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_7de7ded97bed_0 | e24b35f0586fc973 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/Balance.lean | Balance | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "balancedInteractions_of_perm",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rintro ⟨ lt_ringChar, balance ⟩ perm\n constructor\n · simp_all [perm.length_eq]\n intro msg\n rw [← balan... | [
{
"name": "balanceOf_perm",
"text": "lemma balanceOf_perm {as bs : List (Interaction F)} {msg : Array F} :\n List.Perm as bs → balanceOf as msg = balanceOf bs msg := by\n intro perm\n apply List.Perm.sum_eq\n exact perm.filter (·.msg = msg) |>.map (·.mult)\n\n",
"fan_in": 1,
"n_lines": 7,
... | [
{
"name": "balancedInteractions_of_perm",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 361,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
... | 1 | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | @@ -25,9 +25,20 @@
(interactions.length < ringChar F ∨ ringChar F = 0) ∧
∀ msg : Array F, balanceOf interactions msg = 0
+lemma balanceOf_perm {as bs : List (Interaction F)} {msg : Array F} :
+ List.Perm as bs → balanceOf as msg = balanceOf bs msg := by
+ intro perm
+ apply List.Perm.sum_eq
+ exact perm.f... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7de7ded97bed_1 | 2e7fc0d187d330c2 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/Balance.lean | Balance | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "balanceOf_eq_of_const_mult'",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n fun constant_mult => balanceOf_eq_of_const_mult (fun i hi _ => constant_mult i hi)",
"n_chars": 85,
"n_sub... | [
{
"name": "balanceOf_eq_of_const_mult",
"text": "/--\nUseful mechanical lemma: if all multiplicities for a given message are the same,\nthe balance sum can be written as multiplicity times message count.\n-/\nlemma balanceOf_eq_of_const_mult {interactions : List (Interaction F)} {msg : Array F} {mult : F} :... | [
{
"name": "balanceOf_eq_of_const_mult'",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 413,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 1 | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | @@ -26,11 +26,34 @@
∀ msg : Array F, balanceOf interactions msg = 0
/--
+Useful mechanical lemma: if all multiplicities for a given message are the same,
+the balance sum can be written as multiplicity times message count.
+-/
+lemma balanceOf_eq_of_const_mult {interactions : List (Interaction F)} {msg : Array F}... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7de7ded97bed_2 | 2516945679c9f933 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/Balance.lean | Balance | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "balanceOf_eq_of_const_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro const_zero\n rw [balanceOf_eq_of_const_mult' const_zero]\n simp",
"n_chars": 75,
"n_subproofs": ... | [
{
"name": "balanceOf_eq_of_const_mult'",
"text": "/--\nSpecial case of `balanceOf_eq_of_const_mult` for when the exact message doesn't matter.\n-/\nlemma balanceOf_eq_of_const_mult' {interactions : List (Interaction F)} {msg : Array F} {mult : F} :\n (∀ i ∈ interactions, i.mult = mult) →\n balanceOf i... | [
{
"name": "balanceOf_eq_of_const_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 244,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"... | 2 | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | @@ -47,8 +47,19 @@
simp only [List.mem_filter, decide_eq_true_eq] at a_mem_filter
apply constant_mult a <;> simp_all
+/--
+Special case of `balanceOf_eq_of_const_mult` for when the exact message doesn't matter.
+-/
+lemma balanceOf_eq_of_const_mult' {interactions : List (Interaction F)} {msg : Array F} {mult : ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7de7ded97bed_3 | bf84efa2c62efc2b | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/Balance.lean | Balance | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "balanceOf_eq_filter_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [balanceOf_eq_add_filter (· = 0)]\n simp only [balanceOf, List.filter_filter, decide_not, ne_eq, add_eq_rig... | [
{
"name": "balanceOf_eq_of_const_zero",
"text": "lemma balanceOf_eq_of_const_zero {interactions : List (Interaction F)} {msg : Array F} :\n (∀ i ∈ interactions, i.mult = 0) → balanceOf interactions msg = 0 := by\n intro const_zero\n rw [balanceOf_eq_of_const_mult' const_zero]\n simp\n\n",
"fan_in"... | [
{
"name": "balanceOf_eq_of_mult_or_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 27,
"n_chars": 1305,
"n_subproofs": 2,
"n_tactics": 17,
"cyclomatic": 2,
"n_automation": 10,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,... | 5 | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | @@ -55,6 +55,12 @@
balanceOf interactions msg = mult * ↑(interactions.countP (·.msg = msg)) :=
fun constant_mult => balanceOf_eq_of_const_mult (fun i hi _ => constant_mult i hi)
+lemma balanceOf_eq_of_const_zero {interactions : List (Interaction F)} {msg : Array F} :
+ (∀ i ∈ interactions, i.mult = 0) → ba... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7de7ded97bed_4 | ca2461b41846382b | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/Balance.lean | Balance | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "balanceOf_eq_filter_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [balanceOf_eq_add_filter (· = 0)]\n simp only [balanceOf, List.filter_filter, decide_not, ne_eq, add_eq_rig... | [
{
"name": "balanceOf_eq_add_filter",
"text": "lemma balanceOf_eq_add_filter {interactions : List (Interaction F)} {msg : Array F} (p : F → Prop) [DecidablePred p] :\n balanceOf interactions msg =\n balanceOf (interactions.filter (fun i => decide (p i.mult))) msg\n + balanceOf (interactions.filt... | [
{
"name": "consistent_of_normal",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 25,
"n_chars": 1350,
"n_subproofs": 5,
"n_tactics": 18,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 5,
"automation_only": false,
"max... | 7 | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | @@ -61,9 +61,26 @@
rw [balanceOf_eq_of_const_mult' const_zero]
simp
+lemma balanceOf_eq_add_filter {interactions : List (Interaction F)} {msg : Array F} (p : F → Prop) [DecidablePred p] :
+ balanceOf interactions msg =
+ balanceOf (interactions.filter (fun i => decide (p i.mult))) msg
+ + balanceOf... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7de7ded97bed_5 | b765d835150298ae | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/Balance.lean | Balance | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "balanceOf_eq_filter_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [balanceOf_eq_add_filter (· = 0)]\n simp only [balanceOf, List.filter_filter, decide_not, ne_eq, add_eq_rig... | [
{
"name": "balanceOf_eq_add_filter",
"text": "lemma balanceOf_eq_add_filter {interactions : List (Interaction F)} {msg : Array F} (p : F → Prop) [DecidablePred p] :\n balanceOf interactions msg =\n balanceOf (interactions.filter (fun i => decide (p i.mult))) msg\n + balanceOf (interactions.filt... | [
{
"name": "guarantees_of_requirements_of_requirements_of_guarantees",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 10,
"n_lines": 143,
"n_chars": 8529,
"n_subproofs": 26,
"n_tactics": 119,
"cyclomatic": 14,
"n_automation": 38,
"n_rewrites": 12,
"n_structural"... | 10 | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | @@ -65,9 +65,26 @@
rw [balanceOf_eq_of_const_mult' const_zero]
simp
+lemma balanceOf_eq_add_filter {interactions : List (Interaction F)} {msg : Array F} (p : F → Prop) [DecidablePred p] :
+ balanceOf interactions msg =
+ balanceOf (interactions.filter (fun i => decide (p i.mult))) msg
+ + balanceOf... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7de7ded97bed_6 | 04a95eeea357a431 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/Balance.lean | Balance | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "guarantees_of_requirements_of_requirements_of_guarantees",
"depth": 1,
"n_commands": 0,
"n_lines": 114,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro constraints\n induction n generalizing pulls pushes with\n | zero => int... | [
{
"name": "balanceOf_append",
"text": "lemma balanceOf_append {as bs : List (Interaction F)} {msg : Array F} :\n balanceOf (as ++ bs) msg = balanceOf as msg + balanceOf bs msg := by\n simp [balanceOf, List.filter_append, List.map_append, List.sum_append]\n\n",
"fan_in": 2,
"n_lines": 5,
"n_c... | [
{
"name": "balanceOf_active_append_eq",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 33,
"n_chars": 1538,
"n_subproofs": 4,
"n_tactics": 27,
"cyclomatic": 5,
"n_automation": 12,
"n_rewrites": 0,
"n_structural": 9,
"automation_only": false,
... | 2 | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | @@ -25,6 +25,10 @@
(interactions.length < ringChar F ∨ ringChar F = 0) ∧
∀ msg : Array F, balanceOf interactions msg = 0
+lemma balanceOf_append {as bs : List (Interaction F)} {msg : Array F} :
+ balanceOf (as ++ bs) msg = balanceOf as msg + balanceOf bs msg := by
+ simp [balanceOf, List.filter_append, List... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7de7ded97bed_7 | 2e2940ca60b20ba4 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/Balance.lean | Balance | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "balanceOf_active_append_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction pulls generalizing pushes with\n | nil =>\n cases pushes <;> simp [activeInteractions, balanceOf]... | [
{
"name": "balanceOf_cons",
"text": "lemma balanceOf_cons {i : Interaction F} {is : List (Interaction F)} {msg : Array F} :\n balanceOf (i :: is) msg = (if i.msg = msg then i.mult else 0) + balanceOf is msg := by\n by_cases h : i.msg = msg <;> simp [balanceOf, h]\n\n",
"fan_in": 1,
"n_lines": 5,... | [
{
"name": "balancedInteractions_active_append",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 25,
"n_chars": 1020,
"n_subproofs": 3,
"n_tactics": 18,
"cyclomatic": 3,
"n_automation": 3,
"n_rewrites": 3,
"n_structural": 6,
"automation_only": f... | 3 | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | @@ -29,6 +29,10 @@
balanceOf (as ++ bs) msg = balanceOf as msg + balanceOf bs msg := by
simp [balanceOf, List.filter_append, List.map_append, List.sum_append]
+lemma balanceOf_cons {i : Interaction F} {is : List (Interaction F)} {msg : Array F} :
+ balanceOf (i :: is) msg = (if i.msg = msg then i.mult else... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7de7ded97bed_8 | 6679353ccbf8ef07 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/Balance.lean | Balance | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "balanceOf_eq_of_mult_or_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro constant_mult\n set count : ℕ := interactions.countP fun i => i.msg = msg && i.mult ≠ 0\n suffices (i... | [
{
"name": "balanceOf_eq_filter_ne_zero",
"text": "lemma balanceOf_eq_filter_ne_zero {interactions : List (Interaction F)} {msg : Array F} :\n balanceOf interactions msg =\n (interactions.filter (fun i => i.msg = msg && i.mult ≠ 0) |>.map (·.mult) |>.sum) := by\n rw [balanceOf_eq_add_filter (· = 0)]... | [
{
"name": "guarantees_of_requirements_of_requirements_of_guarantees_of_mult_zero_iff",
"fan_in": 0,
"n_deps_direct": 9,
"n_deps_transitive": 15,
"n_lines": 66,
"n_chars": 3853,
"n_subproofs": 10,
"n_tactics": 40,
"cyclomatic": 3,
"n_automation": 10,
"n_rewrites": 1,
"... | 14 | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | import Clean.Circuit
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {Message : TypeMap} [ProvableType Message]
/-
## Channel balance
This module treats channel interactions as multisets and asks what properties can be
deduced from the condition of _balance_: that each element has multiplicity 0.
-/
/-... | @@ -79,6 +79,17 @@
simp_rw [← List.filter_filter]
rw [List.sum_map_filter_add_sum_map_filter_not]
+lemma balanceOf_eq_filter_ne_zero {interactions : List (Interaction F)} {msg : Array F} :
+ balanceOf interactions msg =
+ (interactions.filter (fun i => i.msg = msg && i.mult ≠ 0) |>.map (·.mult) |>.sum) ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c58e565cf790_0 | 9b8d46986d746e82 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/Rotation32/Theorems.lean | Theorems | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "rotation32_bits_soundness",
"depth": 1,
"n_commands": 0,
"n_lines": 20,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- simplify the goal\n simp only [rotRight32, rotRight32_u32, U32.valueNat]\n\n have offset_mod_32 : o % 32 = ... | [
{
"name": "h_x0_const32",
"text": "lemma h_x0_const32 {o : ℕ} (ho : o < 8) :\n 2^(8-o) * 256^3 = 2^(32-o) := by\n rw [show 256 = 2^8 by rfl, ←Nat.pow_mul, ←Nat.pow_add, pow_right_inj₀ (by norm_num) (by norm_num)]\n omega\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 197,
"n_subproofs": 0,... | [
{
"name": "rotation32_bits_soundness",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 23,
"n_chars": 912,
"n_subproofs": 1,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 7,
"n_structural": 0,
"automation_only": false,
... | 3 | import Clean.Utils.Field
import Clean.Utils.Bitwise
import Clean.Utils.Rotation
import Clean.Types.U32
import Clean.Gadgets.ByteDecomposition.ByteDecomposition
variable {p : ℕ} [Fact p.Prime]
variable [p_large_enough: Fact (p > 2^16 + 2^8)]
namespace Gadgets.Rotation32.Theorems
open Gadgets.ByteDecomposition.Theorems... | import Clean.Utils.Field
import Clean.Utils.Bitwise
import Clean.Utils.Rotation
import Clean.Types.U32
import Clean.Gadgets.ByteDecomposition.ByteDecomposition
variable {p : ℕ} [Fact p.Prime]
variable [p_large_enough: Fact (p > 2^16 + 2^8)]
namespace Gadgets.Rotation32.Theorems
open Gadgets.ByteDecomposition.Theorems... | @@ -47,8 +47,32 @@
rw [mul_div_256_off ho 3 (by simp only [Nat.ofNat_pos])]
simp only [tsub_self, pow_zero, mul_one, Nat.add_one_sub_one, pow_one, Nat.reducePow]
+lemma h_x0_const32 {o : ℕ} (ho : o < 8) :
+ 2^(8-o) * 256^3 = 2^(32-o) := by
+ rw [show 256 = 2^8 by rfl, ←Nat.pow_mul, ←Nat.pow_add, pow_right_i... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_da5546447cf8_0 | 48100087061467de | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/SHA256Schedule.lean | SHA256Schedule | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 3 | [
{
"theorem_name": "foldlAcc_eq_varSchedule",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [Circuit.FoldlM.foldlAcc, Vector.getElem_finRange]\n induction k with\n | zero => simp [varSchedule, F... | [
{
"name": "scheduleStep_localLength",
"text": "/-- The localLength of `scheduleStep w i` is 227. -/\nprivate lemma scheduleStep_localLength (w : SHA256Schedule (Expression (F p))) (i : Fin 48) (n : ℕ) :\n (scheduleStep w i).localLength n = 227 := by\n simp [circuit_norm, scheduleStep, LowerSigma1.circui... | [
{
"name": "foldlAcc_eq_varSchedule",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 31,
"n_chars": 1493,
"n_subproofs": 5,
"n_tactics": 26,
"cyclomatic": 2,
"n_automation": 9,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
"... | 2 | import Clean.Gadgets.SHA256.LowerSigma0
import Clean.Gadgets.SHA256.LowerSigma1
import Clean.Gadgets.SHA256.Add32
import Clean.Specs.SHA256
section
variable {p : ℕ} [Fact p.Prime] [Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# SHA-256 Message Schedule
Expands a 16-word block into a 64-word message schedule.
For ... | import Clean.Gadgets.SHA256.LowerSigma0
import Clean.Gadgets.SHA256.LowerSigma1
import Clean.Gadgets.SHA256.Add32
import Clean.Specs.SHA256
section
variable {p : ℕ} [Fact p.Prime] [Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# SHA-256 Message Schedule
Expands a 16-word block into a 64-word message schedule.
For ... | @@ -142,6 +142,11 @@
w.set (i.val + 16) (varFromOffset (fields 32) (n + 194)) (by omega) := by
simp [scheduleStep, circuit_norm, LowerSigma1.circuit, LowerSigma0.circuit, Add32.circuit]
+/-- The localLength of `scheduleStep w i` is 227. -/
+private lemma scheduleStep_localLength (w : SHA256Schedule (Express... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_da5546447cf8_1 | cf50178924380c5c | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/SHA256Schedule.lean | SHA256Schedule | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "foldlAcc_eq_varSchedule",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [Circuit.FoldlM.foldlAcc, Vector.getElem_finRange]\n induction k with\n | zero => simp [varSchedule, F... | [
{
"name": "scheduleStep_output",
"text": "/-- The output of `scheduleStep w i` at offset `n` is `w.set (i.val + 16) (varFromOffset ...)`. -/\nprivate lemma scheduleStep_output (w : SHA256Schedule (Expression (F p))) (i : Fin 48) (n : ℕ) :\n (scheduleStep w i).output n =\n w.set (i.val + 16) (varFrom... | [
{
"name": "finFoldl_eq_varSchedule_48",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 42,
"n_chars": 1982,
"n_subproofs": 7,
"n_tactics": 34,
"cyclomatic": 2,
"n_automation": 8,
"n_rewrites": 7,
"n_structural": 3,
"automation_only": false,
... | 1 | import Clean.Gadgets.SHA256.LowerSigma0
import Clean.Gadgets.SHA256.LowerSigma1
import Clean.Gadgets.SHA256.Add32
import Clean.Specs.SHA256
section
variable {p : ℕ} [Fact p.Prime] [Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# SHA-256 Message Schedule
Expands a 16-word block into a 64-word message schedule.
For ... | import Clean.Gadgets.SHA256.LowerSigma0
import Clean.Gadgets.SHA256.LowerSigma1
import Clean.Gadgets.SHA256.Add32
import Clean.Specs.SHA256
section
variable {p : ℕ} [Fact p.Prime] [Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# SHA-256 Message Schedule
Expands a 16-word block into a 64-word message schedule.
For ... | @@ -136,6 +136,12 @@
(fun w (i : Fin k) => body w i.val) from rfl, ih]
simp only [Fin.val_last, hbody_def, dif_pos (show k < 48 from by omega)]
+/-- The output of `scheduleStep w i` at offset `n` is `w.set (i.val + 16) (varFromOffset ...)`. -/
+private lemma scheduleStep_output (w : SHA256Schedule (E... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_da5546447cf8_2 | a489046b97df1c08 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/SHA256Schedule.lean | SHA256Schedule | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "soundness_inv",
"depth": 1,
"n_commands": 0,
"n_lines": 146,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro k hk\n induction k with\n | zero =>\n refine ⟨?_, ?_⟩\n · intro j hj\n simp only [varSchedule, valSchedu... | [
{
"name": "foldlAcc_eq_varSchedule",
"text": "/-- `Circuit.FoldlM.foldlAcc` at index `⟨k, h⟩ : Fin 48` equals `varSchedule i₀ input_var k`. -/\nprivate lemma foldlAcc_eq_varSchedule (i₀ : ℕ) (input_var_block : SHA256Block (Expression (F p)))\n (k : ℕ) (h : k < 48) :\n Circuit.FoldlM.foldlAcc i₀ (Vecto... | [
{
"name": "soundness_inv",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 169,
"n_chars": 8760,
"n_subproofs": 20,
"n_tactics": 134,
"cyclomatic": 2,
"n_automation": 44,
"n_rewrites": 53,
"n_structural": 21,
"automation_only": false,
"max_... | 3 | import Clean.Gadgets.SHA256.LowerSigma0
import Clean.Gadgets.SHA256.LowerSigma1
import Clean.Gadgets.SHA256.Add32
import Clean.Specs.SHA256
section
variable {p : ℕ} [Fact p.Prime] [Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# SHA-256 Message Schedule
Expands a 16-word block into a 64-word message schedule.
For ... | import Clean.Gadgets.SHA256.LowerSigma0
import Clean.Gadgets.SHA256.LowerSigma1
import Clean.Gadgets.SHA256.Add32
import Clean.Specs.SHA256
section
variable {p : ℕ} [Fact p.Prime] [Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# SHA-256 Message Schedule
Expands a 16-word block into a 64-word message schedule.
For ... | @@ -147,6 +147,36 @@
(scheduleStep w i).localLength n = 227 := by
simp [circuit_norm, scheduleStep, LowerSigma1.circuit, LowerSigma0.circuit, Add32.circuit]
+/-- `Circuit.FoldlM.foldlAcc` at index `⟨k, h⟩ : Fin 48` equals `varSchedule i₀ input_var k`. -/
+private lemma foldlAcc_eq_varSchedule (i₀ : ℕ) (input_... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_da5546447cf8_3 | 791d27c6eed434c4 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/SHA256Schedule.lean | SHA256Schedule | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "soundness",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n circuit_proof_start [messageSchedule]\n simp only [show ∀ (w : SHA256Schedule (Expression (F p))) (i : Fin 48) (n : ℕ),\n Op... | [
{
"name": "soundness_inv",
"text": "/-- The soundness inductive invariant. Given the constraints `h_holds` hold for every step,\n the variable-level schedule at step `k` matches the value-level schedule and is normalized. -/\nprivate lemma soundness_inv (i₀ : ℕ) (input_var : SHA256Block (Expression (F p)... | [
{
"name": "soundness",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 26,
"n_chars": 1174,
"n_subproofs": 3,
"n_tactics": 23,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 8,
"automation_only": false,
"max_nesting": ... | 5 | import Clean.Gadgets.SHA256.LowerSigma0
import Clean.Gadgets.SHA256.LowerSigma1
import Clean.Gadgets.SHA256.Add32
import Clean.Specs.SHA256
section
variable {p : ℕ} [Fact p.Prime] [Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# SHA-256 Message Schedule
Expands a 16-word block into a 64-word message schedule.
For ... | import Clean.Gadgets.SHA256.LowerSigma0
import Clean.Gadgets.SHA256.LowerSigma1
import Clean.Gadgets.SHA256.Add32
import Clean.Specs.SHA256
section
variable {p : ℕ} [Fact p.Prime] [Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# SHA-256 Message Schedule
Expands a 16-word block into a 64-word message schedule.
For ... | @@ -218,6 +218,174 @@
change (scheduleStep _ ⟨k, hk''⟩).output (i₀ + k * 227) = _
rw [scheduleStep_output]
+/-- The soundness inductive invariant. Given the constraints `h_holds` hold for every step,
+ the variable-level schedule at step `k` matches the value-level schedule and is normalized. -/
+private... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_95b99b90bad8_0 | 0775996c7b4857a5 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Table/Inductive.lean | Inductive | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "table_soundness_aux",
"depth": 1,
"n_commands": 0,
"n_lines": 173,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro input_spec\n\n -- add a condition on the trace length to the goal,\n -- so that we can change the induction t... | [
{
"name": "composite_vars_first",
"text": "/--\nHelper for reasoning about the cell assignment produced by `inductiveConstraint`:\nvariables at indices below `size S` are assigned to the first row's input cells.\nStated for generic `ops`/`ops2`, so that all vector lengths stay symbolic and clean.\n-/\npriva... | [
{
"name": "table_soundness_aux",
"fan_in": 1,
"n_deps_direct": 7,
"n_deps_transitive": 4,
"n_lines": 180,
"n_chars": 8499,
"n_subproofs": 20,
"n_tactics": 165,
"cyclomatic": 8,
"n_automation": 54,
"n_rewrites": 21,
"n_structural": 32,
"automation_only": false,
... | 2 | /-
"Inductive" tables are specified by a circuit on a `k`-row window of cells, which
take the first `k-1` rows as input variables and return the `k`-th row as output.
Assignment of cells is handled in the background, which simplifies reasoning about the table.
Thus far, only the common `k=2` case is handled.
-/
impor... | /-
"Inductive" tables are specified by a circuit on a `k`-row window of cells, which
take the first `k-1` rows as input variables and return the `k`-th row as output.
Assignment of cells is handled in the background, which simplifies reasoning about the table.
Thus far, only the common `k=2` case is handled.
-/
impor... | @@ -149,6 +149,22 @@
rw [traceInputs, List.length_map, trace.val.toList_length, trace.prop]
/--
+Helper for reasoning about the cell assignment produced by `inductiveConstraint`:
+variables at indices below `size S` are assigned to the first row's input cells.
+Stated for generic `ops`/`ops2`, so that all vector ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c4156273e45b_2 | 6243e1df42ca9901 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/Add32.lean | Add32 | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "fromBitsExpr_eval_normalized",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n show Expression.eval env (Utils.Bits.fieldFromBitsExpr bits_var) = _\n simp only [Utils.Bits.fieldFromBits_ev... | [
{
"name": "fieldFromBits_eq_valueBits",
"text": "/-- fieldFromBits bits = (valueBits bits : F p) -/\nprivate lemma fieldFromBits_eq_valueBits (bits : Vector (F p) 32) :\n Utils.Bits.fieldFromBits bits = (valueBits bits : F p) := by\n unfold Utils.Bits.fieldFromBits\n rw [fromBits_map_val_eq_valueBits]\... | [
{
"name": "fromBitsExpr_eval_normalized",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 526,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
... | 2 | import Clean.Gadgets.SHA256.BitwiseOps
section
variable {p : ℕ} [Fact p.Prime] [h_large : Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# 32-bit Modular Addition for SHA-256
Adds two 32-bit words (as `fields 32` bit vectors, LSB first) modulo 2^32.
R1CS structure (per call):
- 32 witnesses for output bits z[0..31]... | import Clean.Gadgets.SHA256.BitwiseOps
section
variable {p : ℕ} [Fact p.Prime] [h_large : Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# 32-bit Modular Addition for SHA-256
Adds two 32-bit words (as `fields 32` bit vectors, LSB first) modulo 2^32.
R1CS structure (per call):
- 32 witnesses for output bits z[0..31]... | @@ -113,11 +113,23 @@
rfl
omit h_large in
+/-- fieldFromBits bits = (valueBits bits : F p) -/
+private lemma fieldFromBits_eq_valueBits (bits : Vector (F p) 32) :
+ Utils.Bits.fieldFromBits bits = (valueBits bits : F p) := by
+ unfold Utils.Bits.fieldFromBits
+ rw [fromBits_map_val_eq_valueBits]
+
+omit h_la... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c4156273e45b_3 | c72b3d4d46b2ed9d | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/Add32.lean | Add32 | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 2 | [
{
"theorem_name": "fromBitsExpr_val_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [fromBitsExpr_eval_normalized env bits_var bits h_eval]\n exact ZMod.val_natCast_of_lt (by linarith [valueBits_lt_t... | [
{
"name": "fromBitsExpr_eval_normalized",
"text": "/-- fromBitsExpr evaluated at concrete inputs = (valueBits bits : F p) -/\nprivate lemma fromBitsExpr_eval_normalized (env : Environment (F p))\n (bits_var : Var (fields 32) (F p)) (bits : Vector (F p) 32)\n (h_eval : Vector.map (Expression.eval env) ... | [
{
"name": "fromBitsExpr_val_eq",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 11,
"n_chars": 559,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_ne... | 5 | import Clean.Gadgets.SHA256.BitwiseOps
section
variable {p : ℕ} [Fact p.Prime] [h_large : Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# 32-bit Modular Addition for SHA-256
Adds two 32-bit words (as `fields 32` bit vectors, LSB first) modulo 2^32.
R1CS structure (per call):
- 32 witnesses for output bits z[0..31]... | import Clean.Gadgets.SHA256.BitwiseOps
section
variable {p : ℕ} [Fact p.Prime] [h_large : Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# 32-bit Modular Addition for SHA-256
Adds two 32-bit words (as `fields 32` bit vectors, LSB first) modulo 2^32.
R1CS structure (per call):
- 32 witnesses for output bits z[0..31]... | @@ -120,12 +120,26 @@
rw [fromBits_map_val_eq_valueBits]
omit h_large in
+/-- fromBitsExpr evaluated at concrete inputs = (valueBits bits : F p) -/
+private lemma fromBitsExpr_eval_normalized (env : Environment (F p))
+ (bits_var : Var (fields 32) (F p)) (bits : Vector (F p) 32)
+ (h_eval : Vector.map (Expr... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c4156273e45b_4 | c4273d155fdb9f51 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/Add32.lean | Add32 | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 2 | [
{
"theorem_name": "normalized_of_bool_holds",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro i\n have hi := h i\n have h_get : (Vector.ofFn fun j : Fin 32 => env.get (i₀ + j.val))[i] = env.get (i₀ + ... | [
{
"name": "isbool_of_bool_constraint",
"text": "/-- IsBool from boolean constraint x * (x - 1) = 0 -/\nprivate lemma isbool_of_bool_constraint {x : F p} (h : x * (x - 1) = 0) : IsBool x := by\n rwa [← IsBool.iff_mul_sub_one] at h\n\nomit h_large in\n",
"fan_in": 2,
"n_lines": 6,
"n_chars": 200,... | [
{
"name": "normalized_of_bool_holds",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 514,
"n_subproofs": 2,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"m... | 1 | import Clean.Gadgets.SHA256.BitwiseOps
section
variable {p : ℕ} [Fact p.Prime] [h_large : Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# 32-bit Modular Addition for SHA-256
Adds two 32-bit words (as `fields 32` bit vectors, LSB first) modulo 2^32.
R1CS structure (per call):
- 32 witnesses for output bits z[0..31]... | import Clean.Gadgets.SHA256.BitwiseOps
section
variable {p : ℕ} [Fact p.Prime] [h_large : Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# 32-bit Modular Addition for SHA-256
Adds two 32-bit words (as `fields 32` bit vectors, LSB first) modulo 2^32.
R1CS structure (per call):
- 32 witnesses for output bits z[0..31]... | @@ -148,10 +148,23 @@
ext i; simp [Vector.getElem_map, Vector.getElem_mapRange, Expression.eval]
omit h_large in
+/-- IsBool from boolean constraint x * (x - 1) = 0 -/
+private lemma isbool_of_bool_constraint {x : F p} (h : x * (x - 1) = 0) : IsBool x := by
+ rwa [← IsBool.iff_mul_sub_one] at h
+
+omit h_large i... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c4156273e45b_5 | 26a11b251276703d | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/Add32.lean | Add32 | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "bit_decomp_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv_rhs => rw [← Utils.Bits.fromBits_toBits h_n_lt]\n unfold Utils.Bits.fromBits Utils.Bits.toBits\n rw [Fin.foldl_to_sum... | [
{
"name": "testBit_ite_eq",
"text": "/-- testBit equals div/mod expression -/\nprivate lemma testBit_ite_eq (n i : ℕ) : (if n.testBit i = true then 1 else 0 : ℕ) = n / 2^i % 2 := by\n simp only [Nat.testBit, Nat.shiftRight_eq_div_pow, Nat.one_and_eq_mod_two]\n rcases Nat.mod_two_eq_zero_or_one (n / 2^i) w... | [
{
"name": "bit_decomp_sum",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 420,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
"max_nesting... | 1 | import Clean.Gadgets.SHA256.BitwiseOps
section
variable {p : ℕ} [Fact p.Prime] [h_large : Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# 32-bit Modular Addition for SHA-256
Adds two 32-bit words (as `fields 32` bit vectors, LSB first) modulo 2^32.
R1CS structure (per call):
- 32 witnesses for output bits z[0..31]... | import Clean.Gadgets.SHA256.BitwiseOps
section
variable {p : ℕ} [Fact p.Prime] [h_large : Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# 32-bit Modular Addition for SHA-256
Adds two 32-bit words (as `fields 32` bit vectors, LSB first) modulo 2^32.
R1CS structure (per call):
- 32 witnesses for output bits z[0..31]... | @@ -176,9 +176,22 @@
intro i _
simp [Vector.getElem_map]
+/-- testBit equals div/mod expression -/
+private lemma testBit_ite_eq (n i : ℕ) : (if n.testBit i = true then 1 else 0 : ℕ) = n / 2^i % 2 := by
+ simp only [Nat.testBit, Nat.shiftRight_eq_div_pow, Nat.one_and_eq_mod_two]
+ rcases Nat.mod_two_eq_zero_o... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c4156273e45b_6 | 49a2439f73ab8e2f | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/Add32.lean | Add32 | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "fieldFromBits_bit_decomp",
"depth": 1,
"n_commands": 0,
"n_lines": 20,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [Utils.Bits.fieldFromBits, Utils.Bits.fromBits, Fin.foldl_to_sum]\n have h_val_eq : ∀ i : Fin 32, ((Ve... | [
{
"name": "bit_decomp_sum",
"text": "/-- Bit decomposition: ∑ i, (n / 2^i % 2) * 2^i = n for n < 2^32 -/\nprivate lemma bit_decomp_sum (n : ℕ) (h_n_lt : n < 2^32) :\n ∑ i : Fin 32, n / 2^i.val % 2 * 2^i.val = n := by\n conv_rhs => rw [← Utils.Bits.fromBits_toBits h_n_lt]\n unfold Utils.Bits.fromBits Ut... | [
{
"name": "fieldFromBits_bit_decomp",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 30,
"n_chars": 1353,
"n_subproofs": 4,
"n_tactics": 20,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 5,
"automation_only": false,
... | 2 | import Clean.Gadgets.SHA256.BitwiseOps
section
variable {p : ℕ} [Fact p.Prime] [h_large : Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# 32-bit Modular Addition for SHA-256
Adds two 32-bit words (as `fields 32` bit vectors, LSB first) modulo 2^32.
R1CS structure (per call):
- 32 witnesses for output bits z[0..31]... | import Clean.Gadgets.SHA256.BitwiseOps
section
variable {p : ℕ} [Fact p.Prime] [h_large : Fact (p > 2^33)]
namespace Gadgets.SHA256
/-!
# 32-bit Modular Addition for SHA-256
Adds two 32-bit words (as `fields 32` bit vectors, LSB first) modulo 2^32.
R1CS structure (per call):
- 32 witnesses for output bits z[0..31]... | @@ -181,6 +181,17 @@
simp only [Nat.testBit, Nat.shiftRight_eq_div_pow, Nat.one_and_eq_mod_two]
rcases Nat.mod_two_eq_zero_or_one (n / 2^i) with h | h <;> rw [h] <;> rfl
+/-- Bit decomposition: ∑ i, (n / 2^i % 2) * 2^i = n for n < 2^32 -/
+private lemma bit_decomp_sum (n : ℕ) (h_n_lt : n < 2^32) :
+ ∑ i : Fi... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_9b9dad0b560c_0 | f6a77597a408899e | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Combinatorics/InfiniteGraphRamsey.lean | InfiniteGraphRamsey | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "goodSelection_exists",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n obtain ⟨v, h_v⟩ := Set.Infinite.nonempty ivs.inf\n let f u := color {v, u}\n obtain ⟨c, vs, h_inf, h_v... | [
{
"name": "infinite_pigeonhole_principle",
"text": "/-- An infinite pigeonhole principle. -/\ntheorem infinite_pigeonhole_principle {X Y : Type*} [Finite Y] (f : X → Y) {s : Set X}\n (h_inf : s.Infinite) : ∃ y, ∃ t, t.Infinite ∧ t ⊆ s ∧ ∀ x ∈ t, f x = y := by\n have := h_inf.to_subtype\n obtain ⟨y, h_i... | [
{
"name": "goodSelection_exists",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 559,
"n_subproofs": 2,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2026 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Data.Set.Finite.... | /-
Copyright (c) 2026 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Data.Set.Finite.... | @@ -25,6 +25,18 @@
open Function Set
+/-- An infinite pigeonhole principle. -/
+theorem infinite_pigeonhole_principle {X Y : Type*} [Finite Y] (f : X → Y) {s : Set X}
+ (h_inf : s.Infinite) : ∃ y, ∃ t, t.Infinite ∧ t ⊆ s ∧ ∀ x ∈ t, f x = y := by
+ have := h_inf.to_subtype
+ obtain ⟨y, h_inf'⟩ := Finite.exists... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_9b9dad0b560c_1 | d1eca26a3456bbf5 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Combinatorics/InfiniteGraphRamsey.lean | InfiniteGraphRamsey | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "goodSelection_exists",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n obtain ⟨v, h_v⟩ := Set.Infinite.nonempty ivs.inf\n let f u := color {v, u}\n obtain ⟨c, vs, h_inf, h_v... | [
{
"name": "infinite_pigeonhole_principle",
"text": "/-- An infinite pigeonhole principle. -/\ntheorem infinite_pigeonhole_principle {X Y : Type*} [Finite Y] (f : X → Y) {s : Set X}\n (h_inf : s.Infinite) : ∃ y, ∃ t, t.Infinite ∧ t ⊆ s ∧ ∀ x ∈ t, f x = y := by\n have := h_inf.to_subtype\n obtain ⟨y, h_i... | [
{
"name": "infinite_graph_ramsey",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 28,
"n_chars": 1221,
"n_subproofs": 7,
"n_tactics": 21,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 10,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2026 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Data.Set.Finite.... | /-
Copyright (c) 2026 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Group.Nat
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Data.Set.Finite.... | @@ -25,6 +25,18 @@
open Function Set
+/-- An infinite pigeonhole principle. -/
+theorem infinite_pigeonhole_principle {X Y : Type*} [Finite Y] (f : X → Y) {s : Set X}
+ (h_inf : s.Infinite) : ∃ y, ∃ t, t.Infinite ∧ t ⊆ s ∧ ∀ x ∈ t, f x = y := by
+ have := h_inf.to_subtype
+ obtain ⟨y, h_inf'⟩ := Finite.exists... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7493f90bfd2d_0 | b0bb0cb1dbd7a04c | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Automata/NA/Concat.lean | Concat | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "concat_run_left_right",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨s1, t1, h_mtr, _⟩ := concat_run_left hc (n - 1) (by grind)\n obtain ⟨t1', h_tr, _⟩ : ∃ t1', na1.Tr t1 (xs (n... | [
{
"name": "concat_run_left",
"text": "lemma concat_run_left {xs : ωSequence Symbol} {ss : ωSequence (State1 ⊕ State2)}\n (hc : (concat na1 na2).Run xs ss) (n : ℕ) (hl : ∀ k ≤ n, (ss k).isLeft) :\n ∃ s1 t1, na1.MTr s1 (xs.take n) t1 ∧ s1 ∈ na1.start ∧ ss 0 = inl s1 ∧ ss n = inl t1 := by\n obtain ⟨s1, ... | [
{
"name": "concat_run_left_right",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 532,
"n_subproofs": 2,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.NA.Total
public import Cslib.Foundations.Data.OmegaSequence.Temporal
/-! # Concatenation of nondeterministic au... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.NA.Total
public import Cslib.Foundations.Data.OmegaSequence.Temporal
/-! # Concatenation of nondeterministic au... | @@ -38,9 +38,27 @@
(hc : (concat na1 na2).Run xs ss) (hr : (ss 0).isRight) : [] ∈ language na1 := by
grind [concat, hc.start]
+lemma concat_run_left {xs : ωSequence Symbol} {ss : ωSequence (State1 ⊕ State2)}
+ (hc : (concat na1 na2).Run xs ss) (n : ℕ) (hl : ∀ k ≤ n, (ss k).isLeft) :
+ ∃ s1 t1, na1.MTr s... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7493f90bfd2d_1 | 875dd45eb09ccbf4 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Automata/NA/Concat.lean | Concat | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "concat_run_proj",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hr' : ∃ k, (ss k).isRight := by grind\n let n := Nat.find hr'\n have hl (k) (h_k : k < n) := not_isRight.mp <| Nat.f... | [
{
"name": "concat_run_left_right",
"text": "lemma concat_run_left_right {xs : ωSequence Symbol} {ss : ωSequence (State1 ⊕ State2)}\n (hc : (concat na1 na2).Run xs ss) (n : ℕ) (hn : 0 < n)\n (hl : ∀ k < n, (ss k).isLeft) (hr : (ss n).isRight) : (xs.take n) ∈ language na1 := by\n obtain ⟨s1, t1, h_mtr,... | [
{
"name": "concat_run_proj",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 16,
"n_chars": 768,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nestin... | 4 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.NA.Total
public import Cslib.Foundations.Data.OmegaSequence.Temporal
/-! # Concatenation of nondeterministic au... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.NA.Total
public import Cslib.Foundations.Data.OmegaSequence.Temporal
/-! # Concatenation of nondeterministic au... | @@ -51,6 +51,15 @@
grind [concat, hc.trans n]
grind [LTS.MTr.stepR na1.toLTS h_mtr h_tr]
+lemma concat_run_left_right {xs : ωSequence Symbol} {ss : ωSequence (State1 ⊕ State2)}
+ (hc : (concat na1 na2).Run xs ss) (n : ℕ) (hn : 0 < n)
+ (hl : ∀ k < n, (ss k).isLeft) (hr : (ss n).isRight) : (xs.take n... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7493f90bfd2d_2 | 5d90396162ef0f98 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Automata/NA/Concat.lean | Concat | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "concat_run_proj",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hr' : ∃ k, (ss k).isRight := by grind\n let n := Nat.find hr'\n have hl (k) (h_k : k < n) := not_isRight.mp <| Nat.f... | [
{
"name": "concat_run_right",
"text": "lemma concat_run_right {xs : ωSequence Symbol} {ss : ωSequence (State1 ⊕ State2)}\n (hc : (concat na1 na2).Run xs ss) (n : ℕ) (hl : ∀ k < n, (ss k).isLeft) (hr : (ss n).isRight) :\n ∃ ss2, na2.Run (xs.drop n) ss2 ∧ ss.drop n = ss2.map inr := by\n have h2 k : ∃ s... | [
{
"name": "concat_language_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 21,
"n_chars": 900,
"n_subproofs": 3,
"n_tactics": 14,
"cyclomatic": 4,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 11,
"automation_only": false,
"max_n... | 5 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.NA.Total
public import Cslib.Foundations.Data.OmegaSequence.Temporal
/-! # Concatenation of nondeterministic au... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.NA.Total
public import Cslib.Foundations.Data.OmegaSequence.Temporal
/-! # Concatenation of nondeterministic au... | @@ -60,6 +60,21 @@
use s1, by grind, t1', by grind
grind [LTS.MTr.stepR na1.toLTS h_mtr h_tr]
+lemma concat_run_right {xs : ωSequence Symbol} {ss : ωSequence (State1 ⊕ State2)}
+ (hc : (concat na1 na2).Run xs ss) (n : ℕ) (hl : ∀ k < n, (ss k).isLeft) (hr : (ss n).isRight) :
+ ∃ ss2, na2.Run (xs.drop n) ss... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7493f90bfd2d_3 | 76cc747803fbc510 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Automata/NA/Concat.lean | Concat | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "concat_run_proj",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hr' : ∃ k, (ss k).isRight := by grind\n let n := Nat.find hr'\n have hl (k) (h_k : k < n) := not_isRight.mp <| Nat.f... | [
{
"name": "concat_run_right",
"text": "lemma concat_run_right {xs : ωSequence Symbol} {ss : ωSequence (State1 ⊕ State2)}\n (hc : (concat na1 na2).Run xs ss) (n : ℕ) (hl : ∀ k < n, (ss k).isLeft) (hr : (ss n).isRight) :\n ∃ ss2, na2.Run (xs.drop n) ss2 ∧ ss.drop n = ss2.map inr := by\n have h2 k : ∃ s... | [
{
"name": "finConcat_language_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 37,
"n_chars": 2109,
"n_subproofs": 14,
"n_tactics": 32,
"cyclomatic": 6,
"n_automation": 14,
"n_rewrites": 1,
"n_structural": 14,
"automation_only": false,
... | 5 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.NA.Total
public import Cslib.Foundations.Data.OmegaSequence.Temporal
/-! # Concatenation of nondeterministic au... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.NA.Total
public import Cslib.Foundations.Data.OmegaSequence.Temporal
/-! # Concatenation of nondeterministic au... | @@ -60,6 +60,21 @@
use s1, by grind, t1', by grind
grind [LTS.MTr.stepR na1.toLTS h_mtr h_tr]
+lemma concat_run_right {xs : ωSequence Symbol} {ss : ωSequence (State1 ⊕ State2)}
+ (hc : (concat na1 na2).Run xs ss) (n : ℕ) (hl : ∀ k < n, (ss k).isLeft) (hr : (ss n).isRight) :
+ ∃ ss2, na2.Run (xs.drop n) ss... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_be50075cada2_0 | e308422987953c5a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/StrongNorm.lean | StrongNorm | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "neutral_step",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction Hneut generalizing t' with grind only [Neutral, cases Xi, sn_step]",
"n_chars": 82,
"n_subproofs": 0,
"n... | [
{
"name": "sn_step",
"text": "/-- A single β-reduction step preserves strong normalization. -/\nlemma sn_step (t_st_t' : t ⭢βᶠ t') (sn_t : SN FullBeta t) : SN FullBeta t' :=\n sn_t.of_rel t_st_t'\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 172,
"n_subproofs": 0,
"n_tactics": 1,
"cyc... | [
{
"name": "neutral_step",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 235,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2025 David Wegmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wegmann
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.MultiApp
pub... | /-
Copyright (c) 2025 David Wegmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wegmann
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.MultiApp
pub... | @@ -29,6 +29,10 @@
attribute [grind =] Finset.union_singleton
+/-- A single β-reduction step preserves strong normalization. -/
+lemma sn_step (t_st_t' : t ⭢βᶠ t') (sn_t : SN FullBeta t) : SN FullBeta t' :=
+ sn_t.of_rel t_st_t'
+
set_option linter.tacticAnalysis.verifyGrindOnly false in
/-- Free variables are ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_be50075cada2_1 | 0956a738cf2f7d83 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/StrongNorm.lean | StrongNorm | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "neutral_steps",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction Hsteps <;> grind [neutral_step]",
"n_chars": 47,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,... | [
{
"name": "neutral_step",
"text": "/-- Neutral terms only reduce to other neutral terms in a single step -/\nlemma neutral_step (Hneut : Neutral t) (Hstep : t ⭢βᶠ t') : Neutral t' := by\n induction Hneut generalizing t' with grind only [Neutral, cases Xi, sn_step]\n\n",
"fan_in": 1,
"n_lines": 5,
... | [
{
"name": "neutral_steps",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 203,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 2 | /-
Copyright (c) 2025 David Wegmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wegmann
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.MultiApp
pub... | /-
Copyright (c) 2025 David Wegmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wegmann
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.MultiApp
pub... | @@ -70,8 +70,13 @@
--attribute [scoped grind .] Neutral.bvar Neutral.fvar Neutral.app
+/-- Neutral terms only reduce to other neutral terms in a single step -/
+lemma neutral_step (Hneut : Neutral t) (Hstep : t ⭢βᶠ t') : Neutral t' := by
+ induction Hneut generalizing t' with grind only [Neutral, cases Xi, sn_ste... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_be50075cada2_2 | e99d977dc8d53b9b | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/StrongNorm.lean | StrongNorm | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "sn_abs_app_multiApp",
"depth": 1,
"n_commands": 0,
"n_lines": 31,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction Ps with\n | nil =>\n apply sn_app\n · grind [sn_abs]\n · exact sn_N\n · grind [→ steps_open_con... | [
{
"name": "sn_abs",
"text": "/-- A lambda abstraction is strongly normalizing if its body is strongly normalizing. -/\nlemma sn_abs [DecidableEq Var] [HasFresh Var] {M N : Term Var} (sn_MN : SN FullBeta (M ^ N))\n (lc_N : LC N) : SN FullBeta (abs M) := by\n generalize h : (M ^ N) = M_open at sn_MN\n in... | [
{
"name": "sn_abs_app_multiApp",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 5,
"n_lines": 41,
"n_chars": 1816,
"n_subproofs": 2,
"n_tactics": 32,
"cyclomatic": 7,
"n_automation": 11,
"n_rewrites": 1,
"n_structural": 15,
"automation_only": false,
"ma... | 4 | /-
Copyright (c) 2025 David Wegmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wegmann
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.MultiApp
pub... | /-
Copyright (c) 2025 David Wegmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wegmann
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.MultiApp
pub... | @@ -103,6 +103,18 @@
rw [SN_iff_SN_of_rel]
grind only [cases Xi]
+/-- A lambda abstraction is strongly normalizing if its body is strongly normalizing. -/
+lemma sn_abs [DecidableEq Var] [HasFresh Var] {M N : Term Var} (sn_MN : SN FullBeta (M ^ N))
+ (lc_N : LC N) : SN FullBeta (abs M) := by
+ generaliz... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_97a9085be8c6_0 | b7624eed77593593 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Relation/Euclidean.lean | Euclidean | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 7 | [
{
"theorem_name": "trichotomous_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Std.Trichotomous.trichotomous (r := r) a c\n have cc := reflOn_cod.of_cod bc\n have (ca : r c a) := righ... | [
{
"name": "reflOn_cod",
"text": "/-- A `RightEuclidean` relation is reflexive on its codomain -/\ntheorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab\n\n",
"fan_in": 7,
"n_lines": 4,
"n_chars": 149,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_a... | [
{
"name": "trichotomous_trans",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 243,
"n_subproofs": 3,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | @@ -47,11 +47,18 @@
variable [RightEuclidean r]
+/-- A `RightEuclidean` relation is reflexive on its codomain -/
+theorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab
+
instance [Std.Refl r] : Std.Symm r where
symm a _ ab := rightEuclidean ab (refl a)
theorem trichotomous_trans [Std... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_97a9085be8c6_1 | 7c25cf3d93b4fa5a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Relation/Euclidean.lean | Euclidean | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 7 | [
{
"theorem_name": "trichotomous_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Std.Trichotomous.trichotomous (r := r) a c\n have cc := reflOn_cod.of_cod bc\n have (ca : r c a) := righ... | [
{
"name": "reflOn_cod",
"text": "/-- A `RightEuclidean` relation is reflexive on its codomain -/\ntheorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab\n\n",
"fan_in": 7,
"n_lines": 4,
"n_chars": 149,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_a... | [
{
"name": "rightUnique_antisymm",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 133,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | @@ -47,11 +47,14 @@
variable [RightEuclidean r]
+/-- A `RightEuclidean` relation is reflexive on its codomain -/
+theorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab
+
instance [Std.Refl r] : Std.Symm r where
symm a _ ab := rightEuclidean ab (refl a)
theorem rightUnique_antisymm (h... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_97a9085be8c6_2 | 158a6d22cdf94591 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Relation/Euclidean.lean | Euclidean | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 7 | [
{
"theorem_name": "trichotomous_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Std.Trichotomous.trichotomous (r := r) a c\n have cc := reflOn_cod.of_cod bc\n have (ca : r c a) := righ... | [
{
"name": "reflOn_cod",
"text": "/-- A `RightEuclidean` relation is reflexive on its codomain -/\ntheorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab\n\n",
"fan_in": 7,
"n_lines": 4,
"n_chars": 149,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_a... | [
{
"name": "rightUnique_trans",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 168,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | @@ -47,12 +47,15 @@
variable [RightEuclidean r]
+/-- A `RightEuclidean` relation is reflexive on its codomain -/
+theorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab
+
instance [Std.Refl r] : Std.Symm r where
symm a _ ab := rightEuclidean ab (refl a)
theorem rightUnique_trans (h : ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_97a9085be8c6_4 | f10d82a72892d7e3 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Relation/Euclidean.lean | Euclidean | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 7 | [
{
"theorem_name": "trichotomous_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Std.Trichotomous.trichotomous (r := r) a c\n have cc := reflOn_cod.of_cod bc\n have (ca : r c a) := righ... | [
{
"name": "reflOn_cod",
"text": "/-- A `RightEuclidean` relation is reflexive on its codomain -/\ntheorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab\n\n",
"fan_in": 7,
"n_lines": 4,
"n_chars": 149,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_a... | [
{
"name": "three_contra",
"fan_in": 4,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 12,
"n_chars": 468,
"n_subproofs": 5,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 2 | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | @@ -47,6 +47,9 @@
variable [RightEuclidean r]
+/-- A `RightEuclidean` relation is reflexive on its codomain -/
+theorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab
+
instance [Std.Refl r] : Std.Symm r where
symm a _ ab := rightEuclidean ab (refl a)
@@ -55,7 +58,15 @@
exact antisy... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_97a9085be8c6_5 | 9722a9d4c858aaaa | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Relation/Euclidean.lean | Euclidean | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 7 | [
{
"theorem_name": "trichotomous_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Std.Trichotomous.trichotomous (r := r) a c\n have cc := reflOn_cod.of_cod bc\n have (ca : r c a) := righ... | [
{
"name": "reflOn_cod",
"text": "/-- A `RightEuclidean` relation is reflexive on its codomain -/\ntheorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab\n\n",
"fan_in": 7,
"n_lines": 4,
"n_chars": 149,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_a... | [
{
"name": "trichotomous_antisymm_finite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 292,
"n_subproofs": 2,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
... | 2 | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | @@ -47,6 +47,9 @@
variable [RightEuclidean r]
+/-- A `RightEuclidean` relation is reflexive on its codomain -/
+theorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab
+
instance [Std.Refl r] : Std.Symm r where
symm a _ ab := rightEuclidean ab (refl a)
@@ -55,7 +58,15 @@
exact antisy... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_97a9085be8c6_6 | a26b87c288b9b6a7 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Relation/Euclidean.lean | Euclidean | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 7 | [
{
"theorem_name": "trichotomous_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Std.Trichotomous.trichotomous (r := r) a c\n have cc := reflOn_cod.of_cod bc\n have (ca : r c a) := righ... | [
{
"name": "reflOn_cod",
"text": "/-- A `RightEuclidean` relation is reflexive on its codomain -/\ntheorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab\n\n",
"fan_in": 7,
"n_lines": 4,
"n_chars": 149,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_a... | [
{
"name": "trichotomous_antisymm_card",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 8,
"n_chars": 236,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"... | 2 | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | @@ -47,6 +47,9 @@
variable [RightEuclidean r]
+/-- A `RightEuclidean` relation is reflexive on its codomain -/
+theorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab
+
instance [Std.Refl r] : Std.Symm r where
symm a _ ab := rightEuclidean ab (refl a)
@@ -55,7 +58,15 @@
exact antisy... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_97a9085be8c6_7 | c075d382a02890da | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Relation/Euclidean.lean | Euclidean | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 7 | [
{
"theorem_name": "trichotomous_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Std.Trichotomous.trichotomous (r := r) a c\n have cc := reflOn_cod.of_cod bc\n have (ca : r c a) := righ... | [
{
"name": "reflOn_cod",
"text": "/-- A `RightEuclidean` relation is reflexive on its codomain -/\ntheorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab\n\n",
"fan_in": 7,
"n_lines": 4,
"n_chars": 149,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_a... | [
{
"name": "cod_subset_dom",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 3,
"n_chars": 97,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | @@ -47,10 +47,13 @@
variable [RightEuclidean r]
+/-- A `RightEuclidean` relation is reflexive on its codomain -/
+theorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab
+
instance [Std.Refl r] : Std.Symm r where
symm a _ ab := rightEuclidean ab (refl a)
-theorem cod_subset_dom : cod r ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_97a9085be8c6_8 | b4e34d0a75adbecd | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Relation/Euclidean.lean | Euclidean | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 7 | [
{
"theorem_name": "trichotomous_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Std.Trichotomous.trichotomous (r := r) a c\n have cc := reflOn_cod.of_cod bc\n have (ca : r c a) := righ... | [
{
"name": "reflOn_cod",
"text": "/-- A `RightEuclidean` relation is reflexive on its codomain -/\ntheorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab\n\n",
"fan_in": 7,
"n_lines": 4,
"n_chars": 149,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_a... | [
{
"name": "rightTotal_cod",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 130,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | @@ -47,10 +47,14 @@
variable [RightEuclidean r]
+/-- A `RightEuclidean` relation is reflexive on its codomain -/
+theorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab
+
instance [Std.Refl r] : Std.Symm r where
symm a _ ab := rightEuclidean ab (refl a)
-theorem rightTotal_cod : Relato... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_97a9085be8c6_10 | 36cbc45127ba6cda | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Relation/Euclidean.lean | Euclidean | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 7 | [
{
"theorem_name": "trichotomous_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Std.Trichotomous.trichotomous (r := r) a c\n have aa := reflOn_dom.of_dom ab\n have (ca : r c a) := left... | [
{
"name": "reflOn_dom",
"text": "/-- A `LeftEuclidean` relation is reflexive on its domain -/\ntheorem reflOn_dom : (dom r).ReflOn r := fun _ ⟨_, ab⟩ ↦ leftEuclidean ab ab\n\n",
"fan_in": 7,
"n_lines": 4,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_autom... | [
{
"name": "leftUnique_antisymm",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 131,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | @@ -56,11 +56,14 @@
variable [LeftEuclidean r]
+/-- A `LeftEuclidean` relation is reflexive on its domain -/
+theorem reflOn_dom : (dom r).ReflOn r := fun _ ⟨_, ab⟩ ↦ leftEuclidean ab ab
+
instance [Std.Refl r] : Std.Symm r where
symm _ b ab := leftEuclidean (refl b) ab
theorem leftUnique_antisymm (h : Rela... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_97a9085be8c6_11 | 4cb1634f858d689d | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Relation/Euclidean.lean | Euclidean | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 7 | [
{
"theorem_name": "trichotomous_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Std.Trichotomous.trichotomous (r := r) a c\n have aa := reflOn_dom.of_dom ab\n have (ca : r c a) := left... | [
{
"name": "reflOn_dom",
"text": "/-- A `LeftEuclidean` relation is reflexive on its domain -/\ntheorem reflOn_dom : (dom r).ReflOn r := fun _ ⟨_, ab⟩ ↦ leftEuclidean ab ab\n\n",
"fan_in": 7,
"n_lines": 4,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_autom... | [
{
"name": "leftUnique_trans",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 166,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | @@ -56,12 +56,15 @@
variable [LeftEuclidean r]
+/-- A `LeftEuclidean` relation is reflexive on its domain -/
+theorem reflOn_dom : (dom r).ReflOn r := fun _ ⟨_, ab⟩ ↦ leftEuclidean ab ab
+
instance [Std.Refl r] : Std.Symm r where
symm _ b ab := leftEuclidean (refl b) ab
theorem leftUnique_trans (h : Relator... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_97a9085be8c6_13 | 8e9ccc8dee85fca0 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Relation/Euclidean.lean | Euclidean | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 7 | [
{
"theorem_name": "trichotomous_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Std.Trichotomous.trichotomous (r := r) a c\n have aa := reflOn_dom.of_dom ab\n have (ca : r c a) := left... | [
{
"name": "reflOn_dom",
"text": "/-- A `LeftEuclidean` relation is reflexive on its domain -/\ntheorem reflOn_dom : (dom r).ReflOn r := fun _ ⟨_, ab⟩ ↦ leftEuclidean ab ab\n\n",
"fan_in": 7,
"n_lines": 4,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_autom... | [
{
"name": "dom_subset_cod",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 3,
"n_chars": 97,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | @@ -56,10 +56,13 @@
variable [LeftEuclidean r]
+/-- A `LeftEuclidean` relation is reflexive on its domain -/
+theorem reflOn_dom : (dom r).ReflOn r := fun _ ⟨_, ab⟩ ↦ leftEuclidean ab ab
+
instance [Std.Refl r] : Std.Symm r where
symm _ b ab := leftEuclidean (refl b) ab
-theorem dom_subset_cod : dom r ⊆ cod ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_97a9085be8c6_14 | 661e4a6e23b68ad9 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Relation/Euclidean.lean | Euclidean | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 7 | [
{
"theorem_name": "trichotomous_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Std.Trichotomous.trichotomous (r := r) a c\n have aa := reflOn_dom.of_dom ab\n have (ca : r c a) := left... | [
{
"name": "reflOn_dom",
"text": "/-- A `LeftEuclidean` relation is reflexive on its domain -/\ntheorem reflOn_dom : (dom r).ReflOn r := fun _ ⟨_, ab⟩ ↦ leftEuclidean ab ab\n\n",
"fan_in": 7,
"n_lines": 4,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_autom... | [
{
"name": "leftTotal_dom",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 144,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | @@ -56,10 +56,14 @@
variable [LeftEuclidean r]
+/-- A `LeftEuclidean` relation is reflexive on its domain -/
+theorem reflOn_dom : (dom r).ReflOn r := fun _ ⟨_, ab⟩ ↦ leftEuclidean ab ab
+
instance [Std.Refl r] : Std.Symm r where
symm _ b ab := leftEuclidean (refl b) ab
-theorem leftTotal_dom : Relator.LeftT... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_97a9085be8c6_16 | f9ff33121be5d85a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Relation/Euclidean.lean | Euclidean | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 7 | [
{
"theorem_name": "trichotomous_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Std.Trichotomous.trichotomous (r := r) a c\n have cc := reflOn_cod.of_cod bc\n have (ca : r c a) := righ... | [
{
"name": "reflOn_cod",
"text": "/-- A `RightEuclidean` relation is reflexive on its codomain -/\ntheorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab\n\n",
"fan_in": 7,
"n_lines": 4,
"n_chars": 149,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_a... | [
{
"name": "leftEuclidean_rightEuclidean_dom_cod_eq",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 7,
"n_chars": 235,
"n_subproofs": 2,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only":... | 4 | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | /-
Copyright (c) 2025 Fabrizio Montesi and Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring, Chris Henson
-/
module
public import Cslib.Foundations.Relation.Restriction
public import Mathlib.Data.Fintype.EquivFin
public im... | @@ -47,10 +47,13 @@
variable [RightEuclidean r]
+/-- A `RightEuclidean` relation is reflexive on its codomain -/
+theorem reflOn_cod : (cod r).ReflOn r := fun _ ⟨_, ab⟩ ↦ rightEuclidean ab ab
+
instance [Std.Refl r] : Std.Symm r where
symm a _ ab := rightEuclidean ab (refl a)
-theorem cod_subset_dom : cod r ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_acd54e9c238e_0 | 90240df9daec56ed | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Crypto/Protocols/SecretSharing/Defs.lean | Defs | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "perfectlyPrivate",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro s hs secretDist v hv\n exact Cslib.Probability.PMF.posteriorDist_eq_prior_of_outputIndist\n (p := secretDist) (f... | [
{
"name": "viewDist_eq_of_not_authorized",
"text": "/-- Unauthorized coalitions receive secret-independent view distributions. -/\ntheorem viewDist_eq_of_not_authorized\n (scheme : Scheme Secret Randomness Party Share)\n {s : Finset Party} (hs : ¬ scheme.authorized s)\n (secret₀ secret₁ : Secret) :... | [
{
"name": "perfectlyPrivate",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 426,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Probability.PMF
public import Cslib.Crypto.Protocols.SecretSharing.Scheme
/-!
# Secret Sharing: Definitions
Privacy for secret ... | /-
Copyright (c) 2026 Samuel Schlesinger. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Samuel Schlesinger
-/
module
public import Cslib.Probability.PMF
public import Cslib.Crypto.Protocols.SecretSharing.Scheme
/-!
# Secret Sharing: Definitions
Privacy for secret ... | @@ -53,6 +53,15 @@
(s : Finset Party) (secret : Secret) : PMF (s → Share) :=
viewDistOf scheme.gen scheme.share s secret
+/-- Unauthorized coalitions receive secret-independent view distributions. -/
+theorem viewDist_eq_of_not_authorized
+ (scheme : Scheme Secret Randomness Party Share)
+ {s : Finset P... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f1170da1cd64_0 | 1bf0e6a9549b2e22 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/MultiApp.lean | MultiApp | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "multiApp_steps_lc",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction step <;> grind [FullBeta.step_lc_r, multiApp_step_lc_r]",
"n_chars": 71,
"n_subproofs": 0,
"n_tacti... | [
{
"name": "multiApp_step_lc_r",
"text": "/-- Just like ordinary beta reduction, the right-hand side\n of a multi-application step is locally closed -/\nlemma multiApp_step_lc_r (step : Ns ⭢lβᶠ Ns') : ∀ N ∈ Ns', LC N := by\n induction step <;> grind [FullBeta.step_lc_r]\n\n",
"fan_in": 1,
"n_line... | [
{
"name": "multiApp_steps_lc",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 272,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2025 David Wegmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wegmann
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
/-! Multiple application for untyped lambda calculus. -/
set_option linter.unus... | /-
Copyright (c) 2025 David Wegmann. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Wegmann
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
/-! Multiple application for untyped lambda calculus. -/
set_option linter.unus... | @@ -89,8 +89,14 @@
variable [DecidableEq Var] [HasFresh Var]
+/-- Just like ordinary beta reduction, the right-hand side
+ of a multi-application step is locally closed -/
+lemma multiApp_step_lc_r (step : Ns ⭢lβᶠ Ns') : ∀ N ∈ Ns', LC N := by
+ induction step <;> grind [FullBeta.step_lc_r]
+
/-- Just like ord... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_05451edaf168_0 | b4e907ec040ed921 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/CallByName.lean | CallByName | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "CBN.to_redex",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction step\n · rfl\n · grind [CBN.step_to_redex, Relation.ReflTransGen.trans]",
"n_chars": 89,
"n_subproofs": 0,... | [
{
"name": "CBN.step_to_redex",
"text": "/-- A single Call-by-Name step is a full β-reduction. -/\nlemma CBN.step_to_redex (step : M ⭢ₙ N) : M ↠βᶠ N := by\n induction step with\n | base h => exact .single (.base h)\n | app lc_Z _ ih => exact FullBeta.redex_app_l_cong ih lc_Z\n\n",
"fan_in": 1,
"n_... | [
{
"name": "CBN.to_redex",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 212,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 Maximiliano Onofre Martínez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Maximiliano Onofre Martínez
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
public import Cslib.Languages.LambdaCalculus.LocallyN... | /-
Copyright (c) 2026 Maximiliano Onofre Martínez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Maximiliano Onofre Martínez
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
public import Cslib.Languages.LambdaCalculus.LocallyN... | @@ -33,11 +33,17 @@
variable {M M' N N' : Term Var}
+/-- A single Call-by-Name step is a full β-reduction. -/
+lemma CBN.step_to_redex (step : M ⭢ₙ N) : M ↠βᶠ N := by
+ induction step with
+ | base h => exact .single (.base h)
+ | app lc_Z _ ih => exact FullBeta.redex_app_l_cong ih lc_Z
+
/-- Call-by-Name redu... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_05451edaf168_1 | e4a92571b077661e | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/CallByName.lean | CallByName | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "CBN.steps_lc_r",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction step\n · exact lc_M\n · grind [CBN.lc_r]",
"n_chars": 58,
"n_subproofs": 0,
"n_tactics": 4,
"cyc... | [
{
"name": "CBN.lc_r",
"text": "/-- The right side of a Call-by-Name step is locally closed. -/\nlemma CBN.lc_r (step : M ⭢ₙ N) : LC N := by\n induction step with grind\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 141,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 2,
"n_automati... | [
{
"name": "CBN.steps_lc_r",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 193,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2026 Maximiliano Onofre Martínez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Maximiliano Onofre Martínez
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
public import Cslib.Languages.LambdaCalculus.LocallyN... | /-
Copyright (c) 2026 Maximiliano Onofre Martínez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Maximiliano Onofre Martínez
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
public import Cslib.Languages.LambdaCalculus.LocallyN... | @@ -35,11 +35,15 @@
variable [HasFresh Var] [DecidableEq Var]
+/-- The right side of a Call-by-Name step is locally closed. -/
+lemma CBN.lc_r (step : M ⭢ₙ N) : LC N := by
+ induction step with grind
+
/-- The right side of a Call-by-Name reduction is locally closed. -/
lemma CBN.steps_lc_r (lc_M : LC M) (step ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_05451edaf168_2 | 7e25d60a834314a3 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Untyped/CallByName.lean | CallByName | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "CBN.steps_subst",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction step\n · rfl\n · grind [CBN.step_subst]",
"n_chars": 57,
"n_subproofs": 0,
"n_tactics": 4,
"cyc... | [
{
"name": "CBN.step_subst",
"text": "/-- Substitution preserves a single Call-by-Name step. -/\nlemma CBN.step_subst (x : Var) (h : M ⭢ₙ M') (lc_N : LC N) :\n M[x := N] ⭢ₙ M'[x := N] := by\n induction h\n · grind [Term.subst_open, CBN.base]\n · grind [CBN.app]\n\n",
"fan_in": 1,
"n_lines": 8,
... | [
{
"name": "CBN.steps_subst",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 216,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2026 Maximiliano Onofre Martínez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Maximiliano Onofre Martínez
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
public import Cslib.Languages.LambdaCalculus.LocallyN... | /-
Copyright (c) 2026 Maximiliano Onofre Martínez. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Maximiliano Onofre Martínez
-/
module
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Untyped.FullBeta
public import Cslib.Languages.LambdaCalculus.LocallyN... | @@ -35,12 +35,19 @@
variable [HasFresh Var] [DecidableEq Var]
+/-- Substitution preserves a single Call-by-Name step. -/
+lemma CBN.step_subst (x : Var) (h : M ⭢ₙ M') (lc_N : LC N) :
+ M[x := N] ⭢ₙ M'[x := N] := by
+ induction h
+ · grind [Term.subst_open, CBN.base]
+ · grind [CBN.app]
+
/-- Substitution pr... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_661740b935c9_0 | 9f1c924de37e605f | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/URM/Execution.lean | Execution | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "isHalted_iff_normal",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro hhalted ⟨s', hstep⟩\n exact Step.no_step_of_halted hhalted hstep\n · intro hnormal\n -- ... | [
{
"name": "no_step_of_halted",
"text": "/-- A halted state has no successor in the step relation. -/\ntheorem no_step_of_halted {s s' : State} (hhalted : s.isHalted p) : ¬Step p s s' := by\n grind [State.isHalted]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 175,
"n_subproofs": 0,
"n_tac... | [
{
"name": "isHalted_iff_normal",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 23,
"n_chars": 1052,
"n_subproofs": 2,
"n_tactics": 17,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 10,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Defs
public import Cslib.Foundations.Relation.Confluence
public import Mathlib.Data.Part
/-! # URM Execution Semantics
Singl... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Defs
public import Cslib.Foundations.Relation.Confluence
public import Mathlib.Data.Part
/-! # URM Execution Semantics
Singl... | @@ -86,6 +86,10 @@
/-- The step relation is deterministic: each state has at most one successor. -/
theorem deterministic : Relator.RightUnique (Step p) := by grind only [Relator.RightUnique]
+/-- A halted state has no successor in the step relation. -/
+theorem no_step_of_halted {s s' : State} (hhalted : s.isHalte... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_661740b935c9_1 | c6903534e0502040 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/URM/Execution.lean | Execution | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "isHalted_iff_normal",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro hhalted ⟨s', hstep⟩\n exact Step.no_step_of_halted hhalted hstep\n · intro hnormal\n -- ... | [
{
"name": "no_step_of_halted",
"text": "/-- A halted state has no successor in the step relation. -/\ntheorem no_step_of_halted {s s' : State} (hhalted : s.isHalted p) : ¬Step p s s' := by\n grind [State.isHalted]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 175,
"n_subproofs": 0,
"n_tac... | [
{
"name": "eq_of_halts",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 17,
"n_chars": 761,
"n_subproofs": 5,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": ... | 3 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Defs
public import Cslib.Foundations.Relation.Confluence
public import Mathlib.Data.Part
/-! # URM Execution Semantics
Singl... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Defs
public import Cslib.Foundations.Relation.Confluence
public import Mathlib.Data.Part
/-! # URM Execution Semantics
Singl... | @@ -86,6 +86,10 @@
/-- The step relation is deterministic: each state has at most one successor. -/
theorem deterministic : Relator.RightUnique (Step p) := by grind only [Relator.RightUnique]
+/-- A halted state has no successor in the step relation. -/
+theorem no_step_of_halted {s s' : State} (hhalted : s.isHalte... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_661740b935c9_2 | be4ed88e39fade5d | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/URM/Execution.lean | Execution | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "isHalted_iff_normal",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro hhalted ⟨s', hstep⟩\n exact Step.no_step_of_halted hhalted hstep\n · intro hnormal\n -- ... | [
{
"name": "no_step_of_halted",
"text": "/-- A halted state has no successor in the step relation. -/\ntheorem no_step_of_halted {s s' : State} (hhalted : s.isHalted p) : ¬Step p s s' := by\n grind [State.isHalted]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 175,
"n_subproofs": 0,
"n_tac... | [
{
"name": "halts_iff_normalizable",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 6,
"n_chars": 258,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_n... | 2 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Defs
public import Cslib.Foundations.Relation.Confluence
public import Mathlib.Data.Part
/-! # URM Execution Semantics
Singl... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Defs
public import Cslib.Foundations.Relation.Confluence
public import Mathlib.Data.Part
/-! # URM Execution Semantics
Singl... | @@ -86,6 +86,10 @@
/-- The step relation is deterministic: each state has at most one successor. -/
theorem deterministic : Relator.RightUnique (Step p) := by grind only [Relator.RightUnique]
+/-- A halted state has no successor in the step relation. -/
+theorem no_step_of_halted {s s' : State} (hhalted : s.isHalte... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_661740b935c9_3 | dfb95804b788a5c6 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/URM/Execution.lean | Execution | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "toHaltsWithResult",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n let s := (evalState p inputs).get h\n let ⟨hsteps, hhalted⟩ := evalState_spec p h\n ⟨s, hsteps, hhalted, rfl⟩",
"n_cha... | [
{
"name": "evalState_spec",
"text": "/-- Specification: the state from evalState satisfies Steps and isHalted. -/\ntheorem evalState_spec {inputs : List ℕ} (h : (evalState p inputs).Dom) :\n let s := (evalState p inputs).get h\n Steps p (State.init inputs) s ∧ s.isHalted p :=\n Classical.choose_spec ... | [
{
"name": "toHaltsWithResult",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 325,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nestin... | 1 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Defs
public import Cslib.Foundations.Relation.Confluence
public import Mathlib.Data.Part
/-! # URM Execution Semantics
Singl... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Defs
public import Cslib.Foundations.Relation.Confluence
public import Mathlib.Data.Part
/-! # URM Execution Semantics
Singl... | @@ -128,13 +128,22 @@
noncomputable def evalState (inputs : List ℕ) : Part State :=
⟨Halts p inputs, fun h => Classical.choose h⟩
+/-- Specification: the state from evalState satisfies Steps and isHalted. -/
+theorem evalState_spec {inputs : List ℕ} (h : (evalState p inputs).Dom) :
+ let s := (evalState p inpu... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_661740b935c9_4 | e088620e8b0c8f00 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/URM/Execution.lean | Execution | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "eq_of_halts",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Use confluence: both s₁ and s₂ are reachable from init, so they're joinable\n have ⟨w, hw1, hw2⟩ := step_confluent p h1 h2\... | [
{
"name": "isHalted_iff_normal",
"text": "/-- A state is halted iff it is normal (has no successor) in the reduction system. -/\ntheorem isHalted_iff_normal {p : Program} {s : State} :\n s.isHalted p ↔ Relation.Normal (Step p) s := by\n constructor\n · intro hhalted ⟨s', hstep⟩\n exact Step.no_step_... | [
{
"name": "haltsWithResult_iff_eval",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 17,
"n_chars": 830,
"n_subproofs": 4,
"n_tactics": 13,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 6,
"automation_only": false,
"... | 5 | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Defs
public import Cslib.Foundations.Relation.Confluence
public import Mathlib.Data.Part
/-! # URM Execution Semantics
Singl... | /-
Copyright (c) 2026 Jesse Alama. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jesse Alama
-/
module
public import Cslib.Computability.URM.Defs
public import Cslib.Foundations.Relation.Confluence
public import Mathlib.Data.Part
/-! # URM Execution Semantics
Singl... | @@ -94,6 +94,28 @@
/-! ### Step Properties -/
+/-- A state is halted iff it is normal (has no successor) in the reduction system. -/
+theorem isHalted_iff_normal {p : Program} {s : State} :
+ s.isHalted p ↔ Relation.Normal (Step p) s := by
+ constructor
+ · intro hhalted ⟨s', hstep⟩
+ exact Step.no_step_of... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_9d2b5dd1ff7e_0 | fd15e440f988b11a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Fsub/Opening.lean | Opening | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "openRec_lc",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction lc generalizing X with\n | all => grind [fresh_exists <| free_union Var, openRec_neq_eq]\n | _ => grind\n\nomit [Has... | [
{
"name": "openRec_neq_eq",
"text": "/-- An opening appearing in both sides of an equality of types can be removed. -/\nlemma openRec_neq_eq {σ τ γ : Ty Var} (neq : X ≠ Y) (h : σ⟦Y ↝ τ⟧ᵞ = σ⟦Y ↝ τ⟧ᵞ⟦X ↝ γ⟧ᵞ) :\n σ = σ⟦X ↝ γ⟧ᵞ := by induction σ generalizing Y X <;> grind\n\n",
"fan_in": 2,
"n_line... | [
{
"name": "openRec_lc",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 274,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Foundations.Syntax.HasSubstitution
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.Basic
/-! # λ-calculus
The λ-calculus ... | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Foundations.Syntax.HasSubstitution
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.Basic
/-! # λ-calculus
The λ-calculus ... | @@ -80,10 +80,14 @@
variable {σ τ δ γ : Ty Var}
omit [HasFresh Var] [DecidableEq Var] in
+/-- An opening appearing in both sides of an equality of types can be removed. -/
+lemma openRec_neq_eq {σ τ γ : Ty Var} (neq : X ≠ Y) (h : σ⟦Y ↝ τ⟧ᵞ = σ⟦Y ↝ τ⟧ᵞ⟦X ↝ γ⟧ᵞ) :
+ σ = σ⟦X ↝ γ⟧ᵞ := by induction σ generalizing Y X... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_9d2b5dd1ff7e_1 | 79ee7d361e91f7ac | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Fsub/Opening.lean | Opening | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "openRec_lc",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction lc generalizing X with\n | all => grind [fresh_exists <| free_union Var, openRec_neq_eq]\n | _ => grind\n\nomit [Has... | [
{
"name": "openRec_neq_eq",
"text": "/-- An opening appearing in both sides of an equality of types can be removed. -/\nlemma openRec_neq_eq {σ τ γ : Ty Var} (neq : X ≠ Y) (h : σ⟦Y ↝ τ⟧ᵞ = σ⟦Y ↝ τ⟧ᵞ⟦X ↝ γ⟧ᵞ) :\n σ = σ⟦X ↝ γ⟧ᵞ := by induction σ generalizing Y X <;> grind\n\n",
"fan_in": 2,
"n_line... | [
{
"name": "openRec_subst",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 6,
"n_chars": 278,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 2 | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Foundations.Syntax.HasSubstitution
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.Basic
/-! # λ-calculus
The λ-calculus ... | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Foundations.Syntax.HasSubstitution
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.Basic
/-! # λ-calculus
The λ-calculus ... | @@ -80,10 +80,14 @@
variable {σ τ δ γ : Ty Var}
omit [HasFresh Var] [DecidableEq Var] in
+/-- An opening appearing in both sides of an equality of types can be removed. -/
+lemma openRec_neq_eq {σ τ γ : Ty Var} (neq : X ≠ Y) (h : σ⟦Y ↝ τ⟧ᵞ = σ⟦Y ↝ τ⟧ᵞ⟦X ↝ γ⟧ᵞ) :
+ σ = σ⟦X ↝ γ⟧ᵞ := by induction σ generalizing Y X... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_9d2b5dd1ff7e_2 | 0fcf55d58810d35f | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Fsub/Opening.lean | Opening | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "openRec_lc",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction lc generalizing X with\n | all => grind [fresh_exists <| free_union Var, openRec_neq_eq]\n | _ => grind\n\nomit [Has... | [
{
"name": "openRec_neq_eq",
"text": "/-- An opening appearing in both sides of an equality of types can be removed. -/\nlemma openRec_neq_eq {σ τ γ : Ty Var} (neq : X ≠ Y) (h : σ⟦Y ↝ τ⟧ᵞ = σ⟦Y ↝ τ⟧ᵞ⟦X ↝ γ⟧ᵞ) :\n σ = σ⟦X ↝ γ⟧ᵞ := by induction σ generalizing Y X <;> grind\n\n",
"fan_in": 2,
"n_line... | [
{
"name": "open_subst",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 204,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 1
... | 3 | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Foundations.Syntax.HasSubstitution
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.Basic
/-! # λ-calculus
The λ-calculus ... | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Foundations.Syntax.HasSubstitution
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.Basic
/-! # λ-calculus
The λ-calculus ... | @@ -80,10 +80,14 @@
variable {σ τ δ γ : Ty Var}
omit [HasFresh Var] [DecidableEq Var] in
+/-- An opening appearing in both sides of an equality of types can be removed. -/
+lemma openRec_neq_eq {σ τ γ : Ty Var} (neq : X ≠ Y) (h : σ⟦Y ↝ τ⟧ᵞ = σ⟦Y ↝ τ⟧ᵞ⟦X ↝ γ⟧ᵞ) :
+ σ = σ⟦X ↝ γ⟧ᵞ := by induction σ generalizing Y X... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_9d2b5dd1ff7e_12 | f1dafaba3689bb4b | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Fsub/Opening.lean | Opening | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "openRecTm_lc",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction lc generalizing x with\n | let' | case | tabs | abs =>\n grind [fresh_exists <| free_union Var, openRecTm_neq_eq... | [
{
"name": "openRecTm_neq_eq",
"text": "/-- An opening (term to term) appearing in both sides of an equality of terms can be removed. -/\nlemma openRecTm_neq_eq (neq : x ≠ y) (eq : t⟦y ↝ s₁⟧ᵗᵗ = t⟦y ↝ s₁⟧ᵗᵗ⟦x ↝ s₂⟧ᵗᵗ) :\n t = t⟦x ↝ s₂⟧ᵗᵗ := by\n induction t generalizing x y <;> grind\n\nomit [DecidableEq... | [
{
"name": "openRecTm_lc",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 303,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 2 | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Foundations.Syntax.HasSubstitution
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.Basic
/-! # λ-calculus
The λ-calculus ... | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Foundations.Syntax.HasSubstitution
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.Basic
/-! # λ-calculus
The λ-calculus ... | @@ -236,6 +236,12 @@
lemma substTm_def : substTm (x : Var) (s : Term Var) (t : Term Var) = t[x := s] := by rfl
omit [DecidableEq Var] in
+/-- An opening (term to term) appearing in both sides of an equality of terms can be removed. -/
+lemma openRecTm_neq_eq (neq : x ≠ y) (eq : t⟦y ↝ s₁⟧ᵗᵗ = t⟦y ↝ s₁⟧ᵗᵗ⟦x ↝ s₂⟧ᵗᵗ) ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_9d2b5dd1ff7e_15 | c40642080729ebdc | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Fsub/Opening.lean | Opening | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "openTm_substTy",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " openRecTm_substTy 0 t₁ t₂ δ X",
"n_chars": 35,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automatio... | [
{
"name": "openRecTm_substTy",
"text": "/-- Substitution of a locally closed type distributes with term opening to a term. -/\nlemma openRecTm_substTy (y : ℕ) (t₁ t₂ : Term Var) (δ : Ty Var) (X : Var) :\n (t₁⟦y ↝ t₂⟧ᵗᵗ)[X := δ] = (t₁[X := δ])⟦y ↝ t₂[X := δ]⟧ᵗᵗ := by\n induction t₁ generalizing y <;> gr... | [
{
"name": "openTm_substTy",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 246,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Foundations.Syntax.HasSubstitution
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.Basic
/-! # λ-calculus
The λ-calculus ... | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Foundations.Syntax.HasSubstitution
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.Basic
/-! # λ-calculus
The λ-calculus ... | @@ -259,9 +259,14 @@
variable {t s : Term Var} {δ : Ty Var} {x : Var}
omit [HasFresh Var] in
+/-- Substitution of a locally closed type distributes with term opening to a term. -/
+lemma openRecTm_substTy (y : ℕ) (t₁ t₂ : Term Var) (δ : Ty Var) (X : Var) :
+ (t₁⟦y ↝ t₂⟧ᵗᵗ)[X := δ] = (t₁[X := δ])⟦y ↝ t₂[X := δ]⟧... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_9d2b5dd1ff7e_16 | 08871ce40b64c4e1 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/LambdaCalculus/LocallyNameless/Fsub/Opening.lean | Opening | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "openTm_substTy",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " openRecTm_substTy 0 t₁ t₂ δ X",
"n_chars": 35,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automatio... | [
{
"name": "openRecTm_substTy",
"text": "/-- Substitution of a locally closed type distributes with term opening to a term. -/\nlemma openRecTm_substTy (y : ℕ) (t₁ t₂ : Term Var) (δ : Ty Var) (X : Var) :\n (t₁⟦y ↝ t₂⟧ᵗᵗ)[X := δ] = (t₁[X := δ])⟦y ↝ t₂[X := δ]⟧ᵗᵗ := by\n induction t₁ generalizing y <;> gr... | [
{
"name": "openTm_substTy_var",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 232,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesti... | 2 | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Foundations.Syntax.HasSubstitution
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.Basic
/-! # λ-calculus
The λ-calculus ... | /-
Copyright (c) 2025 Chris Henson. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chris Henson
-/
module
public import Cslib.Foundations.Syntax.HasSubstitution
public import Cslib.Languages.LambdaCalculus.LocallyNameless.Fsub.Basic
/-! # λ-calculus
The λ-calculus ... | @@ -259,9 +259,14 @@
variable {t s : Term Var} {δ : Ty Var} {x : Var}
omit [HasFresh Var] in
+/-- Substitution of a locally closed type distributes with term opening to a term. -/
+lemma openRecTm_substTy (y : ℕ) (t₁ t₂ : Term Var) (δ : Ty Var) (X : Var) :
+ (t₁⟦y ↝ t₂⟧ᵗᵗ)[X := δ] = (t₁[X := δ])⟦y ↝ t₂[X := δ]⟧... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_36ca8164ba2d_0 | 868750907114c44a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Confluence.lean | Confluence | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "reflTransGen_parallelReduction_mRed",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext a b\n constructor\n · apply reflTransGen_le_of_le\n -- TODO: restate `parallelReduction_of_red... | [
{
"name": "mRed_of_parallelReduction",
"text": "/-- The inclusion `⭢ₚ ⊆ ↠` -/\ntheorem mRed_of_parallelReduction {a a' : SKI} (h : a ⭢ₚ a') : a ↠ a' := by\n cases h\n case refl => exact Relation.ReflTransGen.refl\n case par a a' b b' ha hb =>\n apply parallel_mRed\n · exact mRed_of_parallelReductio... | [
{
"name": "reflTransGen_parallelReduction_mRed",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 20,
"n_chars": 712,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 6,
"automation_only": fa... | 2 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | @@ -59,6 +59,18 @@
| par ⦃a a' b b' : SKI⦄ :
ParallelReduction a a' → ParallelReduction b b' → ParallelReduction (a ⬝ b) (a' ⬝ b')
+/-- The inclusion `⭢ₚ ⊆ ↠` -/
+theorem mRed_of_parallelReduction {a a' : SKI} (h : a ⭢ₚ a') : a ↠ a' := by
+ cases h
+ case refl => exact Relation.ReflTransGen.refl
+ case p... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_36ca8164ba2d_1 | 103ac7807ec01f5a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Confluence.lean | Confluence | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "Ka_irreducible",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases h\n case refl => use a, .refl a\n case par b a' h h' => rw [K_irreducible b h]; use a'",
"n_chars": 98,
"n_s... | [
{
"name": "K_irreducible",
"text": "lemma K_irreducible (a : SKI) (h : K ⭢ₚ a) : a = K := by\n cases h\n rfl\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 78,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"au... | [
{
"name": "Ka_irreducible",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 199,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | @@ -59,8 +59,15 @@
| par ⦃a a' b b' : SKI⦄ :
ParallelReduction a a' → ParallelReduction b b' → ParallelReduction (a ⬝ b) (a' ⬝ b')
-lemma Ka_irreducible (a c : SKI) (h : (K ⬝ a) ⭢ₚ c) : ∃ a', a ⭢ₚ a' ∧ c = K ⬝ a' := sorry
+lemma K_irreducible (a : SKI) (h : K ⭢ₚ a) : a = K := by
+ cases h
+ rfl
+lemma K... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_36ca8164ba2d_2 | 4a7f4fa2f4044d72 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Confluence.lean | Confluence | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "Sa_irreducible",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases h\n case refl =>\n exact ⟨a, ParallelReduction.refl a, rfl⟩\n case par b a' h h' => rw [S_irreducible b h]; use a... | [
{
"name": "S_irreducible",
"text": "lemma S_irreducible (a : SKI) (h : S ⭢ₚ a) : a = S := by\n cases h\n rfl\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 78,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"au... | [
{
"name": "Sa_irreducible",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 233,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | @@ -59,8 +59,16 @@
| par ⦃a a' b b' : SKI⦄ :
ParallelReduction a a' → ParallelReduction b b' → ParallelReduction (a ⬝ b) (a' ⬝ b')
-lemma Sa_irreducible (a c : SKI) (h : (S ⬝ a) ⭢ₚ c) : ∃ a', a ⭢ₚ a' ∧ c = S ⬝ a' := sorry
+lemma S_irreducible (a : SKI) (h : S ⭢ₚ a) : a = S := by
+ cases h
+ rfl
+lemma S... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_36ca8164ba2d_3 | b4f762b4fd06acba | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Confluence.lean | Confluence | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "Sa_irreducible",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases h\n case refl =>\n exact ⟨a, ParallelReduction.refl a, rfl⟩\n case par b a' h h' => rw [S_irreducible b h]; use a... | [
{
"name": "S_irreducible",
"text": "lemma S_irreducible (a : SKI) (h : S ⭢ₚ a) : a = S := by\n cases h\n rfl\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 78,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"au... | [
{
"name": "Sab_irreducible",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 10,
"n_chars": 299,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_nestin... | 2 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | @@ -59,8 +59,16 @@
| par ⦃a a' b b' : SKI⦄ :
ParallelReduction a a' → ParallelReduction b b' → ParallelReduction (a ⬝ b) (a' ⬝ b')
-lemma Sa_irreducible (a c : SKI) (h : (S ⬝ a) ⭢ₚ c) : ∃ a', a ⭢ₚ a' ∧ c = S ⬝ a' := sorry
+lemma S_irreducible (a : SKI) (h : S ⭢ₚ a) : a = S := by
+ cases h
+ rfl
+lemma S... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_36ca8164ba2d_4 | a94b4886951d6b16 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Confluence.lean | Confluence | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "parallelReduction_diamond",
"depth": 1,
"n_commands": 0,
"n_lines": 64,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro a a₁ a₂ h₁ h₂\n cases h₁\n case refl => exact ⟨a₂, h₂, .refl a₂⟩\n case par a a' b b' ha' hb' =>\n c... | [
{
"name": "I_irreducible",
"text": "lemma I_irreducible (a : SKI) (h : I ⭢ₚ a) : a = I := by\n cases h\n rfl\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 78,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"au... | [
{
"name": "parallelReduction_diamond",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 70,
"n_chars": 2284,
"n_subproofs": 0,
"n_tactics": 70,
"cyclomatic": 10,
"n_automation": 1,
"n_rewrites": 6,
"n_structural": 40,
"automation_only": false,
... | 6 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | @@ -59,6 +59,10 @@
| par ⦃a a' b b' : SKI⦄ :
ParallelReduction a a' → ParallelReduction b b' → ParallelReduction (a ⬝ b) (a' ⬝ b')
+lemma I_irreducible (a : SKI) (h : I ⭢ₚ a) : a = I := by
+ cases h
+ rfl
+
lemma K_irreducible (a : SKI) (h : K ⭢ₚ a) : a = K := by
cases h
rfl
@@ -91,7 +95,70 @@
The... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_36ca8164ba2d_5 | 91856c73f04d1897 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Confluence.lean | Confluence | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "parallelReduction_diamond",
"depth": 1,
"n_commands": 0,
"n_lines": 64,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro a a₁ a₂ h₁ h₂\n cases h₁\n case refl => exact ⟨a₂, h₂, .refl a₂⟩\n case par a a' b b' ha' hb' =>\n c... | [
{
"name": "I_irreducible",
"text": "lemma I_irreducible (a : SKI) (h : I ⭢ₚ a) : a = I := by\n cases h\n rfl\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 78,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"au... | [
{
"name": "join_parallelReduction_equivalence",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 5,
"n_chars": 182,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": fals... | 7 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | @@ -59,6 +59,10 @@
| par ⦃a a' b b' : SKI⦄ :
ParallelReduction a a' → ParallelReduction b b' → ParallelReduction (a ⬝ b) (a' ⬝ b')
+lemma I_irreducible (a : SKI) (h : I ⭢ₚ a) : a = I := by
+ cases h
+ rfl
+
lemma K_irreducible (a : SKI) (h : K ⭢ₚ a) : a = K := by
cases h
rfl
@@ -91,7 +95,70 @@
The... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_36ca8164ba2d_6 | 98a827d5da4cadf1 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Confluence.lean | Confluence | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "reflTransGen_parallelReduction_mRed",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext a b\n constructor\n · apply reflTransGen_le_of_le\n -- TODO: restate `parallelReduction_of_red... | [
{
"name": "mRed_of_parallelReduction",
"text": "/-- The inclusion `⭢ₚ ⊆ ↠` -/\ntheorem mRed_of_parallelReduction {a a' : SKI} (h : a ⭢ₚ a') : a ↠ a' := by\n cases h\n case refl => exact Relation.ReflTransGen.refl\n case par a a' b b' ha hb =>\n apply parallel_mRed\n · exact mRed_of_parallelReductio... | [
{
"name": "mJoin_red_equivalence",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 11,
"n_lines": 6,
"n_chars": 217,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_... | 11 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | @@ -59,6 +59,18 @@
| par ⦃a a' b b' : SKI⦄ :
ParallelReduction a a' → ParallelReduction b b' → ParallelReduction (a ⬝ b) (a' ⬝ b')
+/-- The inclusion `⭢ₚ ⊆ ↠` -/
+theorem mRed_of_parallelReduction {a a' : SKI} (h : a ⭢ₚ a') : a ↠ a' := by
+ cases h
+ case refl => exact Relation.ReflTransGen.refl
+ case p... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_36ca8164ba2d_7 | 708e549855ca95b2 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Languages/CombinatoryLogic/Confluence.lean | Confluence | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "reflTransGen_parallelReduction_mRed",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext a b\n constructor\n · apply reflTransGen_le_of_le\n -- TODO: restate `parallelReduction_of_red... | [
{
"name": "mRed_of_parallelReduction",
"text": "/-- The inclusion `⭢ₚ ⊆ ↠` -/\ntheorem mRed_of_parallelReduction {a a' : SKI} (h : a ⭢ₚ a') : a ↠ a' := by\n cases h\n case refl => exact Relation.ReflTransGen.refl\n case par a a' b b' ha hb =>\n apply parallel_mRed\n · exact mRed_of_parallelReductio... | [
{
"name": "MRed.diamond",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 12,
"n_lines": 8,
"n_chars": 267,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_nesting":... | 12 | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | /-
Copyright (c) 2025 Thomas Waring. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Thomas Waring
-/
module
public import Cslib.Languages.CombinatoryLogic.Defs
public import Cslib.Foundations.Relation.Confluence
/-!
# SKI reduction is confluent
This file proves the... | @@ -59,6 +59,18 @@
| par ⦃a a' b b' : SKI⦄ :
ParallelReduction a a' → ParallelReduction b b' → ParallelReduction (a ⬝ b) (a' ⬝ b')
+/-- The inclusion `⭢ₚ ⊆ ↠` -/
+theorem mRed_of_parallelReduction {a a' : SKI} (h : a ⭢ₚ a') : a ↠ a' := by
+ cases h
+ case refl => exact Relation.ReflTransGen.refl
+ case p... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_731cdf1bf6c5_0 | 33349f8bbe6b13fc | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/Nat/Segment.lean | Segment | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "nth_of_strictMono",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← nth_comp_of_strictMono hm]\n · simp\n · simp\n · #adaptation_note\n /-- A grind regression found moving to ni... | [
{
"name": "strictMono_infinite",
"text": "/-- Any strictly monotonic function `f : ℕ → ℕ` has an infinite range. -/\ntheorem strictMono_infinite (hm : StrictMono f) :\n (range f).Infinite :=\n infinite_range_of_injective hm.injective\n\n",
"fan_in": 5,
"n_lines": 6,
"n_chars": 200,
"n_su... | [
{
"name": "nth_of_strictMono",
"fan_in": 5,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 468,
"n_subproofs": 1,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | @@ -33,6 +33,11 @@
variable {f : ℕ → ℕ}
+/-- Any strictly monotonic function `f : ℕ → ℕ` has an infinite range. -/
+theorem strictMono_infinite (hm : StrictMono f) :
+ (range f).Infinite :=
+ infinite_range_of_injective hm.injective
+
/-- For a strictly monotonic function `f : ℕ → ℕ`, `f n` is exactly the n-t... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_731cdf1bf6c5_1 | 2d0c66081b485d1f | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/Nat/Segment.lean | Segment | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "strictMono_range_gap",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [nth_of_strictMono hm m] at hl\n rw [nth_of_strictMono hm (m + 1)] at hu\n have h_inf := strictMono_infinite hm\n... | [
{
"name": "nth_of_strictMono",
"text": "/-- For a strictly monotonic function `f : ℕ → ℕ`, `f n` is exactly the n-th\nelement of the range of `f`. -/\ntheorem nth_of_strictMono (hm : StrictMono f) (n : ℕ) :\n f n = nth (· ∈ range f) n := by\n rw [← nth_comp_of_strictMono hm]\n · simp\n · simp\n · #ad... | [
{
"name": "strictMono_range_gap",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 13,
"n_chars": 595,
"n_subproofs": 2,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false,
"max_n... | 3 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | @@ -50,6 +50,19 @@
have h_m_n : m < n + 1 := by apply (nth_lt_nth hf).mp; omega
omega
+/-- For a strictly monotonic function `f : ℕ → ℕ`, `f n` is exactly the n-th
+element of the range of `f`. -/
+theorem nth_of_strictMono (hm : StrictMono f) (n : ℕ) :
+ f n = nth (· ∈ range f) n := by
+ rw [← nth_comp_of_... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_731cdf1bf6c5_2 | e6d06e3c3aa57fe5 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/Nat/Segment.lean | Segment | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "strictMono_range_gap",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [nth_of_strictMono hm m] at hl\n rw [nth_of_strictMono hm (m + 1)] at hu\n have h_inf := strictMono_infinite hm\n... | [
{
"name": "nth_of_strictMono",
"text": "/-- For a strictly monotonic function `f : ℕ → ℕ`, `f n` is exactly the n-th\nelement of the range of `f`. -/\ntheorem nth_of_strictMono (hm : StrictMono f) (n : ℕ) :\n f n = nth (· ∈ range f) n := by\n rw [← nth_comp_of_strictMono hm]\n · simp\n · simp\n · #ad... | [
{
"name": "segment_idem",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 10,
"n_chars": 324,
"n_subproofs": 2,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting":... | 2 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | @@ -38,6 +38,19 @@
(range f).Infinite :=
infinite_range_of_injective hm.injective
+/-- For a strictly monotonic function `f : ℕ → ℕ`, `f n` is exactly the n-th
+element of the range of `f`. -/
+theorem nth_of_strictMono (hm : StrictMono f) (n : ℕ) :
+ f n = nth (· ∈ range f) n := by
+ rw [← nth_comp_of_st... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_731cdf1bf6c5_3 | 87f63c1ac1362c6d | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/Nat/Segment.lean | Segment | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "strictMono_range_gap",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [nth_of_strictMono hm m] at hl\n rw [nth_of_strictMono hm (m + 1)] at hu\n have h_inf := strictMono_infinite hm\n... | [
{
"name": "nth_of_strictMono",
"text": "/-- For a strictly monotonic function `f : ℕ → ℕ`, `f n` is exactly the n-th\nelement of the range of `f`. -/\ntheorem nth_of_strictMono (hm : StrictMono f) (n : ℕ) :\n f n = nth (· ∈ range f) n := by\n rw [← nth_comp_of_strictMono hm]\n · simp\n · simp\n · #ad... | [
{
"name": "segment_upper_bound",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 451,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_ne... | 2 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | @@ -38,6 +38,19 @@
(range f).Infinite :=
infinite_range_of_injective hm.injective
+/-- For a strictly monotonic function `f : ℕ → ℕ`, `f n` is exactly the n-th
+element of the range of `f`. -/
+theorem nth_of_strictMono (hm : StrictMono f) (n : ℕ) :
+ f n = nth (· ∈ range f) n := by
+ rw [← nth_comp_of_st... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_731cdf1bf6c5_4 | 116e841487aab172 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/Nat/Segment.lean | Segment | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "strictMono_range_gap",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [nth_of_strictMono hm m] at hl\n rw [nth_of_strictMono hm (m + 1)] at hu\n have h_inf := strictMono_infinite hm\n... | [
{
"name": "nth_of_strictMono",
"text": "/-- For a strictly monotonic function `f : ℕ → ℕ`, `f n` is exactly the n-th\nelement of the range of `f`. -/\ntheorem nth_of_strictMono (hm : StrictMono f) (n : ℕ) :\n f n = nth (· ∈ range f) n := by\n rw [← nth_comp_of_strictMono hm]\n · simp\n · simp\n · #ad... | [
{
"name": "segment_lower_bound",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 700,
"n_subproofs": 3,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_n... | 2 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | @@ -38,6 +38,19 @@
(range f).Infinite :=
infinite_range_of_injective hm.injective
+/-- For a strictly monotonic function `f : ℕ → ℕ`, `f n` is exactly the n-th
+element of the range of `f`. -/
+theorem nth_of_strictMono (hm : StrictMono f) (n : ℕ) :
+ f n = nth (· ∈ range f) n := by
+ rw [← nth_comp_of_st... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_731cdf1bf6c5_5 | 10f294f5994db851 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/Nat/Segment.lean | Segment | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "strictMono_range_gap",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [nth_of_strictMono hm m] at hl\n rw [nth_of_strictMono hm (m + 1)] at hu\n have h_inf := strictMono_infinite hm\n... | [
{
"name": "nth_of_strictMono",
"text": "/-- For a strictly monotonic function `f : ℕ → ℕ`, `f n` is exactly the n-th\nelement of the range of `f`. -/\ntheorem nth_of_strictMono (hm : StrictMono f) (n : ℕ) :\n f n = nth (· ∈ range f) n := by\n rw [← nth_comp_of_strictMono hm]\n · simp\n · simp\n · #ad... | [
{
"name": "segment_range_val",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 5,
"n_lines": 26,
"n_chars": 1170,
"n_subproofs": 8,
"n_tactics": 20,
"cyclomatic": 3,
"n_automation": 12,
"n_rewrites": 4,
"n_structural": 4,
"automation_only": false,
"max_n... | 5 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | @@ -50,6 +50,19 @@
have h_m_n : m < n + 1 := by apply (nth_lt_nth hf).mp; omega
omega
+/-- For a strictly monotonic function `f : ℕ → ℕ`, `f n` is exactly the n-th
+element of the range of `f`. -/
+theorem nth_of_strictMono (hm : StrictMono f) (n : ℕ) :
+ f n = nth (· ∈ range f) n := by
+ rw [← nth_comp_of_... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_731cdf1bf6c5_6 | 79546731e3ba28f9 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/Nat/Segment.lean | Segment | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "segment_galois_connection",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro m k; constructor\n · intro h\n by_contra! h_con\n have h1 : segment f k + 1 ≤ m := by omega\n ha... | [
{
"name": "segment_upper_bound",
"text": "/-- For a strictly monotonic function `f : ℕ → ℕ` with `f 0 = 0`,\n`k < f (segment f k + 1)` for all `k : ℕ`. -/\ntheorem segment_upper_bound (hm : StrictMono f) (h0 : f 0 = 0) (k : ℕ) :\n k < f (segment f k + 1) := by\n classical\n rw [nth_of_strictMono hm (se... | [
{
"name": "segment_galois_connection",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 18,
"n_chars": 564,
"n_subproofs": 5,
"n_tactics": 14,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
... | 4 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | @@ -94,6 +94,16 @@
apply count_ne_iff_exists.mpr; use 0; grind
/-- For a strictly monotonic function `f : ℕ → ℕ` with `f 0 = 0`,
+`k < f (segment f k + 1)` for all `k : ℕ`. -/
+theorem segment_upper_bound (hm : StrictMono f) (h0 : f 0 = 0) (k : ℕ) :
+ k < f (segment f k + 1) := by
+ classical
+ rw [nth_of_st... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_731cdf1bf6c5_7 | b6bc493157bfcf24 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/Nat/Segment.lean | Segment | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 3 | [
{
"theorem_name": "segment_zero'",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← segment'_eq_segment hm, segment', (show k - f 0 = 0 by omega)]\n grind",
"n_chars": 84,
"n_subproofs": 0,
... | [
{
"name": "segment'_eq_segment",
"text": "/-- For a strictly monotonic function `f : ℕ → ℕ`,\n`segment' f` and `segment f` are actually equal. -/\ntheorem segment'_eq_segment (hm : StrictMono f) :\n segment' f = segment f := by\n classical\n ext k; unfold segment'\n rcases (show k < f 0 ∨ k ≥ f 0 by o... | [
{
"name": "segment_zero'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 277,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | @@ -98,9 +98,36 @@
noncomputable def segment' (f : ℕ → ℕ) (k : ℕ) : ℕ :=
segment (f · - f 0) (k - f 0)
+/-- For a strictly monotonic function `f : ℕ → ℕ`,
+`segment' f` and `segment f` are actually equal. -/
+theorem segment'_eq_segment (hm : StrictMono f) :
+ segment' f = segment f := by
+ classical
+ ext k... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_731cdf1bf6c5_8 | 40dd14ea9780b890 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/Nat/Segment.lean | Segment | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "segment_upper_bound'",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← segment'_eq_segment hm, segment']\n have := segment_upper_bound (base_zero_strictMono hm) (base_zero_shift f) (... | [
{
"name": "base_zero_strictMono",
"text": "theorem base_zero_strictMono (hm : StrictMono f) :\n StrictMono (f · - f 0) := by\n intro m n h_m_n; simp\n have := hm h_m_n\n have : f 0 ≤ f m := by simp [StrictMono.le_iff_le hm]\n have : f 0 ≤ f n := by simp [StrictMono.le_iff_le hm]\n omega\n\n",
"f... | [
{
"name": "segment_upper_bound'",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 8,
"n_chars": 357,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_ne... | 6 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | @@ -112,6 +112,14 @@
(f · - f 0) 0 = 0 := by
simp
+theorem base_zero_strictMono (hm : StrictMono f) :
+ StrictMono (f · - f 0) := by
+ intro m n h_m_n; simp
+ have := hm h_m_n
+ have : f 0 ≤ f m := by simp [StrictMono.le_iff_le hm]
+ have : f 0 ≤ f n := by simp [StrictMono.le_iff_le hm]
+ omega
+
/--... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_731cdf1bf6c5_9 | 904300b1677a1ae6 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Data/Nat/Segment.lean | Segment | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "segment_upper_bound'",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← segment'_eq_segment hm, segment']\n have := segment_upper_bound (base_zero_strictMono hm) (base_zero_shift f) (... | [
{
"name": "base_zero_strictMono",
"text": "theorem base_zero_strictMono (hm : StrictMono f) :\n StrictMono (f · - f 0) := by\n intro m n h_m_n; simp\n have := hm h_m_n\n have : f 0 ≤ f m := by simp [StrictMono.le_iff_le hm]\n have : f 0 ≤ f n := by simp [StrictMono.le_iff_le hm]\n omega\n\n",
"f... | [
{
"name": "segment_lower_bound'",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 8,
"n_chars": 353,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_ne... | 6 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Init
public import Mathlib.Algebra.Order.Sub.Basic
public import Mathlib.Data.Nat.Nth
/-!
# Segments defined by a strictly monotonic f... | @@ -118,6 +118,14 @@
(f · - f 0) 0 = 0 := by
simp
+theorem base_zero_strictMono (hm : StrictMono f) :
+ StrictMono (f · - f 0) := by
+ intro m n h_m_n; simp
+ have := hm h_m_n
+ have : f 0 ≤ f m := by simp [StrictMono.le_iff_le hm]
+ have : f 0 ≤ f n := by simp [StrictMono.le_iff_le hm]
+ omega
+
/--... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_70f20cd84056_0 | 8c611d22fdc03e35 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Bisimulation.lean | Bisimulation | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 4 | [
{
"theorem_name": "IsBisimulation.sup",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [IsBisimulation.isSimulation_iff] at hrb hsb ⊢\n rw [show flip (r ⊔ s) = flip r ⊔ flip s by ext; rfl]\n exact ⟨hrb.... | [
{
"name": "IsBisimulation.isSimulation_iff",
"text": "/-- A relation is a bisimulation iff both it and its inverse are simulations. -/\ntheorem IsBisimulation.isSimulation_iff :\n IsBisimulation lts₁ lts₂ r ↔ (IsSimulation lts₁ lts₂ r ∧ IsSimulation lts₂ lts₁ (flip r)) := by\n have _ (s₁ s₂) : r s₁ s₂ →... | [
{
"name": "IsBisimulation.sup",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 392,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | @@ -101,6 +101,12 @@
theorem IsBisimulation.isSimulation : IsBisimulation lts₁ lts₂ r → IsSimulation lts₁ lts₂ r := by
grind [IsBisimulation, IsSimulation]
+/-- A relation is a bisimulation iff both it and its inverse are simulations. -/
+theorem IsBisimulation.isSimulation_iff :
+ IsBisimulation lts₁ lts₂ r ↔... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_70f20cd84056_1 | 51585ba82e426a20 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Bisimulation.lean | Bisimulation | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "Bisimilarity.bisimilarity_neq_traceEq",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨State, Label, lts, h⟩ := IsBisimulation.traceEq_not_bisim\n use State, Label, lts\n grind [... | [
{
"name": "IsBisimulation.traceEq_not_bisim",
"text": "/-- In general, trace equivalence is not a bisimulation (extra conditions are needed, see for\nexample `Bisimulation.deterministic_trace_eq_is_bisim`). -/\ntheorem IsBisimulation.traceEq_not_bisim :\n ∃ (State : Type) (Label : Type) (lts : LTS State ... | [
{
"name": "Bisimilarity.bisimilarity_neq_traceEq",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 373,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": f... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | @@ -322,10 +322,64 @@
| five2eight : BisimMotTr 5 'a' 8
| eight2nine : BisimMotTr 8 'c' 9
+/-- In general, trace equivalence is not a bisimulation (extra conditions are needed, see for
+example `Bisimulation.deterministic_trace_eq_is_bisim`). -/
+theorem IsBisimulation.traceEq_not_bisim :
+ ∃ (State : Type) (Lab... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_70f20cd84056_2 | 6a68f86142240784 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Bisimulation.lean | Bisimulation | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 4 | [
{
"theorem_name": "IsBisimulation.sup",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [IsBisimulation.isSimulation_iff] at hrb hsb ⊢\n rw [show flip (r ⊔ s) = flip r ⊔ flip s by ext; rfl]\n exact ⟨hrb.... | [
{
"name": "IsBisimulation.isSimulation_iff",
"text": "/-- A relation is a bisimulation iff both it and its inverse are simulations. -/\ntheorem IsBisimulation.isSimulation_iff :\n IsBisimulation lts₁ lts₂ r ↔ (IsSimulation lts₁ lts₂ r ∧ IsSimulation lts₂ lts₁ (flip r)) := by\n have _ (s₁ s₂) : r s₁ s₂ →... | [
{
"name": "IsBisimulation.deterministic_traceEq_isBisimulation",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 453,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"autom... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | @@ -101,6 +101,12 @@
theorem IsBisimulation.isSimulation : IsBisimulation lts₁ lts₂ r → IsSimulation lts₁ lts₂ r := by
grind [IsBisimulation, IsSimulation]
+/-- A relation is a bisimulation iff both it and its inverse are simulations. -/
+theorem IsBisimulation.isSimulation_iff :
+ IsBisimulation lts₁ lts₂ r ↔... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_70f20cd84056_3 | 0b3a90a1ade04533 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Bisimulation.lean | Bisimulation | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "Bisimilarity.deterministic_traceEq_bisim",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n use TraceEq lts₁ lts₂, h, IsBisimulation.deterministic_traceEq_isBisimulation",
"n_chars": 87,... | [
{
"name": "IsBisimulation.deterministic_traceEq_isBisimulation",
"text": "/-- In any deterministic LTS, trace equivalence is a bisimulation. -/\ntheorem IsBisimulation.deterministic_traceEq_isBisimulation\n {lts₁ : LTS State₁ Label} {lts₂ : LTS State₂ Label}\n [lts₁.Deterministic] [lts₂.Deterministic]... | [
{
"name": "Bisimilarity.deterministic_traceEq_bisim",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 390,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only"... | 2 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | @@ -322,10 +322,19 @@
| five2eight : BisimMotTr 5 'a' 8
| eight2nine : BisimMotTr 8 'c' 9
+/-- In any deterministic LTS, trace equivalence is a bisimulation. -/
+theorem IsBisimulation.deterministic_traceEq_isBisimulation
+ {lts₁ : LTS State₁ Label} {lts₂ : LTS State₂ Label}
+ [lts₁.Deterministic] [lts₂.Deter... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_70f20cd84056_4 | c084e5efb812911d | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Bisimulation.lean | Bisimulation | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "Deterministic.bisim_tfae",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n tfae_have 2 ↔ 3 := Deterministic.traceEq_iff_simulationEquiv s₁ s₂\n tfae_have 1 → 2 := Bisimilarity.le_traceEq s... | [
{
"name": "Bisimilarity.deterministic_traceEq_bisim",
"text": "/-- In deterministic LTSs, trace equivalence implies bisimilarity. -/\ntheorem Bisimilarity.deterministic_traceEq_bisim {lts₁ : LTS State₁ Label} {lts₂ : LTS State₂ Label}\n [lts₁.Deterministic] [lts₂.Deterministic] (h : s₁ ~tr[lts₁,lts₂] s₂)... | [
{
"name": "Deterministic.bisim_tfae",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 11,
"n_chars": 621,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"m... | 4 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | @@ -330,11 +330,21 @@
rw [IsBisimulation.isSimulation_iff, TraceEq.flip_eq]
exact ⟨Deterministic.isSimulation_traceEq, Deterministic.isSimulation_traceEq⟩
+/-- In deterministic LTSs, trace equivalence implies bisimilarity. -/
+theorem Bisimilarity.deterministic_traceEq_bisim {lts₁ : LTS State₁ Label} {lts₂ : LT... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_70f20cd84056_5 | 4230d21d523512ea | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Bisimulation.lean | Bisimulation | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "Bisimilarity.deterministic_bisim_eq_traceEq",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext s₁ s₂\n exact (Deterministic.bisim_tfae s₁ s₂).out 0 1",
"n_chars": 72,
"n_subproo... | [
{
"name": "Deterministic.bisim_tfae",
"text": "/-- In a deterministic lts, bisimilarity, trace equivalence, and simulation equivalence are\nequivalent to one-another. -/\ntheorem Deterministic.bisim_tfae {lts₁ : LTS State₁ Label} {lts₂ : LTS State₂ Label}\n [lts₁.Deterministic] [lts₂.Deterministic] (s₁ :... | [
{
"name": "Bisimilarity.deterministic_bisim_eq_traceEq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 8,
"n_chars": 370,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_on... | 5 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | @@ -336,10 +336,22 @@
(s₁ ~[lts₁,lts₂] s₂) := by
use TraceEq lts₁ lts₂, h, IsBisimulation.deterministic_traceEq_isBisimulation
+/-- In a deterministic lts, bisimilarity, trace equivalence, and simulation equivalence are
+equivalent to one-another. -/
+theorem Deterministic.bisim_tfae {lts₁ : LTS State₁ Label}... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_70f20cd84056_6 | 59f067d2ea0dd642 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Bisimulation.lean | Bisimulation | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 4 | [
{
"theorem_name": "IsBisimulation.sup",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [IsBisimulation.isSimulation_iff] at hrb hsb ⊢\n rw [show flip (r ⊔ s) = flip r ⊔ flip s by ext; rfl]\n exact ⟨hrb.... | [
{
"name": "IsBisimulation.isSimulation_iff",
"text": "/-- A relation is a bisimulation iff both it and its inverse are simulations. -/\ntheorem IsBisimulation.isSimulation_iff :\n IsBisimulation lts₁ lts₂ r ↔ (IsSimulation lts₁ lts₂ r ∧ IsSimulation lts₂ lts₁ (flip r)) := by\n have _ (s₁ s₂) : r s₁ s₂ →... | [
{
"name": "HomBisimilarity.symm_simulation",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 15,
"n_chars": 574,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 7,
"automation_only": false... | 1 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | @@ -101,6 +101,12 @@
theorem IsBisimulation.isSimulation : IsBisimulation lts₁ lts₂ r → IsSimulation lts₁ lts₂ r := by
grind [IsBisimulation, IsSimulation]
+/-- A relation is a bisimulation iff both it and its inverse are simulations. -/
+theorem IsBisimulation.isSimulation_iff :
+ IsBisimulation lts₁ lts₂ r ↔... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_70f20cd84056_7 | 838b210ae974ac04 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Bisimulation.lean | Bisimulation | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "isWeakBisimulation_iff_isSWBisimulation",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Iff.intro\n case mp =>\n intro h\n rw [IsSWBisimulation.iff_isSimulation]\n exact ... | [
{
"name": "IsSWBisimulation.iff_isSimulation",
"text": "theorem IsSWBisimulation.iff_isSimulation [HasTau Label] :\n IsSWBisimulation lts₁ lts₂ r ↔\n IsSimulation lts₁ lts₂.saturate r ∧ IsSimulation lts₂ lts₁.saturate (flip r) := by\n refine ⟨fun h => ⟨h.isSimulation, h.isSimulation_flip⟩, ?_⟩\n i... | [
{
"name": "isWeakBisimulation_iff_isSWBisimulation",
"fan_in": 4,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 18,
"n_chars": 774,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 5,
"automation_only... | 2 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | @@ -373,11 +373,29 @@
intro s₂ s₁ hr μ
exact (h hr μ).2
+theorem IsSWBisimulation.iff_isSimulation [HasTau Label] :
+ IsSWBisimulation lts₁ lts₂ r ↔
+ IsSimulation lts₁ lts₂.saturate r ∧ IsSimulation lts₂ lts₁.saturate (flip r) := by
+ refine ⟨fun h => ⟨h.isSimulation, h.isSimulation_flip⟩, ?_⟩
+ intr... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_70f20cd84056_8 | a07eb4785be50942 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Bisimulation.lean | Bisimulation | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 4 | [
{
"theorem_name": "IsWeakBisimulation.isSwBisimulation",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " isWeakBisimulation_iff_isSWBisimulation.1 h",
"n_chars": 44,
"n_subproofs": 0,
"n_tactics": 1,
... | [
{
"name": "isWeakBisimulation_iff_isSWBisimulation",
"text": "/-- We can now prove that any relation is a `WeakBisimulation` iff it is an `SWBisimulation`.\nThis formalises lemma 4.2.10 in [Sangiorgi2011]. -/\ntheorem isWeakBisimulation_iff_isSWBisimulation\n [HasTau Label] {lts₁ : LTS State₁ Label} {lts... | [
{
"name": "IsWeakBisimulation.isSwBisimulation",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 6,
"n_chars": 290,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": fal... | 3 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | @@ -380,22 +380,41 @@
intro ⟨h, hflip⟩ s₁ s₂ hr μ
exact ⟨h s₁ s₂ hr μ, hflip s₂ s₁ hr μ⟩
+/-- We can now prove that any relation is a `WeakBisimulation` iff it is an `SWBisimulation`.
+This formalises lemma 4.2.10 in [Sangiorgi2011]. -/
+theorem isWeakBisimulation_iff_isSWBisimulation
+ [HasTau Label] {lts₁ ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_70f20cd84056_9 | 51e3616afd346f2e | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Bisimulation.lean | Bisimulation | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "HomWeakBisimilarity.refl",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [HomWeakBisimilarity]\n rw [WeakBisimilarity.weakBisim_eq_swBisim lts lts]\n exists Eq\n grind [IsSWB... | [
{
"name": "WeakBisimilarity.weakBisim_eq_swBisim",
"text": "/-- Weak bisimilarity can also be characterized through sw-bisimulations. -/\n@[scoped grind =]\ntheorem WeakBisimilarity.weakBisim_eq_swBisim [HasTau Label]\n (lts₁ : LTS State₁ Label) (lts₂ : LTS State₂ Label) :\n WeakBisimilarity lts₁ lts₂... | [
{
"name": "HomWeakBisimilarity.refl",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 9,
"n_chars": 299,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"ma... | 4 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | @@ -407,9 +407,22 @@
(h : IsSWBisimulation lts₁ lts₂ r) :
IsWeakBisimulation lts₁ lts₂ r := isWeakBisimulation_iff_isSWBisimulation.2 h
+/-- Weak bisimilarity can also be characterized through sw-bisimulations. -/
+@[scoped grind =]
+theorem WeakBisimilarity.weakBisim_eq_swBisim [HasTau Label]
+ (lts₁ : LT... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_70f20cd84056_10 | dc6dae00fec31705 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Bisimulation.lean | Bisimulation | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "IsWeakBisimulation.inv",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n grind [IsWeakBisimulation.isSwBisimulation, IsSWBisimulation,\n flip, IsSWBisimulation.isWeakBisimulation]",
... | [
{
"name": "IsSWBisimulation.isWeakBisimulation",
"text": "theorem IsSWBisimulation.isWeakBisimulation\n [HasTau Label] {lts₁ : LTS State₁ Label} {lts₂ : LTS State₂ Label} {r : State₁ → State₂ → Prop}\n (h : IsSWBisimulation lts₁ lts₂ r) :\n IsWeakBisimulation lts₁ lts₂ r := isWeakBisimulation_iff_isS... | [
{
"name": "IsWeakBisimulation.inv",
"fan_in": 3,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 9,
"n_chars": 424,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_n... | 5 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | @@ -402,6 +402,11 @@
(h : IsWeakBisimulation lts₁ lts₂ r) :
IsSWBisimulation lts₁ lts₂ r := isWeakBisimulation_iff_isSWBisimulation.1 h
+theorem IsSWBisimulation.isWeakBisimulation
+ [HasTau Label] {lts₁ : LTS State₁ Label} {lts₂ : LTS State₂ Label} {r : State₁ → State₂ → Prop}
+ (h : IsSWBisimulation l... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_70f20cd84056_11 | 1723eb98d2f7aad6 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Foundations/Semantics/LTS/Bisimulation.lean | Bisimulation | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "HomWeakBisimilarity.refl",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [HomWeakBisimilarity]\n rw [WeakBisimilarity.weakBisim_eq_swBisim lts lts]\n exists Eq\n grind [IsSWB... | [
{
"name": "WeakBisimilarity.weakBisim_eq_swBisim",
"text": "/-- Weak bisimilarity can also be characterized through sw-bisimulations. -/\n@[scoped grind =]\ntheorem WeakBisimilarity.weakBisim_eq_swBisim [HasTau Label]\n (lts₁ : LTS State₁ Label) (lts₂ : LTS State₂ Label) :\n WeakBisimilarity lts₁ lts₂... | [
{
"name": "HomWeakBisimilarity.eqv",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 11,
"n_lines": 8,
"n_chars": 288,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"ma... | 6 | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | /-
Copyright (c) 2025 Fabrizio Montesi. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fabrizio Montesi, Thomas Waring
-/
module
public import Cslib.Foundations.Relation.Domain
public import Cslib.Foundations.Semantics.LTS.Simulation
public import Cslib.Foundations.S... | @@ -415,9 +415,22 @@
(h : IsSWBisimulation lts₁ lts₂ r) :
IsWeakBisimulation lts₁ lts₂ r := isWeakBisimulation_iff_isSWBisimulation.2 h
+/-- Weak bisimilarity can also be characterized through sw-bisimulations. -/
+@[scoped grind =]
+theorem WeakBisimilarity.weakBisim_eq_swBisim [HasTau Label]
+ (lts₁ : LT... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ce52136f8e4f_0 | 4b5f66cae1f74b4e | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Languages/OmegaLanguage.lean | OmegaLanguage | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 21 | 2 | [
{
"theorem_name": "iSup_def",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext\n simp [iSup, sSup_def]",
"n_chars": 33,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation... | [
{
"name": "sSup_def",
"text": "lemma sSup_def (s : Set (ωLanguage α)) : sSup s = ⟨⋃ p ∈ s, p.toSet⟩ := rfl\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 87,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automa... | [
{
"name": "iSup_def",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 133,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | @@ -109,9 +109,13 @@
lemma bot_def : (⊥ : ωLanguage α) = ⟨∅⟩ := rfl
+lemma sSup_def (s : Set (ωLanguage α)) : sSup s = ⟨⋃ p ∈ s, p.toSet⟩ := rfl
+
lemma sInf_def (s : Set (ωLanguage α)) : sInf s = ⟨⋂ p ∈ s, p.toSet⟩ := rfl
-lemma iSup_def {ι : Sort v} {p : ι → ωLanguage α} : ⨆ i, p i = ⟨⋃ i, (p i).toSet⟩ := sor... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ce52136f8e4f_1 | 1b182ce07f088f12 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Languages/OmegaLanguage.lean | OmegaLanguage | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 21 | 2 | [
{
"theorem_name": "iInf_def",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext\n simp [iInf, sInf_def]",
"n_chars": 33,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation... | [
{
"name": "sInf_def",
"text": "lemma sInf_def (s : Set (ωLanguage α)) : sInf s = ⟨⋂ p ∈ s, p.toSet⟩ := rfl\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 87,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automa... | [
{
"name": "iInf_def",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 133,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | @@ -111,11 +111,15 @@
lemma sSup_def (s : Set (ωLanguage α)) : sSup s = ⟨⋃ p ∈ s, p.toSet⟩ := rfl
+lemma sInf_def (s : Set (ωLanguage α)) : sInf s = ⟨⋂ p ∈ s, p.toSet⟩ := rfl
+
lemma iSup_def {ι : Sort v} {p : ι → ωLanguage α} : ⨆ i, p i = ⟨⋃ i, (p i).toSet⟩ := by
ext
simp [iSup, sSup_def]
-lemma iInf_def... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ce52136f8e4f_2 | 563b6ca630443e2a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Languages/OmegaLanguage.lean | OmegaLanguage | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 21 | 4 | [
{
"theorem_name": "one_hmul",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [hmul_def, Language.one_def, Language.toSet]",
"n_chars": 55,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic":... | [
{
"name": "hmul_def",
"text": "theorem hmul_def (l : Language α) (p : ωLanguage α) : l * p = image2 (· ++ω ·) l.toSet p.toSet :=\n rfl\n\n",
"fan_in": 4,
"n_lines": 4,
"n_chars": 111,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
... | [
{
"name": "one_hmul",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 128,
"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) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | @@ -126,6 +126,9 @@
instance : HMul (Language α) (ωLanguage α) (ωLanguage α) where
hMul l p := ⟨image2 (· ++ω ·) l.toSet p.toSet⟩
+theorem hmul_def (l : Language α) (p : ωLanguage α) : l * p = image2 (· ++ω ·) l.toSet p.toSet :=
+ rfl
+
/-- Concatenation of infinitely many copies of a languages, resulting in an... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ce52136f8e4f_3 | 6387ee76903fa2c0 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Languages/OmegaLanguage.lean | OmegaLanguage | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 21 | 3 | [
{
"theorem_name": "mem_iSup",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [iSup_def]\n exact mem_iUnion",
"n_chars": 45,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"... | [
{
"name": "iSup_def",
"text": "lemma iSup_def {ι : Sort v} {p : ι → ωLanguage α} : ⨆ i, p i = ⟨⋃ i, (p i).toSet⟩ := by\n ext\n simp [iSup, sSup_def]\n\n",
"fan_in": 3,
"n_lines": 5,
"n_chars": 133,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rew... | [
{
"name": "iSup_hmul",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 194,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": 2
... | 3 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | @@ -113,6 +113,10 @@
lemma sInf_def (s : Set (ωLanguage α)) : sInf s = ⟨⋂ p ∈ s, p.toSet⟩ := rfl
+lemma iSup_def {ι : Sort v} {p : ι → ωLanguage α} : ⨆ i, p i = ⟨⋃ i, (p i).toSet⟩ := by
+ ext
+ simp [iSup, sSup_def]
+
lemma iInf_def {ι : Sort v} {p : ι → ωLanguage α} : ⨅ i, p i = ⟨⋂ i, (p i).toSet⟩ := by
ext... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ce52136f8e4f_4 | 7abf4124eb9f54c6 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Languages/OmegaLanguage.lean | OmegaLanguage | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 21 | 3 | [
{
"theorem_name": "mem_iSup",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [iSup_def]\n exact mem_iUnion",
"n_chars": 45,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"... | [
{
"name": "iSup_def",
"text": "lemma iSup_def {ι : Sort v} {p : ι → ωLanguage α} : ⨆ i, p i = ⟨⋃ i, (p i).toSet⟩ := by\n ext\n simp [iSup, sSup_def]\n\n",
"fan_in": 3,
"n_lines": 5,
"n_chars": 133,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rew... | [
{
"name": "hmul_iSup",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 195,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": 2
... | 3 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | @@ -113,6 +113,10 @@
lemma sInf_def (s : Set (ωLanguage α)) : sInf s = ⟨⋂ p ∈ s, p.toSet⟩ := rfl
+lemma iSup_def {ι : Sort v} {p : ι → ωLanguage α} : ⨆ i, p i = ⟨⋃ i, (p i).toSet⟩ := by
+ ext
+ simp [iSup, sSup_def]
+
lemma iInf_def {ι : Sort v} {p : ι → ωLanguage α} : ⨅ i, p i = ⟨⋂ i, (p i).toSet⟩ := by
ext... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ce52136f8e4f_5 | bef51867e03cf4e1 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Languages/OmegaLanguage.lean | OmegaLanguage | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 21 | 2 | [
{
"theorem_name": "le_hmul_congr",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [le_def]\n intros _\n simp_all only [hmul_def, mem_image2]\n tauto",
"n_chars": 82,
"n_subproofs": 0,
... | [
{
"name": "le_def",
"text": "lemma le_def (p q : ωLanguage α) : p ≤ q ↔ p.toSet ⊆ q.toSet := Iff.rfl\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 81,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_o... | [
{
"name": "le_hmul_congr",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 214,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 2 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | @@ -105,6 +105,8 @@
variable {l m : Language α} {p q : ωLanguage α} {a b x : List α} {s t : ωSequence α}
+lemma le_def (p q : ωLanguage α) : p ≤ q ↔ p.toSet ⊆ q.toSet := Iff.rfl
+
lemma bot_def : (⊥ : ωLanguage α) = ⟨∅⟩ := rfl
lemma sSup_def (s : Set (ωLanguage α)) : sSup s = ⟨⋃ p ∈ s, p.toSet⟩ := rfl
@@ -254,... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ce52136f8e4f_6 | a88ff47758e943df | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Languages/OmegaLanguage.lean | OmegaLanguage | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 21 | 2 | [
{
"theorem_name": "omegaPow_of_sub_one",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext\n simp [omegaPow_def]",
"n_chars": 31,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_a... | [
{
"name": "omegaPow_def",
"text": "theorem omegaPow_def [Inhabited α] (l : Language α) :\n l^ω = { s | ∃ xs : ωSequence (List α), xs.flatten = s ∧ ∀ k, xs k ∈ l - 1 }\n := rfl\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 157,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "omegaPow_of_sub_one",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 122,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | @@ -147,6 +147,10 @@
instance [Inhabited α] : OmegaPow (Language α) (ωLanguage α) :=
⟨omegaPow⟩
+theorem omegaPow_def [Inhabited α] (l : Language α) :
+ l^ω = { s | ∃ xs : ωSequence (List α), xs.flatten = s ∧ ∀ k, xs k ∈ l - 1 }
+ := rfl
+
/-- The ω-limit of a language `l` is the ω-language of infinite seque... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ce52136f8e4f_7 | 34ea90f16f276a7b | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Languages/OmegaLanguage.lean | OmegaLanguage | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 21 | 3 | [
{
"theorem_name": "zero_omegaPow",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext\n simp [omegaPow_def, bot_def]",
"n_chars": 40,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"... | [
{
"name": "bot_def",
"text": "lemma bot_def : (⊥ : ωLanguage α) = ⟨∅⟩ := rfl\n\n",
"fan_in": 3,
"n_lines": 3,
"n_chars": 58,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nes... | [
{
"name": "zero_omegaPow",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 6,
"n_chars": 133,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 2 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | @@ -107,6 +107,8 @@
lemma le_def (p q : ωLanguage α) : p ≤ q ↔ p.toSet ⊆ q.toSet := Iff.rfl
+lemma bot_def : (⊥ : ωLanguage α) = ⟨∅⟩ := rfl
+
lemma sSup_def (s : Set (ωLanguage α)) : sSup s = ⟨⋃ p ∈ s, p.toSet⟩ := rfl
lemma sInf_def (s : Set (ωLanguage α)) : sInf s = ⟨⋂ p ∈ s, p.toSet⟩ := rfl
@@ -273,7 +275,9 ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ce52136f8e4f_8 | d65510a104ec1d6a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Languages/OmegaLanguage.lean | OmegaLanguage | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 21 | 3 | [
{
"theorem_name": "zero_omegaPow",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext\n simp [omegaPow_def, bot_def]",
"n_chars": 40,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"... | [
{
"name": "bot_def",
"text": "lemma bot_def : (⊥ : ωLanguage α) = ⟨∅⟩ := rfl\n\n",
"fan_in": 3,
"n_lines": 3,
"n_chars": 58,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nes... | [
{
"name": "omegaPow_eq_empty",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 10,
"n_chars": 345,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | @@ -107,6 +107,8 @@
lemma le_def (p q : ωLanguage α) : p ≤ q ↔ p.toSet ⊆ q.toSet := Iff.rfl
+lemma bot_def : (⊥ : ωLanguage α) = ⟨∅⟩ := rfl
+
lemma sSup_def (s : Set (ωLanguage α)) : sSup s = ⟨⋃ p ∈ s, p.toSet⟩ := rfl
lemma sInf_def (s : Set (ωLanguage α)) : sInf s = ⟨⋂ p ∈ s, p.toSet⟩ := rfl
@@ -273,7 +275,9 ... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ce52136f8e4f_9 | 372a26c15b046d5a | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Languages/OmegaLanguage.lean | OmegaLanguage | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 21 | 1 | [
{
"theorem_name": "omegaPow_le_kstar_omegaPow",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [le_omegaPow_congr]",
"n_chars": 30,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
... | [
{
"name": "le_omegaPow_congr",
"text": "theorem le_omegaPow_congr [Inhabited α] {l1 l2 : Language α} (h : l1 ≤ l2) : l1^ω ≤ l2^ω := by\n rintro s ⟨xs, rfl, h_xs⟩\n refine ⟨xs, rfl, ?_⟩\n intro k; specialize h_xs k\n simp only [Language.mem_sub_one, ne_eq] at h_xs ⊢\n tauto\n\n",
"fan_in": 1,
"n... | [
{
"name": "omegaPow_le_kstar_omegaPow",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 123,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"m... | 1 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | @@ -262,6 +262,13 @@
simp_all only [hmul_def, mem_image2]
tauto
+theorem le_omegaPow_congr [Inhabited α] {l1 l2 : Language α} (h : l1 ≤ l2) : l1^ω ≤ l2^ω := by
+ rintro s ⟨xs, rfl, h_xs⟩
+ refine ⟨xs, rfl, ?_⟩
+ intro k; specialize h_xs k
+ simp only [Language.mem_sub_one, ne_eq] at h_xs ⊢
+ tauto
+
@[sim... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ce52136f8e4f_10 | 555df84d19399493 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Languages/OmegaLanguage.lean | OmegaLanguage | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 21 | 2 | [
{
"theorem_name": "hmul_omegaPow_le_omegaPow",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n suffices h : l * l^ω ≤ (l - 1) * (l * l^ω) by exact omegaPow_coind h\n rw [← mul_hmul, Language.sub_one_mul, ← L... | [
{
"name": "mul_hmul",
"text": "theorem mul_hmul : (l * m) * p = l * (m * p) := by\n ext : 1\n exact image2_assoc append_append_ωSequence\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 108,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
... | [
{
"name": "kstar_omegaPow_le_omegaPow",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 9,
"n_lines": 9,
"n_chars": 384,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"... | 8 | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | /-
Copyright (c) 2025 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Languages.Language
public import Cslib.Foundations.Data.OmegaSequence.Flatten
public import Mathlib.Computability.Languag... | @@ -237,6 +237,10 @@
s ∈ l↗ω ↔ ∃ᶠ m in atTop, s.extract 0 m ∈ l :=
Iff.rfl
+theorem mul_hmul : (l * m) * p = l * (m * p) := by
+ ext : 1
+ exact image2_assoc append_append_ωSequence
+
@[simp, scoped grind =]
theorem zero_hmul : (0 : Language α) * p = ⊥ := by
ext : 1
@@ -357,7 +361,12 @@
· apply sdif... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_66df07ebb69a_0 | 2a1a9cd8f2079476 | lean | lean | github.com/leanprover/cslib | c0120dddfe75d4ab913691c0c184fc436927b19d | Cslib/Computability/Languages/Congruences/BuchiCongruence.lean | BuchiCongruence | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "buchiCongruence_fin_index",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n Finite.of_surjective na.BuchiCongrParam buchiCongrParam_surjective",
"n_chars": 69,
"n_subproofs": 0,
"n... | [
{
"name": "buchiCongrParam_surjective",
"text": "/-- `BuchiCongrParam` is surjective. -/\nlemma buchiCongrParam_surjective : Surjective na.BuchiCongrParam := by\n intro q\n let f s t := (q.out ∈ na.pairLang s t, q.out ∈ na.pairViaLang na.accept s t)\n have h : ∃ u, ∀ s t, ((f s t).1 ↔ u ∈ na.pairLang s t... | [
{
"name": "buchiCongruence_fin_index",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 250,
"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 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.NA.Pair
public import Cslib.Foundations.Combinatorics.InfiniteGraphRamsey
public import Cslib.Foundations.Data.S... | /-
Copyright (c) 2026 Ching-Tsun Chou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ching-Tsun Chou
-/
module
public import Cslib.Computability.Automata.NA.Pair
public import Cslib.Foundations.Combinatorics.InfiniteGraphRamsey
public import Cslib.Foundations.Data.S... | @@ -56,8 +56,24 @@
variable {na : Buchi State Symbol}
+/-- `BuchiCongrParam` is surjective. -/
+lemma buchiCongrParam_surjective : Surjective na.BuchiCongrParam := by
+ intro q
+ let f s t := (q.out ∈ na.pairLang s t, q.out ∈ na.pairViaLang na.accept s t)
+ have h : ∃ u, ∀ s t, ((f s t).1 ↔ u ∈ na.pairLang s t)... | {
"repo": "cslib",
"git_repo": "github.com/leanprover/cslib",
"revision": "c0120dddfe75d4ab913691c0c184fc436927b19d",
"lean_toolchain": "leanprover/lean4:v4.32.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
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