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_555cf1ddf563_5 | 73930ac2b6acf0df | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphAlphaCrownTransferSoundness/Common.lean | Common | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "phaseRelaxLowerScalar_slope_nonneg",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases ph <;> simp [phaseRelaxLowerScalar, alphaRelaxLowerScalar_slope_nonneg, ha0]",
"n_chars": 88,
... | [
{
"name": "alphaRelaxLowerScalar_slope_nonneg",
"text": "lemma alphaRelaxLowerScalar_slope_nonneg (l u a : ℝ) (ha0 : 0 ≤ a) :\n 0 ≤ (alphaRelaxLowerScalar (α := ℝ) l u a).slope := by\n unfold alphaRelaxLowerScalar\n by_cases hu : u > 0\n · by_cases hlpos : l > 0\n · simp [hu, hlpos]\n · simp [hu... | [
{
"name": "phaseRelaxLowerScalar_slope_nonneg",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 243,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": fals... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | @@ -108,8 +108,20 @@
castDimScalar (α := ℝ) h t = t := by
exact castDimScalar_proof_irrel h rfl t
+lemma alphaRelaxLowerScalar_slope_nonneg (l u a : ℝ) (ha0 : 0 ≤ a) :
+ 0 ≤ (alphaRelaxLowerScalar (α := ℝ) l u a).slope := by
+ unfold alphaRelaxLowerScalar
+ by_cases hu : u > 0
+ · by_cases hlpos : l > 0... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_555cf1ddf563_6 | bdcfa000d42f8948 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphAlphaCrownTransferSoundness/Common.lean | Common | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "phaseRelaxLowerScalar_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases ph with\n | inactive =>\n -- rp = 0, so this is `0 ≤ relu(x)`.\n simp [phaseRelaxLowerScalar,... | [
{
"name": "phaseConsistentScalar?_active",
"text": "lemma phaseConsistentScalar?_active {l u : ℝ} :\n phaseConsistentScalar? (α := ℝ) l u ReLUPhase.active = some () → 0 ≤ l := by\n intro h\n unfold phaseConsistentScalar? at h\n by_cases hl : l < 0\n · simp [hl] at h\n ·\n have : ¬ l < (0 : ℝ) := ... | [
{
"name": "phaseRelaxLowerScalar_sound",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 19,
"n_chars": 906,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | @@ -131,6 +131,16 @@
· have hxle : x ≤ 0 := le_trans hxu (le_of_not_gt hu)
simp [hu, Activation.Math.reluSpec, max_eq_right hxle]
+lemma phaseConsistentScalar?_active {l u : ℝ} :
+ phaseConsistentScalar? (α := ℝ) l u ReLUPhase.active = some () → 0 ≤ l := by
+ intro h
+ unfold phaseConsistentScalar? at h
... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_555cf1ddf563_7 | 01b226a89f82dfb2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphAlphaCrownTransferSoundness/Common.lean | Common | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "phaseRelaxLowerScalar_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases ph with\n | inactive =>\n -- rp = 0, so this is `0 ≤ relu(x)`.\n simp [phaseRelaxLowerScalar,... | [
{
"name": "phaseConsistentScalar?_active",
"text": "lemma phaseConsistentScalar?_active {l u : ℝ} :\n phaseConsistentScalar? (α := ℝ) l u ReLUPhase.active = some () → 0 ≤ l := by\n intro h\n unfold phaseConsistentScalar? at h\n by_cases hl : l < 0\n · simp [hl] at h\n ·\n have : ¬ l < (0 : ℝ) := ... | [
{
"name": "phaseRelaxUpperScalar_sound",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 22,
"n_chars": 1012,
"n_subproofs": 4,
"n_tactics": 13,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | @@ -160,6 +160,16 @@
have : ¬ (0 : ℝ) < u := by simpa using hu
exact (not_lt).1 this
+lemma phaseConsistentScalar?_active {l u : ℝ} :
+ phaseConsistentScalar? (α := ℝ) l u ReLUPhase.active = some () → 0 ≤ l := by
+ intro h
+ unfold phaseConsistentScalar? at h
+ by_cases hl : l < 0
+ · simp [hl] at h
... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_555cf1ddf563_8 | 758415f52f28aa67 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphAlphaCrownTransferSoundness/Common.lean | Common | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "mat_vec_add_matrix",
"depth": 1,
"n_commands": 0,
"n_lines": 39,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have htoVec :\n Spec.toVec (Spec.matVecMulSpec (α := ℝ) (Tensor.addSpec (α := ℝ) A B) x) =\n S... | [
{
"name": "get2_add_spec",
"text": "lemma get2_add_spec {m n : Nat}\n (A B : Tensor ℝ (.dim m (.dim n .scalar))) (i : Fin m) (j : Fin n) :\n Spec.get2 (Tensor.addSpec (α := ℝ) A B) i j = Spec.get2 A i j + Spec.get2 B i j := by\n cases A with\n | dim rowsA =>\n cases B with\n | dim rowsB =>\n ... | [
{
"name": "mat_vec_add_matrix",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 47,
"n_chars": 2181,
"n_subproofs": 3,
"n_tactics": 38,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 3,
"n_structural": 4,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | @@ -108,6 +108,24 @@
castDimScalar (α := ℝ) h t = t := by
exact castDimScalar_proof_irrel h rfl t
+lemma get2_add_spec {m n : Nat}
+ (A B : Tensor ℝ (.dim m (.dim n .scalar))) (i : Fin m) (j : Fin n) :
+ Spec.get2 (Tensor.addSpec (α := ℝ) A B) i j = Spec.get2 A i j + Spec.get2 B i j := by
+ cases A wit... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_555cf1ddf563_9 | 89ce8a77bf68ccb6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphAlphaCrownTransferSoundness/Common.lean | Common | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "boundsEvalAt_bounds_identity",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hMat :\n Spec.matVecMulSpec (α := ℝ) (Cert.affIdentity (α := ℝ) n).A x = x :=\n mat_... | [
{
"name": "mat_vec_mul_spec_aff_identity",
"text": "lemma mat_vec_mul_spec_aff_identity {n : Nat}\n (x : Tensor ℝ (.dim n .scalar)) :\n Spec.matVecMulSpec (α := ℝ) (Cert.affIdentity (α := ℝ) n).A x = x := by\n classical\n have htoVec :\n Spec.toVec (Spec.matVecMulSpec (α := ℝ) (Cert.affIdentity... | [
{
"name": "boundsEvalAt_bounds_identity",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 547,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | @@ -108,11 +108,48 @@
castDimScalar (α := ℝ) h t = t := by
exact castDimScalar_proof_irrel h rfl t
+lemma mat_vec_mul_spec_aff_identity {n : Nat}
+ (x : Tensor ℝ (.dim n .scalar)) :
+ Spec.matVecMulSpec (α := ℝ) (Cert.affIdentity (α := ℝ) n).A x = x := by
+ classical
+ have htoVec :
+ Spec.toVec ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_555cf1ddf563_10 | 328d171f186b7552 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphAlphaCrownTransferSoundness/Common.lean | Common | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "boundsEvalAt_bounds_const",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n ext <;> simp [boundsEvalAt, Cert.boundsConst, affineEvalAt, mat_vec_mul_spec_fill_zero]",
"n_cha... | [
{
"name": "mat_vec_mul_spec_fill_zero",
"text": "lemma mat_vec_mul_spec_fill_zero {m n : Nat}\n (x : Tensor ℝ (.dim n .scalar)) :\n Spec.matVecMulSpec (α := ℝ) (Spec.fill (α := ℝ) (0 : ℝ) (.dim m (.dim n .scalar))) x =\n Spec.fill (α := ℝ) (0 : ℝ) (.dim m .scalar) := by\n classical\n have htoVe... | [
{
"name": "boundsEvalAt_bounds_const",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 390,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | @@ -108,12 +108,34 @@
castDimScalar (α := ℝ) h t = t := by
exact castDimScalar_proof_irrel h rfl t
+lemma mat_vec_mul_spec_fill_zero {m n : Nat}
+ (x : Tensor ℝ (.dim n .scalar)) :
+ Spec.matVecMulSpec (α := ℝ) (Spec.fill (α := ℝ) (0 : ℝ) (.dim m (.dim n .scalar))) x =
+ Spec.fill (α := ℝ) (0 : ℝ) ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_555cf1ddf563_11 | bd649cd190fb2f85 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphAlphaCrownTransferSoundness/Common.lean | Common | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "add_spec_pair_distrib",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n calc\n Tensor.addSpec (α := ℝ) (Tensor.addSpec (α := ℝ) a b) (Tensor.addSpec (α := ℝ) c d)\n = Tensor.addS... | [
{
"name": "add_spec_left_comm",
"text": "lemma add_spec_left_comm {s : Shape}\n (a b c : Tensor ℝ s) :\n Tensor.addSpec (α := ℝ) a (Tensor.addSpec (α := ℝ) b c) =\n Tensor.addSpec (α := ℝ) b (Tensor.addSpec (α := ℝ) a c) := by\n -- Derive left-commutativity from `add_spec_assoc` and `add_spec_co... | [
{
"name": "add_spec_pair_distrib",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 1238,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | @@ -108,6 +108,20 @@
castDimScalar (α := ℝ) h t = t := by
exact castDimScalar_proof_irrel h rfl t
+lemma add_spec_left_comm {s : Shape}
+ (a b c : Tensor ℝ s) :
+ Tensor.addSpec (α := ℝ) a (Tensor.addSpec (α := ℝ) b c) =
+ Tensor.addSpec (α := ℝ) b (Tensor.addSpec (α := ℝ) a c) := by
+ -- Derive l... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_555cf1ddf563_12 | de685f8530636b0c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphAlphaCrownTransferSoundness/Common.lean | Common | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "add_spec_pair_distrib",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n calc\n Tensor.addSpec (α := ℝ) (Tensor.addSpec (α := ℝ) a b) (Tensor.addSpec (α := ℝ) c d)\n = Tensor.addS... | [
{
"name": "add_spec_left_comm",
"text": "lemma add_spec_left_comm {s : Shape}\n (a b c : Tensor ℝ s) :\n Tensor.addSpec (α := ℝ) a (Tensor.addSpec (α := ℝ) b c) =\n Tensor.addSpec (α := ℝ) b (Tensor.addSpec (α := ℝ) a c) := by\n -- Derive left-commutativity from `add_spec_assoc` and `add_spec_co... | [
{
"name": "boundsEvalAt_linear_bounds_from_affine",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 61,
"n_chars": 2979,
"n_subproofs": 0,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 5,
"automation_only... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | @@ -172,6 +172,20 @@
(Spec.matVecMulSpec (α := ℝ) A x)
(Spec.matVecMulSpec (α := ℝ) B x)))))
+lemma add_spec_left_comm {s : Shape}
+ (a b c : Tensor ℝ s) :
+ Tensor.addSpec (α := ℝ) a (Tensor.addSpec (α := ℝ) b c) =
+ Tensor.addSpec (α := ℝ) b (Tensor.addSpec (α := ℝ) a c) := by
+ -- Der... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_46545542362a_0 | 043336ea06d41d77 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/Rounding/RoundingApprox.lean | RoundingApprox | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "scalarApprox_roundedAdd",
"depth": 1,
"n_commands": 0,
"n_lines": 29,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Triangle inequality: (rounded(x̂+ŷ) - (x+y)) =\n -- (rounded(x̂+ŷ) - (x̂+ŷ)) + ((x̂+ŷ) - (x+y)).\n have... | [
{
"name": "roundR_abs_error",
"text": "/-- One `neuralRound` step is within half an ulp of the exact real input. -/\nlemma roundR_abs_error (x : ℝ) :\n abs (roundR (β := β) (fexp := fexp) (rnd := rnd) x - x) ≤\n neuralUlp β fexp x TrainingPhase.forward / 2 := by\n simpa [roundR] using neural_error_... | [
{
"name": "scalarApprox_roundedAdd",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 39,
"n_chars": 1992,
"n_subproofs": 5,
"n_tactics": 24,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.NeuralFloat.ErrorBounds
public import NN.Proofs.RuntimeApprox.Core.Tolerance
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# Scalar Rounding Approxima... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.NeuralFloat.ErrorBounds
public import NN.Proofs.RuntimeApprox.Core.Tolerance
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# Scalar Rounding Approxima... | @@ -58,6 +58,14 @@
def roundR (x : ℝ) : ℝ :=
neuralRound (β := β) (fexp := fexp) rnd x
+/-- One `neuralRound` step is within half an ulp of the exact real input. -/
+lemma roundR_abs_error (x : ℝ) :
+ abs (roundR (β := β) (fexp := fexp) (rnd := rnd) x - x) ≤
+ neuralUlp β fexp x TrainingPhase.forward / 2 ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_46545542362a_1 | fad9fda38ea25e7a | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/Rounding/RoundingApprox.lean | RoundingApprox | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "scalarApprox_roundedAdd",
"depth": 1,
"n_commands": 0,
"n_lines": 29,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Triangle inequality: (rounded(x̂+ŷ) - (x+y)) =\n -- (rounded(x̂+ŷ) - (x̂+ŷ)) + ((x̂+ŷ) - (x+y)).\n have... | [
{
"name": "roundR_abs_error",
"text": "/-- One `neuralRound` step is within half an ulp of the exact real input. -/\nlemma roundR_abs_error (x : ℝ) :\n abs (roundR (β := β) (fexp := fexp) (rnd := rnd) x - x) ≤\n neuralUlp β fexp x TrainingPhase.forward / 2 := by\n simpa [roundR] using neural_error_... | [
{
"name": "scalarApprox_roundedMul",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 99,
"n_chars": 4794,
"n_subproofs": 21,
"n_tactics": 74,
"cyclomatic": 1,
"n_automation": 19,
"n_rewrites": 0,
"n_structural": 6,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.NeuralFloat.ErrorBounds
public import NN.Proofs.RuntimeApprox.Core.Tolerance
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# Scalar Rounding Approxima... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.NeuralFloat.ErrorBounds
public import NN.Proofs.RuntimeApprox.Core.Tolerance
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# Scalar Rounding Approxima... | @@ -58,6 +58,14 @@
def roundR (x : ℝ) : ℝ :=
neuralRound (β := β) (fexp := fexp) rnd x
+/-- One `neuralRound` step is within half an ulp of the exact real input. -/
+lemma roundR_abs_error (x : ℝ) :
+ abs (roundR (β := β) (fexp := fexp) (rnd := rnd) x - x) ≤
+ neuralUlp β fexp x TrainingPhase.forward / 2 ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d12612ff115a_0 | bc45b73b1e0366d4 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Ops/Conv/FDeriv.lean | FDeriv | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 3 | [
{
"theorem_name": "toVecT_get1",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases C with\n | zero => exact (Fin.elim0 c)\n | succ C =>\n cases A with\n | dim f =>\n let... | [
{
"name": "toVecT_scalar_apply",
"text": "/-- `toVecT` on scalar tensors always returns the scalar value (the only coordinate is `0`). -/\nprivate lemma toVecT_scalar_apply (x : ℝ) (i : Fin (Shape.size Shape.scalar)) :\n toVecT (t := (Tensor.scalar x : Tensor ℝ Shape.scalar)) i = x := by\n simpa [toVecT... | [
{
"name": "toVecT_get1",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 48,
"n_chars": 2061,
"n_subproofs": 5,
"n_tactics": 42,
"cyclomatic": 4,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 8,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | @@ -76,6 +76,15 @@
Fin (Shape.size (.dim OC (.dim IC (.dim KH (.dim KW .scalar))))) :=
Fin.cast (by simp [Shape.size]) (idx4 (OC := OC) (IC := IC) (KH := KH) (KW := KW) oc ic di dj)
+/-- `toVecT` on scalar tensors always returns the scalar value (the only coordinate is `0`). -/
+private lemma toVecT_scalar_ap... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d12612ff115a_1 | 538084331261fc11 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Ops/Conv/FDeriv.lean | FDeriv | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "get1_ofVecT",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have htv :=\n congrArg (fun w => w (Fin.cast (by simp [Shape.size]) c))\n (toVecT_ofVecT (s := .dim C .scalar) v)\n ex... | [
{
"name": "toVecT_get1",
"text": "/-- Relate 1D tensor `toVecT` coordinates to `get_at_or_zero` via the scalar last-axis encoding. -/\nprivate lemma toVecT_get1\n {C : Nat} (A : Tensor ℝ (.dim C .scalar)) (c : Fin C) :\n toVecT (t := A) (Fin.cast (by simp [Shape.size]) c) =\n getAtOrZero A [c.val... | [
{
"name": "get1_ofVecT",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 12,
"n_chars": 512,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | @@ -85,12 +85,63 @@
(f := fun _ : Fin (Shape.size Shape.scalar) => x)
(i := i))
+/-- Relate 1D tensor `toVecT` coordinates to `get_at_or_zero` via the scalar last-axis encoding. -/
+private lemma toVecT_get1
+ {C : Nat} (A : Tensor ℝ (.dim C .scalar)) (c : Fin C) :
+ toVecT (t := A) (Fin.cast (by ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d12612ff115a_2 | ffd5cf62fb201f7c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Ops/Conv/FDeriv.lean | FDeriv | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "toVecT_get3",
"depth": 1,
"n_commands": 0,
"n_lines": 112,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases W with\n | zero => exact (Fin.elim0 j)\n | succ W =>\n cases H with\n | zero => exact (Fin.elim0 i... | [
{
"name": "idx3S_eq_nested",
"text": "private lemma idx3S_eq_nested\n {C H W : Nat} (c : Fin C) (i : Fin H) (j : Fin W) :\n idx3S (C := C) (H := H) (W := W) c i j =\n finProdFinEquiv (c, finProdFinEquiv (i, finProdFinEquiv (j, (0 : Fin 1)))) := by\n apply Fin.ext\n simp [idx3S, idx3, Shape.size... | [
{
"name": "toVecT_get3",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 119,
"n_chars": 5900,
"n_subproofs": 14,
"n_tactics": 106,
"cyclomatic": 7,
"n_automation": 12,
"n_rewrites": 0,
"n_structural": 14,
"automation_only": false,
"max_nes... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | @@ -143,6 +143,13 @@
(toVecT_ofVecT (s := .dim C .scalar) v)
exact (toVecT_get1 (A := ofVecT (s := .dim C .scalar) v) c).symm.trans htv
+private lemma idx3S_eq_nested
+ {C H W : Nat} (c : Fin C) (i : Fin H) (j : Fin W) :
+ idx3S (C := C) (H := H) (W := W) c i j =
+ finProdFinEquiv (c, finProdFinE... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d12612ff115a_3 | cc863d3f02c13149 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Ops/Conv/FDeriv.lean | FDeriv | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 2 | [
{
"theorem_name": "get3_ofVecT",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have htv :=\n congrArg (fun w => w (idx3S (C := C) (H := H) (W := W) c i j))\n (toVecT_ofVecT (s := .dim C (.dim H (.di... | [
{
"name": "toVecT_get3",
"text": "/-- Relate 3D tensor `toVecT` coordinates to `get_at_or_zero` via the `idx3S` index encoding. -/\nprivate lemma toVecT_get3\n {C H W : Nat} (A : Tensor ℝ (.dim C (.dim H (.dim W .scalar))))\n (c : Fin C) (i : Fin H) (j : Fin W) :\n toVecT (t := A) (idx3S (C := C) (... | [
{
"name": "get3_ofVecT",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 17,
"n_chars": 783,
"n_subproofs": 2,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": ... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | @@ -158,13 +158,139 @@
apply Fin.ext
simp [idx4S, idx4, Shape.size, finProdFinEquiv, Fin.cast]
+/-- Relate 3D tensor `toVecT` coordinates to `get_at_or_zero` via the `idx3S` index encoding. -/
+private lemma toVecT_get3
+ {C H W : Nat} (A : Tensor ℝ (.dim C (.dim H (.dim W .scalar))))
+ (c : Fin C) (i : F... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d12612ff115a_4 | 654ada3a49b445c5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Ops/Conv/FDeriv.lean | FDeriv | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "toVecT_get4",
"depth": 1,
"n_commands": 0,
"n_lines": 148,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases KW with\n | zero => exact (Fin.elim0 dj)\n | succ KW =>\n cases KH with\n | zero => exact (Fin.eli... | [
{
"name": "idx4S_eq_nested",
"text": "private lemma idx4S_eq_nested\n {OC IC KH KW : Nat} (oc : Fin OC) (ic : Fin IC) (di : Fin KH) (dj : Fin KW) :\n idx4S (OC := OC) (IC := IC) (KH := KH) (KW := KW) oc ic di dj =\n finProdFinEquiv\n (oc, finProdFinEquiv (ic, finProdFinEquiv (di, finProdFi... | [
{
"name": "toVecT_get4",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 155,
"n_chars": 8330,
"n_subproofs": 17,
"n_tactics": 148,
"cyclomatic": 9,
"n_automation": 15,
"n_rewrites": 0,
"n_structural": 18,
"automation_only": false,
"max_nes... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | @@ -150,6 +150,14 @@
apply Fin.ext
simp [idx3S, idx3, Shape.size, finProdFinEquiv, Fin.cast]
+private lemma idx4S_eq_nested
+ {OC IC KH KW : Nat} (oc : Fin OC) (ic : Fin IC) (di : Fin KH) (dj : Fin KW) :
+ idx4S (OC := OC) (IC := IC) (KH := KH) (KW := KW) oc ic di dj =
+ finProdFinEquiv
+ (oc,... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d12612ff115a_5 | 74cc2b478d0ee2a7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Ops/Conv/FDeriv.lean | FDeriv | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "get4_ofVecT",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have htv :=\n congrArg (fun w => w (idx4S (OC := OC) (IC := IC) (KH := KH) (KW := KW) oc ic di dj))\n (toVecT_ofVecT (s... | [
{
"name": "toVecT_get4",
"text": "/-- Relate 4D kernel `toVecT` coordinates to `get_at_or_zero` via the `idx4S` index encoding. -/\nprivate lemma toVecT_get4\n {OC IC KH KW : Nat} (K : Tensor ℝ (.dim OC (.dim IC (.dim KH (.dim KW .scalar)))))\n (oc : Fin OC) (ic : Fin IC) (di : Fin KH) (dj : Fin KW) :... | [
{
"name": "get4_ofVecT",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 18,
"n_chars": 833,
"n_subproofs": 2,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": ... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | @@ -292,6 +292,160 @@
(toVecT_get3 (A := ofVecT (s := .dim C (.dim H (.dim W .scalar))) v) c i j).symm
simpa using hget.trans htv
+/-- Relate 4D kernel `toVecT` coordinates to `get_at_or_zero` via the `idx4S` index encoding. -/
+private lemma toVecT_get4
+ {OC IC KH KW : Nat} (K : Tensor ℝ (.dim OC (.dim I... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d12612ff115a_6 | 0d4c3f70caf02bb6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Ops/Conv/FDeriv.lean | FDeriv | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "convBilin_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 1132,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [convBilin]\n\n /-- Output height of `conv2d`, computed from input height, kernel height, stride, and padding. -/\... | [
{
"name": "ite_or_eq_ite2",
"text": "/-- Rewrite a disjunction test into the corresponding nested `if` form. -/\nprivate lemma ite_or_eq_ite2 {P Q : Prop} [Decidable P] [Decidable Q] (a : ℝ) :\n (if P ∨ Q then (0 : ℝ) else a) = (if P then 0 else if Q then 0 else a) := by\n by_cases hP : P <;> by_cases h... | [
{
"name": "convBilin_apply",
"fan_in": 0,
"n_deps_direct": 6,
"n_deps_transitive": 11,
"n_lines": 1141,
"n_chars": 61412,
"n_subproofs": 88,
"n_tactics": 1006,
"cyclomatic": 3,
"n_automation": 89,
"n_rewrites": 4,
"n_structural": 42,
"automation_only": false,
... | 11 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Ops.Conv.BackwardDot
public import Mathlib.Analysis.Calculus.FDeriv.Bilinear
public import ... | @@ -547,6 +547,11 @@
(if P then 0 else if Q then 0 else a) + (if P then 0 else if Q then 0 else b) := by
by_cases hP : P <;> by_cases hQ : Q <;> simp [hP, hQ]
+/-- Rewrite a disjunction test into the corresponding nested `if` form. -/
+private lemma ite_or_eq_ite2 {P Q : Prop} [Decidable P] [Decidable Q] (a... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_30141d3b4f1c_0 | 0053bec2104e940e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MarkovMDP.lean | MarkovMDP | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "valueSupDist_eq_zero_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hBddDiff : BddAbove (Set.range fun s => |values₁ s - values₂ s|) :=\n bddAbove_abs_sub_of_bddAbove_abs (S... | [
{
"name": "abs_sub_le_valueSupDist",
"text": "/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/\ntheorem abs_sub_le_valueSupDist [Nonempty S]\n (values₁ values₂ : ValueFunction S)\n (hBdd : BddAbove (Set.range fun s => |values₁ s - values₂ s|))\n (stat... | [
{
"name": "valueSupDist_eq_zero_iff",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 30,
"n_chars": 1289,
"n_subproofs": 5,
"n_tactics": 18,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 5,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | @@ -60,6 +60,17 @@
noncomputable def valueSupDist [Nonempty S] (values₁ values₂ : ValueFunction S) : ℝ :=
sSup (Set.range fun s => |values₁ s - values₂ s|)
+/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/
+theorem abs_sub_le_valueSupDist [Nonempty S]
+ (values₁ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_30141d3b4f1c_1 | ead46cc126fe361b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MarkovMDP.lean | MarkovMDP | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "valueSupDist_eq_zero_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hBddDiff : BddAbove (Set.range fun s => |values₁ s - values₂ s|) :=\n bddAbove_abs_sub_of_bddAbove_abs (S... | [
{
"name": "abs_sub_le_valueSupDist",
"text": "/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/\ntheorem abs_sub_le_valueSupDist [Nonempty S]\n (values₁ values₂ : ValueFunction S)\n (hBdd : BddAbove (Set.range fun s => |values₁ s - values₂ s|))\n (stat... | [
{
"name": "expectedNextValue_abs_sub_le",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 49,
"n_chars": 2870,
"n_subproofs": 6,
"n_tactics": 34,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | @@ -60,6 +60,17 @@
noncomputable def valueSupDist [Nonempty S] (values₁ values₂ : ValueFunction S) : ℝ :=
sSup (Set.range fun s => |values₁ s - values₂ s|)
+/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/
+theorem abs_sub_le_valueSupDist [Nonempty S]
+ (values₁ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_30141d3b4f1c_2 | 027c34c12ae34bcf | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MarkovMDP.lean | MarkovMDP | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "valueSupDist_eq_zero_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hBddDiff : BddAbove (Set.range fun s => |values₁ s - values₂ s|) :=\n bddAbove_abs_sub_of_bddAbove_abs (S... | [
{
"name": "abs_sub_le_valueSupDist",
"text": "/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/\ntheorem abs_sub_le_valueSupDist [Nonempty S]\n (values₁ values₂ : ValueFunction S)\n (hBdd : BddAbove (Set.range fun s => |values₁ s - values₂ s|))\n (stat... | [
{
"name": "actionValue_abs_sub_le",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 48,
"n_chars": 2678,
"n_subproofs": 6,
"n_tactics": 33,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"m... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | @@ -60,6 +60,17 @@
noncomputable def valueSupDist [Nonempty S] (values₁ values₂ : ValueFunction S) : ℝ :=
sSup (Set.range fun s => |values₁ s - values₂ s|)
+/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/
+theorem abs_sub_le_valueSupDist [Nonempty S]
+ (values₁ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_30141d3b4f1c_3 | 52a57a9b14786204 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MarkovMDP.lean | MarkovMDP | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "valueSupDist_eq_zero_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hBddDiff : BddAbove (Set.range fun s => |values₁ s - values₂ s|) :=\n bddAbove_abs_sub_of_bddAbove_abs (S... | [
{
"name": "abs_sub_le_valueSupDist",
"text": "/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/\ntheorem abs_sub_le_valueSupDist [Nonempty S]\n (values₁ values₂ : ValueFunction S)\n (hBdd : BddAbove (Set.range fun s => |values₁ s - values₂ s|))\n (stat... | [
{
"name": "bellmanPolicy_contraction",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 30,
"n_chars": 1333,
"n_subproofs": 0,
"n_tactics": 15,
"cyclomatic": 3,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,
... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | @@ -60,6 +60,17 @@
noncomputable def valueSupDist [Nonempty S] (values₁ values₂ : ValueFunction S) : ℝ :=
sSup (Set.range fun s => |values₁ s - values₂ s|)
+/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/
+theorem abs_sub_le_valueSupDist [Nonempty S]
+ (values₁ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_30141d3b4f1c_4 | 7661ea692a5506dc | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MarkovMDP.lean | MarkovMDP | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "valueSupDist_eq_zero_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hBddDiff : BddAbove (Set.range fun s => |values₁ s - values₂ s|) :=\n bddAbove_abs_sub_of_bddAbove_abs (S... | [
{
"name": "abs_sub_le_valueSupDist",
"text": "/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/\ntheorem abs_sub_le_valueSupDist [Nonempty S]\n (values₁ values₂ : ValueFunction S)\n (hBdd : BddAbove (Set.range fun s => |values₁ s - values₂ s|))\n (stat... | [
{
"name": "bellmanOptimality_abs_sub_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 50,
"n_chars": 2332,
"n_subproofs": 8,
"n_tactics": 36,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 6,
"automation_only": false,
... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | @@ -60,6 +60,17 @@
noncomputable def valueSupDist [Nonempty S] (values₁ values₂ : ValueFunction S) : ℝ :=
sSup (Set.range fun s => |values₁ s - values₂ s|)
+/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/
+theorem abs_sub_le_valueSupDist [Nonempty S]
+ (values₁ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_30141d3b4f1c_5 | 3c336e6de311f044 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MarkovMDP.lean | MarkovMDP | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "valueSupDist_eq_zero_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hBddDiff : BddAbove (Set.range fun s => |values₁ s - values₂ s|) :=\n bddAbove_abs_sub_of_bddAbove_abs (S... | [
{
"name": "abs_sub_le_valueSupDist",
"text": "/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/\ntheorem abs_sub_le_valueSupDist [Nonempty S]\n (values₁ values₂ : ValueFunction S)\n (hBdd : BddAbove (Set.range fun s => |values₁ s - values₂ s|))\n (stat... | [
{
"name": "bellmanOptimality_contraction",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 38,
"n_chars": 1601,
"n_subproofs": 0,
"n_tactics": 15,
"cyclomatic": 3,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | @@ -60,6 +60,17 @@
noncomputable def valueSupDist [Nonempty S] (values₁ values₂ : ValueFunction S) : ℝ :=
sSup (Set.range fun s => |values₁ s - values₂ s|)
+/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/
+theorem abs_sub_le_valueSupDist [Nonempty S]
+ (values₁ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_30141d3b4f1c_6 | ffe19da4784f2ace | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MarkovMDP.lean | MarkovMDP | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "valueSupDist_eq_zero_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hBddDiff : BddAbove (Set.range fun s => |values₁ s - values₂ s|) :=\n bddAbove_abs_sub_of_bddAbove_abs (S... | [
{
"name": "abs_sub_le_valueSupDist",
"text": "/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/\ntheorem abs_sub_le_valueSupDist [Nonempty S]\n (values₁ values₂ : ValueFunction S)\n (hBdd : BddAbove (Set.range fun s => |values₁ s - values₂ s|))\n (stat... | [
{
"name": "bellmanPolicy_fixedPoint_unique",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 7,
"n_lines": 55,
"n_chars": 2273,
"n_subproofs": 16,
"n_tactics": 35,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 6,
"automation_only": fal... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | @@ -60,6 +60,17 @@
noncomputable def valueSupDist [Nonempty S] (values₁ values₂ : ValueFunction S) : ℝ :=
sSup (Set.range fun s => |values₁ s - values₂ s|)
+/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/
+theorem abs_sub_le_valueSupDist [Nonempty S]
+ (values₁ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_30141d3b4f1c_7 | c2d9530419a03033 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MarkovMDP.lean | MarkovMDP | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "valueSupDist_eq_zero_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hBddDiff : BddAbove (Set.range fun s => |values₁ s - values₂ s|) :=\n bddAbove_abs_sub_of_bddAbove_abs (S... | [
{
"name": "abs_sub_le_valueSupDist",
"text": "/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/\ntheorem abs_sub_le_valueSupDist [Nonempty S]\n (values₁ values₂ : ValueFunction S)\n (hBdd : BddAbove (Set.range fun s => |values₁ s - values₂ s|))\n (stat... | [
{
"name": "bellmanOptimality_fixedPoint_unique",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 8,
"n_lines": 54,
"n_chars": 2216,
"n_subproofs": 16,
"n_tactics": 35,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 6,
"automation_only":... | 8 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.MeasureTheory.Integral.Bochner.Basic
public import Mathlib.MeasureTheory.Measure.Typeclasses.Probability
public import NN.Proofs.RL... | @@ -60,6 +60,17 @@
noncomputable def valueSupDist [Nonempty S] (values₁ values₂ : ValueFunction S) : ℝ :=
sSup (Set.range fun s => |values₁ s - values₂ s|)
+/-- Every pointwise absolute difference is bounded by the sup distance (boundedness assumed). -/
+theorem abs_sub_le_valueSupDist [Nonempty S]
+ (values₁ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_f912af3bffb2_0 | 3ea4f87b79b437d6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32MulSoundness.lean | IEEEExec32MulSoundness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "mul_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 152,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro x y hx hy\n\n -- Real corner bounds.\n have hxy := mul_bounds_Icc (a := toReal A.lo) (b := toReal A.hi) (c := toReal B.... | [
{
"name": "isNaN_mulUp_eq_false_of_isFinite",
"text": "/--\n`mulUp x y` is non-NaN on finite inputs.\n\nAs for `isNaN_mulDown_eq_false_of_isFinite`, this is used to justify that the IEEE `maximum`/`minOfFour`\nhelpers behave like `max`/`min` on the `EReal` semantics of the rounded corner products.\n-/\npriv... | [
{
"name": "mul_sound",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 169,
"n_chars": 8527,
"n_subproofs": 35,
"n_tactics": 129,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 2,
"n_structural": 8,
"automation_only": false,
"max_nesting... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.ERealSemantics
public ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.ERealSemantics
public ... | @@ -101,6 +101,49 @@
simp [h0, isNaN_roundDyadicDown_eq_false]
/--
+`mulUp x y` is non-NaN on finite inputs.
+
+As for `isNaN_mulDown_eq_false_of_isFinite`, this is used to justify that the IEEE `maximum`/`minOfFour`
+helpers behave like `max`/`min` on the `EReal` semantics of the rounded corner product... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_4a06ec6d1024_0 | 87f3654f772918af | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/Scale/ScaleApprox.lean | ScaleApprox | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "approxTTol_from_scale",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `approxT` -> `absOnly eps`, then enlarge tolerance (abs+rel) via monotonicity.\n have habsOnly : approxTTol (α :... | [
{
"name": "absOnly_le_tolFromEpsScale",
"text": "lemma absOnly_le_tolFromEpsScale (eps : ℝ) (B : ℝ≥0) :\n (ApproxTol.absOnly eps).abs ≤ (tolFromEpsScale eps B).abs ∧\n (ApproxTol.absOnly eps).rel ≤ (tolFromEpsScale eps B).rel ∧\n (ApproxTol.absOnly eps).slack ≤ (tolFromEpsScale eps B).slack := by\n... | [
{
"name": "approxTTol_from_scale",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 1103,
"n_subproofs": 2,
"n_tactics": 10,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
public import NN.Proofs.RuntimeApprox.Graph.ForwardApprox
/-!
# ScaleApprox
Scale-aware approximation helpers.
This module adds an *optional* layer t... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
public import NN.Proofs.RuntimeApprox.Graph.ForwardApprox
/-!
# ScaleApprox
Scale-aware approximation helpers.
This module adds an *optional* layer t... | @@ -131,10 +131,32 @@
let rel : ℝ := if (B : ℝ) = 0 then 0 else eps / (B : ℝ)
ApproxTol.ofReal eps rel 1
+lemma absOnly_le_tolFromEpsScale (eps : ℝ) (B : ℝ≥0) :
+ (ApproxTol.absOnly eps).abs ≤ (tolFromEpsScale eps B).abs ∧
+ (ApproxTol.absOnly eps).rel ≤ (tolFromEpsScale eps B).rel ∧
+ (ApproxTol.absOn... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_4a06ec6d1024_1 | 663868281bcfb99c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/Scale/ScaleApprox.lean | ScaleApprox | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "approxCtx_get_tolFromEpsScale",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hi : approxT (α := α) (toSpec := toSpec)\n (TList.get (α := SpecScalar) xS i)\n (TList.get (α... | [
{
"name": "approxTTol_from_scale",
"text": "lemma approxTTol_from_scale {α : Type} {s : Shape} {toSpec : α → SpecScalar}\n {spec : SpecTensor s} {runtime : Tensor α s} (eps : ℝ) (B : ℝ≥0)\n (h : approxT (α := α) (toSpec := toSpec) spec runtime eps) :\n approxTTol (α := α) (toSpec := toSpec) spec ru... | [
{
"name": "approxCtx_get_tolFromEpsScale",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 19,
"n_chars": 932,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
public import NN.Proofs.RuntimeApprox.Graph.ForwardApprox
/-!
# ScaleApprox
Scale-aware approximation helpers.
This module adds an *optional* layer t... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
public import NN.Proofs.RuntimeApprox.Graph.ForwardApprox
/-!
# ScaleApprox
Scale-aware approximation helpers.
This module adds an *optional* layer t... | @@ -142,6 +142,22 @@
simp [ApproxTol.absOnly, tolFromEpsScale, ApproxTol.ofReal]
· simp [ApproxTol.absOnly, tolFromEpsScale, ApproxTol.ofReal]
+lemma approxTTol_from_scale {α : Type} {s : Shape} {toSpec : α → SpecScalar}
+ {spec : SpecTensor s} {runtime : Tensor α s} (eps : ℝ) (B : ℝ≥0)
+ (h : approxT (... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6f400ffe1956_0 | 7f48e00b44f6118f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Algebra/Soundness.lean | Soundness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "dotList_single",
"depth": 1,
"n_commands": 0,
"n_lines": 70,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n revert dx idx\n induction Γ with\n | nil =>\n intro dx idx\n cases idx with\n | mk i _h =>\n cases i with\n... | [
{
"name": "dotList_zero_right",
"text": "/-- Dotting with the all-zero context on the right yields `0`. -/\ntheorem dotList_zero_right {ss : List Shape} (x : TList α ss) :\n dotList (α := α) x (zero (α := α) (ss := ss)) = 0 := by\n induction ss with\n | nil =>\n cases x\n simp [dotList, zero]\n ... | [
{
"name": "dotList_single",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 79,
"n_chars": 3842,
"n_subproofs": 6,
"n_tactics": 66,
"cyclomatic": 10,
"n_automation": 10,
"n_rewrites": 1,
"n_structural": 16,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Algebra
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness (algebraic, backend-generic).
This is a backend-generic analogue of the tensor-tape sound... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Algebra
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness (algebraic, backend-generic).
This is a backend-generic analogue of the tensor-tape sound... | @@ -150,6 +150,18 @@
| [], nil, nil => 0
| _ :: ss, cons a as, cons b bs => dot (α := α) a b + dotList (ss := ss) as bs
+/-- Dotting with the all-zero context on the right yields `0`. -/
+theorem dotList_zero_right {ss : List Shape} (x : TList α ss) :
+ dotList (α := α) x (zero (α := α) (ss := ss)) = 0 := by... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6f400ffe1956_1 | 7f721f4e9dc917f9 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Algebra/Soundness.lean | Soundness | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "backprop_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 60,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction g with\n | nil =>\n intro x dx d seed\n simpa [jvpCtx, backpropCtx] using\n (TList.dotList_cast_lef... | [
{
"name": "dotList_snoc",
"text": "/-- Dot respects appending: dot of two `snoc`ed contexts splits into prefix + last entry. -/\ntheorem dotList_snoc {ss : List Shape} {τ : Shape} (x y : TList α ss) (a b : Tensor α τ) :\n dotList (α := α) (snoc (α := α) (ss := ss) x a) (snoc (α := α) (ss := ss) y b) =\n ... | [
{
"name": "backprop_correct",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 71,
"n_chars": 3706,
"n_subproofs": 5,
"n_tactics": 60,
"cyclomatic": 2,
"n_automation": 10,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_ne... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Algebra
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness (algebraic, backend-generic).
This is a backend-generic analogue of the tensor-tape sound... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Algebra
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness (algebraic, backend-generic).
This is a backend-generic analogue of the tensor-tape sound... | @@ -173,6 +173,25 @@
simp [dotList, add, TensorAlgebra.dot_add_right (α := α) (a := xh) (b := yh) (c := zh),
ih, add_assoc, add_left_comm]
+/-- Dot respects appending: dot of two `snoc`ed contexts splits into prefix + last entry. -/
+theorem dotList_snoc {ss : List Shape} {τ : Shape} (x y : TL... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_5c4d5825839c_0 | bec602cdcff4ea45 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/Linalg.lean | Linalg | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "approx_dot_finRange",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- base approximation for the initial accumulator `0`\n have h0 :\n abs (toSpec (β := β) (fexp := fexp) (rnd :... | [
{
"name": "approx_dot_list",
"text": "/--\nDot-product approximation bound over an arbitrary list of indices.\n\nIn words: if `aR` and `bR` approximate `aS` and `bS` entrywise (within `epsa`/`epsb`),\n then\nfolding `acc + aR k * bR k` approximates the corresponding spec fold, with error bounded by the\nac... | [
{
"name": "approx_dot_finRange",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 36,
"n_chars": 1898,
"n_subproofs": 1,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.Ops
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Core.Tensor.Linalg
/-!
# NF Linear Algebra
Forward (runtime→spec) approxima... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.Ops
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Core.Tensor.Linalg
/-!
# NF Linear Algebra
Forward (runtime→spec) approxima... | @@ -250,6 +250,93 @@
exact hto
/--
+Dot-product approximation bound over an arbitrary list of indices.
+
+In words: if `aR` and `bR` approximate `aS` and `bS` entrywise (within `epsa`/`epsb`),
+ then
+folding `acc + aR k * bR k` approximates the corresponding spec fold, with error bounded by the
+acc... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_5c4d5825839c_1 | 6d712ecb5aaf8b66 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/Linalg.lean | Linalg | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "approxT_mat_vec_mul_spec",
"depth": 1,
"n_commands": 0,
"n_lines": 241,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro AS vS AR vR epsA epsV hA hv\n -- unfold the concrete shapes\n cases AS with\n | dim ASf =>\n cases... | [
{
"name": "approx_dot_finRange",
"text": "/--\nDot-product approximation bound specialized to `List.finRange n`.\n\nThis packages `approx_dot_list` with the appropriate initial accumulator bound for `0`.\n-/\nprivate theorem approx_dot_finRange {n : Nat}\n {aS bS : Fin n → SpecScalar} {aR bR : Fin n → R}... | [
{
"name": "approxT_mat_vec_mul_spec",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 264,
"n_chars": 14991,
"n_subproofs": 23,
"n_tactics": 223,
"cyclomatic": 15,
"n_automation": 12,
"n_rewrites": 0,
"n_structural": 22,
"automation_only": fals... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.Ops
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Core.Tensor.Linalg
/-!
# NF Linear Algebra
Forward (runtime→spec) approxima... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.Ops
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Core.Tensor.Linalg
/-!
# NF Linear Algebra
Forward (runtime→spec) approxima... | @@ -337,6 +337,41 @@
simpa [List.foldl, dotStep, add_assoc, add_left_comm, add_comm] using ih'
/--
+Dot-product approximation bound specialized to `List.finRange n`.
+
+This packages `approx_dot_list` with the appropriate initial accumulator bound for `0`.
+-/
+private theorem approx_dot_finRange {n : Nat}
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_5c4d5825839c_2 | 3b8f8c836a77437b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/Linalg.lean | Linalg | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "approxT_mat_mul_spec",
"depth": 1,
"n_commands": 0,
"n_lines": 265,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro AS BS AR BR epsA epsB hA hB\n cases AS with\n | dim ASf =>\n cases AR with\n | dim ARf =>\n ... | [
{
"name": "mat_get_mat_mul_spec",
"text": "/-- The matrix entry `(i,j)` of `Spec.mat_mul_spec` is the dot-product of row `i` of `A` with column\n `j` of `B`. -/\nprivate lemma mat_get_mat_mul_spec {m n p : Nat}\n (A : Tensor R (.dim m (.dim n .scalar))) (B : Tensor R (.dim n (.dim p .scalar)))\n (i :... | [
{
"name": "approxT_mat_mul_spec",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 289,
"n_chars": 16892,
"n_subproofs": 31,
"n_tactics": 245,
"cyclomatic": 23,
"n_automation": 15,
"n_rewrites": 0,
"n_structural": 29,
"automation_only": false,
... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.Ops
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Core.Tensor.Linalg
/-!
# NF Linear Algebra
Forward (runtime→spec) approxima... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.Ops
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Core.Tensor.Linalg
/-!
# NF Linear Algebra
Forward (runtime→spec) approxima... | @@ -663,6 +663,38 @@
(fun k => matGet (β := β) (fexp := fexp) (rnd := rnd) B k j))))
omit [NeuralValidRndToNearest rnd] in
+/-- The matrix entry `(i,j)` of `Spec.mat_mul_spec` is the dot-product of row `i` of `A` with column
+ `j` of `B`. -/
+private lemma mat_get_mat_mul_spec {m n p : Nat}
+ (A : Tenso... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_850c93e1b5d0_0 | b2280dbe55ccdd14 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/Factorizations.lean | Factorizations | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "getD_foldl_snoc_read",
"depth": 1,
"n_commands": 0,
"n_lines": 20,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have htake : l.take (k + 1) = l.take k ++ [l[k]'hk] := List.take_succ_eq_append_getElem hk\n have hplen : ((l.take k... | [
{
"name": "getD_foldl_snoc_lt",
"text": "/-- A fold that only appends never changes an index already inside the accumulator. -/\ntheorem getD_foldl_snoc_lt (g : List β → ι → β) (d : β) (l : List ι) (acc : List β)\n (k : Nat) (hk : k < acc.length) :\n (l.foldl (fun s a => s ++ [g s a]) acc).getD k d = ... | [
{
"name": "getD_foldl_snoc_read",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 27,
"n_chars": 1492,
"n_subproofs": 2,
"n_tactics": 20,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 7,
"n_structural": 2,
"automation_only": false,
"max... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.LinearAlgebra
public import Mathlib.Data.List.GetD
/-!
# Correctness of the exact matrix factorizations ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.LinearAlgebra
public import Mathlib.Data.List.GetD
/-!
# Correctness of the exact matrix factorizations ... | @@ -85,12 +85,42 @@
simp only [List.length_append, List.length_cons, List.length_nil]
grind
+/-- A fold that only appends never changes an index already inside the accumulator. -/
+theorem getD_foldl_snoc_lt (g : List β → ι → β) (d : β) (l : List ι) (acc : List β)
+ (k : Nat) (hk : k < acc.length) :
... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_850c93e1b5d0_1 | f72bac0838170213 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/Factorizations.lean | Factorizations | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "getD_foldl_snoc_read",
"depth": 1,
"n_commands": 0,
"n_lines": 20,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have htake : l.take (k + 1) = l.take k ++ [l[k]'hk] := List.take_succ_eq_append_getElem hk\n have hplen : ((l.take k... | [
{
"name": "getD_foldl_snoc_lt",
"text": "/-- A fold that only appends never changes an index already inside the accumulator. -/\ntheorem getD_foldl_snoc_lt (g : List β → ι → β) (d : β) (l : List ι) (acc : List β)\n (k : Nat) (hk : k < acc.length) :\n (l.foldl (fun s a => s ++ [g s a]) acc).getD k d = ... | [
{
"name": "getD_foldl_finRange",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 36,
"n_chars": 1950,
"n_subproofs": 3,
"n_tactics": 31,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 10,
"n_structural": 3,
"automation_only": false,
"max... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.LinearAlgebra
public import Mathlib.Data.List.GetD
/-!
# Correctness of the exact matrix factorizations ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.LinearAlgebra
public import Mathlib.Data.List.GetD
/-!
# Correctness of the exact matrix factorizations ... | @@ -85,11 +85,51 @@
simp only [List.length_append, List.length_cons, List.length_nil]
grind
+/-- A fold that only appends never changes an index already inside the accumulator. -/
+theorem getD_foldl_snoc_lt (g : List β → ι → β) (d : β) (l : List ι) (acc : List β)
+ (k : Nat) (hk : k < acc.length) :
... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_850c93e1b5d0_2 | a4b469903a7ba34e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/Factorizations.lean | Factorizations | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "choleskyFn_lower_triangular",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold Spec.choleskyFn Spec.choleskyColsFn\n rw [getD_foldl_finRange]\n rw [if_pos hij]",
"n_chars": 93,
... | [
{
"name": "getD_foldl_finRange",
"text": "/-- The element at position `j` of the snoc-fold over `finRange n` is `g` applied to the fold of the\nlength-`j` prefix and the index `j`. -/\ntheorem getD_foldl_finRange (g : List β → Fin n → β) (d : β) (j : Fin n) :\n ((List.finRange n).foldl (fun s a => s ++ [... | [
{
"name": "choleskyFn_lower_triangular",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 8,
"n_chars": 334,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 0,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.LinearAlgebra
public import Mathlib.Data.List.GetD
/-!
# Correctness of the exact matrix factorizations ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.LinearAlgebra
public import Mathlib.Data.List.GetD
/-!
# Correctness of the exact matrix factorizations ... | @@ -96,6 +96,41 @@
ih (acc ++ [g acc a]) (by rw [List.length_append]; grind),
List.getD_append _ _ _ _ hk]
+/-- The element at position `j` of the snoc-fold over `finRange n` is `g` applied to the fold of the
+length-`j` prefix and the index `j`. -/
+theorem getD_foldl_finRange (g : List β → Fin n →... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_850c93e1b5d0_3 | 70464c3cc3d197be | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/Factorizations.lean | Factorizations | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "choleskySpec_lower_triangular",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [show Spec.choleskySpec A = Spec.ofMatFn (Spec.choleskyFn (Spec.toMatFn A)) from rfl,\n get2_ofMatFn]\n... | [
{
"name": "choleskyFn_lower_triangular",
"text": "/-- The executable Cholesky factor is lower-triangular: entries strictly above the diagonal vanish. -/\ntheorem choleskyFn_lower_triangular (A : Fin n → Fin n → ℝ) {i j : Fin n} (hij : i.val < j.val) :\n Spec.choleskyFn A i j = 0 := by\n unfold Spec.chol... | [
{
"name": "choleskySpec_lower_triangular",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 8,
"n_chars": 418,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.LinearAlgebra
public import Mathlib.Data.List.GetD
/-!
# Correctness of the exact matrix factorizations ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.LinearAlgebra
public import Mathlib.Data.List.GetD
/-!
# Correctness of the exact matrix factorizations ... | @@ -142,9 +142,19 @@
theorem get2_ofMatFn {m k : Nat} (f : Fin m → Fin k → ℝ) (i : Fin m) (j : Fin k) :
Spec.get2 (Spec.ofMatFn f) i j = f i j := rfl
+/-- The executable Cholesky factor is lower-triangular: entries strictly above the diagonal vanish. -/
+theorem choleskyFn_lower_triangular (A : Fin n → Fin n → ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e232b08abe58_0 | 78aedbff4b74aff2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundDyadicToIEEE32Bounds.lean | RoundDyadicToIEEE32Bounds | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "shiftRightCeilPow2_le_shiftRight_add1",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hor := shiftRightCeilPow2_eq_shiftRight_or_shiftRight_add1 (n := n) (shift := shift)\n rcases h... | [
{
"name": "shiftRightCeilPow2_eq_shiftRight_or_shiftRight_add1",
"text": "/--\n`shiftRightCeilPow2 n shift` is always either `n >>> shift` or `(n >>> shift) + 1`.\nThis is the “two-point” characterization of the ceil-quotient; it complements\n`roundShiftRightEven_eq_shiftRight_or_shiftRight_add1` for neares... | [
{
"name": "shiftRightCeilPow2_le_shiftRight_add1",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 270,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": f... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | @@ -46,8 +46,32 @@
namespace IEEE32Exec
open TorchLean.Floats
noncomputable section
+/--
+`shiftRightCeilPow2 n shift` is always either `n >>> shift` or `(n >>> shift) + 1`.
+This is the “two-point” characterization of the ceil-quotient; it complements
+`roundShiftRightEven_eq_shiftRight_or_shiftRight_add1` for near... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e232b08abe58_1 | 94c32cc7dfed7fc5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundDyadicToIEEE32Bounds.lean | RoundDyadicToIEEE32Bounds | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "shiftRight_lt_pow2_of_lt_pow",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `n >>> k = n / 2^k`, and `2^(k+t) = 2^k * 2^t`.\n have hn' : n < (2 ^ k) * (2 ^ t) := by\n simpa [Nat.p... | [
{
"name": "shiftRight_eq_div_pow",
"text": "/-! ## Small Nat helpers -/\nprivate lemma shiftRight_eq_div_pow (n k : Nat) : Nat.shiftRight n k = n / 2 ^ k := by\n simp [Nat.shiftRight_eq_div_pow]\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 150,
"n_subproofs": 0,
"n_tactics": 2,
"cyclom... | [
{
"name": "shiftRight_lt_pow2_of_lt_pow",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 859,
"n_subproofs": 2,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | @@ -46,6 +46,9 @@
namespace IEEE32Exec
open TorchLean.Floats
noncomputable section
+/-! ## Small Nat helpers -/
+private lemma shiftRight_eq_div_pow (n k : Nat) : Nat.shiftRight n k = n / 2 ^ k := by
+ simp [Nat.shiftRight_eq_div_pow]
/-!
## Bit-length bounds used to rule out impossible carries
In the normal reg... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e232b08abe58_2 | d1762821913dcc35 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundDyadicToIEEE32Bounds.lean | RoundDyadicToIEEE32Bounds | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "shiftRight_lt_pow2_of_lt_pow",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `n >>> k = n / 2^k`, and `2^(k+t) = 2^k * 2^t`.\n have hn' : n < (2 ^ k) * (2 ^ t) := by\n simpa [Nat.p... | [
{
"name": "shiftRight_eq_div_pow",
"text": "/-! ## Small Nat helpers -/\nprivate lemma shiftRight_eq_div_pow (n k : Nat) : Nat.shiftRight n k = n / 2 ^ k := by\n simp [Nat.shiftRight_eq_div_pow]\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 150,
"n_subproofs": 0,
"n_tactics": 2,
"cyclom... | [
{
"name": "shiftRight_log2_sub_lt_pow2_24",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 24,
"n_chars": 1368,
"n_subproofs": 7,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | @@ -46,6 +46,9 @@
namespace IEEE32Exec
open TorchLean.Floats
noncomputable section
+/-! ## Small Nat helpers -/
+private lemma shiftRight_eq_div_pow (n k : Nat) : Nat.shiftRight n k = n / 2 ^ k := by
+ simp [Nat.shiftRight_eq_div_pow]
/-!
## Bit-length bounds used to rule out impossible carries
In the normal reg... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e232b08abe58_3 | 5717ed7b4fb04e39 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundDyadicToIEEE32Bounds.lean | RoundDyadicToIEEE32Bounds | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "shiftRight_log2_sub_lt_pow2_24",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Use the generic `lt_pow_succ_log_self` bound with base 2.\n have hlt : mant < 2 ^ (Nat.log 2 mant).succ... | [
{
"name": "shiftRight_lt_pow2_of_lt_pow",
"text": "/-!\n## Bit-length bounds used to rule out impossible carries\nIn the normal regime, `roundDyadicToIEEE32` computes a 24-bit mantissa `m24`.\nIf `m24 = 2^24` we carry into the exponent (this is the IEEE rule when rounding pushes us across a\npower-of-two bo... | [
{
"name": "roundDyadicToIEEE32_eq_roundDyadicDown_or_roundDyadicUp_pos",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 6,
"n_lines": 812,
"n_chars": 50824,
"n_subproofs": 274,
"n_tactics": 674,
"cyclomatic": 10,
"n_automation": 211,
"n_rewrites": 6,
"n_structu... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | @@ -75,6 +75,22 @@
shiftRightCeilPow2 n shift ≤ Nat.shiftRight n shift + 1 := by
have hor := shiftRightCeilPow2_eq_shiftRight_or_shiftRight_add1 (n := n) (shift := shift)
rcases hor with hq | hq <;> simp [hq]
+/-!
+## Bit-length bounds used to rule out impossible carries
+In the normal regime, `roundDyadicTo... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e232b08abe58_4 | 47c4411b3516d51b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundDyadicToIEEE32Bounds.lean | RoundDyadicToIEEE32Bounds | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "toEReal_ofBits_mkBits_fin_signFlip",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hETrue :=\n toEReal_ofBits_mkBits_fin_eq_toReal (sign := true) (exp := exp) (frac := frac) hexp... | [
{
"name": "toEReal_ofBits_mkBits_fin_eq_toReal",
"text": "private lemma toEReal_ofBits_mkBits_fin_eq_toReal (sign : Bool) (exp frac : Nat)\n (hexp : exp < 255) (hfrac : frac < 2 ^ 23) :\n toEReal (ofBits (mkBits sign exp frac) : IEEE32Exec) =\n (toReal (ofBits (mkBits sign exp frac) : IEEE32Exec)... | [
{
"name": "toEReal_ofBits_mkBits_fin_signFlip",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 23,
"n_chars": 1241,
"n_subproofs": 4,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": f... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | @@ -91,6 +91,35 @@
have hto : toReal (negZero : IEEE32Exec) = 0 := by
simp [toReal_eq, hdy, dyadicToReal]
simp [hE, hto]
+private lemma toEReal_ofBits_mkBits_fin_eq_toReal (sign : Bool) (exp frac : Nat)
+ (hexp : exp < 255) (hfrac : frac < 2 ^ 23) :
+ toEReal (ofBits (mkBits sign exp frac) : IEEE32Exec... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e232b08abe58_5 | 231406a34b39cf83 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundDyadicToIEEE32Bounds.lean | RoundDyadicToIEEE32Bounds | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "roundDyadicToIEEE32_eq_roundDyadicDown_or_roundDyadicUp_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 796,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n intro d\n by_cases hm : mant = 0\n · subst hm\n simp [d, ro... | [
{
"name": "shiftRight_log2_sub_lt_pow2_24",
"text": "private lemma shiftRight_log2_sub_lt_pow2_24 (mant : Nat) (_hm : mant ≠ 0) (hlog : 23 ≤ mant.log2) :\n Nat.shiftRight mant (mant.log2 - 23) < pow2 24 := by\n -- Use the generic `lt_pow_succ_log_self` bound with base 2.\n have hlt : mant < 2 ^ (Nat.lo... | [
{
"name": "toEReal_roundDyadicDown_le_roundDyadicToIEEE32_le_roundDyadicUp",
"fan_in": 2,
"n_deps_direct": 5,
"n_deps_transitive": 11,
"n_lines": 513,
"n_chars": 31422,
"n_subproofs": 92,
"n_tactics": 473,
"cyclomatic": 34,
"n_automation": 106,
"n_rewrites": 1,
"n_str... | 11 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | @@ -91,6 +91,29 @@
simpa [Nat.pow_add, Nat.mul_assoc, Nat.mul_left_comm, Nat.mul_comm] using hn
have hdiv : n / 2 ^ k < 2 ^ t := Nat.div_lt_of_lt_mul hn'
simpa [Nat.shiftRight_eq_div_pow] using hdiv
+private lemma shiftRight_log2_sub_lt_pow2_24 (mant : Nat) (_hm : mant ≠ 0) (hlog : 23 ≤ mant.log2) :
+ Nat... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e232b08abe58_6 | 57a5019922ec7eaf | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundDyadicToIEEE32Bounds.lean | RoundDyadicToIEEE32Bounds | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "roundDyadicToIEEE32_eq_roundDyadicDown_or_roundDyadicUp_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 796,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n intro d\n by_cases hm : mant = 0\n · subst hm\n simp [d, ro... | [
{
"name": "shiftRight_log2_sub_lt_pow2_24",
"text": "private lemma shiftRight_log2_sub_lt_pow2_24 (mant : Nat) (_hm : mant ≠ 0) (hlog : 23 ≤ mant.log2) :\n Nat.shiftRight mant (mant.log2 - 23) < pow2 24 := by\n -- Use the generic `lt_pow_succ_log_self` bound with base 2.\n have hlt : mant < 2 ^ (Nat.lo... | [
{
"name": "toEReal_roundDyadicDown_le_roundDyadicToIEEE32",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 12,
"n_lines": 5,
"n_chars": 314,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automatio... | 12 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | @@ -91,6 +91,29 @@
simpa [Nat.pow_add, Nat.mul_assoc, Nat.mul_left_comm, Nat.mul_comm] using hn
have hdiv : n / 2 ^ k < 2 ^ t := Nat.div_lt_of_lt_mul hn'
simpa [Nat.shiftRight_eq_div_pow] using hdiv
+private lemma shiftRight_log2_sub_lt_pow2_24 (mant : Nat) (_hm : mant ≠ 0) (hlog : 23 ≤ mant.log2) :
+ Nat... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e232b08abe58_7 | 15684f4a3944b0ba | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundDyadicToIEEE32Bounds.lean | RoundDyadicToIEEE32Bounds | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "roundDyadicToIEEE32_eq_roundDyadicDown_or_roundDyadicUp_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 796,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n intro d\n by_cases hm : mant = 0\n · subst hm\n simp [d, ro... | [
{
"name": "shiftRight_log2_sub_lt_pow2_24",
"text": "private lemma shiftRight_log2_sub_lt_pow2_24 (mant : Nat) (_hm : mant ≠ 0) (hlog : 23 ≤ mant.log2) :\n Nat.shiftRight mant (mant.log2 - 23) < pow2 24 := by\n -- Use the generic `lt_pow_succ_log_self` bound with base 2.\n have hlt : mant < 2 ^ (Nat.lo... | [
{
"name": "toEReal_roundDyadicToIEEE32_le_roundDyadicUp",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 12,
"n_lines": 5,
"n_chars": 310,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_... | 12 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Floats.IEEEExec.NatLemmas
publi... | @@ -91,6 +91,29 @@
simpa [Nat.pow_add, Nat.mul_assoc, Nat.mul_left_comm, Nat.mul_comm] using hn
have hdiv : n / 2 ^ k < 2 ^ t := Nat.div_lt_of_lt_mul hn'
simpa [Nat.shiftRight_eq_div_pow] using hdiv
+private lemma shiftRight_log2_sub_lt_pow2_24 (mant : Nat) (_hm : mant ≠ 0) (hlog : 23 ≤ mant.log2) :
+ Nat... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_68e7447ccc2e_0 | ca20c2898697c5c5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/SpecialRules.lean | SpecialRules | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "expField_quietNaN_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hx : isNaN x = true\n · -- `quietNaN` ORs `quietBit` into the fraction field; exponent bits are unchanged.\n... | [
{
"name": "expField_ofBits_or_quietBit",
"text": "private lemma expField_ofBits_or_quietBit (b : UInt32) :\n expField (ofBits (b ||| quietBit)) = expField (ofBits b) := by\n -- `quietNaN` is implemented by OR-ing a fixed bit (`quietBit`) into the fraction field.\n -- This lemma records the key invarian... | [
{
"name": "expField_quietNaN_eq",
"fan_in": 4,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 546,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | @@ -66,6 +66,52 @@
/-! ## Bitfield facts used by special-case lemmas -/
+private lemma expField_ofBits_or_quietBit (b : UInt32) :
+ expField (ofBits (b ||| quietBit)) = expField (ofBits b) := by
+ -- `quietNaN` is implemented by OR-ing a fixed bit (`quietBit`) into the fraction field.
+ -- This lemma records ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_68e7447ccc2e_1 | 90e8ff75d40813f8 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/SpecialRules.lean | SpecialRules | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "expField_quietNaN_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hx : isNaN x = true\n · -- `quietNaN` ORs `quietBit` into the fraction field; exponent bits are unchanged.\n... | [
{
"name": "expField_ofBits_or_quietBit",
"text": "private lemma expField_ofBits_or_quietBit (b : UInt32) :\n expField (ofBits (b ||| quietBit)) = expField (ofBits b) := by\n -- `quietNaN` is implemented by OR-ing a fixed bit (`quietBit`) into the fraction field.\n -- This lemma records the key invarian... | [
{
"name": "expField_quietNaN",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 192,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | @@ -66,6 +66,52 @@
/-! ## Bitfield facts used by special-case lemmas -/
+private lemma expField_ofBits_or_quietBit (b : UInt32) :
+ expField (ofBits (b ||| quietBit)) = expField (ofBits b) := by
+ -- `quietNaN` is implemented by OR-ing a fixed bit (`quietBit`) into the fraction field.
+ -- This lemma records ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_68e7447ccc2e_2 | 27efb156baf42d89 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/SpecialRules.lean | SpecialRules | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "expField_allOnes_of_isNaN",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n expField_eq_expAllOnes_of_isNaN x hx",
"n_chars": 39,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic"... | [
{
"name": "expField_eq_expAllOnes_of_isNaN",
"text": "/-- If `x` is a NaN, then its exponent field is all ones. -/\ntheorem expField_eq_expAllOnes_of_isNaN (x : IEEE32Exec) (hx : isNaN x = true) :\n expField x = expAllOnes := by\n -- By definition, `isNaN x` checks `(expField x == expAllOnes) && (fracFi... | [
{
"name": "expField_allOnes_of_isNaN",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 207,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | @@ -66,9 +66,23 @@
/-! ## Bitfield facts used by special-case lemmas -/
+/-- If `x` is a NaN, then its exponent field is all ones. -/
+theorem expField_eq_expAllOnes_of_isNaN (x : IEEE32Exec) (hx : isNaN x = true) :
+ expField x = expAllOnes := by
+ -- By definition, `isNaN x` checks `(expField x == expAllOnes... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_68e7447ccc2e_3 | 531fd8872b401400 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/SpecialRules.lean | SpecialRules | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "expField_allOnes_of_isInf",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n expField_eq_expAllOnes_of_isInf x hx",
"n_chars": 39,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic"... | [
{
"name": "expField_eq_expAllOnes_of_isInf",
"text": "/-- If `x` is an infinity, then its exponent field is all ones. -/\ntheorem expField_eq_expAllOnes_of_isInf (x : IEEE32Exec) (hx : isInf x = true) :\n expField x = expAllOnes := by\n -- By definition, `isInf x` checks `(expField x == expAllOnes) && (... | [
{
"name": "expField_allOnes_of_isInf",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 207,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | @@ -66,9 +66,22 @@
/-! ## Bitfield facts used by special-case lemmas -/
+/-- If `x` is an infinity, then its exponent field is all ones. -/
+theorem expField_eq_expAllOnes_of_isInf (x : IEEE32Exec) (hx : isInf x = true) :
+ expField x = expAllOnes := by
+ -- By definition, `isInf x` checks `(expField x == expA... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_68e7447ccc2e_4 | 137166028a867fef | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/SpecialRules.lean | SpecialRules | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "expField_quietNaN",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n expField_quietNaN_eq x",
"n_chars": 25,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation... | [
{
"name": "expField_quietNaN_eq",
"text": "/--\nQuieting a NaN does not change the exponent field.\n\nInformal: `quietNaN` only ORs `quietBit` into the fraction payload; exponent bits are preserved.\n-/\ntheorem expField_quietNaN_eq (x : IEEE32Exec) :\n expField (quietNaN x) = expField x := by\n by_case... | [
{
"name": "isFinite_eq_false_of_chooseNaN1_some",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 25,
"n_chars": 952,
"n_subproofs": 4,
"n_tactics": 15,
"cyclomatic": 3,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": ... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | @@ -112,6 +112,21 @@
simpa [hExpMask, hi] using (Nat.testBit_two_pow_sub_one 8 i)
simp [expField, ofBits, UInt32.toNat_and, UInt32.toNat_shiftRight, UInt32.toNat_or, hmask]
+/--
+Quieting a NaN does not change the exponent field.
+
+Informal: `quietNaN` only ORs `quietBit` into the fraction payload; expon... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_68e7447ccc2e_5 | c09d0c5c921b5281 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/SpecialRules.lean | SpecialRules | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "expField_quietNaN",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n expField_quietNaN_eq x",
"n_chars": 25,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation... | [
{
"name": "expField_quietNaN_eq",
"text": "/--\nQuieting a NaN does not change the exponent field.\n\nInformal: `quietNaN` only ORs `quietBit` into the fraction payload; exponent bits are preserved.\n-/\ntheorem expField_quietNaN_eq (x : IEEE32Exec) :\n expField (quietNaN x) = expField x := by\n by_case... | [
{
"name": "isFinite_eq_false_of_chooseNaN2_some",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 65,
"n_chars": 3149,
"n_subproofs": 17,
"n_tactics": 52,
"cyclomatic": 6,
"n_automation": 15,
"n_rewrites": 0,
"n_structural": 11,
"automation_onl... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | @@ -112,6 +112,21 @@
simpa [hExpMask, hi] using (Nat.testBit_two_pow_sub_one 8 i)
simp [expField, ofBits, UInt32.toNat_and, UInt32.toNat_shiftRight, UInt32.toNat_or, hmask]
+/--
+Quieting a NaN does not change the exponent field.
+
+Informal: `quietNaN` only ORs `quietBit` into the fraction payload; expon... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_68e7447ccc2e_6 | 7f604a1ae8901d05 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/SpecialRules.lean | SpecialRules | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "expField_quietNaN",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n expField_quietNaN_eq x",
"n_chars": 25,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation... | [
{
"name": "expField_quietNaN_eq",
"text": "/--\nQuieting a NaN does not change the exponent field.\n\nInformal: `quietNaN` only ORs `quietBit` into the fraction payload; exponent bits are preserved.\n-/\ntheorem expField_quietNaN_eq (x : IEEE32Exec) :\n expField (quietNaN x) = expField x := by\n by_case... | [
{
"name": "isFinite_eq_false_of_chooseNaN3_some",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 107,
"n_chars": 5475,
"n_subproofs": 25,
"n_tactics": 76,
"cyclomatic": 8,
"n_automation": 22,
"n_rewrites": 0,
"n_structural": 16,
"automation_on... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | @@ -112,6 +112,21 @@
simpa [hExpMask, hi] using (Nat.testBit_two_pow_sub_one 8 i)
simp [expField, ofBits, UInt32.toNat_and, UInt32.toNat_shiftRight, UInt32.toNat_or, hmask]
+/--
+Quieting a NaN does not change the exponent field.
+
+Informal: `quietNaN` only ORs `quietBit` into the fraction payload; expon... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_68e7447ccc2e_7 | e8ee38df934a3fe2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/SpecialRules.lean | SpecialRules | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "chooseNaN3_of_isSNaN_left",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n chooseNaN3_of_isSNaN_x x y z hx",
"n_chars": 34,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "chooseNaN3_of_isSNaN_x",
"text": "/-- If `x` is a signaling NaN, `chooseNaN3` returns it (quieted), regardless of `y` and `z`. -/\ntheorem chooseNaN3_of_isSNaN_x (x y z : IEEE32Exec) (hx : isSNaN x = true) :\n chooseNaN3 x y z = some (quietNaN x) := by\n simp [chooseNaN3, hx]\n\n",
"fan_i... | [
{
"name": "chooseNaN3_of_isSNaN_left",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 236,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | @@ -66,9 +66,15 @@
/-! ## Bitfield facts used by special-case lemmas -/
+/-- If `x` is a signaling NaN, `chooseNaN3` returns it (quieted), regardless of `y` and `z`. -/
+theorem chooseNaN3_of_isSNaN_x (x y z : IEEE32Exec) (hx : isSNaN x = true) :
+ chooseNaN3 x y z = some (quietNaN x) := by
+ simp [chooseNaN3,... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_68e7447ccc2e_8 | 3f5ab79111b68d08 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/SpecialRules.lean | SpecialRules | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "chooseNaN3_of_isSNaN_mid",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n chooseNaN3_of_isSNaN_y x y z hx hy",
"n_chars": 37,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1... | [
{
"name": "chooseNaN3_of_isSNaN_y",
"text": "/--\nIf `y` is a signaling NaN and `x` is not, `chooseNaN3` returns `y` (quieted).\n\nThis is the same precedence rule as `chooseNaN2`: signaling NaNs win (and get quieted).\n-/\ntheorem chooseNaN3_of_isSNaN_y (x y z : IEEE32Exec)\n (hx : isSNaN x = false) (hy... | [
{
"name": "chooseNaN3_of_isSNaN_mid",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 268,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | @@ -66,10 +66,21 @@
/-! ## Bitfield facts used by special-case lemmas -/
+/--
+If `y` is a signaling NaN and `x` is not, `chooseNaN3` returns `y` (quieted).
+
+This is the same precedence rule as `chooseNaN2`: signaling NaNs win (and get quieted).
+-/
+theorem chooseNaN3_of_isSNaN_y (x y z : IEEE32Exec)
+ (hx :... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_68e7447ccc2e_9 | 135e9e396059f153 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/SpecialRules.lean | SpecialRules | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "chooseNaN3_of_isSNaN_right",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n chooseNaN3_of_isSNaN_z x y z hx hy hz",
"n_chars": 40,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomati... | [
{
"name": "chooseNaN3_of_isSNaN_z",
"text": "/-- If only `z` is a signaling NaN, `chooseNaN3` returns `z` (quieted). -/\ntheorem chooseNaN3_of_isSNaN_z (x y z : IEEE32Exec)\n (hx : isSNaN x = false) (hy : isSNaN y = false) (hz : isSNaN z = true) :\n chooseNaN3 x y z = some (quietNaN z) := by\n simp [... | [
{
"name": "chooseNaN3_of_isSNaN_right",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 586,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Special-value rules for `IEEE32Exec`
`IEEE32Exec` is the executable, proof-relevant bit-level IEEE-754 b... | @@ -66,10 +66,18 @@
/-! ## Bitfield facts used by special-case lemmas -/
+/-- If only `z` is a signaling NaN, `chooseNaN3` returns `z` (quieted). -/
+theorem chooseNaN3_of_isSNaN_z (x y z : IEEE32Exec)
+ (hx : isSNaN x = false) (hy : isSNaN y = false) (hz : isSNaN z = true) :
+ chooseNaN3 x y z = some (quiet... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_5652cd31010d_0 | 9cd521bafff7abe6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Nodes/GraphComposition.lean | GraphComposition | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "weakenContext_backpropVec_eq_adjoint_fderiv",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n Graph.backpropVec_eq_adjoint_fderiv\n (Γ := Γ ++ extra) (ss := ss) (weakenContext dg extra).g (... | [
{
"name": "backpropVec_eq_adjoint_fderiv",
"text": "/--\nEnd-to-end analytic theorem for bundled graphs.\n\nThis is just `Graph.backpropVec_eq_adjoint_fderiv` with the bundled proof `dg.hg`.\n-/\ntheorem backpropVec_eq_adjoint_fderiv\n {Γ : List Shape} {ss : List Shape} (dg : DGraph Γ ss) :\n ∀ (xV : ... | [
{
"name": "weakenContext_backpropVec_eq_adjoint_fderiv",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 920,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_o... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.Piecewise
/-!
# Differentiable graph composition
The `DGraph` wrapper packages a tape graph together with node-local `NodeFDerivCorrect` proofs.
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.Piecewise
/-!
# Differentiable graph composition
The `DGraph` wrapper packages a tape graph together with node-local `NodeFDerivCorrect` proofs.
... | @@ -290,7 +290,9 @@
=
(fderiv ℝ
(Graph.evalVec (Γ := Γ ++ extra) (ss := ss) (weakenContext dg extra).g) xV).adjoint
- seedV := sorry
+ seedV :=
+ Graph.backpropVec_eq_adjoint_fderiv
+ (Γ := Γ ++ extra) (ss := ss) (weakenContext dg extra).g (weakenContext dg extra).hg
/--
... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_5652cd31010d_1 | b578e8b955f8eda9 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Nodes/GraphComposition.lean | GraphComposition | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "weakenContext_backpropVec_eq_adjoint_fderiv",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n Graph.backpropVec_eq_adjoint_fderiv\n (Γ := Γ ++ extra) (ss := ss) (weakenContext dg extra).g (... | [
{
"name": "backpropVec_eq_adjoint_fderiv",
"text": "/--\nEnd-to-end analytic theorem for bundled graphs.\n\nThis is just `Graph.backpropVec_eq_adjoint_fderiv` with the bundled proof `dg.hg`.\n-/\ntheorem backpropVec_eq_adjoint_fderiv\n {Γ : List Shape} {ss : List Shape} (dg : DGraph Γ ss) :\n ∀ (xV : ... | [
{
"name": "append_backpropVec_eq_adjoint_fderiv",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 19,
"n_chars": 921,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": f... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.Piecewise
/-!
# Differentiable graph composition
The `DGraph` wrapper packages a tape graph together with node-local `NodeFDerivCorrect` proofs.
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.Piecewise
/-!
# Differentiable graph composition
The `DGraph` wrapper packages a tape graph together with node-local `NodeFDerivCorrect` proofs.
... | @@ -289,7 +289,9 @@
Graph.backpropVec (Γ := Γ) (ss := ss₁ ++ ss₂) (append dg₁ dg₂).g xV seedV
=
(fderiv ℝ (Graph.evalVec (Γ := Γ) (ss := ss₁ ++ ss₂) (append dg₁ dg₂).g) xV).adjoint
- seedV := sorry
+ seedV :=
+ Graph.backpropVec_eq_adjoint_fderiv
+ (Γ := Γ) (ss := ss₁ ++ ss₂) (a... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_80f77d82dd08_0 | 6d58b548e4562dc1 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/Graph/BackwardApprox.lean | BackwardApprox | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "backprop_approx",
"depth": 1,
"n_commands": 0,
"n_lines": 94,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro xS xR epsIn seedS seedR epsSeed hx hseed\n induction g with\n | nil =>\n -- backprop is just a cast along `Γ ... | [
{
"name": "eval_approx",
"text": "/--\nForward approximation theorem for `RevGraph` (just `FwdGraph.eval_approx` via `toFwdGraph`).\n-/\ntheorem eval_approx {Γ : List Shape} {ss : List Shape} (g : RevGraph (α := α) toSpec Γ ss) :\n ∀ (xS : TList SpecScalar Γ) (xR : TList α Γ) (epsIn : EList Γ),\n ap... | [
{
"name": "backprop_approx",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 125,
"n_chars": 6661,
"n_subproofs": 7,
"n_tactics": 78,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.Graph.ForwardApprox
public import NN.Spec.Core.TensorOps
/-!
# BackwardApprox
Reverse-mode (backward) runtime→spec approximation framework.
This is th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.Graph.ForwardApprox
public import NN.Spec.Core.TensorOps
/-!
# BackwardApprox
Reverse-mode (backward) runtime→spec approximation framework.
This is th... | @@ -132,6 +132,22 @@
xR
/--
+Forward approximation theorem for `RevGraph` (just `FwdGraph.eval_approx` via `toFwdGraph`).
+-/
+theorem eval_approx {Γ : List Shape} {ss : List Shape} (g : RevGraph (α := α) toSpec Γ ss) :
+ ∀ (xS : TList SpecScalar Γ) (xR : TList α Γ) (epsIn : EList Γ),
+ approxCtx (α := ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_832c686a191f_0 | 3050bd76688704a2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/Boundary.lean | Boundary | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "observationHolds_of_checkObservation_eq_ok",
"depth": 1,
"n_commands": 0,
"n_lines": 51,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro hFiniteSwitch\n -- With `checkObsFinite=true`, `checkObservation` mus... | [
{
"name": "tensorFinite_of_checkTensorFinite_eq_ok",
"text": "private theorem tensorFinite_of_checkTensorFinite_eq_ok {s : Spec.Shape} (field : String)\n (t : Spec.Tensor Float s)\n (h : Internal.checkTensorFinite (s := s) (field := field) t = .ok ()) :\n tensorFinite (s := s) t = true := by\n -- ... | [
{
"name": "observationHolds_of_checkObservation_eq_ok",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 57,
"n_chars": 3090,
"n_subproofs": 6,
"n_tactics": 48,
"cyclomatic": 11,
"n_automation": 8,
"n_rewrites": 0,
"n_structural": 15,
"automatio... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.RL.Boundary.Core
public import NN.Proofs.RL.Tactics
/-!
# RL Trust-Boundary Proofs
`NN.Runtime.RL.Boundary.Core` provides executable “trust-boundary” checkers for e... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.RL.Boundary.Core
public import NN.Proofs.RL.Tactics
/-!
# RL Trust-Boundary Proofs
`NN.Runtime.RL.Boundary.Core` provides executable “trust-boundary” checkers for e... | @@ -51,6 +51,17 @@
These facts are purely about the small executable helpers in `Runtime.RL.Boundary.Internal`.
-/
+private theorem tensorFinite_of_checkTensorFinite_eq_ok {s : Spec.Shape} (field : String)
+ (t : Spec.Tensor Float s)
+ (h : Internal.checkTensorFinite (s := s) (field := field) t = .ok ()) :
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_832c686a191f_1 | 57b217729c330b56 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/Boundary.lean | Boundary | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "rewardHolds_of_checkReward_eq_ok",
"depth": 1,
"n_commands": 0,
"n_lines": 39,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro hFiniteSwitch\n have h' := h\n simp [checkReward, hFiniteSwitch, Bind.bind, ... | [
{
"name": "isFiniteFloat_of_checkFloatFinite_eq_ok",
"text": "private theorem isFiniteFloat_of_checkFloatFinite_eq_ok (field : String) (x : Float)\n (h : Internal.checkFloatFinite (field := field) x = .ok ()) :\n isFiniteFloat x = true := by\n cases hOk : isFiniteFloat x with\n | false =>\n sim... | [
{
"name": "rewardHolds_of_checkReward_eq_ok",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 45,
"n_chars": 2314,
"n_subproofs": 5,
"n_tactics": 38,
"cyclomatic": 9,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 12,
"automation_only": fa... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.RL.Boundary.Core
public import NN.Proofs.RL.Tactics
/-!
# RL Trust-Boundary Proofs
`NN.Runtime.RL.Boundary.Core` provides executable “trust-boundary” checkers for e... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.RL.Boundary.Core
public import NN.Proofs.RL.Tactics
/-!
# RL Trust-Boundary Proofs
`NN.Runtime.RL.Boundary.Core` provides executable “trust-boundary” checkers for e... | @@ -72,6 +72,15 @@
| true =>
simp
+private theorem isFiniteFloat_of_checkFloatFinite_eq_ok (field : String) (x : Float)
+ (h : Internal.checkFloatFinite (field := field) x = .ok ()) :
+ isFiniteFloat x = true := by
+ cases hOk : isFiniteFloat x with
+ | false =>
+ simp [Internal.checkFloatFinit... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d8ba3c3df87a_0 | a210b0a24e813d9d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/Quantized.lean | Quantized | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "mem_sub",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hy' : (-y) ∈ neg B := by\n constructor\n · have : -B.hi ≤ -y := neg_le_neg hy.2\n simpa [neg] using this\n · hav... | [
{
"name": "mem_add",
"text": "/-- Soundness of `add`: membership is preserved by real addition. -/\ntheorem mem_add {R : Rounder} {A B : RInterval} {x y : ℝ}\n (hx : x ∈ A) (hy : y ∈ B) :\n x + y ∈ add R A B := by\n constructor\n · have : A.lo + B.lo ≤ x + y := add_le_add hx.1 hy.1\n exact le_tra... | [
{
"name": "mem_sub",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 524,
"n_subproofs": 3,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 6
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Complex.Trigonometric
public import Mathlib.Data.EReal.Basic
public import NN.Floats.Interval.Rounders
/-!
# Quantized interval arithmetic (rounding-on-`ℝ`, ov... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Complex.Trigonometric
public import Mathlib.Data.EReal.Basic
public import NN.Floats.Interval.Rounders
/-!
# Quantized interval arithmetic (rounding-on-`ℝ`, ov... | @@ -112,10 +112,28 @@
let m : ℝ := absMax A * absMax B
⟨R.down (-m), R.up m⟩
+/-- Soundness of `add`: membership is preserved by real addition. -/
+theorem mem_add {R : Rounder} {A B : RInterval} {x y : ℝ}
+ (hx : x ∈ A) (hy : y ∈ B) :
+ x + y ∈ add R A B := by
+ constructor
+ · have : A.lo + B.lo ≤ x +... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d8ba3c3df87a_1 | 8f02bb143042a175 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/Quantized.lean | Quantized | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "mem_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hxabs : |x| ≤ absMax A := abs_le_absMax (I := A) hx\n have hyabs : |y| ≤ absMax B := abs_le_absMax (I := B) hy\n have hxyab... | [
{
"name": "abs_le_absMax",
"text": "/-- If `x ∈ I`, then `|x| ≤ absMax I`. -/\ntheorem abs_le_absMax {I : RInterval} {x : ℝ} (hx : x ∈ I) :\n |x| ≤ absMax I := by\n -- `abs` is convex on ℝ; max on an interval occurs at endpoints.\n exact abs_le_max_abs_abs hx.1 hx.2\n\n",
"fan_in": 2,
"n_lines"... | [
{
"name": "mem_mul",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 21,
"n_chars": 928,
"n_subproofs": 6,
"n_tactics": 13,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
"max_nesting": 4
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Complex.Trigonometric
public import Mathlib.Data.EReal.Basic
public import NN.Floats.Interval.Rounders
/-!
# Quantized interval arithmetic (rounding-on-`ℝ`, ov... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Complex.Trigonometric
public import Mathlib.Data.EReal.Basic
public import NN.Floats.Interval.Rounders
/-!
# Quantized interval arithmetic (rounding-on-`ℝ`, ov... | @@ -98,6 +98,12 @@
noncomputable def absMax (I : RInterval) : ℝ :=
max |I.lo| |I.hi|
+/-- If `x ∈ I`, then `|x| ≤ absMax I`. -/
+theorem abs_le_absMax {I : RInterval} {x : ℝ} (hx : x ∈ I) :
+ |x| ≤ absMax I := by
+ -- `abs` is convex on ℝ; max on an interval occurs at endpoints.
+ exact abs_le_max_abs_abs hx... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d8ba3c3df87a_2 | a19d019dbba858a6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/Quantized.lean | Quantized | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "mem_tanh",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [tanh] using (mem_tanhBounds (R := R) x)",
"n_chars": 52,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,... | [
{
"name": "mem_tanhBounds",
"text": "/-- Soundness of `tanhBounds`: `Real.tanh x ∈ [-1,1]`. -/\ntheorem mem_tanhBounds {R : Rounder} (x : ℝ) :\n Real.tanh x ∈ tanhBounds R := by\n -- `tanh x = sinh x / cosh x`, `cosh x > 0`, and `sinh x < cosh x`.\n have hcosh : 0 < Real.cosh x := Real.cosh_pos x\n ha... | [
{
"name": "mem_tanh",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 247,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2
}... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Complex.Trigonometric
public import Mathlib.Data.EReal.Basic
public import NN.Floats.Interval.Rounders
/-!
# Quantized interval arithmetic (rounding-on-`ℝ`, ov... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Complex.Trigonometric
public import Mathlib.Data.EReal.Basic
public import NN.Floats.Interval.Rounders
/-!
# Quantized interval arithmetic (rounding-on-`ℝ`, ov... | @@ -125,6 +125,34 @@
noncomputable def tanhBounds (R : Rounder) : RInterval :=
⟨R.down (-1), R.up 1⟩
+/-- Soundness of `tanhBounds`: `Real.tanh x ∈ [-1,1]`. -/
+theorem mem_tanhBounds {R : Rounder} (x : ℝ) :
+ Real.tanh x ∈ tanhBounds R := by
+ -- `tanh x = sinh x / cosh x`, `cosh x > 0`, and `sinh x < cosh x... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d8ba3c3df87a_3 | 83f7d549e7d5788a | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/Quantized.lean | Quantized | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "mem_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hxabs : |x| ≤ absMax A := abs_le_absMax (I := A) hx\n have hyabs : |y| ≤ absMax B := abs_le_absMax (I := B) hy\n have hxyab... | [
{
"name": "abs_le_absMax",
"text": "/-- If `x ∈ I`, then `|x| ≤ absMax I`. -/\ntheorem abs_le_absMax {I : RInterval} {x : ℝ} (hx : x ∈ I) :\n |x| ≤ absMax I := by\n -- `abs` is convex on ℝ; max on an interval occurs at endpoints.\n exact abs_le_max_abs_abs hx.1 hx.2\n\n",
"fan_in": 2,
"n_lines"... | [
{
"name": "mem_div_of_nozero",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 79,
"n_chars": 3726,
"n_subproofs": 34,
"n_tactics": 67,
"cyclomatic": 4,
"n_automation": 9,
"n_rewrites": 2,
"n_structural": 15,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Complex.Trigonometric
public import Mathlib.Data.EReal.Basic
public import NN.Floats.Interval.Rounders
/-!
# Quantized interval arithmetic (rounding-on-`ℝ`, ov... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Complex.Trigonometric
public import Mathlib.Data.EReal.Basic
public import NN.Floats.Interval.Rounders
/-!
# Quantized interval arithmetic (rounding-on-`ℝ`, ov... | @@ -98,6 +98,12 @@
noncomputable def absMax (I : RInterval) : ℝ :=
max |I.lo| |I.hi|
+/-- If `x ∈ I`, then `|x| ≤ absMax I`. -/
+theorem abs_le_absMax {I : RInterval} {x : ℝ} (hx : x ∈ I) :
+ |x| ≤ absMax I := by
+ -- `abs` is convex on ℝ; max on an interval occurs at endpoints.
+ exact abs_le_max_abs_abs hx... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6ed7da6fa2a9_0 | c800304f561ef9f9 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/SignedOps.lean | SignedOps | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "signBit_eq_testBit31",
"depth": 1,
"n_commands": 0,
"n_lines": 27,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hSignMask : signMask.toNat = 2 ^ 31 := signMask_toNat\n by_cases hb : x.bits.toNat.testBit 31\n ·... | [
{
"name": "signMask_toNat",
"text": "/-- `signMask` is the single bit `2^31` (as a `Nat`). -/\n@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "signBit_eq_testBit31",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 36,
"n_chars": 1679,
"n_subproofs": 9,
"n_tactics": 24,
"cyclomatic": 1,
"n_automation": 8,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | @@ -25,6 +25,9 @@
noncomputable section
+/-- `signMask` is the single bit `2^31` (as a `Nat`). -/
+@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide
+
/-- `expAllOnes` is the mask `2^8-1` (as a `Nat`). -/
@[simp] private lemma expAllOnes_toNat : (expAllOnes : UInt32).toNat = ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6ed7da6fa2a9_1 | c0f43342c5dc4771 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/SignedOps.lean | SignedOps | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "signBit_eq_testBit31",
"depth": 1,
"n_commands": 0,
"n_lines": 27,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hSignMask : signMask.toNat = 2 ^ 31 := signMask_toNat\n by_cases hb : x.bits.toNat.testBit 31\n ·... | [
{
"name": "signMask_toNat",
"text": "/-- `signMask` is the single bit `2^31` (as a `Nat`). -/\n@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "signBit_neg_of_isNaN_eq_false",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 32,
"n_chars": 1252,
"n_subproofs": 5,
"n_tactics": 18,
"cyclomatic": 3,
"n_automation": 4,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | @@ -25,6 +25,9 @@
noncomputable section
+/-- `signMask` is the single bit `2^31` (as a `Nat`). -/
+@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide
+
/-- `expAllOnes` is the mask `2^8-1` (as a `Nat`). -/
@[simp] private lemma expAllOnes_toNat : (expAllOnes : UInt32).toNat = ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6ed7da6fa2a9_2 | 266fe067bc13b2b6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/SignedOps.lean | SignedOps | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "toEReal_neg_of_isNaN_eq_false",
"depth": 1,
"n_commands": 0,
"n_lines": 32,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases hx : toDyadic? x with\n | some d =>\n exact toEReal_neg_of_toDyadic?_some (x := x) ... | [
{
"name": "toEReal_neg_of_toDyadic?_some",
"text": "/--\n`toEReal` respects negation on the finite/dyadic branch.\n\nWe phrase this lemma using the dyadic decode witness `toDyadic? x = some d`, which guarantees:\n- `x` is finite (hence `toEReal` agrees with `toReal`), and\n- `toReal (neg x) = -toReal x` (vi... | [
{
"name": "toEReal_neg_of_isNaN_eq_false",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 42,
"n_chars": 2060,
"n_subproofs": 10,
"n_tactics": 30,
"cyclomatic": 4,
"n_automation": 9,
"n_rewrites": 2,
"n_structural": 3,
"automation_only": false... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | @@ -25,6 +25,49 @@
noncomputable section
+/--
+`toEReal` respects negation on the finite/dyadic branch.
+
+We phrase this lemma using the dyadic decode witness `toDyadic? x = some d`, which guarantees:
+- `x` is finite (hence `toEReal` agrees with `toReal`), and
+- `toReal (neg x) = -toReal x` (via `toReal_neg_eq_... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6ed7da6fa2a9_3 | 5582a9a1f0ce1565 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/SignedOps.lean | SignedOps | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "signBit_eq_testBit31",
"depth": 1,
"n_commands": 0,
"n_lines": 27,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hSignMask : signMask.toNat = 2 ^ 31 := signMask_toNat\n by_cases hb : x.bits.toNat.testBit 31\n ·... | [
{
"name": "signMask_toNat",
"text": "/-- `signMask` is the single bit `2^31` (as a `Nat`). -/\n@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "toEReal_roundDyadicDown_le",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 7,
"n_lines": 80,
"n_chars": 4132,
"n_subproofs": 20,
"n_tactics": 63,
"cyclomatic": 5,
"n_automation": 10,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | @@ -68,6 +68,9 @@
need directly using the `Nat.testBit` API from Lean's core bitwise theory.
-/
+/-- `signMask` is the single bit `2^31` (as a `Nat`). -/
+@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide
+
/-- `expAllOnes` is the mask `2^8-1` (as a `Nat`). -/
@[simp] private ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6ed7da6fa2a9_4 | 1b29e6c45ca08f66 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/SignedOps.lean | SignedOps | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "signBit_eq_testBit31",
"depth": 1,
"n_commands": 0,
"n_lines": 27,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hSignMask : signMask.toNat = 2 ^ 31 := signMask_toNat\n by_cases hb : x.bits.toNat.testBit 31\n ·... | [
{
"name": "signMask_toNat",
"text": "/-- `signMask` is the single bit `2^31` (as a `Nat`). -/\n@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "toEReal_roundDyadicUp_ge",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 74,
"n_chars": 3740,
"n_subproofs": 20,
"n_tactics": 62,
"cyclomatic": 5,
"n_automation": 10,
"n_rewrites": 1,
"n_structural": 5,
"automation_only": false,
... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | @@ -68,6 +68,9 @@
need directly using the `Nat.testBit` API from Lean's core bitwise theory.
-/
+/-- `signMask` is the single bit `2^31` (as a `Nat`). -/
+@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide
+
/-- `expAllOnes` is the mask `2^8-1` (as a `Nat`). -/
@[simp] private ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6ed7da6fa2a9_5 | 4a0efa013360bbbd | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/SignedOps.lean | SignedOps | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "signBit_eq_testBit31",
"depth": 1,
"n_commands": 0,
"n_lines": 27,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hSignMask : signMask.toNat = 2 ^ 31 := signMask_toNat\n by_cases hb : x.bits.toNat.testBit 31\n ·... | [
{
"name": "signMask_toNat",
"text": "/-- `signMask` is the single bit `2^31` (as a `Nat`). -/\n@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "toEReal_addDown_le",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 8,
"n_lines": 43,
"n_chars": 2040,
"n_subproofs": 14,
"n_tactics": 34,
"cyclomatic": 3,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_... | 8 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | @@ -68,6 +68,9 @@
need directly using the `Nat.testBit` API from Lean's core bitwise theory.
-/
+/-- `signMask` is the single bit `2^31` (as a `Nat`). -/
+@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide
+
/-- `expAllOnes` is the mask `2^8-1` (as a `Nat`). -/
@[simp] private ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6ed7da6fa2a9_6 | bd80c31af6e6d3a7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/SignedOps.lean | SignedOps | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "signBit_eq_testBit31",
"depth": 1,
"n_commands": 0,
"n_lines": 27,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hSignMask : signMask.toNat = 2 ^ 31 := signMask_toNat\n by_cases hb : x.bits.toNat.testBit 31\n ·... | [
{
"name": "signMask_toNat",
"text": "/-- `signMask` is the single bit `2^31` (as a `Nat`). -/\n@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "toEReal_addUp_ge",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 41,
"n_chars": 1917,
"n_subproofs": 14,
"n_tactics": 34,
"cyclomatic": 3,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_ne... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | @@ -68,6 +68,9 @@
need directly using the `Nat.testBit` API from Lean's core bitwise theory.
-/
+/-- `signMask` is the single bit `2^31` (as a `Nat`). -/
+@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide
+
/-- `expAllOnes` is the mask `2^8-1` (as a `Nat`). -/
@[simp] private ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6ed7da6fa2a9_7 | 1e9b55b92b2a4f7a | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/SignedOps.lean | SignedOps | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "signBit_eq_testBit31",
"depth": 1,
"n_commands": 0,
"n_lines": 27,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hSignMask : signMask.toNat = 2 ^ 31 := signMask_toNat\n by_cases hb : x.bits.toNat.testBit 31\n ·... | [
{
"name": "signMask_toNat",
"text": "/-- `signMask` is the single bit `2^31` (as a `Nat`). -/\n@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "toEReal_mulDown_le",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 8,
"n_lines": 92,
"n_chars": 4979,
"n_subproofs": 26,
"n_tactics": 80,
"cyclomatic": 7,
"n_automation": 16,
"n_rewrites": 6,
"n_structural": 10,
"automation_only": false,
"ma... | 8 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | @@ -68,6 +68,9 @@
need directly using the `Nat.testBit` API from Lean's core bitwise theory.
-/
+/-- `signMask` is the single bit `2^31` (as a `Nat`). -/
+@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide
+
/-- `expAllOnes` is the mask `2^8-1` (as a `Nat`). -/
@[simp] private ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6ed7da6fa2a9_8 | 47d0c988e44bf716 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/SignedOps.lean | SignedOps | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "signBit_eq_testBit31",
"depth": 1,
"n_commands": 0,
"n_lines": 27,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hSignMask : signMask.toNat = 2 ^ 31 := signMask_toNat\n by_cases hb : x.bits.toNat.testBit 31\n ·... | [
{
"name": "signMask_toNat",
"text": "/-- `signMask` is the single bit `2^31` (as a `Nat`). -/\n@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "toEReal_mulUp_ge",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 90,
"n_chars": 4627,
"n_subproofs": 28,
"n_tactics": 84,
"cyclomatic": 7,
"n_automation": 18,
"n_rewrites": 7,
"n_structural": 11,
"automation_only": false,
"max_... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness.Positive
/-!
Signed directed-rounding soundness.
The lemmas in this file handle sign-sensitive arithmetic cases for lower and uppe... | @@ -68,6 +68,9 @@
need directly using the `Nat.testBit` API from Lean's core bitwise theory.
-/
+/-- `signMask` is the single bit `2^31` (as a `Nat`). -/
+@[simp] private lemma signMask_toNat : (signMask : UInt32).toNat = 2 ^ 31 := by decide
+
/-- `expAllOnes` is the mask `2^8-1` (as a `Nat`). -/
@[simp] private ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_1b91e764f479_0 | 66350207f04e3c11 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/ConvBackward/BiasKernel.lean | BiasKernel | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "approxT_conv2d_bias_deriv_spec",
"depth": 1,
"n_commands": 0,
"n_lines": 64,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro layerS layerR outS outR bT\n classical\n have hε : 0 ≤ linfNorm bT := linf_norm_nonneg (t := bT)\n ... | [
{
"name": "approx_conv2d_bias_point",
"text": "/--\nSoundness of the Conv2D **bias**-gradient pointwise bound.\n\nGiven `approxT` for `grad_output`, this shows the spec bias-gradient entry is approximated by the\nNF runtime entry within `conv2dBiasPointBound`.\n-/\ntheorem approx_conv2d_bias_point\n {inC... | [
{
"name": "approxT_conv2d_bias_deriv_spec",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 100,
"n_chars": 4820,
"n_subproofs": 11,
"n_tactics": 62,
"cyclomatic": 3,
"n_automation": 8,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": fal... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.ConvBackward.Common
/-!
# NeuralFloat Conv2D Bias/Kernel Backward Bounds
This file proves pointwise NeuralFloat approximation bounds for the Conv2D ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.ConvBackward.Common
/-!
# NeuralFloat Conv2D Bias/Kernel Backward Bounds
This file proves pointwise NeuralFloat approximation bounds for the Conv2D ... | @@ -60,6 +60,239 @@
(foldAddState (β := β) (fexp := fexp) (rnd := rnd) idxs termR epsTerm).2
/--
+Soundness of the Conv2D **bias**-gradient pointwise bound.
+
+Given `approxT` for `grad_output`, this shows the spec bias-gradient entry is approximated by the
+NF runtime entry within `conv2dBiasPointBound`.
+-/
+th... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_1b91e764f479_1 | 411afdea061ba7fe | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/ConvBackward/BiasKernel.lean | BiasKernel | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "approxT_conv2d_kernel_deriv_spec",
"depth": 1,
"n_commands": 0,
"n_lines": 138,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro layerS layerR outS outR bT\n classical\n have hε : 0 ≤ linfNorm bT := linf_norm_nonneg (t := bT)... | [
{
"name": "approx_conv2d_kernel_point",
"text": "/--\nSoundness of the Conv2D **kernel**-gradient pointwise bound.\n\nGiven `approxT` hypotheses for the input and upstream gradient (`grad_output`), this shows the spec\nkernel-gradient entry is approximated by the NF runtime entry within `conv2dKernelPointBo... | [
{
"name": "approxT_conv2d_kernel_deriv_spec",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 181,
"n_chars": 7665,
"n_subproofs": 15,
"n_tactics": 131,
"cyclomatic": 25,
"n_automation": 12,
"n_rewrites": 1,
"n_structural": 9,
"automation_only"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.ConvBackward.Common
/-!
# NeuralFloat Conv2D Bias/Kernel Backward Bounds
This file proves pointwise NeuralFloat approximation bounds for the Conv2D ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.ConvBackward.Common
/-!
# NeuralFloat Conv2D Bias/Kernel Backward Bounds
This file proves pointwise NeuralFloat approximation bounds for the Conv2D ... | @@ -123,6 +123,361 @@
(foldAddState (β := β) (fexp := fexp) (rnd := rnd) idxs termR epsTerm).2
/--
+Soundness of the Conv2D **kernel**-gradient pointwise bound.
+
+Given `approxT` hypotheses for the input and upstream gradient (`grad_output`), this shows the spec
+kernel-gradient entry is approximated by the NF r... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c749e2b40b82_0 | 3717de19910cc242 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/MlpMse.lean | MlpMse | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "reluDerivCLM_inner",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Expand inner products into coordinate sums and commute scalars.\n simp [inner_eq_sum_mul, reluDerivCLM_... | [
{
"name": "reluDerivCLM_apply",
"text": "/-- Coordinate formula for `reluDerivCLM`: it scales each coordinate by `relu'(xᵢ)`. -/\nlemma reluDerivCLM_apply {n : Nat} (x dx : Vec n) (i : Fin n) :\n (reluDerivCLM (n := n) x) dx i = dx i * Activation.Math.reluDerivSpec (x i) := by\n -- `reluDerivCLM` is imp... | [
{
"name": "reluDerivCLM_inner",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 457,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nest... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | @@ -67,13 +67,29 @@
WithLp.toLp 2 fun j : Fin n =>
Spec.get2 W i j
+/-- Coordinate formula for `reluDerivCLM`: it scales each coordinate by `relu'(xᵢ)`. -/
+lemma reluDerivCLM_apply {n : Nat} (x dx : Vec n) (i : Fin n) :
+ (reluDerivCLM (n := n) x) dx i = dx i * Activation.Math.reluDerivSpec (x i) := b... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c749e2b40b82_1 | 085392775a81aea3 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/MlpMse.lean | MlpMse | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "reluDerivCLM_adjoint_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n let A := reluDerivCLM (n := n) x\n have hforall : ∀ dx : Vec n, inner ℝ dx (A.adjoint δ) = inner ... | [
{
"name": "reluDerivCLM_inner",
"text": "/--\nReLU derivative map is self-adjoint w.r.t. the Euclidean inner product.\n\nThis is because it is a diagonal scaling map on `ℝⁿ`.\n-/\nlemma reluDerivCLM_inner {n : Nat} (x dx δ : Vec n) :\n inner ℝ ((reluDerivCLM (n := n) x) dx) δ = inner ℝ dx ((reluDerivCLM ... | [
{
"name": "reluDerivCLM_adjoint_apply",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 32,
"n_chars": 1476,
"n_subproofs": 7,
"n_tactics": 23,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | @@ -80,12 +80,29 @@
ContinuousLinearMap.smulRight_apply, ContinuousLinearMap.proj_apply, smul_eq_mul]
simpa [e] using this
+/--
+ReLU derivative map is self-adjoint w.r.t. the Euclidean inner product.
+
+This is because it is a diagonal scaling map on `ℝⁿ`.
+-/
+lemma reluDerivCLM_inner {n : Nat} (x dx δ : ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c749e2b40b82_2 | fda37503b3c1afdf | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/MlpMse.lean | MlpMse | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 6 | [
{
"theorem_name": "mseGrad_eq_adjoint_fderiv",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hf : fderiv ℝ (mse (n := n) t) y = (2 / (n : ℝ)) • innerSL ℝ (y - t) := by\n simpa using (hasFDerivAt_ms... | [
{
"name": "hasFDerivAt_mse",
"text": "/-- Fréchet derivative of MSE, packaged as a continuous linear map `Vec n →L ℝ`. -/\nlemma hasFDerivAt_mse {n : Nat} (t y : Vec n) :\n HasFDerivAt (mse (n := n) t) ((2 / (n : ℝ)) • (innerSL ℝ (y - t))) y := by\n have hsub : HasFDerivAt (fun y : Vec n => y - t) (1 : ... | [
{
"name": "mseGrad_eq_adjoint_fderiv",
"fan_in": 5,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 23,
"n_chars": 1054,
"n_subproofs": 2,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | @@ -102,6 +102,39 @@
def mseGrad {n : Nat} (y t : Vec n) : Vec n :=
(2 / (n : ℝ)) • (y - t)
+/-- Fréchet derivative of MSE, packaged as a continuous linear map `Vec n →L ℝ`. -/
+lemma hasFDerivAt_mse {n : Nat} (t y : Vec n) :
+ HasFDerivAt (mse (n := n) t) ((2 / (n : ℝ)) • (innerSL ℝ (y - t))) y := by
+ have ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c749e2b40b82_3 | 9b7417f83f102dda | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/MlpMse.lean | MlpMse | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "grad_W2_mse",
"depth": 1,
"n_commands": 0,
"n_lines": 36,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Compose `mse` with the `W2`-slice of the network.\n let f : Mat outDim hidDim → Vec outDim :=\n fun W2 => mlpVecMat (in... | [
{
"name": "mseGrad_eq_adjoint_fderiv",
"text": "/--\nThe VJP of MSE at `y` with upstream seed `1` equals the usual gradient `mseGrad y t`.\n\nThis is the scalar-loss specialization: for scalar loss `ℓ`, the gradient is `(fderiv ℓ)† 1`.\n-/\nlemma mseGrad_eq_adjoint_fderiv {n : Nat} (t y : Vec n) :\n VJP[... | [
{
"name": "grad_W2_mse",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 52,
"n_chars": 2637,
"n_subproofs": 5,
"n_tactics": 34,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting"... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | @@ -136,6 +136,28 @@
exact hscaled.congr_fderiv hcoef
/--
+The VJP of MSE at `y` with upstream seed `1` equals the usual gradient `mseGrad y t`.
+
+This is the scalar-loss specialization: for scalar loss `ℓ`, the gradient is `(fderiv ℓ)† 1`.
+-/
+lemma mseGrad_eq_adjoint_fderiv {n : Nat} (t y : Vec n) :
+ VJP[... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c749e2b40b82_4 | 9909c9bcde7534c9 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/MlpMse.lean | MlpMse | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "grad_W2_mse",
"depth": 1,
"n_commands": 0,
"n_lines": 36,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Compose `mse` with the `W2`-slice of the network.\n let f : Mat outDim hidDim → Vec outDim :=\n fun W2 => mlpVecMat (in... | [
{
"name": "mseGrad_eq_adjoint_fderiv",
"text": "/--\nThe VJP of MSE at `y` with upstream seed `1` equals the usual gradient `mseGrad y t`.\n\nThis is the scalar-loss specialization: for scalar loss `ℓ`, the gradient is `(fderiv ℓ)† 1`.\n-/\nlemma mseGrad_eq_adjoint_fderiv {n : Nat} (t y : Vec n) :\n VJP[... | [
{
"name": "grad_b2_mse",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 52,
"n_chars": 2603,
"n_subproofs": 5,
"n_tactics": 35,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
"max_nesting"... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | @@ -136,6 +136,28 @@
exact hscaled.congr_fderiv hcoef
/--
+The VJP of MSE at `y` with upstream seed `1` equals the usual gradient `mseGrad y t`.
+
+This is the scalar-loss specialization: for scalar loss `ℓ`, the gradient is `(fderiv ℓ)† 1`.
+-/
+lemma mseGrad_eq_adjoint_fderiv {n : Nat} (t y : Vec n) :
+ VJP[... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c749e2b40b82_5 | 8aad37f05b8cab2c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/MlpMse.lean | MlpMse | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "grad_W2_mse",
"depth": 1,
"n_commands": 0,
"n_lines": 36,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Compose `mse` with the `W2`-slice of the network.\n let f : Mat outDim hidDim → Vec outDim :=\n fun W2 => mlpVecMat (in... | [
{
"name": "mseGrad_eq_adjoint_fderiv",
"text": "/--\nThe VJP of MSE at `y` with upstream seed `1` equals the usual gradient `mseGrad y t`.\n\nThis is the scalar-loss specialization: for scalar loss `ℓ`, the gradient is `(fderiv ℓ)† 1`.\n-/\nlemma mseGrad_eq_adjoint_fderiv {n : Nat} (t y : Vec n) :\n VJP[... | [
{
"name": "grad_b1_mse",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 7,
"n_lines": 51,
"n_chars": 2897,
"n_subproofs": 5,
"n_tactics": 36,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting"... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | @@ -191,6 +191,28 @@
exact hscaled.congr_fderiv hcoef
/--
+The VJP of MSE at `y` with upstream seed `1` equals the usual gradient `mseGrad y t`.
+
+This is the scalar-loss specialization: for scalar loss `ℓ`, the gradient is `(fderiv ℓ)† 1`.
+-/
+lemma mseGrad_eq_adjoint_fderiv {n : Nat} (t y : Vec n) :
+ VJP[... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c749e2b40b82_6 | 925e82c11046d16e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/MlpMse.lean | MlpMse | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "grad_W2_mse",
"depth": 1,
"n_commands": 0,
"n_lines": 36,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Compose `mse` with the `W2`-slice of the network.\n let f : Mat outDim hidDim → Vec outDim :=\n fun W2 => mlpVecMat (in... | [
{
"name": "mseGrad_eq_adjoint_fderiv",
"text": "/--\nThe VJP of MSE at `y` with upstream seed `1` equals the usual gradient `mseGrad y t`.\n\nThis is the scalar-loss specialization: for scalar loss `ℓ`, the gradient is `(fderiv ℓ)† 1`.\n-/\nlemma mseGrad_eq_adjoint_fderiv {n : Nat} (t y : Vec n) :\n VJP[... | [
{
"name": "grad_x_mse",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 7,
"n_lines": 51,
"n_chars": 2909,
"n_subproofs": 5,
"n_tactics": 35,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | @@ -191,6 +191,28 @@
exact hscaled.congr_fderiv hcoef
/--
+The VJP of MSE at `y` with upstream seed `1` equals the usual gradient `mseGrad y t`.
+
+This is the scalar-loss specialization: for scalar loss `ℓ`, the gradient is `(fderiv ℓ)† 1`.
+-/
+lemma mseGrad_eq_adjoint_fderiv {n : Nat} (t y : Vec n) :
+ VJP[... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c749e2b40b82_7 | d3e363a1e6038407 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/MlpMse.lean | MlpMse | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "grad_W2_mse",
"depth": 1,
"n_commands": 0,
"n_lines": 36,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Compose `mse` with the `W2`-slice of the network.\n let f : Mat outDim hidDim → Vec outDim :=\n fun W2 => mlpVecMat (in... | [
{
"name": "mseGrad_eq_adjoint_fderiv",
"text": "/--\nThe VJP of MSE at `y` with upstream seed `1` equals the usual gradient `mseGrad y t`.\n\nThis is the scalar-loss specialization: for scalar loss `ℓ`, the gradient is `(fderiv ℓ)† 1`.\n-/\nlemma mseGrad_eq_adjoint_fderiv {n : Nat} (t y : Vec n) :\n VJP[... | [
{
"name": "grad_W1_mse",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 7,
"n_lines": 63,
"n_chars": 3582,
"n_subproofs": 5,
"n_tactics": 44,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting"... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Params
public import NN.Proofs.Autograd.Notation
public import NN.Spec.Models.Mlp
public import Mathlib.Analysis.InnerProductSpace.Calculus
/-!
# Mlp... | @@ -191,6 +191,28 @@
exact hscaled.congr_fderiv hcoef
/--
+The VJP of MSE at `y` with upstream seed `1` equals the usual gradient `mseGrad y t`.
+
+This is the scalar-loss specialization: for scalar loss `ℓ`, the gradient is `(fderiv ℓ)† 1`.
+-/
+lemma mseGrad_eq_adjoint_fderiv {n : Nat} (t y : Vec n) :
+ VJP[... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b885a515799a_0 | fdce1bf32681619e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/SelfSupervised/PredictiveView.lean | PredictiveView | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "graphAlignmentEnergy_nonneg",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold graphAlignmentEnergy\n induction graph.positiveEdges with\n | nil => simp\n | cons edge rest ih =>\n ... | [
{
"name": "sqDist_nonneg",
"text": "/-- Squared Euclidean distance is nonnegative. -/\ntheorem sqDist_nonneg {d : Nat} (z w : EuclideanRep d) :\n 0 ≤ sqDist z w := by\n unfold sqDist\n exact Finset.sum_nonneg (fun j _ => sq_nonneg (z j - w j))\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 212... | [
{
"name": "graphAlignmentEnergy_nonneg",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 415,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.SelfSupervised.JEPA
public import NN.MLTheory.SelfSupervised.MAE
public import NN.MLTheory.SelfSupervised.VICReg
public import Mathlib.Algebra.BigOperators.Fin
publi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.SelfSupervised.JEPA
public import NN.MLTheory.SelfSupervised.MAE
public import NN.MLTheory.SelfSupervised.VICReg
public import Mathlib.Algebra.BigOperators.Fin
publi... | @@ -260,6 +260,12 @@
noncomputable def sqDist {d : Nat} (z w : EuclideanRep d) : ℝ :=
∑ j : Fin d, (z j - w j) ^ 2
+/-- Squared Euclidean distance is nonnegative. -/
+theorem sqDist_nonneg {d : Nat} (z w : EuclideanRep d) :
+ 0 ≤ sqDist z w := by
+ unfold sqDist
+ exact Finset.sum_nonneg (fun j _ => sq_nonne... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b885a515799a_1 | 7cd284ffc3fa79a3 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/SelfSupervised/PredictiveView.lean | PredictiveView | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "graphAlignmentEnergy_eq_zero_of_collapsed",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hcollapsed with ⟨z, hz⟩\n unfold graphAlignmentEnergy\n induction graph.positiveEdges wi... | [
{
"name": "sqDist_self",
"text": "/-- A vector has zero squared distance from itself. -/\n@[simp] theorem sqDist_self {d : Nat} (z : EuclideanRep d) :\n sqDist z z = 0 := by\n simp [sqDist]\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 158,
"n_subproofs": 0,
"n_tactics": 2,
"cyclom... | [
{
"name": "graphAlignmentEnergy_eq_zero_of_collapsed",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 570,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 2,
"automation_onl... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.SelfSupervised.JEPA
public import NN.MLTheory.SelfSupervised.MAE
public import NN.MLTheory.SelfSupervised.VICReg
public import Mathlib.Algebra.BigOperators.Fin
publi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.SelfSupervised.JEPA
public import NN.MLTheory.SelfSupervised.MAE
public import NN.MLTheory.SelfSupervised.VICReg
public import Mathlib.Algebra.BigOperators.Fin
publi... | @@ -260,6 +260,11 @@
noncomputable def sqDist {d : Nat} (z w : EuclideanRep d) : ℝ :=
∑ j : Fin d, (z j - w j) ^ 2
+/-- A vector has zero squared distance from itself. -/
+@[simp] theorem sqDist_self {d : Nat} (z : EuclideanRep d) :
+ sqDist z z = 0 := by
+ simp [sqDist]
+
/-- Real-valued alignment energy in... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b885a515799a_2 | 5a4706f6ffe7091c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/SelfSupervised/PredictiveView.lean | PredictiveView | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "realVarianceFloorGuard_zero_spread_positive",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [realVarianceFloorGuard_zero_spread (d := d) (gamma := gamma) (le_of_lt hgamma)]\n exact mu... | [
{
"name": "realVarianceFloorGuard_zero_spread",
"text": "/-- Zero spread in every coordinate pays exactly `d * gamma` when `gamma` is nonnegative. -/\ntheorem realVarianceFloorGuard_zero_spread {d : Nat} {gamma : ℝ}\n (hgamma : 0 ≤ gamma) :\n realVarianceFloorGuard (d := d) gamma (fun _ => 0) = d * ga... | [
{
"name": "realVarianceFloorGuard_zero_spread_positive",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 416,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_on... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.SelfSupervised.JEPA
public import NN.MLTheory.SelfSupervised.MAE
public import NN.MLTheory.SelfSupervised.VICReg
public import Mathlib.Algebra.BigOperators.Fin
publi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.SelfSupervised.JEPA
public import NN.MLTheory.SelfSupervised.MAE
public import NN.MLTheory.SelfSupervised.VICReg
public import Mathlib.Algebra.BigOperators.Fin
publi... | @@ -293,10 +293,18 @@
(gamma : ℝ) (spread : Fin d → ℝ) : ℝ :=
∑ j : Fin d, realVarianceFloorPenalty gamma (spread j)
+/-- Zero spread in every coordinate pays exactly `d * gamma` when `gamma` is nonnegative. -/
+theorem realVarianceFloorGuard_zero_spread {d : Nat} {gamma : ℝ}
+ (hgamma : 0 ≤ gamma) :
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b885a515799a_3 | 57724dd69fdfd157 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/SelfSupervised/PredictiveView.lean | PredictiveView | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "graphSSLObjective_eq_guard_of_collapsed",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [graphSSLObjective, graphAlignmentEnergy_eq_zero_of_collapsed graph rep hcollapsed,\n coord... | [
{
"name": "coordinateSpread_eq_zero_of_collapsed",
"text": "/-- A collapsed representation has zero spread in every coordinate. -/\ntheorem coordinateSpread_eq_zero_of_collapsed {n d : Nat}\n (rep : Fin n → EuclideanRep d) (hcollapsed : CollapsedRep rep) (j : Fin d) :\n coordinateSpread rep j = 0 := b... | [
{
"name": "graphSSLObjective_eq_guard_of_collapsed",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 13,
"n_chars": 585,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only"... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.SelfSupervised.JEPA
public import NN.MLTheory.SelfSupervised.MAE
public import NN.MLTheory.SelfSupervised.VICReg
public import Mathlib.Algebra.BigOperators.Fin
publi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.SelfSupervised.JEPA
public import NN.MLTheory.SelfSupervised.MAE
public import NN.MLTheory.SelfSupervised.VICReg
public import Mathlib.Algebra.BigOperators.Fin
publi... | @@ -299,6 +299,13 @@
(rep : Fin n → EuclideanRep d) (j : Fin d) : ℝ :=
∑ i : Fin n, ∑ k : Fin n, (rep i j - rep k j) ^ 2
+/-- A collapsed representation has zero spread in every coordinate. -/
+theorem coordinateSpread_eq_zero_of_collapsed {n d : Nat}
+ (rep : Fin n → EuclideanRep d) (hcollapsed : Collapse... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b885a515799a_4 | fb3c54091fd37479 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/SelfSupervised/PredictiveView.lean | PredictiveView | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "graphSSLObjective_collapsed_positive",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [graphSSLObjective_eq_guard_of_collapsed graph rep gamma hcollapsed]\n exact realVarianceFloorGuar... | [
{
"name": "realVarianceFloorGuard_zero_spread_positive",
"text": "/-- Collapsed coordinate-spread summaries pay a positive variance-floor guard in nonzero dimension. -/\ntheorem realVarianceFloorGuard_zero_spread_positive {d : Nat} {gamma : ℝ}\n (hd : 0 < d) (hgamma : 0 < gamma) :\n 0 < realVarianceFl... | [
{
"name": "graphSSLObjective_collapsed_positive",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 13,
"n_chars": 602,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": f... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.SelfSupervised.JEPA
public import NN.MLTheory.SelfSupervised.MAE
public import NN.MLTheory.SelfSupervised.VICReg
public import Mathlib.Algebra.BigOperators.Fin
publi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.SelfSupervised.JEPA
public import NN.MLTheory.SelfSupervised.MAE
public import NN.MLTheory.SelfSupervised.VICReg
public import Mathlib.Algebra.BigOperators.Fin
publi... | @@ -321,6 +321,13 @@
realVarianceFloorGuard (d := d) gamma (fun _ => 0) = d * gamma := by
simp [realVarianceFloorGuard, realVarianceFloorPenalty, hgamma]
+/-- Collapsed coordinate-spread summaries pay a positive variance-floor guard in nonzero dimension. -/
+theorem realVarianceFloorGuard_zero_spread_positive... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e8870efd22bc_0 | 877e08c8bfb08c56 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/ReLU/Bridge/ReLUMlpBridge.lean | ReLUMlpBridge | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "mlp_eval_affine_id",
"depth": 1,
"n_commands": 0,
"n_lines": 87,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Unfold evaluation and rewrite the MLP as `linear ∘ relu ∘ linear`.\n unfold mlpEvalNd\n rw [mlp_forwa... | [
{
"name": "toVec_dim_toVec",
"text": "/-- Rewrapping a vector by `Tensor.dim` preserves the underlying coordinate function `toVec`. -/\nlemma toVec_dim_toVec {n : Nat} (x : TensorVec n) :\n toVec (Tensor.dim (fun j : Fin n => Tensor.scalar (toVec x j))) = toVec x := by\n funext j\n cases x with\n | di... | [
{
"name": "mlp_eval_affine_id",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 96,
"n_chars": 4669,
"n_subproofs": 8,
"n_tactics": 72,
"cyclomatic": 5,
"n_automation": 8,
"n_rewrites": 9,
"n_structural": 9,
"automation_only": false,
"max_n... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.MLTheory.Proofs.Approximation.Universal.UniversalApproximation
public import NN.Spec.Core.Tensor
public import NN.Spec.Layers.Activation... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.MLTheory.Proofs.Approximation.Universal.UniversalApproximation
public import NN.Spec.Core.Tensor
public import NN.Spec.Layers.Activation... | @@ -50,6 +50,14 @@
noncomputable def toVec {n : Nat} (x : TensorVec n) : Fin n → ℝ :=
(Tensor.dimScalarEquiv (α := ℝ) n).toFun x
+/-- Rewrapping a vector by `Tensor.dim` preserves the underlying coordinate function `toVec`. -/
+lemma toVec_dim_toVec {n : Nat} (x : TensorVec n) :
+ toVec (Tensor.dim (fun j : Fi... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e8870efd22bc_1 | e000f1aae111ba5a | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/ReLU/Bridge/ReLUMlpBridge.lean | ReLUMlpBridge | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "mlp_eval_affine_id",
"depth": 1,
"n_commands": 0,
"n_lines": 87,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Unfold evaluation and rewrite the MLP as `linear ∘ relu ∘ linear`.\n unfold mlpEvalNd\n rw [mlp_forwa... | [
{
"name": "toVec_dim_toVec",
"text": "/-- Rewrapping a vector by `Tensor.dim` preserves the underlying coordinate function `toVec`. -/\nlemma toVec_dim_toVec {n : Nat} (x : TensorVec n) :\n toVec (Tensor.dim (fun j : Fin n => Tensor.scalar (toVec x j))) = toVec x := by\n funext j\n cases x with\n | di... | [
{
"name": "mlp_eval_coord",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 17,
"n_chars": 679,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting"... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.MLTheory.Proofs.Approximation.Universal.UniversalApproximation
public import NN.Spec.Core.Tensor
public import NN.Spec.Layers.Activation... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.MLTheory.Proofs.Approximation.Universal.UniversalApproximation
public import NN.Spec.Core.Tensor
public import NN.Spec.Layers.Activation... | @@ -50,6 +50,14 @@
noncomputable def toVec {n : Nat} (x : TensorVec n) : Fin n → ℝ :=
(Tensor.dimScalarEquiv (α := ℝ) n).toFun x
+/-- Rewrapping a vector by `Tensor.dim` preserves the underlying coordinate function `toVec`. -/
+lemma toVec_dim_toVec {n : Nat} (x : TensorVec n) :
+ toVec (Tensor.dim (fun j : Fi... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e8870efd22bc_2 | 4db4da77b186b857 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/ReLU/Bridge/ReLUMlpBridge.lean | ReLUMlpBridge | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "mlp_eval_affine_id",
"depth": 1,
"n_commands": 0,
"n_lines": 87,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Unfold evaluation and rewrite the MLP as `linear ∘ relu ∘ linear`.\n unfold mlpEvalNd\n rw [mlp_forwa... | [
{
"name": "toVec_dim_toVec",
"text": "/-- Rewrapping a vector by `Tensor.dim` preserves the underlying coordinate function `toVec`. -/\nlemma toVec_dim_toVec {n : Nat} (x : TensorVec n) :\n toVec (Tensor.dim (fun j : Fin n => Tensor.scalar (toVec x j))) = toVec x := by\n funext j\n cases x with\n | di... | [
{
"name": "mlp_eval_lift_from_1d",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 78,
"n_chars": 3753,
"n_subproofs": 6,
"n_tactics": 62,
"cyclomatic": 5,
"n_automation": 7,
"n_rewrites": 9,
"n_structural": 10,
"automation_only": false,
"m... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.MLTheory.Proofs.Approximation.Universal.UniversalApproximation
public import NN.Spec.Core.Tensor
public import NN.Spec.Layers.Activation... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.MLTheory.Proofs.Approximation.Universal.UniversalApproximation
public import NN.Spec.Core.Tensor
public import NN.Spec.Layers.Activation... | @@ -50,6 +50,14 @@
noncomputable def toVec {n : Nat} (x : TensorVec n) : Fin n → ℝ :=
(Tensor.dimScalarEquiv (α := ℝ) n).toFun x
+/-- Rewrapping a vector by `Tensor.dim` preserves the underlying coordinate function `toVec`. -/
+lemma toVec_dim_toVec {n : Nat} (x : TensorVec n) :
+ toVec (Tensor.dim (fun j : Fi... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_7f3e5b1971b7_0 | 2f10307ea83ec58e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/Scale/BackwardScale.lean | BackwardScale | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "evalSpec_eq_rev",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n by\n -- `RevGraph.evalSpec` is `FwdGraph.evalSpec` of `RevGraph.toFwdGraph`.\n simpa [evalSpec, RevGraph.evalSpec, Fwd... | [
{
"name": "toFwdGraph_toFwdGraphScale_eq",
"text": "theorem toFwdGraph_toFwdGraphScale_eq {Γ : List Shape} {ss : List Shape}\n (g : RevGraphScale (α := α) toSpec Γ ss) :\n FwdGraphScale.toFwdGraph (toFwdGraphScale (α := α) (toSpec := toSpec) g) =\n RevGraph.toFwdGraph (toRevGraph (α := α) (toSpec... | [
{
"name": "evalSpec_eq_rev",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 666,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
public import NN.Proofs.RuntimeApprox.Graph.BackwardApprox
public import NN.Proofs.RuntimeApprox.Scale.ForwardScale
/-!
# BackwardScale
Backward (reve... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
public import NN.Proofs.RuntimeApprox.Graph.BackwardApprox
public import NN.Proofs.RuntimeApprox.Scale.ForwardScale
/-!
# BackwardScale
Backward (reve... | @@ -95,6 +95,15 @@
scaleBound := node.fwdScaleBound
scaleSound := node.fwdScaleSound }
+theorem toFwdGraph_toFwdGraphScale_eq {Γ : List Shape} {ss : List Shape}
+ (g : RevGraphScale (α := α) toSpec Γ ss) :
+ FwdGraphScale.toFwdGraph (toFwdGraphScale (α := α) (toSpec := toSpec) g) =
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_7f3e5b1971b7_1 | 995786ad592b65b5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/Scale/BackwardScale.lean | BackwardScale | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "backprop_scale",
"depth": 1,
"n_commands": 0,
"n_lines": 105,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro xS xR epsIn bIn seedS seedR bSeed hx hB hinSeed\n revert xS xR epsIn bIn seedS seedR bSeed hx hB hinSeed\n inducti... | [
{
"name": "eval_scale",
"text": "theorem eval_scale {Γ : List Shape} {ss : List Shape} (g : RevGraphScale (α := α) toSpec Γ ss) :\n ∀ (xS : TList SpecScalar Γ) (xR : TList α Γ) (epsIn : EList Γ) (bIn : BList Γ),\n approxCtx (α := α) toSpec xS xR epsIn →\n scaleCtx (α := α) toSpec xS xR bIn →\n ... | [
{
"name": "backprop_scale",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 122,
"n_chars": 7062,
"n_subproofs": 10,
"n_tactics": 86,
"cyclomatic": 2,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
public import NN.Proofs.RuntimeApprox.Graph.BackwardApprox
public import NN.Proofs.RuntimeApprox.Scale.ForwardScale
/-!
# BackwardScale
Backward (reve... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
public import NN.Proofs.RuntimeApprox.Graph.BackwardApprox
public import NN.Proofs.RuntimeApprox.Scale.ForwardScale
/-!
# BackwardScale
Backward (reve... | @@ -149,6 +149,21 @@
FwdGraphScale.evalScales (α := α) (toSpec := toSpec) (Γ := Γ) (ss := ss) (toFwdGraphScale (α := α)
g) bIn xR
+theorem eval_scale {Γ : List Shape} {ss : List Shape} (g : RevGraphScale (α := α) toSpec Γ ss) :
+ ∀ (xS : TList SpecScalar Γ) (xR : TList α Γ) (epsIn : EList Γ) (bIn : BList Γ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_f6a2180c1006_0 | 73b6c575a5f7b112 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/Exec32/Compare.lean | Compare | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "le_self_of_isFinite_eq_true",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hne : (expField x != expAllOnes) = true := by simpa [isFinite] using hx\n have hexp : (expField x == exp... | [
{
"name": "cmpDyadic_self",
"text": "private lemma cmpDyadic_self (d : Dyadic) : cmpDyadic d d = .eq := by\n by_cases hm : d.mant == 0 <;> simp [cmpDyadic, hm]\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 124,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 2,
"n_automation": 1,
... | [
{
"name": "le_self_of_isFinite_eq_true",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 29,
"n_chars": 1274,
"n_subproofs": 6,
"n_tactics": 17,
"cyclomatic": 7,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32.Directed
/-!
Comparisons for executable IEEE32 values.
The definitions here implement the ordering and classification behavior used by the executable... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32.Directed
/-!
Comparisons for executable IEEE32 values.
The definitions here implement the ordering and classification behavior used by the executable... | @@ -69,6 +69,9 @@
For the interval layer, we mainly need the basic fact that `le` is reflexive on finite values.
-/
+private lemma cmpDyadic_self (d : Dyadic) : cmpDyadic d d = .eq := by
+ by_cases hm : d.mant == 0 <;> simp [cmpDyadic, hm]
+
/--
`IEEE32Exec.le` is reflexive on finite values.
@@ -78,7 +81,24 @@... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_f6a2180c1006_1 | 6488e1f22b6c6573 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/Exec32/Compare.lean | Compare | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "le_self_of_isFinite_eq_true_imp",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro hx\n exact le_self_of_isFinite_eq_true (x := x) hx",
"n_chars": 62,
"n_subproofs": 0,
"n... | [
{
"name": "le_self_of_isFinite_eq_true",
"text": "/--\n`IEEE32Exec.le` is reflexive on finite values.\n\nInformally: if `x` is a finite float32, then `x ≤ x`. (NaNs are excluded by the `isFinite` premise:\nfor NaN, `isFinite x = false` and `x ≤ x` is false because `compare` returns `none`.)\n\nThis lemma is... | [
{
"name": "isFinite_imp_le_self_iff_true",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 16,
"n_chars": 502,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32.Directed
/-!
Comparisons for executable IEEE32 values.
The definitions here implement the ordering and classification behavior used by the executable... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32.Directed
/-!
Comparisons for executable IEEE32 values.
The definitions here implement the ordering and classification behavior used by the executable... | @@ -72,8 +72,38 @@
private lemma cmpDyadic_self (d : Dyadic) : cmpDyadic d d = .eq := by
by_cases hm : d.mant == 0 <;> simp [cmpDyadic, hm]
+/--
+`IEEE32Exec.le` is reflexive on finite values.
+
+Informally: if `x` is a finite float32, then `x ≤ x`. (NaNs are excluded by the `isFinite` premise:
+for NaN, `isFinit... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_cf81d9a917ce_0 | ecba29122892bf79 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Spec/Models/Mamba.lean | Mamba | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "runList_outputs_length",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [runList] using m.runListAux_outputs_length h0 [] xs",
"n_chars": 64,
"n_subproofs": 0,
"n_tactics... | [
{
"name": "runListAux_outputs_length",
"text": "/-- The full Mamba recurrent pass emits one output token per input token. -/\ntheorem runListAux_outputs_length\n (m : SelectiveMambaBlockSpec α inputDim innerDim stateDim outputDim convWidth)\n (h0 : Tensor α (.dim innerDim (.dim stateDim .scalar)))\n ... | [
{
"name": "runList_outputs_length",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 417,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_n... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Dynamics.StateSpace
public import NN.Spec.Layers.Activation
/-!
# Mamba-style selective state-space blocks
Mamba replaces quad... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Dynamics.StateSpace
public import NN.Spec.Layers.Activation
/-!
# Mamba-style selective state-space blocks
Mamba replaces quad... | @@ -302,12 +302,26 @@
m.runList h0 [] = (h0, []) := by
rfl
+/-- The full Mamba recurrent pass emits one output token per input token. -/
+theorem runListAux_outputs_length
+ (m : SelectiveMambaBlockSpec α inputDim innerDim stateDim outputDim convWidth)
+ (h0 : Tensor α (.dim innerDim (.dim stateDim .sca... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_1f62d1ca269d_0 | 214f53494648c13c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Utils/List.lean | List | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "le_foldl_max_of_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction l generalizing acc with\n | nil =>\n cases hi\n | cons hd tl ih =>\n rcases (List.mem_cons.1 hi)... | [
{
"name": "le_foldl_max_init",
"text": "/--\nLower bound helper for `foldl max`.\n\nThe folded maximum is always at least as large as the initial accumulator.\n-/\nlemma le_foldl_max_init {ι β : Type} [LinearOrder β] (l : List ι) (f : ι → β) (acc : β) :\n acc ≤ l.foldl (fun a i => max a (f i)) acc := by\... | [
{
"name": "le_foldl_max_of_mem",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 809,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 4,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Group.MinMax
public import Mathlib.Algebra.Ring.Basic
public import Mathlib.Data.Fintype.BigOperators
public import Mathlib.Data.List.FinRange
public impor... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Group.MinMax
public import Mathlib.Algebra.Ring.Basic
public import Mathlib.Data.Fintype.BigOperators
public import Mathlib.Data.List.FinRange
public impor... | @@ -25,6 +25,22 @@
namespace List
/--
+Lower bound helper for `foldl max`.
+
+The folded maximum is always at least as large as the initial accumulator.
+-/
+lemma le_foldl_max_init {ι β : Type} [LinearOrder β] (l : List ι) (f : ι → β) (acc : β) :
+ acc ≤ l.foldl (fun a i => max a (f i)) acc := by
+ induction l... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_1f62d1ca269d_1 | 3166bbfeef9e8c7d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Utils/List.lean | List | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "add_foldl_add0",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa using (foldl_add_init (l := l) (f := f) (acc := acc)).symm",
"n_chars": 70,
"n_subproofs": 0,
"n_tactics":... | [
{
"name": "foldl_add_init",
"text": "/--\nTurn `foldl (fun a x => a + f x) acc` into `acc + foldl (fun a x => a + f x) 0`.\n\nThis is the standard \"peel off the initial accumulator\" lemma for left folds over `+`.\n-/\nlemma foldl_add_init {α β : Type} [AddMonoid β] (l : List α) (f : α → β) (acc : β) :\n ... | [
{
"name": "add_foldl_add0",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 244,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Group.MinMax
public import Mathlib.Algebra.Ring.Basic
public import Mathlib.Data.Fintype.BigOperators
public import Mathlib.Data.List.FinRange
public impor... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Group.MinMax
public import Mathlib.Algebra.Ring.Basic
public import Mathlib.Data.Fintype.BigOperators
public import Mathlib.Data.List.FinRange
public impor... | @@ -24,8 +24,29 @@
namespace List
+/--
+Turn `foldl (fun a x => a + f x) acc` into `acc + foldl (fun a x => a + f x) 0`.
+
+This is the standard "peel off the initial accumulator" lemma for left folds over `+`.
+-/
+lemma foldl_add_init {α β : Type} [AddMonoid β] (l : List α) (f : α → β) (acc : β) :
+ l.foldl (... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_1f62d1ca269d_2 | c9f5450372699d00 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Utils/List.lean | List | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "finRange_foldl_add_acc",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h1 := foldl_add_init (l := List.finRange n) (f := f) (acc := acc)\n have h2 := finRange_foldl_add_eq_finset_su... | [
{
"name": "finRange_foldl_add_eq_finset_sum",
"text": "/--\nRewrite the canonical `List.finRange` addition fold into a `Finset.univ` sum.\n\nSpecs use `List.foldl` because it computes well; proofs usually want `Finset.sum` so standard\nbig-operator lemmas apply.\n-/\nlemma finRange_foldl_add_eq_finset_sum {... | [
{
"name": "finRange_foldl_add_acc",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 550,
"n_subproofs": 2,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Group.MinMax
public import Mathlib.Algebra.Ring.Basic
public import Mathlib.Data.Fintype.BigOperators
public import Mathlib.Data.List.FinRange
public impor... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Group.MinMax
public import Mathlib.Algebra.Ring.Basic
public import Mathlib.Data.Fintype.BigOperators
public import Mathlib.Data.List.FinRange
public impor... | @@ -45,6 +45,32 @@
simp [List.foldl, h1, h2, add_assoc]
/--
+Rewrite the canonical `List.finRange` addition fold into a `Finset.univ` sum.
+
+Specs use `List.foldl` because it computes well; proofs usually want `Finset.sum` so standard
+big-operator lemmas apply.
+-/
+lemma finRange_foldl_add_eq_finset_sum {β... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_0 | c39764cbbf5bb8c5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 3 | [
{
"theorem_name": "toReal?_eq_none_of_isFinite_eq_false",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hdy : toDyadic? x = none := toDyadic?_eq_none_of_isFinite_eq_false (x := x) hx\n simp [toReal?, ... | [
{
"name": "toDyadic?_eq_none_of_isFinite_eq_false",
"text": "/-- If `x` is not finite, then `toDyadic? x = none`. -/\ntheorem toDyadic?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :\n toDyadic? x = none := by\n -- By cases on the fraction field: expField=all-ones gives either... | [
{
"name": "toReal?_eq_none_of_isFinite_eq_false",
"fan_in": 7,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 280,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": fa... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -49,10 +49,32 @@
/-! ## Basic facts: `isFinite` ↔ `toDyadic?`/`toReal?` -/
+/-- If `x` is not finite, then `toDyadic? x = none`. -/
+theorem toDyadic?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :
+ toDyadic? x = none := by
+ -- By cases on the fraction field: expField=all-ones g... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.