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_9f470b8a1f5e_0 | 1dfed12c3611bbe2 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/OracleReduction/Security/TranscriptTree/Composition.lean | Composition | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "transcript_msg",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv_lhs => rw [peelMsg_spec path]\n rfl",
"n_chars": 46,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1... | [
{
"name": "peelMsg_spec",
"text": "/-- A `LeafPath` at a message node is `.msg` of its peel. -/\ntheorem peelMsg_spec {k : Fin m} {h : pSpec₁.dir k = .P_to_V} {msg : pSpec₁.Message ⟨k, h⟩}\n {child : ChallengeTree pSpec₁ arity₁ k.succ} (p : LeafPath (.msgNode k h msg child)) :\n p = @LeafPath.msg _ _ ... | [
{
"name": "transcript_msg",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 452,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree.Basic
/-!
# Trees of transcripts — sequential composition
This file relates trees of transcrip... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree.Basic
/-!
# Trees of transcripts — sequential composition
This file relates trees of transcrip... | @@ -361,6 +361,11 @@
{child : ChallengeTree pSpec₁ arity₁ k.succ} (p : LeafPath (.msgNode k h msg child)) :
LeafPath child := (peelMsgAux p).1
+/-- A `LeafPath` at a message node is `.msg` of its peel. -/
+theorem peelMsg_spec {k : Fin m} {h : pSpec₁.dir k = .P_to_V} {msg : pSpec₁.Message ⟨k, h⟩}
+ {chil... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_9f470b8a1f5e_1 | 139b3ca85597e72b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/OracleReduction/Security/TranscriptTree/Composition.lean | Composition | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "transcript_chal",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv_lhs => rw [chalPeel_spec path]\n rfl",
"n_chars": 47,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic":... | [
{
"name": "chalPeel_spec",
"text": "/-- A `LeafPath` at a challenge node is `.chal` of its peeled index and child path. -/\ntheorem chalPeel_spec {k : Fin m} {h : pSpec₁.dir k = .V_to_P}\n {challenges : Fin (arity₁ ⟨k, h⟩) → pSpec₁.Challenge ⟨k, h⟩}\n {children : Fin (arity₁ ⟨k, h⟩) → ChallengeTree pS... | [
{
"name": "transcript_chal",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 585,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree.Basic
/-!
# Trees of transcripts — sequential composition
This file relates trees of transcrip... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree.Basic
/-!
# Trees of transcripts — sequential composition
This file relates trees of transcrip... | @@ -402,6 +402,14 @@
(p : LeafPath (.chalNode k h challenges children)) :
(j : Fin (arity₁ ⟨k, h⟩)) × LeafPath (children j) := (chalPeelAux p).1
+/-- A `LeafPath` at a challenge node is `.chal` of its peeled index and child path. -/
+theorem chalPeel_spec {k : Fin m} {h : pSpec₁.dir k = .V_to_P}
+ {chall... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_9f470b8a1f5e_2 | ddc2b165f7e611a9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/OracleReduction/Security/TranscriptTree/Composition.lean | Composition | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 3 | [
{
"theorem_name": "appendSplit_fst_isStructured",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n SplitData.fst_isStructured (splitDataOfTree (r := 0) T)\n (by rw [splitDataOfTree_src]; exact hT)",
"n_cha... | [
{
"name": "splitDataOfTree_src",
"text": "/-- The `SplitData` certificate built from an appended tree faithfully represents it. -/\ntheorem splitDataOfTree_src {r : Fin (m + 1)}\n (T : ChallengeTree (pSpec₁ ++ₚ pSpec₂) (appendArity arity₁ arity₂) (leftRound r)) :\n (splitDataOfTree (arity₁ := arity₁) ... | [
{
"name": "appendSplit_fst_isStructured",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 399,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree.Basic
/-!
# Trees of transcripts — sequential composition
This file relates trees of transcrip... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree.Basic
/-!
# Trees of transcripts — sequential composition
This file relates trees of transcrip... | @@ -547,6 +547,12 @@
(T : ChallengeTree (pSpec₁ ++ₚ pSpec₂) (appendArity arity₁ arity₂) (leftRound r)) :
SplitData arity₁ arity₂ r := (splitDataOfTreeAux T r rfl).1
+/-- The `SplitData` certificate built from an appended tree faithfully represents it. -/
+theorem splitDataOfTree_src {r : Fin (m + 1)}
+ (... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_9f470b8a1f5e_3 | c3e83c6374cf9315 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/OracleReduction/Security/TranscriptTree/Composition.lean | Composition | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 3 | [
{
"theorem_name": "appendSplit_fst_isStructured",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n SplitData.fst_isStructured (splitDataOfTree (r := 0) T)\n (by rw [splitDataOfTree_src]; exact hT)",
"n_cha... | [
{
"name": "splitDataOfTree_src",
"text": "/-- The `SplitData` certificate built from an appended tree faithfully represents it. -/\ntheorem splitDataOfTree_src {r : Fin (m + 1)}\n (T : ChallengeTree (pSpec₁ ++ₚ pSpec₂) (appendArity arity₁ arity₂) (leftRound r)) :\n (splitDataOfTree (arity₁ := arity₁) ... | [
{
"name": "appendSplit_sndAt_isStructured",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 479,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree.Basic
/-!
# Trees of transcripts — sequential composition
This file relates trees of transcrip... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree.Basic
/-!
# Trees of transcripts — sequential composition
This file relates trees of transcrip... | @@ -547,6 +547,12 @@
(T : ChallengeTree (pSpec₁ ++ₚ pSpec₂) (appendArity arity₁ arity₂) (leftRound r)) :
SplitData arity₁ arity₂ r := (splitDataOfTreeAux T r rfl).1
+/-- The `SplitData` certificate built from an appended tree faithfully represents it. -/
+theorem splitDataOfTree_src {r : Fin (m + 1)}
+ (... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_9f470b8a1f5e_4 | 8097e270c822462b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/OracleReduction/Security/TranscriptTree/Composition.lean | Composition | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "rightPrefix_concat",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext idx\n have hidx : idx.val < m + i.val + 1 := by\n have := idx.isLt; simp only [rightRound, Fin.val_natAdd, F... | [
{
"name": "cast_eq_cast_of_heq",
"text": "/-- Two casts into a common type are equal as soon as their arguments are `HEq`. Lets cast-equality\ngoals be discharged by reasoning about the (cast-free) underlying values. -/\ntheorem cast_eq_cast_of_heq {α α' β : Sort _} (h1 : α = β) (h2 : α' = β) {a : α} {a' : ... | [
{
"name": "rightPrefix_concat",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 28,
"n_chars": 1229,
"n_subproofs": 3,
"n_tactics": 21,
"cyclomatic": 5,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree.Basic
/-!
# Trees of transcripts — sequential composition
This file relates trees of transcrip... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree.Basic
/-!
# Trees of transcripts — sequential composition
This file relates trees of transcrip... | @@ -715,6 +715,12 @@
Fin.val_castAdd, Fin.val_succ] <;>
exact cast_eq_iff_heq.mpr (cast_heq _ _).symm
+/-- Two casts into a common type are equal as soon as their arguments are `HEq`. Lets cast-equality
+goals be discharged by reasoning about the (cast-free) underlying values. -/
+theorem cast_eq_cast_of_... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_9f470b8a1f5e_5 | 89954bf2ed9d8c81 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/OracleReduction/Security/TranscriptTree/Composition.lean | Composition | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 3 | [
{
"theorem_name": "appendSplit_fst_isStructured",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n SplitData.fst_isStructured (splitDataOfTree (r := 0) T)\n (by rw [splitDataOfTree_src]; exact hT)",
"n_cha... | [
{
"name": "splitDataOfTree_src",
"text": "/-- The `SplitData` certificate built from an appended tree faithfully represents it. -/\ntheorem splitDataOfTree_src {r : Fin (m + 1)}\n (T : ChallengeTree (pSpec₁ ++ₚ pSpec₂) (appendArity arity₁ arity₂) (leftRound r)) :\n (splitDataOfTree (arity₁ := arity₁) ... | [
{
"name": "appendSplit_fullTranscripts_append_of_mem",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 805,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 3,
"automation_onl... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree.Basic
/-!
# Trees of transcripts — sequential composition
This file relates trees of transcrip... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree.Basic
/-!
# Trees of transcripts — sequential composition
This file relates trees of transcrip... | @@ -547,6 +547,12 @@
(T : ChallengeTree (pSpec₁ ++ₚ pSpec₂) (appendArity arity₁ arity₂) (leftRound r)) :
SplitData arity₁ arity₂ r := (splitDataOfTreeAux T r rfl).1
+/-- The `SplitData` certificate built from an appended tree faithfully represents it. -/
+theorem splitDataOfTree_src {r : Fin (m + 1)}
+ (... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4fd2cbfff6a2_0 | 2926205ea720ef51 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon.lean | ReedSolomon | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "evalOnPoints_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n aesop (add unsafe (by rw [←evalOnPointsRingHom_eq_evalOnPoints]))",
"n_chars": 73,
"n_subproofs": 0,
"n_tactic... | [
{
"name": "evalOnPointsRingHom_eq_evalOnPoints",
"text": "lemma evalOnPointsRingHom_eq_evalOnPoints [CommSemiring F] {p : F[X]} {domain : ι ↪ F} :\n evalOnPointsRingHom domain p = evalOnPoints domain p := rfl\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 155,
"n_subproofs": 0,
"n_tactics"... | [
{
"name": "evalOnPoints_mul",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 238,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | @@ -49,9 +49,13 @@
map_add' := by aesop
map_mul' := by aesop
+lemma evalOnPointsRingHom_eq_evalOnPoints [CommSemiring F] {p : F[X]} {domain : ι ↪ F} :
+ evalOnPointsRingHom domain p = evalOnPoints domain p := rfl
+
@[simp]
lemma evalOnPoints_mul [CommSemiring F] {domain : ι ↪ F} {p q : F[X]} :
- evalOnPoi... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4fd2cbfff6a2_1 | 1dde47fbbc5f1a63 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon.lean | ReedSolomon | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "mem_code_of_polynomial_of_natDegree_lt_of_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases h0 : p = 0\n · have hf : f = 0 := by aesop\n simp [hf]\n · rw [Polynomial.natD... | [
{
"name": "mem_code_of_polynomial_of_degree_lt_of_eval",
"text": "lemma mem_code_of_polynomial_of_degree_lt_of_eval {n : ℕ} {α : ι ↪ F} {f : ι → F}\n (p : Polynomial F)\n (hdeg : p.degree < n) (heval : ∀ i, f i = p.eval (α i)) :\n f ∈ code α n := by\n aesop\n (add simp [code, evalOnPoints,\n ... | [
{
"name": "mem_code_of_polynomial_of_natDegree_lt_of_eval",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 401,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automatio... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | @@ -151,6 +151,15 @@
variable [Semiring F]
+lemma mem_code_of_polynomial_of_degree_lt_of_eval {n : ℕ} {α : ι ↪ F} {f : ι → F}
+ (p : Polynomial F)
+ (hdeg : p.degree < n) (heval : ∀ i, f i = p.eval (α i)) :
+ f ∈ code α n := by
+ aesop
+ (add simp [code, evalOnPoints,
+ Polynomial.degreeLT,
+ ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4fd2cbfff6a2_2 | eb6f8c3aeb465dc3 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon.lean | ReedSolomon | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "dim_eq_deg_of_le",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n rw [\n ← genMatIsVandermonde, ← rank_eq_dim_fromColGenMat, Vandermonde.rank_nonsquare_rows_eq_min\n... | [
{
"name": "genMatIsVandermonde",
"text": "/-- The Vandermonde matrix is the generator matrix for an RS code of length `ι` and dimension `deg`.\n-/\nlemma genMatIsVandermonde [Fintype ι] [Field F] [inst : NeZero m] {α : ι ↪ F} :\n fromColGenMat (Vandermonde.nonsquare (ι' := m) α) = ReedSolomon.code α m :=... | [
{
"name": "dim_eq_deg_of_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 284,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | @@ -128,6 +128,25 @@
open LinearCode
+/-- The Vandermonde matrix is the generator matrix for an RS code of length `ι` and dimension `deg`.
+-/
+lemma genMatIsVandermonde [Fintype ι] [Field F] [inst : NeZero m] {α : ι ↪ F} :
+ fromColGenMat (Vandermonde.nonsquare (ι' := m) α) = ReedSolomon.code α m := by
+ clas... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4fd2cbfff6a2_3 | fba3762f486a1d9c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon.lean | ReedSolomon | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "dim_eq_card_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [LinearCode.dim]\n let f := ReedSolomon.evalOnPoints (F := F) α\n let S := Polynomial.degreeLT F n\n have h_code :... | [
{
"name": "dim_eq_deg_of_le'",
"text": "/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/\nlemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]\n {n : ℕ} {α : ι ↪ F} (h : n ≤ Fintype.card ι) :\n LinearCode.dim (ReedSolomon.code α n) = n := by\n by_c... | [
{
"name": "dim_eq_card_of_lt",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 30,
"n_chars": 1052,
"n_subproofs": 5,
"n_tactics": 24,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 3,
"n_structural": 5,
"automation_only": false,
"max_ne... | 2 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | @@ -190,11 +190,89 @@
← genMatIsVandermonde, ← rank_eq_dim_fromColGenMat, Vandermonde.rank_nonsquare_rows_eq_min
] <;> simp [inj, h]
+/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/
+lemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]
+ {n : ℕ} ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4fd2cbfff6a2_4 | 4e970c7dd8fe15b5 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon.lean | ReedSolomon | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "dim_eq_card_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [LinearCode.dim]\n let f := ReedSolomon.evalOnPoints (F := F) α\n let S := Polynomial.degreeLT F n\n have h_code :... | [
{
"name": "dim_eq_deg_of_le'",
"text": "/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/\nlemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]\n {n : ℕ} {α : ι ↪ F} (h : n ≤ Fintype.card ι) :\n LinearCode.dim (ReedSolomon.code α n) = n := by\n by_c... | [
{
"name": "dim_eq_min_deg_card",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 14,
"n_chars": 502,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_ne... | 3 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | @@ -190,11 +190,89 @@
← genMatIsVandermonde, ← rank_eq_dim_fromColGenMat, Vandermonde.rank_nonsquare_rows_eq_min
] <;> simp [inj, h]
+/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/
+lemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]
+ {n : ℕ} ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4fd2cbfff6a2_5 | a6165f6de2afceb4 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon.lean | ReedSolomon | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "dim_eq_deg_of_le",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n rw [\n ← genMatIsVandermonde, ← rank_eq_dim_fromColGenMat, Vandermonde.rank_nonsquare_rows_eq_min\n... | [
{
"name": "genMatIsVandermonde",
"text": "/-- The Vandermonde matrix is the generator matrix for an RS code of length `ι` and dimension `deg`.\n-/\nlemma genMatIsVandermonde [Fintype ι] [Field F] [inst : NeZero m] {α : ι ↪ F} :\n fromColGenMat (Vandermonde.nonsquare (ι' := m) α) = ReedSolomon.code α m :=... | [
{
"name": "rateOfLinearCode_eq_div",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 5,
"n_chars": 200,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | @@ -128,6 +128,25 @@
open LinearCode
+/-- The Vandermonde matrix is the generator matrix for an RS code of length `ι` and dimension `deg`.
+-/
+lemma genMatIsVandermonde [Fintype ι] [Field F] [inst : NeZero m] {α : ι ↪ F} :
+ fromColGenMat (Vandermonde.nonsquare (ι' := m) α) = ReedSolomon.code α m := by
+ clas... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4fd2cbfff6a2_6 | be7fe170f63b19b0 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon.lean | ReedSolomon | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "dim_eq_card_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [LinearCode.dim]\n let f := ReedSolomon.evalOnPoints (F := F) α\n let S := Polynomial.degreeLT F n\n have h_code :... | [
{
"name": "dim_eq_deg_of_le'",
"text": "/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/\nlemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]\n {n : ℕ} {α : ι ↪ F} (h : n ≤ Fintype.card ι) :\n LinearCode.dim (ReedSolomon.code α n) = n := by\n by_c... | [
{
"name": "rateOfLinearCode_eq_div'",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 8,
"n_chars": 410,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | @@ -190,6 +190,61 @@
← genMatIsVandermonde, ← rank_eq_dim_fromColGenMat, Vandermonde.rank_nonsquare_rows_eq_min
] <;> simp [inj, h]
+/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/
+lemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]
+ {n : ℕ} {... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4fd2cbfff6a2_7 | e08f6d609d0a7d0d | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon.lean | ReedSolomon | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "dim_eq_card_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [LinearCode.dim]\n let f := ReedSolomon.evalOnPoints (F := F) α\n let S := Polynomial.degreeLT F n\n have h_code :... | [
{
"name": "dim_eq_deg_of_le'",
"text": "/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/\nlemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]\n {n : ℕ} {α : ι ↪ F} (h : n ≤ Fintype.card ι) :\n LinearCode.dim (ReedSolomon.code α n) = n := by\n by_c... | [
{
"name": "rateOfLinearCode_eq_min_div",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 7,
"n_chars": 261,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
... | 4 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | @@ -190,11 +190,89 @@
← genMatIsVandermonde, ← rank_eq_dim_fromColGenMat, Vandermonde.rank_nonsquare_rows_eq_min
] <;> simp [inj, h]
+/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/
+lemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]
+ {n : ℕ} ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4fd2cbfff6a2_8 | e431ad3cfe034840 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon.lean | ReedSolomon | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "dim_eq_card_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [LinearCode.dim]\n let f := ReedSolomon.evalOnPoints (F := F) α\n let S := Polynomial.degreeLT F n\n have h_code :... | [
{
"name": "dim_eq_deg_of_le'",
"text": "/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/\nlemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]\n {n : ℕ} {α : ι ↪ F} (h : n ≤ Fintype.card ι) :\n LinearCode.dim (ReedSolomon.code α n) = n := by\n by_c... | [
{
"name": "minDist'",
"fan_in": 3,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 43,
"n_chars": 2022,
"n_subproofs": 7,
"n_tactics": 39,
"cyclomatic": 2,
"n_automation": 9,
"n_rewrites": 3,
"n_structural": 10,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | @@ -190,6 +190,61 @@
← genMatIsVandermonde, ← rank_eq_dim_fromColGenMat, Vandermonde.rank_nonsquare_rows_eq_min
] <;> simp [inj, h]
+/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/
+lemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]
+ {n : ℕ} {... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4fd2cbfff6a2_9 | 76c3a22ceccddf5c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon.lean | ReedSolomon | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "dim_eq_card_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [LinearCode.dim]\n let f := ReedSolomon.evalOnPoints (F := F) α\n let S := Polynomial.degreeLT F n\n have h_code :... | [
{
"name": "dim_eq_deg_of_le'",
"text": "/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/\nlemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]\n {n : ℕ} {α : ι ↪ F} (h : n ≤ Fintype.card ι) :\n LinearCode.dim (ReedSolomon.code α n) = n := by\n by_c... | [
{
"name": "isMDS_code",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 9,
"n_chars": 370,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 2 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | @@ -190,6 +190,61 @@
← genMatIsVandermonde, ← rank_eq_dim_fromColGenMat, Vandermonde.rank_nonsquare_rows_eq_min
] <;> simp [inj, h]
+/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/
+lemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]
+ {n : ℕ} {... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4fd2cbfff6a2_10 | 8ff4f83e848699f6 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon.lean | ReedSolomon | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "dim_eq_card_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [LinearCode.dim]\n let f := ReedSolomon.evalOnPoints (F := F) α\n let S := Polynomial.degreeLT F n\n have h_code :... | [
{
"name": "dim_eq_deg_of_le'",
"text": "/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/\nlemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]\n {n : ℕ} {α : ι ↪ F} (h : n ≤ Fintype.card ι) :\n LinearCode.dim (ReedSolomon.code α n) = n := by\n by_c... | [
{
"name": "uniqueDecodingRadius_RS_eq'",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 12,
"n_chars": 505,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
... | 2 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | @@ -190,6 +190,61 @@
← genMatIsVandermonde, ← rank_eq_dim_fromColGenMat, Vandermonde.rank_nonsquare_rows_eq_min
] <;> simp [inj, h]
+/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/
+lemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]
+ {n : ℕ} {... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4fd2cbfff6a2_11 | f46fb26478cdfd75 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon.lean | ReedSolomon | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "dim_eq_card_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [LinearCode.dim]\n let f := ReedSolomon.evalOnPoints (F := F) α\n let S := Polynomial.degreeLT F n\n have h_code :... | [
{
"name": "dim_eq_deg_of_le'",
"text": "/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/\nlemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]\n {n : ℕ} {α : ι ↪ F} (h : n ≤ Fintype.card ι) :\n LinearCode.dim (ReedSolomon.code α n) = n := by\n by_c... | [
{
"name": "uniqueDecodingRadius_RS_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 10,
"n_chars": 595,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
... | 3 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | @@ -190,6 +190,61 @@
← genMatIsVandermonde, ← rank_eq_dim_fromColGenMat, Vandermonde.rank_nonsquare_rows_eq_min
] <;> simp [inj, h]
+/-- Generalized dimension formula for RS code with arbitrary finite index type `ι`. -/
+lemma dim_eq_deg_of_le' {ι : Type*} [Fintype ι] {F : Type*} [Field F]
+ {n : ℕ} {... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4fd2cbfff6a2_12 | ada9397a0567a72d | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon.lean | ReedSolomon | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "toPolynomial_lt_min_deg_card",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases h0 : toPolynomial c = 0\n · simp [h0]\n · rw [←Polynomial.natDegree_lt_iff_degree_lt h0, lt_min_iff... | [
{
"name": "toPolynomial_def",
"text": "lemma toPolynomial_def {f : ReedSolomon.code domain deg} :\n toPolynomial f = Lagrange.interpolate univ domain f := rfl\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 121,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
... | [
{
"name": "toPolynomial_lt_min_deg_card",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 534,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 3,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 3,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland, Ilia Vlasov,
Mirco Richter, Chung Thai Nguyen
-/
import ArkLib.Data.Matrix.Vandermonde
import ArkLib.Data.MvPo... | @@ -455,6 +455,9 @@
(interpolate (domain := domain))
(ReedSolomon.code domain deg)
+lemma toPolynomial_def {f : ReedSolomon.code domain deg} :
+ toPolynomial f = Lagrange.interpolate univ domain f := rfl
+
/-- The polynomials corresponding to Reed-Solomon codewords are of degree smaller than `deg`. -/
le... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_307bb5c1b6da_0 | 3a2d9925eddb55cb | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/NormBounds/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "valMinAbs_sub_natAbs_le",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h : ((a.valMinAbs - b.valMinAbs : ℤ) : ZMod q) = a - b := by\n rw [Int.cast_sub, ZMod.coe_valMinAbs, ZMod.c... | [
{
"name": "valMinAbs_natAbs_le",
"text": "/-- The centered representative `valMinAbs` has the least absolute value among all\ninteger representatives of a residue class. -/\ntheorem valMinAbs_natAbs_le {a : ZMod q} (m : ℤ) (h : (m : ZMod q) = a) :\n a.valMinAbs.natAbs ≤ m.natAbs := by\n have hmem := ZMo... | [
{
"name": "valMinAbs_sub_natAbs_le",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 445,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Rq
import ArkLib.Data.Lattices.Vectors
import Mathlib.Algebra.Field.ZMod
import Mathlib.Data.ZMod.ValMinAbs
/-!... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Rq
import ArkLib.Data.Lattices.Vectors
import Mathlib.Algebra.Field.ZMod
import Mathlib.Data.ZMod.ValMinAbs
/-!... | @@ -40,10 +40,33 @@
/-! ## Minimality and triangle inequality for the centered representative -/
+/-- The centered representative `valMinAbs` has the least absolute value among all
+integer representatives of a residue class. -/
+theorem valMinAbs_natAbs_le {a : ZMod q} (m : ℤ) (h : (m : ZMod q) = a) :
+ a.valM... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_307bb5c1b6da_1 | 4c2b54793f012f41 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/NormBounds/Basic.lean | Basic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "Rq.l1Norm_one",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hq2 : 2 ≤ q := (Fact.out (p := Nat.Prime q)).two_le\n unfold Rq.l1Norm\n rw [Finset.sum_eq_single (0 : ℕ)]\n · rw [R... | [
{
"name": "Rq.one_val",
"text": "/-- The underlying polynomial of `1 : Rq Φ` is the constant `1` (no reduction occurs, as\n`deg 1 = 0 < deg φ`). -/\ntheorem Rq.one_val (h : 1 ≤ Φ.φ.natDegree) : (1 : Rq Φ).1 = 1 := by\n change Φ.reduce 1 = 1\n apply Φ.reduce_eq_self_of_degree_lt\n rw [CompPoly.CPolynomial... | [
{
"name": "Rq.l1Norm_one",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 18,
"n_chars": 767,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 6,
"n_structural": 3,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Rq
import ArkLib.Data.Lattices.Vectors
import Mathlib.Algebra.Field.ZMod
import Mathlib.Data.ZMod.ValMinAbs
/-!... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Rq
import ArkLib.Data.Lattices.Vectors
import Mathlib.Algebra.Field.ZMod
import Mathlib.Data.ZMod.ValMinAbs
/-!... | @@ -81,14 +81,30 @@
notation "‖" z "‖₂²" => vecL2NormSq _ z
omit [NeZero q] in
+/-- The underlying polynomial of `1 : Rq Φ` is the constant `1` (no reduction occurs, as
+`deg 1 = 0 < deg φ`). -/
+theorem Rq.one_val (h : 1 ≤ Φ.φ.natDegree) : (1 : Rq Φ).1 = 1 := by
+ change Φ.reduce 1 = 1
+ apply Φ.reduce_eq_self_o... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_307bb5c1b6da_2 | 91b4e6de7895a016 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/NormBounds/Basic.lean | Basic | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "valMinAbs_sub_natAbs_le",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h : ((a.valMinAbs - b.valMinAbs : ℤ) : ZMod q) = a - b := by\n rw [Int.cast_sub, ZMod.coe_valMinAbs, ZMod.c... | [
{
"name": "valMinAbs_natAbs_le",
"text": "/-- The centered representative `valMinAbs` has the least absolute value among all\ninteger representatives of a residue class. -/\ntheorem valMinAbs_natAbs_le {a : ZMod q} (m : ℤ) (h : (m : ZMod q) = a) :\n a.valMinAbs.natAbs ≤ m.natAbs := by\n have hmem := ZMo... | [
{
"name": "Rq.l2NormSq_sub_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 20,
"n_chars": 1074,
"n_subproofs": 4,
"n_tactics": 16,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false,
"max_n... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Rq
import ArkLib.Data.Lattices.Vectors
import Mathlib.Algebra.Field.ZMod
import Mathlib.Data.ZMod.ValMinAbs
/-!... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Rq
import ArkLib.Data.Lattices.Vectors
import Mathlib.Algebra.Field.ZMod
import Mathlib.Data.ZMod.ValMinAbs
/-!... | @@ -40,10 +40,33 @@
/-! ## Minimality and triangle inequality for the centered representative -/
+/-- The centered representative `valMinAbs` has the least absolute value among all
+integer representatives of a residue class. -/
+theorem valMinAbs_natAbs_le {a : ZMod q} (m : ℤ) (h : (m : ZMod q) = a) :
+ a.valM... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_307bb5c1b6da_3 | 6697eb9fa815aac8 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/NormBounds/Basic.lean | Basic | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "valMinAbs_sub_natAbs_le",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h : ((a.valMinAbs - b.valMinAbs : ℤ) : ZMod q) = a - b := by\n rw [Int.cast_sub, ZMod.coe_valMinAbs, ZMod.c... | [
{
"name": "valMinAbs_natAbs_le",
"text": "/-- The centered representative `valMinAbs` has the least absolute value among all\ninteger representatives of a residue class. -/\ntheorem valMinAbs_natAbs_le {a : ZMod q} (m : ℤ) (h : (m : ZMod q) = a) :\n a.valMinAbs.natAbs ≤ m.natAbs := by\n have hmem := ZMo... | [
{
"name": "sub_l2NormSq_le",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 17,
"n_chars": 725,
"n_subproofs": 1,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": false,
"max_nestin... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Rq
import ArkLib.Data.Lattices.Vectors
import Mathlib.Algebra.Field.ZMod
import Mathlib.Data.ZMod.ValMinAbs
/-!... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Rq
import ArkLib.Data.Lattices.Vectors
import Mathlib.Algebra.Field.ZMod
import Mathlib.Data.ZMod.ValMinAbs
/-!... | @@ -40,10 +40,33 @@
/-! ## Minimality and triangle inequality for the centered representative -/
+/-- The centered representative `valMinAbs` has the least absolute value among all
+integer representatives of a residue class. -/
+theorem valMinAbs_natAbs_le {a : ZMod q} (m : ℤ) (h : (m : ZMod q) = a) :
+ a.valM... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_307bb5c1b6da_4 | 1e97516567564b8c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/NormBounds/Basic.lean | Basic | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "valMinAbs_sub_natAbs_le",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h : ((a.valMinAbs - b.valMinAbs : ℤ) : ZMod q) = a - b := by\n rw [Int.cast_sub, ZMod.coe_valMinAbs, ZMod.c... | [
{
"name": "valMinAbs_natAbs_le",
"text": "/-- The centered representative `valMinAbs` has the least absolute value among all\ninteger representatives of a residue class. -/\ntheorem valMinAbs_natAbs_le {a : ZMod q} (m : ℤ) (h : (m : ZMod q) = a) :\n a.valMinAbs.natAbs ≤ m.natAbs := by\n have hmem := ZMo... | [
{
"name": "Rq.lInftyNorm_sub_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 18,
"n_chars": 932,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": false,
"max_... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Rq
import ArkLib.Data.Lattices.Vectors
import Mathlib.Algebra.Field.ZMod
import Mathlib.Data.ZMod.ValMinAbs
/-!... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Rq
import ArkLib.Data.Lattices.Vectors
import Mathlib.Algebra.Field.ZMod
import Mathlib.Data.ZMod.ValMinAbs
/-!... | @@ -40,10 +40,33 @@
/-! ## Minimality and triangle inequality for the centered representative -/
+/-- The centered representative `valMinAbs` has the least absolute value among all
+integer representatives of a residue class. -/
+theorem valMinAbs_natAbs_le {a : ZMod q} (m : ℤ) (h : (m : ZMod q) = a) :
+ a.valM... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_307bb5c1b6da_5 | 7c320b948476eb31 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/NormBounds/Basic.lean | Basic | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "valMinAbs_sub_natAbs_le",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h : ((a.valMinAbs - b.valMinAbs : ℤ) : ZMod q) = a - b := by\n rw [Int.cast_sub, ZMod.coe_valMinAbs, ZMod.c... | [
{
"name": "valMinAbs_natAbs_le",
"text": "/-- The centered representative `valMinAbs` has the least absolute value among all\ninteger representatives of a residue class. -/\ntheorem valMinAbs_natAbs_le {a : ZMod q} (m : ℤ) (h : (m : ZMod q) = a) :\n a.valMinAbs.natAbs ≤ m.natAbs := by\n have hmem := ZMo... | [
{
"name": "sub_lInftyNorm_le",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 20,
"n_chars": 1102,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_ne... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Rq
import ArkLib.Data.Lattices.Vectors
import Mathlib.Algebra.Field.ZMod
import Mathlib.Data.ZMod.ValMinAbs
/-!... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Rq
import ArkLib.Data.Lattices.Vectors
import Mathlib.Algebra.Field.ZMod
import Mathlib.Data.ZMod.ValMinAbs
/-!... | @@ -40,10 +40,33 @@
/-! ## Minimality and triangle inequality for the centered representative -/
+/-- The centered representative `valMinAbs` has the least absolute value among all
+integer representatives of a residue class. -/
+theorem valMinAbs_natAbs_le {a : ZMod q} (m : ℤ) (h : (m : ZMod q) = a) :
+ a.valM... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_093489f3c6d4_0 | 353cc2b8485fc2b9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/ToMathlib/Finset/ToListWithProof.lean | ToListWithProof | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "toListWithProof_eq_toList",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [toListWithProof]\n exact list_reduceOption_helper (fun x hx ↦ Finset.mem_toList.mp hx)",
"n_chars... | [
{
"name": "list_reduceOption_helper",
"text": "private lemma list_reduceOption_helper\n {α : Type*} [DecidableEq α] {s : Finset α}\n {l : List α} (h : ∀ x ∈ l, x ∈ s) :\n List.map Subtype.val\n (List.reduceOption (l.map (fun x ↦ if hx : x ∈ s then some ⟨x, hx⟩ else none)))\n = l := by\n in... | [
{
"name": "toListWithProof_eq_toList",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 261,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Data.Finset.Defs
import Mathlib.Data.Finset.Empty
import Mathlib.Data.Finset.Dedup
namespace Finset
/-- A helper to con... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Data.Finset.Defs
import Mathlib.Data.Finset.Empty
import Mathlib.Data.Finset.Dedup
namespace Finset
/-- A helper to con... | @@ -25,11 +25,28 @@
toListWithProof (∅ : Finset α) = [] := by
simp [toListWithProof, List.reduceOption]
+private lemma list_reduceOption_helper
+ {α : Type*} [DecidableEq α] {s : Finset α}
+ {l : List α} (h : ∀ x ∈ l, x ∈ s) :
+ List.map Subtype.val
+ (List.reduceOption (l.map (fun x ↦ if hx : x ∈ s t... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_87757f51176a_0 | dc989cf022e54a89 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/ToMathlib/Polynomial/EvalExt.lean | EvalExt | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "eq_of_eval_eq_natDegree",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros hs h_eval; use eq_of_eval_eq_degree (by\n exact lt_of_le_of_lt (Polynomial.degree_le_natDegree) (WithBo... | [
{
"name": "eq_of_eval_eq_degree",
"text": "lemma eq_of_eval_eq_degree {p q : 𝔽[X]} {n : ℕ}\n (hp : p.degree < .some n) (hq : q.degree < .some n) (s : Finset 𝔽) :\n s.card ≥ n → (∀ x ∈ s, p.eval x = q.eval x) → p = q := by\n intros h h'\n by_cases h'' : p = 0 ∧ q = 0\n · rw [h''.1, h''.2]\n · h... | [
{
"name": "eq_of_eval_eq_natDegree",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 442,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max... | 1 | import Mathlib.LinearAlgebra.Lagrange
namespace Polynomial
variable {𝔽 : Type*} [Field 𝔽]
lemma eq_of_eval_eq_natDegree {p q : 𝔽[X]} {n : ℕ}
(hp : p.natDegree < n) (hq : q.natDegree < n) (s : Finset 𝔽) :
s.card ≥ n → (∀ x ∈ s, p.eval x = q.eval x) → p = q := sorry
end Polynomial
| import Mathlib.LinearAlgebra.Lagrange
namespace Polynomial
variable {𝔽 : Type*} [Field 𝔽]
lemma eq_of_eval_eq_degree {p q : 𝔽[X]} {n : ℕ}
(hp : p.degree < .some n) (hq : q.degree < .some n) (s : Finset 𝔽) :
s.card ≥ n → (∀ x ∈ s, p.eval x = q.eval x) → p = q := by
intros h h'
by_cases h'' : p = 0 ∧... | @@ -4,9 +4,47 @@
variable {𝔽 : Type*} [Field 𝔽]
+lemma eq_of_eval_eq_degree {p q : 𝔽[X]} {n : ℕ}
+ (hp : p.degree < .some n) (hq : q.degree < .some n) (s : Finset 𝔽) :
+ s.card ≥ n → (∀ x ∈ s, p.eval x = q.eval x) → p = q := by
+ intros h h'
+ by_cases h'' : p = 0 ∧ q = 0
+ · rw [h''.1, h''.2]
+ · ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6d18d2ea051a_0 | 1958c4a726448faf | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/DivergenceOfSets.lean | DivergenceOfSets | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "finite_possibleDeltas",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n Set.Finite.subset finite_relHammingDistRange possibleDeltas_subset_relHammingDistRange",
"n_chars": 89,
"n_subpr... | [
{
"name": "possibleDeltas_subset_relHammingDistRange",
"text": "/-- The set of possible relative Hamming distances between two sets is well-defined. -/\n@[simp]\nlemma possibleDeltas_subset_relHammingDistRange :\n possibleDeltas U V ⊆ relHammingDistRange ι :=\n fun x hx_mem_deltas ↦ by\n simp only [p... | [
{
"name": "finite_possibleDeltas",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 241,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import ArkLib.... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import ArkLib.... | @@ -39,9 +39,26 @@
def possibleDeltas (U V : Set (ι → F)) [Nonempty V] [Fintype V] : Set ℚ≥0 :=
{d : ℚ≥0 | ∃ u ∈ U, δᵣ'(u,V) = d}
+/-- The set of possible relative Hamming distances between two sets is well-defined. -/
+@[simp]
+lemma possibleDeltas_subset_relHammingDistRange :
+ possibleDeltas U V ⊆ relHammin... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6d18d2ea051a_1 | f86e51f97381d98a | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/DivergenceOfSets.lean | DivergenceOfSets | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "reedSolomon_rate_mul_card_le_deg",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Rewrite the rate expression in terms of the dimension\n rw [reedSolomon_rate_mul_card_eq_dim (deg := d... | [
{
"name": "reedSolomon_rate_mul_card_eq_dim",
"text": "theorem reedSolomon_rate_mul_card_eq_dim {ι : Type} [Fintype ι] [Nonempty ι]\n {F : Type} [Field F]\n {deg : ℕ} {domain : ι ↪ F} :\n (Fintype.card ι : ℝ≥0) * (LinearCode.rate (ReedSolomon.code domain deg) : ℝ≥0)\n = (LinearCode.dim (ReedSolomon.... | [
{
"name": "reedSolomon_rate_mul_card_le_deg",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 12,
"n_chars": 511,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import ArkLib.... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import ArkLib.... | @@ -359,11 +359,35 @@
simpa using h_le
exact_mod_cast hdim_le_len_nat
+theorem reedSolomon_rate_mul_card_eq_dim {ι : Type} [Fintype ι] [Nonempty ι]
+ {F : Type} [Field F]
+ {deg : ℕ} {domain : ι ↪ F} :
+ (Fintype.card ι : ℝ≥0) * (LinearCode.rate (ReedSolomon.code domain deg) : ℝ≥0)
+ = (LinearCode.dim... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6d18d2ea051a_2 | 59216140c8104eeb | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/DivergenceOfSets.lean | DivergenceOfSets | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "errorBound_ge_const",
"depth": 1,
"n_commands": 0,
"n_lines": 137,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n set r : ℝ≥0 := (LinearCode.rate (ReedSolomon.code domain deg) : ℝ≥0) with hr\n by_cases hUD : δ ≤ (1 - ... | [
{
"name": "reedSolomon_rate_mul_card_le_deg",
"text": "theorem reedSolomon_rate_mul_card_le_deg {ι : Type} [Fintype ι] [Nonempty ι]\n {F : Type} [Field F]\n {deg : ℕ} {domain : ι ↪ F} :\n (Fintype.card ι : ℝ≥0) * (LinearCode.rate (ReedSolomon.code domain deg) : ℝ≥0)\n ≤ (deg : ℝ≥0) := by\n -- Rewri... | [
{
"name": "errorBound_ge_const",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 146,
"n_chars": 7401,
"n_subproofs": 62,
"n_tactics": 130,
"cyclomatic": 1,
"n_automation": 35,
"n_rewrites": 2,
"n_structural": 5,
"automation_only": false,
"... | 6 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import ArkLib.... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import ArkLib.... | @@ -379,6 +379,16 @@
rw [← mul_div_assoc]
simp
+theorem reedSolomon_rate_mul_card_le_deg {ι : Type} [Fintype ι] [Nonempty ι]
+ {F : Type} [Field F]
+ {deg : ℕ} {domain : ι ↪ F} :
+ (Fintype.card ι : ℝ≥0) * (LinearCode.rate (ReedSolomon.code domain deg) : ℝ≥0)
+ ≤ (deg : ℝ≥0) := by
+ -- Rewrite the rate... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6d18d2ea051a_3 | f5f543620746593b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/DivergenceOfSets.lean | DivergenceOfSets | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "errorBound_ge_const",
"depth": 1,
"n_commands": 0,
"n_lines": 137,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n set r : ℝ≥0 := (LinearCode.rate (ReedSolomon.code domain deg) : ℝ≥0) with hr\n by_cases hUD : δ ≤ (1 - ... | [
{
"name": "reedSolomon_rate_pos",
"text": "theorem reedSolomon_rate_pos {ι : Type} [Fintype ι] [Nonempty ι]\n {F : Type} [Field F]\n {deg : ℕ} {domain : ι ↪ F}\n (hdeg : 0 < deg) :\n 0 < LinearCode.rate (ReedSolomon.code domain deg) := by\n classical\n haveI : NeZero deg := ⟨Nat.ne_of_gt hdeg⟩\n ha... | [
{
"name": "errorBound_johnson_mono",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 101,
"n_chars": 5294,
"n_subproofs": 26,
"n_tactics": 77,
"cyclomatic": 1,
"n_automation": 13,
"n_rewrites": 1,
"n_structural": 6,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import ArkLib.... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import ArkLib.... | @@ -389,6 +389,40 @@
-- Cast the dimension bound to `ℝ≥0`
exact_mod_cast (reedSolomon_dim_le_deg (deg := deg) (domain := domain))
+theorem reedSolomon_rate_pos {ι : Type} [Fintype ι] [Nonempty ι]
+ {F : Type} [Field F]
+ {deg : ℕ} {domain : ι ↪ F}
+ (hdeg : 0 < deg) :
+ 0 < LinearCode.rate (ReedSolomon.co... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6d18d2ea051a_4 | 38e69a6c5b56a96d | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/DivergenceOfSets.lean | DivergenceOfSets | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "divergence_pred_spec",
"depth": 1,
"n_commands": 0,
"n_lines": 58,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n haveI : Fintype (possibleDeltas U V) :=\n @Fintype.ofFinite _ (finite_possibleDeltas (U := U) (V := V... | [
{
"name": "relDistFromCode'_le_divergence",
"text": "theorem relDistFromCode'_le_divergence {ι : Type} [Fintype ι] [Nonempty ι]\n {F : Type} [DecidableEq F]\n {U V : Set (ι → F)} [Nonempty U] [Nonempty V] [Fintype V]\n (u : ι → F) (hu : u ∈ U) :\n δᵣ'(u, V) ≤ divergence U V := by\n classical\n have ... | [
{
"name": "divergence_pred_spec",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 66,
"n_chars": 2818,
"n_subproofs": 17,
"n_tactics": 55,
"cyclomatic": 4,
"n_automation": 11,
"n_rewrites": 0,
"n_structural": 20,
"automation_only": false,
"... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import ArkLib.... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import ArkLib.... | @@ -702,6 +702,23 @@
(δ₁ := δ₁) (δ₂ := δ₂) hδ ht1' hδ₂
simpa [ProximityGap.errorBound, t, ρ, Set.mem_Icc, Set.mem_Ioo, h1, h2, ht1, ht2] using hmono
+theorem relDistFromCode'_le_divergence {ι : Type} [Fintype ι] [Nonempty ι]
+ {F : Type} [DecidableEq F]
+ {U V : Set (ι → F)} [Nonempty U] [Nonemp... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_faff92a173d4_0 | ce5f82e0996aefdc | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/RestrictDegreeVar.lean | RestrictDegreeVar | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "mem_restrictDegreeVar_iff_degreeOf_le",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [mem_restrictDegreeVar]\n exact ⟨fun h i => degreeOf_le_iff.mpr (fun s hs => h s hs i),\n ... | [
{
"name": "mem_restrictDegreeVar",
"text": "theorem mem_restrictDegreeVar {b : σ → ℕ} (p : MvPolynomial σ R) :\n p ∈ restrictDegreeVar σ R b ↔ ∀ s ∈ p.support, ∀ i, (s : σ →₀ ℕ) i ≤ b i := by\n simp only [restrictDegreeVar, mem_restrictSupport_iff, Set.subset_def, Finset.mem_coe,\n Set.mem_setOf_eq]\... | [
{
"name": "mem_restrictDegreeVar_iff_degreeOf_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 517,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": f... | 1 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import ArkLib.Data.MvPolynomial.Degrees
/-!
# Per-variable degree restriction ("prismalinear" polynomials)
`MvPo... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import ArkLib.Data.MvPolynomial.Degrees
/-!
# Per-variable degree restriction ("prismalinear" polynomials)
`MvPo... | @@ -36,6 +36,11 @@
Submodule R (MvPolynomial σ R) :=
restrictSupport R { n | ∀ i, n i ≤ b i }
+theorem mem_restrictDegreeVar {b : σ → ℕ} (p : MvPolynomial σ R) :
+ p ∈ restrictDegreeVar σ R b ↔ ∀ s ∈ p.support, ∀ i, (s : σ →₀ ℕ) i ≤ b i := by
+ simp only [restrictDegreeVar, mem_restrictSupport_iff, Set.su... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_faff92a173d4_1 | dd71d918d4a905c0 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/RestrictDegreeVar.lean | RestrictDegreeVar | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "restrictDegreeVar_mono",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro p hp\n rw [mem_restrictDegreeVar_iff_degreeOf_le] at hp ⊢\n exact fun i => (hp i).trans (h i)",
"n_chars... | [
{
"name": "mem_restrictDegreeVar_iff_degreeOf_le",
"text": "/-- Characterisation by per-variable degree: `p` is prismalinear with bound `b` iff `degreeOf i p ≤\nb i` for every variable `i`. The per-variable analogue of `mem_restrictDegree_iff_degreeOf_le`. -/\ntheorem mem_restrictDegreeVar_iff_degreeOf_le {... | [
{
"name": "restrictDegreeVar_mono",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 330,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_... | 2 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import ArkLib.Data.MvPolynomial.Degrees
/-!
# Per-variable degree restriction ("prismalinear" polynomials)
`MvPo... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import ArkLib.Data.MvPolynomial.Degrees
/-!
# Per-variable degree restriction ("prismalinear" polynomials)
`MvPo... | @@ -47,9 +47,20 @@
@[simp] theorem restrictDegreeVar_const (m : ℕ) :
restrictDegreeVar σ R (fun _ => m) = restrictDegree σ R m := rfl
+/-- Characterisation by per-variable degree: `p` is prismalinear with bound `b` iff `degreeOf i p ≤
+b i` for every variable `i`. The per-variable analogue of `mem_restrictDegre... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_faff92a173d4_2 | ddf96fe6eb811164 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/RestrictDegreeVar.lean | RestrictDegreeVar | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "restrictDegreeVar_le_restrictDegree",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← restrictDegreeVar_const (σ := σ) (R := R) m]\n exact restrictDegreeVar_mono h",
"n_chars": 9... | [
{
"name": "restrictDegreeVar_mono",
"text": "/-- `restrictDegreeVar` is monotone in the per-variable bound. -/\ntheorem restrictDegreeVar_mono {b₁ b₂ : σ → ℕ} (h : ∀ i, b₁ i ≤ b₂ i) :\n restrictDegreeVar σ R b₁ ≤ restrictDegreeVar σ R b₂ := by\n intro p hp\n rw [mem_restrictDegreeVar_iff_degreeOf_le] a... | [
{
"name": "restrictDegreeVar_le_restrictDegree",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 8,
"n_chars": 401,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": fal... | 4 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import ArkLib.Data.MvPolynomial.Degrees
/-!
# Per-variable degree restriction ("prismalinear" polynomials)
`MvPo... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import ArkLib.Data.MvPolynomial.Degrees
/-!
# Per-variable degree restriction ("prismalinear" polynomials)
`MvPo... | @@ -55,10 +55,19 @@
exact ⟨fun h i => degreeOf_le_iff.mpr (fun s hs => h s hs i),
fun h s hs i => degreeOf_le_iff.mp (h i) s hs⟩
+/-- `restrictDegreeVar` is monotone in the per-variable bound. -/
+theorem restrictDegreeVar_mono {b₁ b₂ : σ → ℕ} (h : ∀ i, b₁ i ≤ b₂ i) :
+ restrictDegreeVar σ R b₁ ≤ rest... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_faff92a173d4_3 | 302fee5244cbcb38 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/RestrictDegreeVar.lean | RestrictDegreeVar | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "sumAlgEquiv_mem_restrictDegreeVar",
"depth": 1,
"n_commands": 0,
"n_lines": 21,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro s hs\n obtain ⟨m, hm, hs_eq⟩ : ∃ m : (S₁ ⊕ S₂) →₀ ℕ,\n m ∈ p.support ∧ s = m.comapDomain Sum... | [
{
"name": "sumToIter_monomial_aux",
"text": "lemma sumToIter_monomial_aux {R : Type*} [CommSemiring R]\n {S₁ S₂ : Type*}\n (m : (S₁ ⊕ S₂) →₀ ℕ) (c : R) :\n MvPolynomial.sumToIter R S₁ S₂ (MvPolynomial.monomial m c) =\n MvPolynomial.monomial (m.comapDomain Sum.inl Sum.inl_injective.injOn)\n ... | [
{
"name": "sumAlgEquiv_mem_restrictDegreeVar",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 29,
"n_chars": 1375,
"n_subproofs": 2,
"n_tactics": 22,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 6,
"n_structural": 6,
"automation_only": fa... | 1 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import ArkLib.Data.MvPolynomial.Degrees
/-!
# Per-variable degree restriction ("prismalinear" polynomials)
`MvPo... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import ArkLib.Data.MvPolynomial.Degrees
/-!
# Per-variable degree restriction ("prismalinear" polynomials)
`MvPo... | @@ -56,6 +56,30 @@
`fixFirstVariablesOfMQP_degreeVarLE` (the prismalinear analog of `fixFirstVariablesOfMQP_degreeLE`).
-/
+lemma sumToIter_monomial_aux {R : Type*} [CommSemiring R]
+ {S₁ S₂ : Type*}
+ (m : (S₁ ⊕ S₂) →₀ ℕ) (c : R) :
+ MvPolynomial.sumToIter R S₁ S₂ (MvPolynomial.monomial m c) =
+ MvPo... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6cbae307a9f6_0 | 61b646789229e8c9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/ProofSystem/Sumcheck/Domain.lean | Domain | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "card_cube",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [cube, Fintype.card_piFinset, card_points]",
"n_chars": 58,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomat... | [
{
"name": "card_points",
"text": "/-- Coordinate `i` has exactly `size i` evaluation points. -/\n@[simp] lemma card_points (D : SumcheckDomain R k) (i : Fin k) :\n (D.points i).card = D.size i := by\n simp [points]\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 183,
"n_subproofs": 0,
"n... | [
{
"name": "card_cube",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 312,
"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 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks
-/
import Mathlib.Data.Fintype.Pi
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Data.Fin.VecNotation
import Mathlib.Data.Fin.Tuple.Basic
import Mathlib.... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks
-/
import Mathlib.Data.Fintype.Pi
import Mathlib.Data.Fintype.BigOperators
import Mathlib.Data.Fin.VecNotation
import Mathlib.Data.Fin.Tuple.Basic
import Mathlib.... | @@ -129,9 +129,15 @@
@[simp] lemma mem_points {D : SumcheckDomain R k} {i : Fin k} {x : R} :
x ∈ D.points i ↔ ∃ j, D.embed i j = x := by simp [points]
+/-- Coordinate `i` has exactly `size i` evaluation points. -/
+@[simp] lemma card_points (D : SumcheckDomain R k) (i : Fin k) :
+ (D.points i).card = D.size ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_55d8b653e67e_0 | e1d14502b13d032e | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Galois/Trace.lean | Trace | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "traceHComp_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n traceOverComp_eq _ _ _",
"n_chars": 25,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0... | [
{
"name": "traceOverComp_eq",
"text": "/-- The computable trace agrees with `traceOver`. -/\ntheorem traceOverComp_eq (S : Finset ℕ) (a : Rq Φ) : traceOverComp Φ S a = traceOver Φ S a := by\n rw [traceOverComp, Rq.mk_sum]\n simp only [traceOver, galoisAut]\n\n",
"fan_in": 1,
"n_lines": 6,
"n_c... | [
{
"name": "traceHComp_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 195,
"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) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Galois.Group
/-!
# The Trace Map `Tr_H`
For a subgroup `H` of Galois automorphisms, the relative trace is `Tr_... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Galois.Group
/-!
# The Trace Map `Tr_H`
For a subgroup `H` of Galois automorphisms, the relative trace is `Tr_... | @@ -52,6 +52,11 @@
Rq.mk Φ (∑ i ∈ S, ∑ k ∈ Finset.range Φ.φ.natDegree,
CompPoly.CPolynomial.monomial (k * i) (a.1.coeff k))
+/-- The computable trace agrees with `traceOver`. -/
+theorem traceOverComp_eq (S : Finset ℕ) (a : Rq Φ) : traceOverComp Φ S a = traceOver Φ S a := by
+ rw [traceOverComp, Rq.mk_sum]
+... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_55d8b653e67e_1 | 1bea614d5799860b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Galois/Trace.lean | Trace | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "traceH_mem_fixed",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨traceH_fixed_of_smul α k (conjExp α) (conjExp_odd α)\n (Hexp_generator_smul α k (conjExp α) hk2pow hk (Or.inl rfl)) a,\... | [
{
"name": "traceH_fixed_of_smul",
"text": "/-- If multiplication by `g` permutes `Hexp` (`Hexp_generator_smul`), then `σ_g` fixes `Tr_H`.\nThe per-term step uses `σ_g(σ_i a) = σ_{g·i} a = σ_{(g·i) mod 2^{α+1}} a` (composition +\nexponent-periodicity, both proven); the sum then reindexes along the permutatio... | [
{
"name": "traceH_mem_fixed",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 870,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nestin... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Galois.Group
/-!
# The Trace Map `Tr_H`
For a subgroup `H` of Galois automorphisms, the relative trace is `Tr_... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Galois.Group
/-!
# The Trace Map `Tr_H`
For a subgroup `H` of Galois automorphisms, the relative trace is `Tr_... | @@ -62,6 +62,23 @@
Rq (powTwoCyclotomic (R := R) α) :=
traceOverComp (powTwoCyclotomic α) (Hexp α k) a
+/-- If multiplication by `g` permutes `Hexp` (`Hexp_generator_smul`), then `σ_g` fixes `Tr_H`.
+The per-term step uses `σ_g(σ_i a) = σ_{g·i} a = σ_{(g·i) mod 2^{α+1}} a` (composition +
+exponent-periodicity... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4affc39c7b98_0 | 4d5d8897a3b2684a | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Galois/Order.lean | Order | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "two_pow_dvd_four_pow_sub_one_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [pow_dvd_iff_le_emultiplicity, emultiplicity_four_pow_sub_one,\n ← Int.natCast_dvd_natCast (m := 2 ^... | [
{
"name": "emultiplicity_four_pow_sub_one",
"text": "/-- **2-adic LTE for `g = 4·2^κ + 1`**: `v₂(gⁿ − 1) = (κ+2) + v₂(n)`. -/\ntheorem emultiplicity_four_pow_sub_one (κ n : ℕ) :\n emultiplicity 2 ((4 * 2 ^ κ + 1 : ℤ) ^ n - 1)\n = (κ + 2 : ℕ) + emultiplicity 2 (n : ℤ) := by\n have hodd : Odd (4 * 2 ... | [
{
"name": "two_pow_dvd_four_pow_sub_one_iff",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 767,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.NumberTheory.Multiplicity
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# The order of `4k+1` modulo `2^{α+1}` (2-adic lifting-the-exponent)... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.NumberTheory.Multiplicity
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# The order of `4k+1` modulo `2^{α+1}` (2-adic lifting-the-exponent)... | @@ -30,10 +30,28 @@
namespace ArkLib.Lattices.CyclotomicModulus
+/-- **2-adic LTE for `g = 4·2^κ + 1`**: `v₂(gⁿ − 1) = (κ+2) + v₂(n)`. -/
+theorem emultiplicity_four_pow_sub_one (κ n : ℕ) :
+ emultiplicity 2 ((4 * 2 ^ κ + 1 : ℤ) ^ n - 1)
+ = (κ + 2 : ℕ) + emultiplicity 2 (n : ℤ) := by
+ have hodd : Odd (4... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4affc39c7b98_1 | bc75626e32005d01 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Galois/Order.lean | Order | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "four_pow_dvd_iff_nat",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hge : (1 : ℕ) ≤ (4 * 2 ^ κ + 1) ^ n := Nat.one_le_pow _ _ (by positivity)\n rw [← two_pow_dvd_four_pow_sub_one_i... | [
{
"name": "two_pow_dvd_four_pow_sub_one_iff",
"text": "/-- **Divisibility characterization**: `2^{α+1} ∣ gⁿ − 1 ↔ 2^{α-κ-1} ∣ n` for `g = 4·2^κ+1`,\nwhen `κ + 1 ≤ α` (so `α - κ - 1` is the genuine order `d/(2k)`). -/\ntheorem two_pow_dvd_four_pow_sub_one_iff (κ α n : ℕ) (hκ : κ + 1 ≤ α) :\n (2 : ℤ) ^ (α ... | [
{
"name": "four_pow_dvd_iff_nat",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 460,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_ne... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.NumberTheory.Multiplicity
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# The order of `4k+1` modulo `2^{α+1}` (2-adic lifting-the-exponent)... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.NumberTheory.Multiplicity
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# The order of `4k+1` modulo `2^{α+1}` (2-adic lifting-the-exponent)... | @@ -42,9 +42,24 @@
rw [one_pow, hsub, emultiplicity_pow_self_of_prime Int.prime_two] at h
exact h
+/-- **Divisibility characterization**: `2^{α+1} ∣ gⁿ − 1 ↔ 2^{α-κ-1} ∣ n` for `g = 4·2^κ+1`,
+when `κ + 1 ≤ α` (so `α - κ - 1` is the genuine order `d/(2k)`). -/
+theorem two_pow_dvd_four_pow_sub_one_iff (κ α n : ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4affc39c7b98_2 | 8981d76a9f9811dd | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Galois/Order.lean | Order | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "four_pow_dvd_iff_nat",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hge : (1 : ℕ) ≤ (4 * 2 ^ κ + 1) ^ n := Nat.one_le_pow _ _ (by positivity)\n rw [← two_pow_dvd_four_pow_sub_one_i... | [
{
"name": "two_pow_dvd_four_pow_sub_one_iff",
"text": "/-- **Divisibility characterization**: `2^{α+1} ∣ gⁿ − 1 ↔ 2^{α-κ-1} ∣ n` for `g = 4·2^κ+1`,\nwhen `κ + 1 ≤ α` (so `α - κ - 1` is the genuine order `d/(2k)`). -/\ntheorem two_pow_dvd_four_pow_sub_one_iff (κ α n : ℕ) (hκ : κ + 1 ≤ α) :\n (2 : ℤ) ^ (α ... | [
{
"name": "four_pow_aux",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 20,
"n_chars": 1062,
"n_subproofs": 8,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false,
"max_nesting... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.NumberTheory.Multiplicity
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# The order of `4k+1` modulo `2^{α+1}` (2-adic lifting-the-exponent)... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.NumberTheory.Multiplicity
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# The order of `4k+1` modulo `2^{α+1}` (2-adic lifting-the-exponent)... | @@ -42,6 +42,17 @@
rw [one_pow, hsub, emultiplicity_pow_self_of_prime Int.prime_two] at h
exact h
+/-- **Divisibility characterization**: `2^{α+1} ∣ gⁿ − 1 ↔ 2^{α-κ-1} ∣ n` for `g = 4·2^κ+1`,
+when `κ + 1 ≤ α` (so `α - κ - 1` is the genuine order `d/(2k)`). -/
+theorem two_pow_dvd_four_pow_sub_one_iff (κ α n : ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4affc39c7b98_3 | 558c23e0548c8c96 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Galois/Order.lean | Order | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "four_pow_dvd_iff_nat",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hge : (1 : ℕ) ≤ (4 * 2 ^ κ + 1) ^ n := Nat.one_le_pow _ _ (by positivity)\n rw [← two_pow_dvd_four_pow_sub_one_i... | [
{
"name": "two_pow_dvd_four_pow_sub_one_iff",
"text": "/-- **Divisibility characterization**: `2^{α+1} ∣ gⁿ − 1 ↔ 2^{α-κ-1} ∣ n` for `g = 4·2^κ+1`,\nwhen `κ + 1 ≤ α` (so `α - κ - 1` is the genuine order `d/(2k)`). -/\ntheorem two_pow_dvd_four_pow_sub_one_iff (κ α n : ℕ) (hκ : κ + 1 ≤ α) :\n (2 : ℤ) ^ (α ... | [
{
"name": "four_pow_injOn",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 12,
"n_chars": 504,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,
"max_nesting... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.NumberTheory.Multiplicity
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# The order of `4k+1` modulo `2^{α+1}` (2-adic lifting-the-exponent)... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.NumberTheory.Multiplicity
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# The order of `4k+1` modulo `2^{α+1}` (2-adic lifting-the-exponent)... | @@ -42,6 +42,17 @@
rw [one_pow, hsub, emultiplicity_pow_self_of_prime Int.prime_two] at h
exact h
+/-- **Divisibility characterization**: `2^{α+1} ∣ gⁿ − 1 ↔ 2^{α-κ-1} ∣ n` for `g = 4·2^κ+1`,
+when `κ + 1 ≤ α` (so `α - κ - 1` is the genuine order `d/(2k)`). -/
+theorem two_pow_dvd_four_pow_sub_one_iff (κ α n : ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4affc39c7b98_4 | 8e7febd8db8d9cd7 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Galois/Order.lean | Order | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "four_pow_dvd_iff_nat",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hge : (1 : ℕ) ≤ (4 * 2 ^ κ + 1) ^ n := Nat.one_le_pow _ _ (by positivity)\n rw [← two_pow_dvd_four_pow_sub_one_i... | [
{
"name": "two_pow_dvd_four_pow_sub_one_iff",
"text": "/-- **Divisibility characterization**: `2^{α+1} ∣ gⁿ − 1 ↔ 2^{α-κ-1} ∣ n` for `g = 4·2^κ+1`,\nwhen `κ + 1 ≤ α` (so `α - κ - 1` is the genuine order `d/(2k)`). -/\ntheorem two_pow_dvd_four_pow_sub_one_iff (κ α n : ℕ) (hκ : κ + 1 ≤ α) :\n (2 : ℤ) ^ (α ... | [
{
"name": "four_pow_order_modEq_one",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 349,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"ma... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.NumberTheory.Multiplicity
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# The order of `4k+1` modulo `2^{α+1}` (2-adic lifting-the-exponent)... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.NumberTheory.Multiplicity
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# The order of `4k+1` modulo `2^{α+1}` (2-adic lifting-the-exponent)... | @@ -42,9 +42,24 @@
rw [one_pow, hsub, emultiplicity_pow_self_of_prime Int.prime_two] at h
exact h
+/-- **Divisibility characterization**: `2^{α+1} ∣ gⁿ − 1 ↔ 2^{α-κ-1} ∣ n` for `g = 4·2^κ+1`,
+when `κ + 1 ≤ α` (so `α - κ - 1` is the genuine order `d/(2k)`). -/
+theorem two_pow_dvd_four_pow_sub_one_iff (κ α n : ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_4affc39c7b98_5 | 8372ffaae6e24be6 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Galois/Order.lean | Order | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "four_pow_dvd_iff_nat",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hge : (1 : ℕ) ≤ (4 * 2 ^ κ + 1) ^ n := Nat.one_le_pow _ _ (by positivity)\n rw [← two_pow_dvd_four_pow_sub_one_i... | [
{
"name": "two_pow_dvd_four_pow_sub_one_iff",
"text": "/-- **Divisibility characterization**: `2^{α+1} ∣ gⁿ − 1 ↔ 2^{α-κ-1} ∣ n` for `g = 4·2^κ+1`,\nwhen `κ + 1 ≤ α` (so `α - κ - 1` is the genuine order `d/(2k)`). -/\ntheorem two_pow_dvd_four_pow_sub_one_iff (κ α n : ℕ) (hκ : κ + 1 ≤ α) :\n (2 : ℤ) ^ (α ... | [
{
"name": "four_pow_mod_period",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 12,
"n_chars": 750,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_ne... | 4 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.NumberTheory.Multiplicity
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# The order of `4k+1` modulo `2^{α+1}` (2-adic lifting-the-exponent)... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.NumberTheory.Multiplicity
import Mathlib.RingTheory.Coprime.Lemmas
/-!
# The order of `4k+1` modulo `2^{α+1}` (2-adic lifting-the-exponent)... | @@ -42,9 +42,24 @@
rw [one_pow, hsub, emultiplicity_pow_self_of_prime Int.prime_two] at h
exact h
+/-- **Divisibility characterization**: `2^{α+1} ∣ gⁿ − 1 ↔ 2^{α-κ-1} ∣ n` for `g = 4·2^κ+1`,
+when `κ + 1 ≤ α` (so `α - κ - 1` is the genuine order `d/(2k)`). -/
+theorem two_pow_dvd_four_pow_sub_one_iff (κ α n : ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_7ddb66513b38_1 | a3cfacaf811f09f5 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ProximityGap/AHIV22Support.lean | AHIV22Support | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "exists_common_support_of_wt_le",
"depth": 1,
"n_commands": 0,
"n_lines": 133,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n letI : Fintype E := Fintype.ofFinite E\n let f : E → ℕ := fun x ↦ (vecSupport (F := F) (x : ... | [
{
"name": "mem_vecSupport",
"text": "/-- Membership in `vecSupport` is exactly nonvanishing at that coordinate. -/\nprivate lemma mem_vecSupport {u : ι → F} {j : ι} :\n j ∈ vecSupport (F := F) u ↔ u j ≠ 0 := by\n simp [vecSupport]\n\nomit [Finite F] in\n",
"fan_in": 1,
"n_lines": 7,
"n_chars... | [
{
"name": "dist_interleaved_code_to_code_lb",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 162,
"n_chars": 8085,
"n_subproofs": 35,
"n_tactics": 146,
"cyclomatic": 2,
"n_automation": 23,
"n_rewrites": 1,
"n_structural": 33,
"automation_only"... | 5 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Chung Thai Nguyen, Elias Judin,
Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.InterleavedCode
import ArkLib.Data.CodingTheo... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Chung Thai Nguyen, Elias Judin,
Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.InterleavedCode
import ArkLib.Data.CodingTheo... | @@ -39,6 +39,12 @@
Finset.filter (fun j ↦ u j ≠ 0) Finset.univ
omit [Finite F] in
+/-- Membership in `vecSupport` is exactly nonvanishing at that coordinate. -/
+private lemma mem_vecSupport {u : ι → F} {j : ι} :
+ j ∈ vecSupport (F := F) u ↔ u j ≠ 0 := by
+ simp [vecSupport]
+
+omit [Finite F] in
/-- Non-me... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_882786c27a4b_0 | 5b087925e8ab3781 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/KZG/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "commit_eq_c_polynomial",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_mem : poly.toPoly ∈ Polynomial.degreeLT (ZMod p) (n + 1) := by\n rw [Polynomial.mem_degreeLT, ← degree_to... | [
{
"name": "commit_eq",
"text": "/-- The commitment to a mathlib polynomial `poly` of maximum degree `n` is equal to\n`g₁ ^ (poly.1.eval a).val` -/\ntheorem commit_eq {a : ZMod p} (hpG1 : Nat.card G₁ = p)\n (poly : Polynomial.degreeLT (ZMod p) (n + 1)) :\n commit (Groups.PowerSrs.tower g₁ a n) (Polynom... | [
{
"name": "commit_eq_c_polynomial",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 18,
"n_chars": 1002,
"n_subproofs": 1,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 5,
"n_structural": 4,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann, Quang Dao
-/
import ArkLib.Commitments.Functional.Basic
import ArkLib.Commitments.Functional.KZG.Algebra
import ArkLib.Commitments.Functional.KZG.Sampling
import... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann, Quang Dao
-/
import ArkLib.Commitments.Functional.Basic
import ArkLib.Commitments.Functional.KZG.Algebra
import ArkLib.Commitments.Functional.KZG.Sampling
import... | @@ -72,13 +72,50 @@
pairing opening (verifySrs[1] / g₂ ^ z.val)
omit [Module (ZMod p) (Additive G₁)] [DecidableEq G₁] [Fact (0 < p)] in
+/-- The commitment to a mathlib polynomial `poly` of maximum degree `n` is equal to
+`g₁ ^ (poly.1.eval a).val` -/
+theorem commit_eq {a : ZMod p} (hpG1 : Nat.card G₁ = p)
+ ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_882786c27a4b_1 | 313c47beeca69715 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/KZG/Basic.lean | Basic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "mod_p_eq_additive",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hxyeq : (Additive.toMul g) ^ x = (Additive.toMul g) ^ y :=\n mod_p_eq (G := G) (p := p) (g := (Additive.toMul g))... | [
{
"name": "mod_p_eq",
"text": "/-- Powers with exponents congruent modulo `p` agree in a group of prime order `p`. -/\nlemma mod_p_eq (x y : ℤ) (g : G) (hxy : x ≡ y [ZMOD p]) : g ^ x = g ^ y := by\n have hordg : g = 1 ∨ orderOf g = p := by\n have ord_g_dvd : orderOf g ∣ p := by\n have hc : Nat.card... | [
{
"name": "mod_p_eq_additive",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 388,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann, Quang Dao
-/
import ArkLib.Commitments.Functional.Basic
import ArkLib.Commitments.Functional.KZG.Algebra
import ArkLib.Commitments.Functional.KZG.Sampling
import... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann, Quang Dao
-/
import ArkLib.Commitments.Functional.Basic
import ArkLib.Commitments.Functional.KZG.Algebra
import ArkLib.Commitments.Functional.KZG.Sampling
import... | @@ -72,10 +72,28 @@
pairing opening (verifySrs[1] / g₂ ^ z.val)
omit [Module (ZMod p) (Additive G₁)] [DecidableEq G₁] [Fact (0 < p)] in
+/-- Powers with exponents congruent modulo `p` agree in a group of prime order `p`. -/
+lemma mod_p_eq (x y : ℤ) (g : G) (hxy : x ≡ y [ZMOD p]) : g ^ x = g ^ y := by
+ have h... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b1cb42ad31b4_0 | 2209db3b7c0db1b8 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ReedSolomon/Multilinear.lean | Multilinear | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "mem_rs_code_of_mle_of_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n aesop (add simp [mem_rs_code_iff_exists_mle])",
"n_chars": 51,
"n_subproofs": 0,
"n_tactics": 2,
... | [
{
"name": "mem_rs_code_iff_exists_mle",
"text": "/-- A word `f` belongs to the RS-code iff there exists a multilinear polynomial `g`\n such that `f` is evaluation of `powAlgHom g` on points from the eval domain. -/\nlemma mem_rs_code_iff_exists_mle\n {f : ι → F} {deg : ℕ} :\n f ∈ code domain (2 ^ deg) ↔\... | [
{
"name": "mem_rs_code_of_mle_of_eval",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 414,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.ReedSolomon
import ArkLib.Data.MvPolynomial.Multilinear
import ArkLib.Data.MvPolynomial.LinearMvExtension
/-! This module pro... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.ReedSolomon
import ArkLib.Data.MvPolynomial.Multilinear
import ArkLib.Data.MvPolynomial.LinearMvExtension
/-! This module pro... | @@ -24,13 +24,35 @@
variable {F : Type*} [Field F] {ι : Type*} (domain : ι ↪ F)
+/-- A word `f` belongs to the RS-code iff there exists a multilinear polynomial `g`
+ such that `f` is evaluation of `powAlgHom g` on points from the eval domain. -/
+lemma mem_rs_code_iff_exists_mle
+ {f : ι → F} {deg : ℕ} :
+ f ∈... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_41e4b4613c7f_0 | 47758cafc67c9ed8 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ProximityGap/Folding.lean | Folding | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "even_add_odd_eq_of_not_charp_2",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n even_add_odd_eq_of_2_ne_0 _ _ _ hz <| fun contra ↦ hchar <|\n ringChar.of_eq (CharP.ringChar_of_prime_eq_zer... | [
{
"name": "even_add_odd_eq_of_2_ne_0",
"text": "private lemma even_add_odd_eq_of_2_ne_0\n (x y z : F) (hz : z ≠ 0) (hchar : (2 : F) ≠ 0) :\n x = (x + y) / 2 + (x - y) / (2 * z) * z := by grind\n\nomit [DecidableEq F] in\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 174,
"n_subproofs": 0,
"... | [
{
"name": "even_add_odd_eq_of_not_charp_2",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 282,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Algebra.Polynomial.Roots
import Mathlib.LinearAlgebra.Lagrange
import ArkLib.Data.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Algebra.Polynomial.Roots
import Mathlib.LinearAlgebra.Lagrange
import ArkLib.Data.... | @@ -70,9 +70,16 @@
variable {k : ℕ} {x : F}
omit [DecidableEq F] in
+private lemma even_add_odd_eq_of_2_ne_0
+ (x y z : F) (hz : z ≠ 0) (hchar : (2 : F) ≠ 0) :
+ x = (x + y) / 2 + (x - y) / (2 * z) * z := by grind
+
+omit [DecidableEq F] in
private lemma even_add_odd_eq_of_not_charp_2
(x y z : F) (hz : z ≠ 0)... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_41e4b4613c7f_5 | fc9751a5eb1181ba | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ProximityGap/Folding.lean | Folding | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "foldValue_k_1",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n aesop\n (add simp [foldValue, foldWordAux_of_k_2])\n (add safe (by grind))",
"n_chars": 84,
"n_subproofs": 0,
... | [
{
"name": "foldWordAux_of_k_2",
"text": "/-- An explicit formula to compute `foldWordAux` when `k = 2`\n not involving Lagrange interpolation. -/\nlemma foldWordAux_of_k_2\n [NeZero n]\n {i : Fin (2 ^ (n - 1))} :\n foldWordAux domain f 2 (domain.subdomain 1 i) =\n let x : domain := CosetFftDomain.two... | [
{
"name": "foldValue_k_1",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 13,
"n_chars": 524,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Algebra.Polynomial.Roots
import Mathlib.LinearAlgebra.Lagrange
import ArkLib.Data.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Algebra.Polynomial.Roots
import Mathlib.LinearAlgebra.Lagrange
import ArkLib.Data.... | @@ -81,6 +81,86 @@
even_add_odd_eq_of_2_ne_0 _ _ _ hz <| fun contra ↦ hchar <|
ringChar.of_eq (CharP.ringChar_of_prime_eq_zero Nat.prime_two contra)
+/-- An explicit formula to compute `foldWordAux` when `k = 2`
+ not involving Lagrange interpolation. -/
+lemma foldWordAux_of_k_2
+ [NeZero n]
+ {i : Fin (2... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_41e4b4613c7f_6 | 5611cbcdaaac72f0 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ProximityGap/Folding.lean | Folding | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "foldValue_k_1",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n aesop\n (add simp [foldValue, foldWordAux_of_k_2])\n (add safe (by grind))",
"n_chars": 84,
"n_subproofs": 0,
... | [
{
"name": "foldWordAux_of_k_2",
"text": "/-- An explicit formula to compute `foldWordAux` when `k = 2`\n not involving Lagrange interpolation. -/\nlemma foldWordAux_of_k_2\n [NeZero n]\n {i : Fin (2 ^ (n - 1))} :\n foldWordAux domain f 2 (domain.subdomain 1 i) =\n let x : domain := CosetFftDomain.two... | [
{
"name": "foldWord_k_1",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 13,
"n_chars": 521,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": ... | 4 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Algebra.Polynomial.Roots
import Mathlib.LinearAlgebra.Lagrange
import ArkLib.Data.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Algebra.Polynomial.Roots
import Mathlib.LinearAlgebra.Lagrange
import ArkLib.Data.... | @@ -81,6 +81,86 @@
even_add_odd_eq_of_2_ne_0 _ _ _ hz <| fun contra ↦ hchar <|
ringChar.of_eq (CharP.ringChar_of_prime_eq_zero Nat.prime_two contra)
+/-- An explicit formula to compute `foldWordAux` when `k = 2`
+ not involving Lagrange interpolation. -/
+lemma foldWordAux_of_k_2
+ [NeZero n]
+ {i : Fin (2... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_413584fcf7b2_6 | 4ff5128148c90c83 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/OracleReduction/Security/CoordinateWiseSpecialSoundness/Composition.lean | Composition | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 1 | [
{
"theorem_name": "toShape_append",
"depth": 1,
"n_commands": 0,
"n_lines": 43,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ChallengeTreeShape.ext rfl (heq_of_eq ?_)\n funext i challenges\n simp only [CWSSStructure.toShape, ChallengeTreeS... | [
{
"name": "append_soundnessParam_inl",
"text": "/-- The appended structure's soundness parameter at a left index is the left component's. -/\n@[simp] theorem append_soundnessParam_inl (i₁ : pSpec₁.ChallengeIdx) :\n (append D₁ D₂).soundnessParam (ChallengeIdx.inl i₁) = D₁.soundnessParam i₁ := by\n simp o... | [
{
"name": "append_coordinateWiseSpecialSound",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 15,
"n_lines": 21,
"n_chars": 1154,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": fa... | 15 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.CoordinateWiseSpecialSoundness.Basic
import ArkLib.OracleReduction.Composition.Sequential.Append
/-!
# Compositi... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.CoordinateWiseSpecialSoundness.Basic
import ArkLib.OracleReduction.Composition.Sequential.Append
/-!
# Compositi... | @@ -133,6 +133,11 @@
(append D₁ D₂).alphabet (ChallengeIdx.inr i₂) = D₂.alphabet i₂ := by
simp only [append, ChallengeIdx.sumEquiv_symm_inr]
+/-- The appended structure's soundness parameter at a left index is the left component's. -/
+@[simp] theorem append_soundnessParam_inl (i₁ : pSpec₁.ChallengeIdx) :
+ ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_529e7c355431_0 | 0e011b2110ecc0e3 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/ProofSystem/Stir/Combine.lean | Combine | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "combine_eq_cases",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext x\n simp only [combine]\n split_ifs\n · aesop\n (add simp [geom_sum_cases])\n (add safe (by ring))\n ... | [
{
"name": "geom_sum_cases",
"text": "private lemma geom_sum_cases (q : F) (n : ℕ) :\n ∑ l ∈ range (n + 1), q ^ l =\n if q ≠ 1 then (1 - q ^ (n + 1)) / (1 - q)\n else (↑(n + 1) : F) := by\n split_ifs with hq\n · rw [←neg_div_neg_eq, geom_sum_eq] <;> aesop\n · aesop\n\n",
"fan_in": 2,
"n_lin... | [
{
"name": "combine_eq_cases",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 23,
"n_chars": 838,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Mirco Richter, Poulami Das (Least Authority), Aristotle (Harmonic)
-/
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Cases
import Mathlib.T... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Mirco Richter, Poulami Das (Least Authority), Aristotle (Harmonic)
-/
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Cases
import Mathlib.T... | @@ -48,6 +48,14 @@
combine φ 0 r fs degs =
∑ i, (r ^ i.val) • fs i := by aesop (add simp [combine, ri])
+private lemma geom_sum_cases (q : F) (n : ℕ) :
+ ∑ l ∈ range (n + 1), q ^ l =
+ if q ≠ 1 then (1 - q ^ (n + 1)) / (1 - q)
+ else (↑(n + 1) : F) := by
+ split_ifs with hq
+ · rw [←neg_div_neg_eq, g... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_529e7c355431_2 | 9fb196ae26c86211 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/ProofSystem/Stir/Combine.lean | Combine | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "combine_eq_cases",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext x\n simp only [combine]\n split_ifs\n · aesop\n (add simp [geom_sum_cases])\n (add safe (by ring))\n ... | [
{
"name": "geom_sum_cases",
"text": "private lemma geom_sum_cases (q : F) (n : ℕ) :\n ∑ l ∈ range (n + 1), q ^ l =\n if q ≠ 1 then (1 - q ^ (n + 1)) / (1 - q)\n else (↑(n + 1) : F) := by\n split_ifs with hq\n · rw [←neg_div_neg_eq, geom_sum_eq] <;> aesop\n · aesop\n\n",
"fan_in": 2,
"n_lin... | [
{
"name": "degreeCor_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 565,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Mirco Richter, Poulami Das (Least Authority), Aristotle (Harmonic)
-/
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Cases
import Mathlib.T... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Mirco Richter, Poulami Das (Least Authority), Aristotle (Harmonic)
-/
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.Cases
import Mathlib.T... | @@ -48,6 +48,14 @@
combine φ 0 r fs degs =
∑ i, (r ^ i.val) • fs i := by aesop (add simp [combine, ri])
+private lemma geom_sum_cases (q : F) (n : ℕ) :
+ ∑ l ∈ range (n + 1), q ^ l =
+ if q ≠ 1 then (1 - q ^ (n + 1)) / (1 - q)
+ else (↑(n + 1) : F) := by
+ split_ifs with hq
+ · rw [←neg_div_neg_eq, g... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_aec3f1513222_0 | b60f987aafbdf61d | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Existence.lean | Existence | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 4 | [
{
"theorem_name": "leadingCoeff_E'",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n generalize he : (E ωs f p e) = E\n rw [←natDegree_E h_dist]\n aesop",
"n_chars": 76,
"n_subproofs": 0,
"n_tac... | [
{
"name": "natDegree_E",
"text": "private lemma natDegree_E\n (h : (Δ₀(f, p.eval ∘ ωs) : ℕ) ≤ e) :\n (E (ωs := ωs) f p e).natDegree = e := by\n simp only [E]\n rw [natDegree_mul (by aesop) (by aesop)]\n aesop\n (add simp natDegree_mul)\n (erase simp BerlekampWelch.elocPolyF_eq_elocPoly')\n (ad... | [
{
"name": "leadingCoeff_E'",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 190,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | @@ -20,6 +20,16 @@
(f : Fin n → F) (p : Polynomial F) (e : ℕ) : Polynomial F :=
X ^ (e - (Δ₀(f, p.eval ∘ ωs) : ℕ)) * ElocPolyF ωs f p
+private lemma natDegree_E
+ (h : (Δ₀(f, p.eval ∘ ωs) : ℕ) ≤ e) :
+ (E (ωs := ωs) f p e).natDegree = e := by
+ simp only [E]
+ rw [natDegree_mul (by aesop) (by aesop)]
+ aes... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_aec3f1513222_1 | 8e0be131935d4428 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Existence.lean | Existence | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 4 | [
{
"theorem_name": "leadingCoeff_E'",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n generalize he : (E ωs f p e) = E\n rw [←natDegree_E h_dist]\n aesop",
"n_chars": 76,
"n_subproofs": 0,
"n_tac... | [
{
"name": "natDegree_E",
"text": "private lemma natDegree_E\n (h : (Δ₀(f, p.eval ∘ ωs) : ℕ) ≤ e) :\n (E (ωs := ωs) f p e).natDegree = e := by\n simp only [E]\n rw [natDegree_mul (by aesop) (by aesop)]\n aesop\n (add simp natDegree_mul)\n (erase simp BerlekampWelch.elocPolyF_eq_elocPoly')\n (ad... | [
{
"name": "natDegree_Q",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 241,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 4... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | @@ -20,6 +20,16 @@
(f : Fin n → F) (p : Polynomial F) (e : ℕ) : Polynomial F :=
X ^ (e - (Δ₀(f, p.eval ∘ ωs) : ℕ)) * ElocPolyF ωs f p
+private lemma natDegree_E
+ (h : (Δ₀(f, p.eval ∘ ωs) : ℕ) ≤ e) :
+ (E (ωs := ωs) f p e).natDegree = e := by
+ simp only [E]
+ rw [natDegree_mul (by aesop) (by aesop)]
+ aes... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_aec3f1513222_2 | 675073a6436c58a6 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Existence.lean | Existence | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 2 | [
{
"theorem_name": "solutionToQ_from_Q",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine Polynomial.ext fun i ↦ ?p₁\n simp only [solutionToQ_coeff, Fin.liftF, E_and_Q_to_a_solution_coeff, add_lt_iff_n... | [
{
"name": "Q_ne_zero",
"text": "private lemma Q_ne_zero (hne : p ≠ 0) : Q ωs f p e ≠ 0 := by\n aesop (add simp [Q, E_ne_zero])\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 101,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_struc... | [
{
"name": "solutionToQ_from_Q",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 18,
"n_chars": 735,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_ne... | 3 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | @@ -50,6 +50,9 @@
(add simp [Q, natDegree_mul, E_ne_zero, natDegree_E])
(add safe (by omega))
+private lemma Q_ne_zero (hne : p ≠ 0) : Q ωs f p e ≠ 0 := by
+ aesop (add simp [Q, E_ne_zero])
+
private lemma solutionToQ_from_Q
(h_p_deg : p.natDegree < k)
(h_dist : (Δ₀(f, p.eval ∘ ωs) : ℕ) ≤ e) :
@@ -6... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_aec3f1513222_3 | c62de86e1ef9fe30 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Existence.lean | Existence | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 2 | [
{
"theorem_name": "solutionToE_from_E",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Polynomial.ext\n intro i\n simp only [coeff_solutionToE]\n split_ifs <;>\n try aesop (config := {warnOnNont... | [
{
"name": "leadingCoeff_E'",
"text": "private lemma leadingCoeff_E'\n (h_dist : (Δ₀(f, p.eval ∘ ωs) : ℕ) ≤ e) : (E ωs f p e).coeff e = 1 := by\n generalize he : (E ωs f p e) = E\n rw [←natDegree_E h_dist]\n aesop\n\n",
"fan_in": 2,
"n_lines": 7,
"n_chars": 190,
"n_subproofs": 0,
"n_t... | [
{
"name": "solutionToE_from_E",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 19,
"n_chars": 665,
"n_subproofs": 1,
"n_tactics": 15,
"cyclomatic": 3,
"n_automation": 8,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_ne... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | @@ -38,6 +38,12 @@
private lemma leadingCoeff_E : (E ωs f p e).leadingCoeff = 1 := by
simp [E]
+private lemma leadingCoeff_E'
+ (h_dist : (Δ₀(f, p.eval ∘ ωs) : ℕ) ≤ e) : (E ωs f p e).coeff e = 1 := by
+ generalize he : (E ωs f p e) = E
+ rw [←natDegree_E h_dist]
+ aesop
+
private noncomputable def Q (ωs : Fi... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_aec3f1513222_4 | 4f32f3c69bfee479 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Existence.lean | Existence | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 2 | [
{
"theorem_name": "solutionToQ_from_Q",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine Polynomial.ext fun i ↦ ?p₁\n simp only [solutionToQ_coeff, Fin.liftF, E_and_Q_to_a_solution_coeff, add_lt_iff_n... | [
{
"name": "natDegree_Q",
"text": "private lemma natDegree_Q\n (h : (Δ₀(f, p.eval ∘ ωs) : ℕ) ≤ e) :\n (Q ωs f p e).natDegree ≤ e + p.natDegree := by\n by_cases p = 0 <;>\n aesop\n (add simp [Q, natDegree_mul, E_ne_zero, natDegree_E])\n (add safe (by omega))\n\n",
"fan_in": 2,
"n_lines": 9,
... | [
{
"name": "E_and_Q_BerlekampWelch_condition",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 19,
"n_chars": 556,
"n_subproofs": 0,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": fals... | 3 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | @@ -48,6 +48,14 @@
(f : Fin n → F) (p : Polynomial F) (e : ℕ) : Polynomial F :=
p * (E ωs f p e)
+private lemma natDegree_Q
+ (h : (Δ₀(f, p.eval ∘ ωs) : ℕ) ≤ e) :
+ (Q ωs f p e).natDegree ≤ e + p.natDegree := by
+ by_cases p = 0 <;>
+ aesop
+ (add simp [Q, natDegree_mul, E_ne_zero, natDegree_E])
+ (ad... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_aec3f1513222_5 | 833722a2d48e8b2a | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Existence.lean | Existence | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 2 | [
{
"theorem_name": "Q'_div_E'_eq_p",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_eq := E_and_Q_unique he hk_n (Q_ne_zero hp) h_Q' h_diff\n (E_and_Q_BerlekampWelch_condition hp_deg h_ham)\n h_c... | [
{
"name": "E_and_Q_BerlekampWelch_condition",
"text": "private lemma E_and_Q_BerlekampWelch_condition\n (h_p_deg : p.natDegree < k)\n (h_dist : (Δ₀(f, p.eval ∘ ωs) : ℕ) ≤ e) :\n BerlekampWelchCondition e k ωs f (E ωs f p e) (Q ωs f p e) := by\n exact ⟨\n by {\n intro i\n by_cases hi : f i = p.eva... | [
{
"name": "Q'_div_E'_eq_p",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 27,
"n_chars": 790,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting... | 5 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | @@ -59,6 +59,24 @@
private lemma Q_ne_zero (hne : p ≠ 0) : Q ωs f p e ≠ 0 := by
aesop (add simp [Q, E_ne_zero])
+private lemma E_and_Q_BerlekampWelch_condition
+ (h_p_deg : p.natDegree < k)
+ (h_dist : (Δ₀(f, p.eval ∘ ωs) : ℕ) ≤ e) :
+ BerlekampWelchCondition e k ωs f (E ωs f p e) (Q ωs f p e) := by
+ exact ⟨... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_aec3f1513222_6 | 3a69cc7fe0968709 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Existence.lean | Existence | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 2 | [
{
"theorem_name": "Q'_div_E'_eq_p",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_eq := E_and_Q_unique he hk_n (Q_ne_zero hp) h_Q' h_diff\n (E_and_Q_BerlekampWelch_condition hp_deg h_ham)\n h_c... | [
{
"name": "E_and_Q_BerlekampWelch_condition",
"text": "private lemma E_and_Q_BerlekampWelch_condition\n (h_p_deg : p.natDegree < k)\n (h_dist : (Δ₀(f, p.eval ∘ ωs) : ℕ) ≤ e) :\n BerlekampWelchCondition e k ωs f (E ωs f p e) (Q ωs f p e) := by\n exact ⟨\n by {\n intro i\n by_cases hi : f i = p.eva... | [
{
"name": "linsolve_always_some_berlekamp_welch",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 8,
"n_lines": 15,
"n_chars": 635,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": f... | 7 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import ArkLib.Data.CodingTheory.BerlekampWelch.Condition
/-! # Berlekamp-Welch Solution Existence -/
namespace BerlekampWelch
variable {α... | @@ -94,12 +94,37 @@
(add simp [E_ne_zero, Polynomial.degree_eq_natDegree])
(add safe (by omega))
+private lemma E_and_Q_BerlekampWelch_condition
+ (h_p_deg : p.natDegree < k)
+ (h_dist : (Δ₀(f, p.eval ∘ ωs) : ℕ) ≤ e) :
+ BerlekampWelchCondition e k ωs f (E ωs f p e) (Q ωs f p e) := by
+ exact ⟨
+ by {
... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1e3500cf2a2e_1 | d6d49e872475d10a | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ProximityGap/DG25/ReedSolomon.lean | ReedSolomon | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "reedSolomon_multilinearCorrelatedAgreement",
"depth": 1,
"n_commands": 0,
"n_lines": 34,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n set n := Fintype.card ι\n intro ϑ hϑ_gt_0 u h_prob_u_close_gt\n let e : ℕ := Nat... | [
{
"name": "reedSolomon_multilinearCorrelatedAgreement_Nat",
"text": "/-- **Corollary 3.7**: RS Codes have Tensor-Style Proximity Gaps (Unique Decoding)\nExample 4.1 shows that ε=n is tight for RS codes (Ben+23 Thm 4.1 is sharp). -/\ntheorem reedSolomon_multilinearCorrelatedAgreement_Nat [Nontrivial (ReedSol... | [
{
"name": "reedSolomon_multilinearCorrelatedAgreement",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 42,
"n_chars": 1911,
"n_subproofs": 2,
"n_tactics": 37,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 7,
"n_structural": 9,
"automation_... | 2 | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import ArkLib.Data.CodingTheory.ProximityGap.DG25.MainResults
/-!
# DG25 Reed-Solomon Corollaries
This module specializes the DG25 proxim... | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import ArkLib.Data.CodingTheory.ProximityGap.DG25.MainResults
/-!
# DG25 Reed-Solomon Corollaries
This module specializes the DG25 proxim... | @@ -116,13 +116,103 @@
rw [h_δ_mul_n_eq_e] at jointProximity₂_u₀_u₁
exact jointProximity₂_u₀_u₁
+/-- **Corollary 3.7**: RS Codes have Tensor-Style Proximity Gaps (Unique Decoding)
+Example 4.1 shows that ε=n is tight for RS codes (Ben+23 Thm 4.1 is sharp). -/
+theorem reedSolomon_multilinearCorrelatedAgreement_... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_a534b9233b5d_0 | 4233f6a60dffb1ae | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Degrees.lean | Degrees | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "ps_coeff_mul_sum_monomial",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hdeg : ∀ N : ℕ, m < N → A.coeff N = 0 := (natDegree_le_iff_coeff_eq_zero).1 hm\n simp [Finset.... | [
{
"name": "ps_coeff_mul_monomial_ite",
"text": "lemma ps_coeff_mul_monomial_ite {R : Type} [Semiring R]\n (A : R[X]) (j i : ℕ) (r : R) :\n (A * Polynomial.monomial j r).coeff i =\n if j ≤ i then A.coeff (i - j) * r else 0 := by\n classical\n simp [← C_mul_X_pow_eq_monomial, ← mul_assoc, coeff_m... | [
{
"name": "ps_coeff_mul_sum_monomial",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 540,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | @@ -35,12 +35,23 @@
open Polynomial.Bivariate Polynomial Finset
open scoped BigOperators
+lemma ps_coeff_mul_monomial_ite {R : Type} [Semiring R]
+ (A : R[X]) (j i : ℕ) (r : R) :
+ (A * Polynomial.monomial j r).coeff i =
+ if j ≤ i then A.coeff (i - j) * r else 0 := by
+ classical
+ simp [← C_mul_X_pow... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_a534b9233b5d_1 | f433601b9a06fba5 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Degrees.lean | Degrees | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 2 | [
{
"theorem_name": "ps_degree_x_swap_le",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_contra h_contra\n obtain ⟨n, hn⟩ : ∃ n ∈ (swap f).support,\n (swap f).coeff n ≠ 0 ∧ (swap f).coeff n ≠ 0 ∧ ((... | [
{
"name": "ps_swap_coeff",
"text": "private lemma ps_swap_coeff {F : Type} [CommRing F] (g : F[X][Y]) (i j : ℕ) :\n Bivariate.coeff (swap g) i j = Bivariate.coeff g j i := by\n have h_swap_coeff : ∀ (g : F[X][Y]) (i j : ℕ),\n Bivariate.coeff (swap g) i j = Bivariate.coeff g j i := by\n unfold Bi... | [
{
"name": "ps_degree_x_swap_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 691,
"n_subproofs": 3,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | @@ -35,6 +35,26 @@
open Polynomial.Bivariate Polynomial Finset
open scoped BigOperators
+private lemma ps_swap_coeff {F : Type} [CommRing F] (g : F[X][Y]) (i j : ℕ) :
+ Bivariate.coeff (swap g) i j = Bivariate.coeff g j i := by
+ have h_swap_coeff : ∀ (g : F[X][Y]) (i j : ℕ),
+ Bivariate.coeff (swap g) i j... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_a534b9233b5d_2 | 5d94e752c20794f3 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Degrees.lean | Degrees | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 2 | [
{
"theorem_name": "ps_degree_x_swap_le",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_contra h_contra\n obtain ⟨n, hn⟩ : ∃ n ∈ (swap f).support,\n (swap f).coeff n ≠ 0 ∧ (swap f).coeff n ≠ 0 ∧ ((... | [
{
"name": "ps_swap_coeff",
"text": "private lemma ps_swap_coeff {F : Type} [CommRing F] (g : F[X][Y]) (i j : ℕ) :\n Bivariate.coeff (swap g) i j = Bivariate.coeff g j i := by\n have h_swap_coeff : ∀ (g : F[X][Y]) (i j : ℕ),\n Bivariate.coeff (swap g) i j = Bivariate.coeff g j i := by\n unfold Bi... | [
{
"name": "ps_degree_x_swap_ge",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 26,
"n_chars": 1505,
"n_subproofs": 7,
"n_tactics": 27,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 5,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | @@ -35,6 +35,26 @@
open Polynomial.Bivariate Polynomial Finset
open scoped BigOperators
+private lemma ps_swap_coeff {F : Type} [CommRing F] (g : F[X][Y]) (i j : ℕ) :
+ Bivariate.coeff (swap g) i j = Bivariate.coeff g j i := by
+ have h_swap_coeff : ∀ (g : F[X][Y]) (i j : ℕ),
+ Bivariate.coeff (swap g) i j... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_a534b9233b5d_3 | 3d566ee709eed2cd | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Degrees.lean | Degrees | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "ps_degree_x_swap",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hf : f = 0\n · subst hf; simp [degreeX, natDegreeY]\n · exact le_antisymm (ps_degree_x_swap_le f) (ps_degree_x_... | [
{
"name": "ps_degree_x_swap_ge",
"text": "private lemma ps_degree_x_swap_ge {F : Type} [CommRing F] (f : F[X][Y]) (hf : f ≠ 0) :\n natDegreeY f ≤ degreeX (swap f) := by\n obtain ⟨N, hN⟩ : ∃ N, N = f.natDegree ∧ f.coeff N ≠ 0 := by\n simp_all only [ne_eq, ↓existsAndEq, coeff_natDegree, leadingCoeff_eq... | [
{
"name": "ps_degree_x_swap",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 244,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | @@ -67,10 +67,35 @@
convert ps_swap_coeff f m n using 1
exact hm.2 (h_coeff_swap.symm ▸ by rw [coeff_eq_zero_of_natDegree_lt hm.1]; aesop)
+private lemma ps_degree_x_swap_ge {F : Type} [CommRing F] (f : F[X][Y]) (hf : f ≠ 0) :
+ natDegreeY f ≤ degreeX (swap f) := by
+ obtain ⟨N, hN⟩ : ∃ N, N = f.natDegree... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_a534b9233b5d_4 | 33d355018e550269 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Degrees.lean | Degrees | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "ps_eval_y_eq_eval_x_swap",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n letI : Algebra F[X] F[X] := Polynomial.algebra (R := F) (A := F)\n convert aveal_eq_map_swap y f using 1\n · unf... | [
{
"name": "ps_eval_x_eq_map",
"text": "lemma ps_eval_x_eq_map {F : Type} [CommSemiring F]\n (x : F) (f : F[X][Y]) :\n evalX x f = f.map (evalRingHom x) := by\n classical\n ext n; simp [evalX, toFinsupp_apply]\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 175,
"n_subproofs": 0,
"n_t... | [
{
"name": "ps_eval_y_eq_eval_x_swap",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 404,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | @@ -35,12 +35,20 @@
open Polynomial.Bivariate Polynomial Finset
open scoped BigOperators
+lemma ps_eval_x_eq_map {F : Type} [CommSemiring F]
+ (x : F) (f : F[X][Y]) :
+ evalX x f = f.map (evalRingHom x) := by
+ classical
+ ext n; simp [evalX, toFinsupp_apply]
+
lemma ps_eval_y_eq_eval_x_swap {F : Type} [Co... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_a534b9233b5d_5 | 235f05e2c718ea9b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Degrees.lean | Degrees | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "ps_filter_nonzero_card_y",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := ps_card_eval_y_eq_zero_le_nat_degree_y A hA P_y;\n simp_all only [ne_eq, ge_iff_le, gt_iff_lt, Finset.fil... | [
{
"name": "ps_card_eval_y_eq_zero_le_nat_degree_y",
"text": "lemma ps_card_eval_y_eq_zero_le_nat_degree_y {F : Type} [Field F] [DecidableEq F]\n (A : F[X][Y]) (hA : A ≠ 0) (P : Finset F) :\n (P.filter (fun y ↦ evalY y A = 0)).card ≤ natDegreeY A := by\n set A_poly : Polynomial (Polynomial F) := A\n ... | [
{
"name": "ps_filter_nonzero_card_y",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 501,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | @@ -35,10 +35,28 @@
open Polynomial.Bivariate Polynomial Finset
open scoped BigOperators
+lemma ps_card_eval_y_eq_zero_le_nat_degree_y {F : Type} [Field F] [DecidableEq F]
+ (A : F[X][Y]) (hA : A ≠ 0) (P : Finset F) :
+ (P.filter (fun y ↦ evalY y A = 0)).card ≤ natDegreeY A := by
+ set A_poly : Polynomial (P... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_a534b9233b5d_6 | fe08c5ce1d3e6b3d | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Degrees.lean | Degrees | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "ps_filter_nonzero_card_x",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_card_splits : P_x.card =\n (P_x.filter (fun x ↦ evalX x A = 0)).card + (P_x.filter (fun x ↦ evalX x A ... | [
{
"name": "ps_card_eval_x_eq_zero_le_degree_x",
"text": "lemma ps_card_eval_x_eq_zero_le_degree_x {F : Type} [Field F] [DecidableEq F]\n (A : F[X][Y]) (hA : A ≠ 0) (P : Finset F) :\n (P.filter (fun x ↦ evalX x A = 0)).card ≤ degreeX A := by\n by_contra! h_contra;\n obtain ⟨j₀, hj₀⟩ : ∃ j₀, (A.coeff ... | [
{
"name": "ps_filter_nonzero_card_x",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 595,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | @@ -35,10 +35,37 @@
open Polynomial.Bivariate Polynomial Finset
open scoped BigOperators
+lemma ps_card_eval_x_eq_zero_le_degree_x {F : Type} [Field F] [DecidableEq F]
+ (A : F[X][Y]) (hA : A ≠ 0) (P : Finset F) :
+ (P.filter (fun x ↦ evalX x A = 0)).card ≤ degreeX A := by
+ by_contra! h_contra;
+ obtain ⟨j... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_a534b9233b5d_7 | 45051e2b8dd91198 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Degrees.lean | Degrees | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "ps_degX_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n by_contra h_contra\n obtain ⟨y, hy⟩ : ∃ y ∈ P_y, (evalY y P).natDegree = degreeX P ∧ evalY y A ≠ 0 := by\n ... | [
{
"name": "ps_filter_nonzero_card_y",
"text": "lemma ps_filter_nonzero_card_y {F : Type} [Field F] [DecidableEq F]\n (A : F[X][Y]) (hA : A ≠ 0) (P_y : Finset F) (bound : ℕ)\n (h_bound_ge : bound ≥ natDegreeY A)\n (h_card_gt : P_y.card > bound) :\n (P_y.filter (fun y ↦ evalY y A ≠ 0)).card > boun... | [
{
"name": "ps_degX_bound",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 24,
"n_chars": 1212,
"n_subproofs": 6,
"n_tactics": 16,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | @@ -106,6 +106,15 @@
· aesop
exact le_antisymm h_deg_y (le_natDegree_of_ne_zero (by aesop))
+lemma ps_filter_nonzero_card_y {F : Type} [Field F] [DecidableEq F]
+ (A : F[X][Y]) (hA : A ≠ 0) (P_y : Finset F) (bound : ℕ)
+ (h_bound_ge : bound ≥ natDegreeY A)
+ (h_card_gt : P_y.card > bound) :
+ (P_y... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_a534b9233b5d_8 | 29ebfd943da8a05b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Degrees.lean | Degrees | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "ps_degY_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n obtain ⟨x, hx⟩ : ∃ x ∈ P_x, (evalX x A) ≠ 0 ∧ (evalX x P).natDegree = natDegreeY P := by\n have h_filter : (... | [
{
"name": "ps_filter_nonzero_card_x",
"text": "lemma ps_filter_nonzero_card_x {F : Type} [Field F] [DecidableEq F]\n (A : F[X][Y]) (hA : A ≠ 0) (P_x : Finset F) (bound : ℕ)\n (h_bound_ge : bound ≥ degreeX A)\n (h_card_gt : P_x.card > bound) :\n (P_x.filter (fun x ↦ evalX x A ≠ 0)).card > bound -... | [
{
"name": "ps_degY_bound",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 23,
"n_chars": 1405,
"n_subproofs": 6,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
"max_nestin... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | @@ -83,6 +83,17 @@
· refine le_natDegree_of_ne_zero ?_
convert hx.2 using 1
+lemma ps_filter_nonzero_card_x {F : Type} [Field F] [DecidableEq F]
+ (A : F[X][Y]) (hA : A ≠ 0) (P_x : Finset F) (bound : ℕ)
+ (h_bound_ge : bound ≥ degreeX A)
+ (h_card_gt : P_x.card > bound) :
+ (P_x.filter (fun x ↦ ev... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_a534b9233b5d_9 | 259587afc4a4d124 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Degrees.lean | Degrees | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "ps_degree_bounds_of_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n letI : DecidableEq F := Classical.decEq F\n by_cases hB0 : B = 0\n · have hP0 : P = 0 := by\n ... | [
{
"name": "ps_degX_bound",
"text": "lemma ps_degX_bound {F : Type} [Field F]\n {A B P : F[X][Y]} (hA : A ≠ 0) (hP : P ≠ 0) (hBA : B = P * A)\n (b_x b_y a_x a_y : ℕ) (n_y : ℕ+) (h_by_ge_ay : b_y ≥ a_y)\n (h_f_degY : a_y ≥ natDegreeY A) (h_g_degY : b_y ≥ natDegreeY B)\n (P_y : Finset F) (h_card_Py... | [
{
"name": "ps_degree_bounds_of_mul",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 10,
"n_lines": 28,
"n_chars": 1481,
"n_subproofs": 3,
"n_tactics": 16,
"cyclomatic": 4,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 5,
"automation_only": false,
... | 10 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | @@ -189,6 +189,29 @@
linarith [ps_card_eval_x_eq_zero_le_degree_x A hA P_x,
Nat.sub_add_cancel (show degreeX A ≤ bound from h_bound_ge)]
+lemma ps_degX_bound {F : Type} [Field F]
+ {A B P : F[X][Y]} (hA : A ≠ 0) (hP : P ≠ 0) (hBA : B = P * A)
+ (b_x b_y a_x a_y : ℕ) (n_y : ℕ+) (h_by_ge_ay : b_y ≥ a_y)
+... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_a534b9233b5d_10 | dbfe170e905bc6b2 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Degrees.lean | Degrees | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "ps_nat_degree_y_swap",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h := ps_degree_x_swap (swap f)\n have hs : swap (swap f) = f := swap.left_inv f\n rw [hs] at h\n exact h.symm"... | [
{
"name": "ps_degree_x_swap",
"text": "lemma ps_degree_x_swap {F : Type} [CommRing F] (f : F[X][Y]) :\n degreeX (swap f) = natDegreeY f := by\n by_cases hf : f = 0\n · subst hf; simp [degreeX, natDegreeY]\n · exact le_antisymm (ps_degree_x_swap_le f) (ps_degree_x_swap_ge f hf)\n\n",
"fan_in": 1,
... | [
{
"name": "ps_nat_degree_y_swap",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 7,
"n_chars": 226,
"n_subproofs": 2,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_ne... | 4 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alexander Hicks, Aleph
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Analysis.Normed.Field.Lemmas
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.RingTheory... | @@ -92,6 +92,16 @@
bv_omega
exact h_final
+lemma ps_degree_x_swap {F : Type} [CommRing F] (f : F[X][Y]) :
+ degreeX (swap f) = natDegreeY f := by
+ by_cases hf : f = 0
+ · subst hf; simp [degreeX, natDegreeY]
+ · exact le_antisymm (ps_degree_x_swap_le f) (ps_degree_x_swap_ge f hf)
+
lemma ps_nat_degree... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6ebbae41ba62_0 | e0bb10935fea8314 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/MDSCode.lean | MDSCode | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "IsMDS_of_matrix_IsMDS",
"depth": 1,
"n_commands": 0,
"n_lines": 41,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_singleton_bound : (Module.finrank F (fromRowGenMat G)) ≤\n (Fintype.card (Fin n)) -... | [
{
"name": "minWt_ge_of_MDS",
"text": "/-- Every nonzero codeword in a code generated by a `k × n` MDS matrix has Hamming weight greater or\nequal to `n - k + 1`. -/\nlemma minWt_ge_of_MDS [Field F] [DecidableEq F] {G : Matrix (Fin k) (Fin n) F}\n(hMDS : Matrix.IsMDS G) {c : Fin n → F} (hc_mem : c ∈ fromRowG... | [
{
"name": "IsMDS_of_matrix_IsMDS",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 45,
"n_chars": 2357,
"n_subproofs": 7,
"n_tactics": 44,
"cyclomatic": 3,
"n_automation": 8,
"n_rewrites": 7,
"n_structural": 11,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova
-/
import ArkLib.Data.CodingTheory.Basic.LinearCode
import Mathlib.Data.Int.Star
/-!
# Basics of MDS codes and MDS matrices
Lay out the fundamental definitio... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova
-/
import ArkLib.Data.CodingTheory.Basic.LinearCode
import Mathlib.Data.Int.Star
/-!
# Basics of MDS codes and MDS matrices
Lay out the fundamental definitio... | @@ -32,6 +32,39 @@
def Matrix.IsMDS [CommRing F] (G : Matrix (Fin k) (Fin n) F) : Prop :=
∀ σ : Fin k ↪ Fin n, (G.submatrix id σ).det ≠ 0
+/-- Every nonzero codeword in a code generated by a `k × n` MDS matrix has Hamming weight greater or
+equal to `n - k + 1`. -/
+lemma minWt_ge_of_MDS [Field F] [DecidableEq F]... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6ebbae41ba62_1 | 2342bf31d330bd2a | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/MDSCode.lean | MDSCode | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "matrix_IsMDS_of_IsMDS",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n contrapose! hCode\n simp_all only [Matrix.IsMDS, ne_eq, not_forall, Decidable.not_not]\n obtain ⟨σ, hσ⟩ := hCode\n... | [
{
"name": "vecMul_injective_of_rank_eq",
"text": "/-- If `G` has full row rank, then every nonzero vector maps to a nonzero codeword. -/\nlemma vecMul_injective_of_rank_eq [Field F] {G : Matrix (Fin k) (Fin n) F} (hrank : G.rank = k) :\n Function.Injective (G.vecMulLinear) := by\n have h_injective : Mod... | [
{
"name": "matrix_IsMDS_of_IsMDS",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 37,
"n_chars": 1763,
"n_subproofs": 9,
"n_tactics": 34,
"cyclomatic": 2,
"n_automation": 10,
"n_rewrites": 1,
"n_structural": 9,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova
-/
import ArkLib.Data.CodingTheory.Basic.LinearCode
import Mathlib.Data.Int.Star
/-!
# Basics of MDS codes and MDS matrices
Lay out the fundamental definitio... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova
-/
import ArkLib.Data.CodingTheory.Basic.LinearCode
import Mathlib.Data.Int.Star
/-!
# Basics of MDS codes and MDS matrices
Lay out the fundamental definitio... | @@ -32,6 +32,19 @@
def Matrix.IsMDS [CommRing F] (G : Matrix (Fin k) (Fin n) F) : Prop :=
∀ σ : Fin k ↪ Fin n, (G.submatrix id σ).det ≠ 0
+/-- If `G` has full row rank, then every nonzero vector maps to a nonzero codeword. -/
+lemma vecMul_injective_of_rank_eq [Field F] {G : Matrix (Fin k) (Fin n) F} (hrank : G.r... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6ebbae41ba62_2 | 0f2201017e413b8b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/MDSCode.lean | MDSCode | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "colRank_genMatrix_eq_dim_of_MDS",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n set G := matrixFromBasis LC with hG\n have hLC : LC = fromRowGenMat G := eq_fromRowGenMat_matrixFromBasis... | [
{
"name": "IsMDS_of_matrix_IsMDS",
"text": "/-- If a generator matrix is MDS with at least one row, then the code it generates is MDS. -/\nlemma IsMDS_of_matrix_IsMDS [Field F] [DecidableEq F] {G : Matrix (Fin k) (Fin n) F}\n (hMDS : Matrix.IsMDS G) (hkn : k ≤ n) (hk : 0 < k) : (fromRowGenMat G).IsMDS :=... | [
{
"name": "colRank_genMatrix_eq_dim_of_MDS",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 28,
"n_chars": 1260,
"n_subproofs": 5,
"n_tactics": 19,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 7,
"automation_only": fals... | 4 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova
-/
import ArkLib.Data.CodingTheory.Basic.LinearCode
import Mathlib.Data.Int.Star
/-!
# Basics of MDS codes and MDS matrices
Lay out the fundamental definitio... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova
-/
import ArkLib.Data.CodingTheory.Basic.LinearCode
import Mathlib.Data.Int.Star
/-!
# Basics of MDS codes and MDS matrices
Lay out the fundamental definitio... | @@ -78,6 +78,50 @@
have := LinearMap.finrank_range_add_finrank_ker (G.vecMulLinear)
simp_all [LinearMap.ker_eq_bot]
+/-- If a generator matrix is MDS with at least one row, then the code it generates is MDS. -/
+lemma IsMDS_of_matrix_IsMDS [Field F] [DecidableEq F] {G : Matrix (Fin k) (Fin n) F}
+ (hMDS : Ma... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_795ea71762b4_0 | c77daaf8a630b485 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Cardinality.lean | Cardinality | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "card_fixedSubring_ge",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hinj := Fintype.card_le_of_injective _ (fixedBasisMap_injective q α κ h2 hκ)\n rwa [Fintype.card_fun, Fintype.ca... | [
{
"name": "fixedBasisMap_injective",
"text": "/-- **`fixedBasisMap` is injective**: distinct coefficient vectors give distinct fixed elements,\nread off at coefficient position `(d/2k)·s` via `vElt_coeff` and cancellation of the unit\n`2 if s=0 else 1`. -/\ntheorem fixedBasisMap_injective (α κ : ℕ) (h2 : (2... | [
{
"name": "card_fixedSubring_ge",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 409,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Subfield.TraceInnerProduct
/-!
# The Cardinality `|R_q^H| = q^k` of the Fixed Subring (Hachi §3, Eq. 7)
The nu... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Subfield.TraceInnerProduct
/-!
# The Cardinality `|R_q^H| = q^k` of the Fixed Subring (Hachi §3, Eq. 7)
The nu... | @@ -42,10 +42,45 @@
fixedSubring (R := ZMod q) α (2 ^ κ) :=
∑ j : Fin (2 ^ κ), (c j).val • vElt (R := ZMod q) α κ hκ j
+/-- **`fixedBasisMap` is injective**: distinct coefficient vectors give distinct fixed elements,
+read off at coefficient position `(d/2k)·s` via `vElt_coeff` and cancellation of the unit
+`... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_795ea71762b4_1 | 6bf3b834e0466289 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Cardinality.lean | Cardinality | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "card_fixedSubring_ge",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hinj := Fintype.card_le_of_injective _ (fixedBasisMap_injective q α κ h2 hκ)\n rwa [Fintype.card_fun, Fintype.ca... | [
{
"name": "fixedBasisMap_injective",
"text": "/-- **`fixedBasisMap` is injective**: distinct coefficient vectors give distinct fixed elements,\nread off at coefficient position `(d/2k)·s` via `vElt_coeff` and cancellation of the unit\n`2 if s=0 else 1`. -/\ntheorem fixedBasisMap_injective (α κ : ℕ) (h2 : (2... | [
{
"name": "card_fixedSubring_eq",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 8,
"n_chars": 472,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_ne... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Subfield.TraceInnerProduct
/-!
# The Cardinality `|R_q^H| = q^k` of the Fixed Subring (Hachi §3, Eq. 7)
The nu... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Subfield.TraceInnerProduct
/-!
# The Cardinality `|R_q^H| = q^k` of the Fixed Subring (Hachi §3, Eq. 7)
The nu... | @@ -54,10 +54,45 @@
fixedSubring (R := ZMod q) α (2 ^ κ) :=
∑ j : Fin (2 ^ κ), (c j).val • vElt (R := ZMod q) α κ hκ j
+/-- **`fixedBasisMap` is injective**: distinct coefficient vectors give distinct fixed elements,
+read off at coefficient position `(d/2k)·s` via `vElt_coeff` and cancellation of the unit
+`... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_9fa9e6e62ab5_0 | 6aef594378414730 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/RestrictDegree.lean | RestrictDegree | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "fixFirstVariablesOfMQP_degreeLE",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n fixFirstVariablesOfMQP_degreeVarLE ℓ (b := fun _ => deg) v hp",
"n_chars": 66,
"n_subproofs": 0,
"... | [
{
"name": "fixFirstVariablesOfMQP_degreeVarLE",
"text": "/-- The per-variable / prismalinear degree-survival lemma: if a polynomial respects a per-variable\ndegree bound `b : Fin ℓ → ℕ`, then fixing the first `v` variables to scalars produces a polynomial\nwhose surviving `Fin (ℓ-v)` variables respect `b` r... | [
{
"name": "fixFirstVariablesOfMQP_degreeLE",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 606,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import ArkLib.Data.MvPolynomial.Degrees
import ArkLib.Data.MvPolynomial.RestrictDegreeVar
/-!
# Operations preserving `MvPolynomial.restrictDegre... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import ArkLib.Data.MvPolynomial.Degrees
import ArkLib.Data.MvPolynomial.RestrictDegreeVar
/-!
# Operations preserving `MvPolynomial.restrictDegre... | @@ -51,12 +51,52 @@
let eval_map : L[X Fin ↑v] →+* L := (eval challenges : MvPolynomial (Fin v) L →+* L)
MvPolynomial.map (f := eval_map) (σ := Fin (ℓ - v)) H_forward
+/-- The per-variable / prismalinear degree-survival lemma: if a polynomial respects a per-variable
+degree bound `b : Fin ℓ → ℕ`, then fixing th... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_dd9350e894dc_0 | 3704806dd0909dda | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Indicator.lean | Indicator | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "indicator_natDegree_lt_of_pos_nonempty",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Polynomial.natDegree_lt_iff_degree_lt\n (indicator_ne_zero_of_pos_nonempty h)]\n exact i... | [
{
"name": "indicator_ne_zero_of_pos_nonempty",
"text": "/-- If `pos` is non-empty then the indicator polynomial is the constant\n zero polynomial. -/\nlemma indicator_ne_zero_of_pos_nonempty {pos neg : Finset F}\n (h : pos.Nonempty) :\n indicator pos neg ≠ 0 := by\n unfold indicator\n intro contra\n o... | [
{
"name": "indicator_natDegree_lt_of_pos_nonempty",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 10,
"n_chars": 374,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only":... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | @@ -71,6 +71,29 @@
[Polynomial.eval_finsetSum,
Finset.sum_eq_single x])])
+/-- If `pos` is non-empty then the indicator polynomial is the constant
+ zero polynomial. -/
+lemma indicator_ne_zero_of_pos_nonempty {pos neg : Finset F}
+ (h : pos.Nonempty) :
+ indicator pos neg ≠ 0 := by
+ unfold ind... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_dd9350e894dc_1 | 30de9e5dfe1f39d2 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Indicator.lean | Indicator | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "indicator_natDegree_lt_of_pos_nonempty",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Polynomial.natDegree_lt_iff_degree_lt\n (indicator_ne_zero_of_pos_nonempty h)]\n exact i... | [
{
"name": "indicator_ne_zero_of_pos_nonempty",
"text": "/-- If `pos` is non-empty then the indicator polynomial is the constant\n zero polynomial. -/\nlemma indicator_ne_zero_of_pos_nonempty {pos neg : Finset F}\n (h : pos.Nonempty) :\n indicator pos neg ≠ 0 := by\n unfold indicator\n intro contra\n o... | [
{
"name": "indicator_natDegree_lt_of_neg_nonempty",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 10,
"n_chars": 352,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only":... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | @@ -71,6 +71,29 @@
[Polynomial.eval_finsetSum,
Finset.sum_eq_single x])])
+/-- If `pos` is non-empty then the indicator polynomial is the constant
+ zero polynomial. -/
+lemma indicator_ne_zero_of_pos_nonempty {pos neg : Finset F}
+ (h : pos.Nonempty) :
+ indicator pos neg ≠ 0 := by
+ unfold ind... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_dd9350e894dc_2 | 2b43b30110e8a6fd | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Indicator.lean | Indicator | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "indicator_natDegree_lt_of_pos_nonempty",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Polynomial.natDegree_lt_iff_degree_lt\n (indicator_ne_zero_of_pos_nonempty h)]\n exact i... | [
{
"name": "indicator_degree_lt",
"text": "/-- The degree of the indicator polynomial\n is less than `#(pos ∪ neg)`. -/\nlemma indicator_degree_lt {pos neg : Finset F} :\n (indicator pos neg).degree < (pos ∪ neg).card := by\n unfold indicator\n exact Lagrange.degree_interpolate_lt _ (by simp)\n\n",
"... | [
{
"name": "indicator_degree_lt_of_pos_subset_neg",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 334,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": ... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | @@ -91,12 +91,22 @@
Finset.prod_eq_one])
(add safe [(by rw [Finset.sum_eq_single x])])
+/-- The degree of the indicator polynomial
+ is less than `#(pos ∪ neg)`. -/
+lemma indicator_degree_lt {pos neg : Finset F} :
+ (indicator pos neg).degree < (pos ∪ neg).card := by
+ unfold indicator
+ exact ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_dd9350e894dc_3 | 016a127802eb6ea9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Indicator.lean | Indicator | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "indicator_natDegree_lt_of_pos_nonempty",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Polynomial.natDegree_lt_iff_degree_lt\n (indicator_ne_zero_of_pos_nonempty h)]\n exact i... | [
{
"name": "indicator_ne_zero_of_pos_nonempty",
"text": "/-- If `pos` is non-empty then the indicator polynomial is the constant\n zero polynomial. -/\nlemma indicator_ne_zero_of_pos_nonempty {pos neg : Finset F}\n (h : pos.Nonempty) :\n indicator pos neg ≠ 0 := by\n unfold indicator\n intro contra\n o... | [
{
"name": "indicator_natDegree_lt_of_pos_nonempty_of_pos_subset_neg",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 11,
"n_chars": 464,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | @@ -71,6 +71,29 @@
[Polynomial.eval_finsetSum,
Finset.sum_eq_single x])])
+/-- If `pos` is non-empty then the indicator polynomial is the constant
+ zero polynomial. -/
+lemma indicator_ne_zero_of_pos_nonempty {pos neg : Finset F}
+ (h : pos.Nonempty) :
+ indicator pos neg ≠ 0 := by
+ unfold ind... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_dd9350e894dc_4 | 9d64babc16ca9c2b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Indicator.lean | Indicator | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "indicator_natDegree_lt_of_pos_nonempty",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Polynomial.natDegree_lt_iff_degree_lt\n (indicator_ne_zero_of_pos_nonempty h)]\n exact i... | [
{
"name": "indicator_degree_lt",
"text": "/-- The degree of the indicator polynomial\n is less than `#(pos ∪ neg)`. -/\nlemma indicator_degree_lt {pos neg : Finset F} :\n (indicator pos neg).degree < (pos ∪ neg).card := by\n unfold indicator\n exact Lagrange.degree_interpolate_lt _ (by simp)\n\n",
"... | [
{
"name": "indicator_natDegree_lt_of_neg_nonempty_of_pos_subset_neg",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 13,
"n_chars": 507,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
... | 4 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | @@ -114,12 +114,22 @@
Finset.prod_eq_one])
(add safe [(by rw [Finset.sum_eq_single x])])
+/-- The degree of the indicator polynomial
+ is less than `#(pos ∪ neg)`. -/
+lemma indicator_degree_lt {pos neg : Finset F} :
+ (indicator pos neg).degree < (pos ∪ neg).card := by
+ unfold indicator
+ exac... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_dd9350e894dc_5 | 8bda26989a215e3f | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Indicator.lean | Indicator | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "singleton_indicator_eq_1_empty",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold singletonIndicator\n rw [indicator_eq_1_of_neg_empty_empty_of_pos_nonempty (by simp)]",
"n_chars... | [
{
"name": "indicator_eq_1_of_neg_empty_empty_of_pos_nonempty",
"text": "/-- The indicator polynomial is a constant one polynomial\n if the set `neg` is empty while `pos` is not. -/\nlemma indicator_eq_1_of_neg_empty_empty_of_pos_nonempty\n {pos : Finset F}\n (h_pos : pos.Nonempty) :\n indicator pos ∅ = ... | [
{
"name": "singleton_indicator_eq_1_empty",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 268,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | @@ -44,6 +44,33 @@
lemma indicator_eq_0_of_pos_empty {neg : Finset F} :
indicator ∅ neg = 0 := by simp [indicator]
+/-- The indicator polynomial is a constant one polynomial
+ if the set `neg` is empty while `pos` is not. -/
+lemma indicator_eq_1_of_neg_empty_empty_of_pos_nonempty
+ {pos : Finset F}
+ (h_pos :... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_dd9350e894dc_6 | f4093d655a344efd | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Indicator.lean | Indicator | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "singleton_indicator_eval_self",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold singletonIndicator\n rw [indicator_eq_1_on_pos (by simp)]",
"n_chars": 70,
"n_subproofs": 0,
... | [
{
"name": "indicator_eq_1_on_pos",
"text": "/-- Indicator evaluated on an element of `pos` is equal to 1. -/\nlemma indicator_eq_1_on_pos {pos neg : Finset F} {x : F}\n (h_pos : x ∈ pos) :\n (indicator pos neg).eval x = 1 := by\n unfold indicator\n have {x} {y} (hy : y ∈ (pos ∪ neg).erase x) :\n (x -... | [
{
"name": "singleton_indicator_eval_self",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 225,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | @@ -71,6 +71,26 @@
[Polynomial.eval_finsetSum,
Finset.sum_eq_single x])])
+/-- Indicator evaluated on an element of `pos` is equal to 1. -/
+lemma indicator_eq_1_on_pos {pos neg : Finset F} {x : F}
+ (h_pos : x ∈ pos) :
+ (indicator pos neg).eval x = 1 := by
+ unfold indicator
+ have {x} {y} (hy... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_dd9350e894dc_7 | e46a0c3aedd55fdb | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Indicator.lean | Indicator | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "singleton_indicator_eval_eq_zero_of_mem_sdiff",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold singletonIndicator\n rw [indicator_eq_0_on_neg_sub_pos (by simp [h])]",
"n_chars"... | [
{
"name": "indicator_eq_0_on_neg_sub_pos",
"text": "/-- The indicator polynomial is zero on `neg \\ pos`. -/\nlemma indicator_eq_0_on_neg_sub_pos {pos neg : Finset F} {x : F}\n (h_pos : x ∈ neg \\ pos) :\n (indicator pos neg).eval x = 0 := by\n have h_basis_zero : ∀ y ∈ pos, Polynomial.eval x (Lagrange.b... | [
{
"name": "singleton_indicator_eval_eq_zero_of_mem_sdiff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 272,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | @@ -91,6 +91,16 @@
Finset.prod_eq_one])
(add safe [(by rw [Finset.sum_eq_single x])])
+/-- The indicator polynomial is zero on `neg \ pos`. -/
+lemma indicator_eq_0_on_neg_sub_pos {pos neg : Finset F} {x : F}
+ (h_pos : x ∈ neg \ pos) :
+ (indicator pos neg).eval x = 0 := by
+ have h_basis_zero :... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_dd9350e894dc_8 | f3ea6cc16a86023c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Indicator.lean | Indicator | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "indicator_natDegree_lt_of_pos_nonempty",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Polynomial.natDegree_lt_iff_degree_lt\n (indicator_ne_zero_of_pos_nonempty h)]\n exact i... | [
{
"name": "indicator_degree_lt",
"text": "/-- The degree of the indicator polynomial\n is less than `#(pos ∪ neg)`. -/\nlemma indicator_degree_lt {pos neg : Finset F} :\n (indicator pos neg).degree < (pos ∪ neg).card := by\n unfold indicator\n exact Lagrange.degree_interpolate_lt _ (by simp)\n\n",
"... | [
{
"name": "singleton_indicator_degree_lt_of_mem",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 278,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": fa... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | @@ -91,12 +91,22 @@
Finset.prod_eq_one])
(add safe [(by rw [Finset.sum_eq_single x])])
+/-- The degree of the indicator polynomial
+ is less than `#(pos ∪ neg)`. -/
+lemma indicator_degree_lt {pos neg : Finset F} :
+ (indicator pos neg).degree < (pos ∪ neg).card := by
+ unfold indicator
+ exact ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_dd9350e894dc_9 | 72f9d422b00f5c96 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Indicator.lean | Indicator | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "indicator_natDegree_lt_of_pos_nonempty",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Polynomial.natDegree_lt_iff_degree_lt\n (indicator_ne_zero_of_pos_nonempty h)]\n exact i... | [
{
"name": "indicator_degree_lt",
"text": "/-- The degree of the indicator polynomial\n is less than `#(pos ∪ neg)`. -/\nlemma indicator_degree_lt {pos neg : Finset F} :\n (indicator pos neg).degree < (pos ∪ neg).card := by\n unfold indicator\n exact Lagrange.degree_interpolate_lt _ (by simp)\n\n",
"... | [
{
"name": "singleton_indicator_natDegree_lt_of_mem",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 8,
"n_chars": 316,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only":... | 4 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.LinearAlgebra.Lagrange
import Mathlib.Tac... | @@ -114,12 +114,22 @@
Finset.prod_eq_one])
(add safe [(by rw [Finset.sum_eq_single x])])
+/-- The degree of the indicator polynomial
+ is less than `#(pos ∪ neg)`. -/
+lemma indicator_degree_lt {pos neg : Finset F} :
+ (indicator pos neg).degree < (pos ∪ neg).card := by
+ unfold indicator
+ exac... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_c553f16e067a_0 | a7e83147ab4d310e | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/OracleReduction/Security/CoordinateWiseSpecialSoundness/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "isSpecialSoundFamily_one_iff_injective",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [isSpecialSoundFamily_one]\n refine ⟨fun h => h.1, fun hinj => ⟨hinj, 0, Finset.univ.erase 0,\n ... | [
{
"name": "isSpecialSoundFamily_one",
"text": "/-- For `ℓ = 1`, coordinate-wise special soundness is ordinary `k`-special soundness: the challenge\n values are distinct, and there is a central vector together with `k - 1` siblings differing in the\n single coordinate — i.e. `k` pairwise-distinct challenge... | [
{
"name": "isSpecialSoundFamily_one_iff_injective",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 941,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 6,
"automation_only"... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree
/-!
# Coordinate-Wise Special Soundness (CWSS) — the notion
This file defines **coordinate-wis... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.TranscriptTree
/-!
# Coordinate-Wise Special Soundness (CWSS) — the notion
This file defines **coordinate-wis... | @@ -84,13 +84,40 @@
∀ i : Fin ℓ, ∃ J : Finset (Fin (ℓ * (k - 1) + 1)),
e ∉ J ∧ J.card = k - 1 ∧ ∀ j ∈ J, CoordEq i (c e) (c j)
+/-- For `ℓ = 1`, coordinate-wise special soundness is ordinary `k`-special soundness: the challenge
+ values are distinct, and there is a central vector together with `k - 1` si... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_df61e9684bfd_0 | 736c1abd476080cd | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/RelativeDistance.lean | RelativeDistance | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "relDistFromCode_eq_distFromCode_div",
"depth": 1,
"n_commands": 0,
"n_lines": 54,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- 1. Unfold definitions\n -- 2. Handle the case where C is empty\n by_cases hC_empty : C = ∅\n · r... | [
{
"name": "exists_relClosest_codeword_of_Nonempty_Code",
"text": "/-- This follows proof strategy from `exists_closest_codeword_of_Nonempty_Code`. However, it's NOT\nused to construct `pickRelClosestCodeword_of_Nonempty_Code`. -/\nlemma exists_relClosest_codeword_of_Nonempty_Code {ι : Type*} [Fintype ι] {F ... | [
{
"name": "relDistFromCode_eq_distFromCode_div",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 57,
"n_chars": 3305,
"n_subproofs": 2,
"n_tactics": 39,
"cyclomatic": 3,
"n_automation": 8,
"n_rewrites": 12,
"n_structural": 6,
"automation_only":... | 2 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | @@ -70,6 +70,88 @@
theorem relDistFromCode_of_empty (u : n → R) : δᵣ(u, (∅ : Set (n → R))) = ⊤ := by
simp [relDistFromCode]
+/-- This follows proof strategy from `exists_closest_codeword_of_Nonempty_Code`. However, it's NOT
+used to construct `pickRelClosestCodeword_of_Nonempty_Code`. -/
+lemma exists_relClosest_... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_df61e9684bfd_1 | 42e5befee618b6dd | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/RelativeDistance.lean | RelativeDistance | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "pairDist_eq_distFromCode_iff_eq_relDistFromCode_div",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv_rhs => rw [relDistFromCode_eq_distFromCode_div]\n constructor\n · intro h_dist_... | [
{
"name": "relDistFromCode_eq_distFromCode_div",
"text": "theorem relDistFromCode_eq_distFromCode_div (u : ι → F) (C : Set (ι → F)) :\n δᵣ(u, C) = (Δ₀(u, C) : ENNReal) / (Fintype.card ι : ENNReal) := by\n -- 1. Unfold definitions\n -- 2. Handle the case where C is empty\n by_cases hC_empty : C = ∅\n ... | [
{
"name": "pairDist_eq_distFromCode_iff_eq_relDistFromCode_div",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 27,
"n_chars": 1301,
"n_subproofs": 0,
"n_tactics": 27,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 6,
"n_structural": 4,
"au... | 3 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | @@ -152,8 +152,87 @@
-- This is exactly `h_sInf_mem`.
exact h_sInf_mem
+theorem relDistFromCode_eq_distFromCode_div (u : ι → F) (C : Set (ι → F)) :
+ δᵣ(u, C) = (Δ₀(u, C) : ENNReal) / (Fintype.card ι : ENNReal) := by
+ -- 1. Unfold definitions
+ -- 2. Handle the case where C is empty
+ by_cases hC_empty :... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_df61e9684bfd_3 | c9d10018e7267c4b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/RelativeDistance.lean | RelativeDistance | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "pairDist_eq_distFromCode_iff_eq_relDistFromCode_div",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv_rhs => rw [relDistFromCode_eq_distFromCode_div]\n constructor\n · intro h_dist_... | [
{
"name": "relDistFromCode_eq_distFromCode_div",
"text": "theorem relDistFromCode_eq_distFromCode_div (u : ι → F) (C : Set (ι → F)) :\n δᵣ(u, C) = (Δ₀(u, C) : ENNReal) / (Fintype.card ι : ENNReal) := by\n -- 1. Unfold definitions\n -- 2. Handle the case where C is empty\n by_cases hC_empty : C = ∅\n ... | [
{
"name": "relCloseToCode_iff_relCloseToCodeword_of_minDist",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 51,
"n_chars": 2434,
"n_subproofs": 4,
"n_tactics": 30,
"cyclomatic": 4,
"n_automation": 4,
"n_rewrites": 4,
"n_structural": 11,
"auto... | 5 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | @@ -152,8 +152,87 @@
-- This is exactly `h_sInf_mem`.
exact h_sInf_mem
+theorem relDistFromCode_eq_distFromCode_div (u : ι → F) (C : Set (ι → F)) :
+ δᵣ(u, C) = (Δ₀(u, C) : ENNReal) / (Fintype.card ι : ENNReal) := by
+ -- 1. Unfold definitions
+ -- 2. Handle the case where C is empty
+ by_cases hC_empty :... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_df61e9684bfd_7 | 1b317885b501f2ca | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/RelativeDistance.lean | RelativeDistance | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 4 | [
{
"theorem_name": "distFromCode_le_iff_relDistFromCode_le",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_n_pos : 0 < Fintype.card ι := Fintype.card_pos\n have h_n_pos_nnreal : 0 < (Fintype.card ι ... | [
{
"name": "pairRelDist_le_iff_pairDist_le",
"text": "/-- Equivalence between relative and natural distance bounds. -/\nlemma pairRelDist_le_iff_pairDist_le (δ : NNReal) :\n (δᵣ(u, v) ≤ δ) ↔ (Δ₀(u, v) ≤ Nat.floor (δ * Fintype.card ι)) := by\n -- 1. Get n > 0 from [Nonempty ι]\n have h_n_pos : 0 < Fintyp... | [
{
"name": "relCloseToWord_iff_exists_possibleDisagreeCols",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 514,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | @@ -64,10 +64,29 @@
have h_M_spec := Classical.choose_spec h_exists
exact ⟨M_val, h_M_spec.1⟩
+/-- Equivalence between relative and natural distance bounds. -/
+lemma pairRelDist_le_iff_pairDist_le (δ : NNReal) :
+ (δᵣ(u, v) ≤ δ) ↔ (Δ₀(u, v) ≤ Nat.floor (δ * Fintype.card ι)) := by
+ -- 1. Get n > 0 from [No... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_df61e9684bfd_8 | 5d53a903b93d1675 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/RelativeDistance.lean | RelativeDistance | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 4 | [
{
"theorem_name": "distFromCode_le_iff_relDistFromCode_le",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_n_pos : 0 < Fintype.card ι := Fintype.card_pos\n have h_n_pos_nnreal : 0 < (Fintype.card ι ... | [
{
"name": "pairRelDist_le_iff_pairDist_le",
"text": "/-- Equivalence between relative and natural distance bounds. -/\nlemma pairRelDist_le_iff_pairDist_le (δ : NNReal) :\n (δᵣ(u, v) ≤ δ) ↔ (Δ₀(u, v) ≤ Nat.floor (δ * Fintype.card ι)) := by\n -- 1. Get n > 0 from [Nonempty ι]\n have h_n_pos : 0 < Fintyp... | [
{
"name": "relCloseToWord_iff_exists_agreementCols",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 567,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only"... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | @@ -64,12 +64,31 @@
have h_M_spec := Classical.choose_spec h_exists
exact ⟨M_val, h_M_spec.1⟩
+/-- Equivalence between relative and natural distance bounds. -/
+lemma pairRelDist_le_iff_pairDist_le (δ : NNReal) :
+ (δᵣ(u, v) ≤ δ) ↔ (Δ₀(u, v) ≤ Nat.floor (δ * Fintype.card ι)) := by
+ -- 1. Get n > 0 from [No... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_df61e9684bfd_9 | b6b77b6cf4aa5162 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/RelativeDistance.lean | RelativeDistance | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "relDist_floor_bound_iff_complement_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 68,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let k := upperBound\n set r : ℝ≥0 := δ * n\n set m : ℕ := Nat.floor r\n have h_m_le_r_NNReal :... | [
{
"name": "NNReal.sub_eq_zero_of_le",
"text": "lemma NNReal.sub_eq_zero_of_le (x y : ℝ≥0) (h : x ≤ y) : x - y = 0 := by\n exact tsub_eq_zero_of_le h\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 109,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewr... | [
{
"name": "relDist_floor_bound_iff_complement_bound",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 80,
"n_chars": 3841,
"n_subproofs": 13,
"n_tactics": 63,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 18,
"n_structural": 13,
"automation... | 2 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | @@ -71,6 +71,9 @@
apply le_of_lt
exact_mod_cast h
+lemma NNReal.sub_eq_zero_of_le (x y : ℝ≥0) (h : x ≤ y) : x - y = 0 := by
+ exact tsub_eq_zero_of_le h
+
/-- The equivalence between the two lowerbound of `upperBound` in Nat and NNReal context.
In which, `upperBound` is viewed as the size of an **agreement s... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_df61e9684bfd_10 | e938162b4b43a6bd | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/RelativeDistance.lean | RelativeDistance | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "finite_possibleRelHammingDists",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n Set.Finite.subset finite_relHammingDistRange possibleRelHammingDists_subset_relHammingDistRange",
"n_chars"... | [
{
"name": "finite_relHammingDistRange",
"text": "/-- The range of the relative Hamming distance function is finite.\n-/\n@[simp]\nlemma finite_relHammingDistRange [Nonempty ι] : (relHammingDistRange ι).Finite := by\n simp only [relHammingDistRange, ← Set.finite_coe_iff, Set.coe_setOf]\n exact\n finite_... | [
{
"name": "finite_possibleRelHammingDists",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 275,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 2 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | @@ -95,6 +95,23 @@
lemma relHammingDist_mem_relHammingDistRange [DecidableEq F] : δᵣ(u, v) ∈ relHammingDistRange ι :=
⟨hammingDist _ _, Finset.card_filter_le _ _, rfl⟩
+/-- The range of the relative Hamming distance function is finite.
+-/
+@[simp]
+lemma finite_relHammingDistRange [Nonempty ι] : (relHammingDistR... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_df61e9684bfd_11 | b407bc830624e30e | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/RelativeDistance.lean | RelativeDistance | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "pairDist_eq_distFromCode_iff_eq_relDistFromCode_div",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv_rhs => rw [relDistFromCode_eq_distFromCode_div]\n constructor\n · intro h_dist_... | [
{
"name": "relDistFromCode_eq_distFromCode_div",
"text": "theorem relDistFromCode_eq_distFromCode_div (u : ι → F) (C : Set (ι → F)) :\n δᵣ(u, C) = (Δ₀(u, C) : ENNReal) / (Fintype.card ι : ENNReal) := by\n -- 1. Unfold definitions\n -- 2. Handle the case where C is empty\n by_cases hC_empty : C = ∅\n ... | [
{
"name": "relDistFromCode'_eq_relDistFromCode",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 63,
"n_chars": 3105,
"n_subproofs": 4,
"n_tactics": 48,
"cyclomatic": 4,
"n_automation": 8,
"n_rewrites": 7,
"n_structural": 17,
"automation_only":... | 3 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.CodingTheory.Basic.Distance
/-!
# Relative Dist... | @@ -152,6 +152,62 @@
-- This is exactly `h_sInf_mem`.
exact h_sInf_mem
+theorem relDistFromCode_eq_distFromCode_div (u : ι → F) (C : Set (ι → F)) :
+ δᵣ(u, C) = (Δ₀(u, C) : ENNReal) / (Fintype.card ι : ENNReal) := by
+ -- 1. Unfold definitions
+ -- 2. Handle the case where C is empty
+ by_cases hC_empty :... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_3b48e1a9add8_9 | 2e131536a748a992 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/GuruswamiSudan.lean | GuruswamiSudan | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 1 | [
{
"theorem_name": "coeff_vec_to_bivariate_ne_zero_of_isWitnessC",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨i, j, hwd, hne⟩ := isWitnessC_nonzero hw\n intro heq\n apply hne\n rw [← coeff_vec_... | [
{
"name": "isWitnessC_nonzero",
"text": "/-- Extract the nonzero-coefficient condition from `isWitnessC`: there exists at least one\n index pair `(i, j)` in the weighted-degree region `i + (k-1)·j ≤ D` where `c(i,j) ≠ 0`. -/\nprivate lemma isWitnessC_nonzero {k D r : ℕ} {ωs : Fin n ↪ F} {f : Fin n → F}\n... | [
{
"name": "coeff_vec_to_bivariate_ne_zero_of_isWitnessC",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 15,
"n_chars": 620,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 3,
"automation_... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Elias Judin
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import Mathlib.RingTh... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Elias Judin
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import Mathlib.RingTh... | @@ -213,6 +213,19 @@
(List.finRange n).all (fun idx ↦
hasseMultiplicityCheck k D r c (ωs idx) (f idx))
+/-- Extract the nonzero-coefficient condition from `isWitnessC`: there exists at least one
+ index pair `(i, j)` in the weighted-degree region `i + (k-1)·j ≤ D` where `c(i,j) ≠ 0`. -/
+private lemma isWi... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
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