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_3b48e1a9add8_11 | a810078490c1ee3a | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/GuruswamiSudan.lean | GuruswamiSudan | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 2 | [
{
"theorem_name": "witness_candidate_set_witness_vanishes",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold witnessCandidateSet at hp\n cases hcw : computeGsWitness (n := n) k D r ωs f\n case none =... | [
{
"name": "isWitnessC_imp_eval_zero_at_points",
"text": "/-- When `r > 0` and the witness predicate `isWitnessC` holds, the bivariate polynomial\n represented by `c` vanishes at every interpolation point `(ωs i, f i)`.\n\n This connects the computable Hasse-derivative multiplicity filter to the classi... | [
{
"name": "guruswami_sudan_for_proximity_gap_existence_strong",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 9,
"n_lines": 22,
"n_chars": 1190,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"auto... | 9 | /-
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... | @@ -246,6 +246,21 @@
(List.finRange n).all (fun idx ↦
hasseMultiplicityCheck k D r c (ωs idx) (f idx))
+/-- When `r > 0` and the witness predicate `isWitnessC` holds, the bivariate polynomial
+ represented by `c` vanishes at every interpolation point `(ωs i, f i)`.
+
+ This connects the computable Hasse... | {
"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_13 | 6ba13f0b90c5f4fd | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/GuruswamiSudan.lean | GuruswamiSudan | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 2 | [
{
"theorem_name": "witness_candidate_set_witness_vanishes",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold witnessCandidateSet at hp\n cases hcw : computeGsWitness (n := n) k D r ωs f\n case none =... | [
{
"name": "isWitnessC_imp_eval_zero_at_points",
"text": "/-- When `r > 0` and the witness predicate `isWitnessC` holds, the bivariate polynomial\n represented by `c` vanishes at every interpolation point `(ωs i, f i)`.\n\n This connects the computable Hasse-derivative multiplicity filter to the classi... | [
{
"name": "guruswami_sudan_for_proximity_gap_property_strong",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 9,
"n_lines": 31,
"n_chars": 1633,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"autom... | 9 | /-
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... | @@ -246,6 +246,21 @@
(List.finRange n).all (fun idx ↦
hasseMultiplicityCheck k D r c (ωs idx) (f idx))
+/-- When `r > 0` and the witness predicate `isWitnessC` holds, the bivariate polynomial
+ represented by `c` vanishes at every interpolation point `(ωs i, f i)`.
+
+ This connects the computable Hasse... | {
"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_6a681e719904_0 | 47d58c52adc2bc99 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/NormBounds/LyubashevskySeiler.lean | LyubashevskySeiler | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "isUnit_of_l1Norm_le",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_contra hc\n -- Algebraic core: a non-unit has `q ∣ ‖c‖₂²`.\n have hdvd : (q : ℤ) ∣ (Rq.l2NormSq Φ c : ℤ) := q_dvd... | [
{
"name": "Rq.l2NormSq_le_l1Norm_sq",
"text": "/-- **Norm bridge.** The centered squared `ℓ₂` norm is at most the square of the\ncentered `ℓ₁` norm: `‖c‖₂² ≤ ‖c‖₁²`. This is `Σ aₖ² ≤ (Σ aₖ)²` for nonnegative `aₖ`. -/\ntheorem Rq.l2NormSq_le_l1Norm_sq (c : Rq Φ) :\n Rq.l2NormSq Φ c ≤ (Rq.l1Norm Φ c) ^ 2 :... | [
{
"name": "isUnit_of_l1Norm_le",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 27,
"n_chars": 1616,
"n_subproofs": 6,
"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.NormBounds.Basic
import ArkLib.Data.Lattices.CyclotomicRing.NormBounds.LsCore
import Mathlib.Data.Nat.Prime.Basi... | /-
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.NormBounds.Basic
import ArkLib.Data.Lattices.CyclotomicRing.NormBounds.LsCore
import Mathlib.Data.Nat.Prime.Basi... | @@ -72,6 +72,14 @@
local notation "Φ" => (powTwoCyclotomic (R := ZMod q) α)
omit [NeZero q] in
+/-- **Norm bridge.** The centered squared `ℓ₂` norm is at most the square of the
+centered `ℓ₁` norm: `‖c‖₂² ≤ ‖c‖₁²`. This is `Σ aₖ² ≤ (Σ aₖ)²` for nonnegative `aₖ`. -/
+theorem Rq.l2NormSq_le_l1Norm_sq (c : Rq Φ) :
+ ... | {
"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_c99ff6759cc3_2 | 0b9e25f1347a7a4c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/KZG/FunctionBinding/Basic.lean | Basic | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "function_binding_cond_ext_output_maps_to_arsdh",
"depth": 1,
"n_commands": 0,
"n_lines": 80,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hsrs : srs = Groups.PowerSrs.generate n τ (g₂ := g₂) (g₁ := g₁) := by\n exact funct... | [
{
"name": "function_binding_game_ext_support_srs",
"text": "/-- Extract the sampled SRS equation from a supported extended function-binding game output. -/\nlemma function_binding_game_ext_support_srs {n L : ℕ} {AuxState : Type} [SampleableType G₁]\n (adversary : KzgFunctionBindingAdversary p G₁ G₂ n uni... | [
{
"name": "function_binding",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 8,
"n_lines": 33,
"n_chars": 1961,
"n_subproofs": 0,
"n_tactics": 21,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nes... | 8 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.KZG.FunctionBinding.EvaluationBindingConflict
import ArkLib.Commitments.Functional.KZG.FunctionBinding.TauInQueries
import... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.KZG.FunctionBinding.EvaluationBindingConflict
import ArkLib.Commitments.Functional.KZG.FunctionBinding.TauInQueries
import... | @@ -270,6 +270,42 @@
omit [DecidableEq G₁] in
include g₁ g₂ pairing in
+/-- Extract the sampled SRS equation from a supported extended function-binding game output. -/
+lemma function_binding_game_ext_support_srs {n L : ℕ} {AuxState : Type} [SampleableType G₁]
+ (adversary : KzgFunctionBindingAdversary p G₁ G₂ 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_b1bec034a9e9_0 | 66b37e4cf3995af2 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/Distance.lean | Distance | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "dist_pos_of_Nontrivial",
"depth": 1,
"n_commands": 0,
"n_lines": 23,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Code.dist_eq_minDist]\n unfold Code.minDist\n let S_eq : Set ℕ := {d | ∃ u ∈ C, ∃ v ∈ C, u ≠ v ∧ hammingDist ... | [
{
"name": "dist_eq_minDist",
"text": "lemma dist_eq_minDist {ι : Type*} [Fintype ι] {F : Type*} [DecidableEq F] (C : Set (ι → F)) :\n Code.dist C = Code.minDist C := by\n -- 1. Define the sets\n let S_le : Set ℕ := {d | ∃ u ∈ C, ∃ v ∈ C, u ≠ v ∧ hammingDist u v ≤ d}\n let S_eq : Set ℕ := {d | ∃ u ∈ C,... | [
{
"name": "dist_pos_of_Nontrivial",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 29,
"n_chars": 1405,
"n_subproofs": 3,
"n_tactics": 15,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 4,
"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: Quang Dao, Katerina Hristova, František Silváši, Julian Sutherland,
Ilia Vlasov, Chung Thai Nguyen
-/
import ArkLib.Data.Fin.Basic
import ArkLib.Data.CodingTheory.Prelim... | /-
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.Fin.Basic
import ArkLib.Data.CodingTheory.Prelim... | @@ -166,11 +166,111 @@
simp only [ne_eq, Set.mem_setOf_eq]
refine ⟨u, And.intro hu ⟨v, And.intro hv ⟨huv, hammingDist_le_card_fintype⟩⟩⟩
+lemma dist_eq_minDist {ι : Type*} [Fintype ι] {F : Type*} [DecidableEq F] (C : Set (ι → F)) :
+ Code.dist C = Code.minDist C := by
+ -- 1. Define the sets
+ let S_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_b1bec034a9e9_1 | 85075e59e6ec9bea | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/Distance.lean | Distance | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "closeToWord_iff_exists_agreementCols",
"depth": 1,
"n_commands": 0,
"n_lines": 80,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n rw [closeToWord_iff_exists_possibleDisagreeCols]\n constructor\n · -- Direction 1: (∃ ... | [
{
"name": "closeToWord_iff_exists_possibleDisagreeCols",
"text": "theorem closeToWord_iff_exists_possibleDisagreeCols\n {ι : Type*} [Fintype ι] {F : Type*} [DecidableEq F] (u v : ι → F) (e : ℕ) :\n Δ₀(u, v) ≤ e ↔ ∃ (D : Finset ι),\n D.card ≤ e ∧ (∀ (colIdx : ι), colIdx ∉ D → u colIdx = v colIdx) ... | [
{
"name": "closeToWord_iff_exists_agreementCols",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 86,
"n_chars": 4046,
"n_subproofs": 8,
"n_tactics": 67,
"cyclomatic": 9,
"n_automation": 9,
"n_rewrites": 5,
"n_structural": 32,
"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.Fin.Basic
import ArkLib.Data.CodingTheory.Prelim... | /-
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.Fin.Basic
import ArkLib.Data.CodingTheory.Prelim... | @@ -224,11 +224,148 @@
have h_M_spec := Classical.choose_spec h_exists
exact ⟨M_val, h_M_spec.1⟩
+theorem closeToWord_iff_exists_possibleDisagreeCols
+ {ι : Type*} [Fintype ι] {F : Type*} [DecidableEq F] (u v : ι → F) (e : ℕ) :
+ Δ₀(u, v) ≤ e ↔ ∃ (D : Finset ι),
+ D.card ≤ e ∧ (∀ (colIdx : ι), colIdx... | {
"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_b1bec034a9e9_2 | 8603e7b9a916543b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/Distance.lean | Distance | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "distFromCode_le_card_index_of_Nonempty",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- exact an element from C since C is nonempty\n letI h_nonempty : Set.Nonempty C := by (expose_na... | [
{
"name": "distFromCode_eq_top_iff_empty",
"text": "theorem distFromCode_eq_top_iff_empty (u : n → R) (C : Set (n → R)) : Δ₀(u, C) = ⊤ ↔ C = ∅ := by\n apply Iff.intro\n · simp only [distFromCode]\n intro h\n apply Set.eq_empty_iff_forall_notMem.mpr\n intro v hv\n apply sInf_eq_top.mp at h\n ... | [
{
"name": "distFromCode_le_card_index_of_Nonempty",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 20,
"n_chars": 1084,
"n_subproofs": 5,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"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.Fin.Basic
import ArkLib.Data.CodingTheory.Prelim... | /-
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.Fin.Basic
import ArkLib.Data.CodingTheory.Prelim... | @@ -242,6 +242,20 @@
theorem distFromCode_of_empty (u : n → R) : Δ₀(u, (∅ : Set (n → R))) = ⊤ := by
simp [distFromCode]
+theorem distFromCode_eq_top_iff_empty (u : n → R) (C : Set (n → R)) : Δ₀(u, C) = ⊤ ↔ C = ∅ := by
+ apply Iff.intro
+ · simp only [distFromCode]
+ intro h
+ apply Set.eq_empty_iff_forall... | {
"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_b1bec034a9e9_3 | 453763881483f77a | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/Distance.lean | Distance | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "distFromCode_eq_of_lt_half_dist",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply eq_of_lt_dist hv hw\n calc\n Δ₀(v, w) ≤ Δ₀(v, u) + Δ₀(u, w) := by exact hammingDist_triangle v u ... | [
{
"name": "eq_of_lt_dist",
"text": "/-- If `u` and `v` are two codewords of `C` with distance less than `dist C`,\nthen they are the same. -/\ntheorem eq_of_lt_dist {C : Set (n → R)} {u v : n → R} (hu : u ∈ C) (hv : v ∈ C)\n (huv : Δ₀(u, v) < ‖C‖₀) : u = v := by\n simp only [dist] at huv\n by_contra hN... | [
{
"name": "distFromCode_eq_of_lt_half_dist",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 487,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"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, Chung Thai Nguyen
-/
import ArkLib.Data.Fin.Basic
import ArkLib.Data.CodingTheory.Prelim... | /-
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.Fin.Basic
import ArkLib.Data.CodingTheory.Prelim... | @@ -224,6 +224,19 @@
have h_M_spec := Classical.choose_spec h_exists
exact ⟨M_val, h_M_spec.1⟩
+/-- If `u` and `v` are two codewords of `C` with distance less than `dist C`,
+then they are the same. -/
+theorem eq_of_lt_dist {C : Set (n → R)} {u v : n → R} (hu : u ∈ C) (hv : v ∈ C)
+ (huv : Δ₀(u, v) < ‖C‖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_b1bec034a9e9_4 | 6ea23af90ef04c39 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/Basic/Distance.lean | Distance | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "closeToCode_iff_closeToCodeword_of_minDist",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · -- Direction 1: (→)\n -- Assume: Δ₀(u, C) ≤ ↑e\n -- Goal: ∃ v ∈ C, Δ₀(u,... | [
{
"name": "distFromPickClosestCodeword_of_Nonempty_Code",
"text": "lemma distFromPickClosestCodeword_of_Nonempty_Code {ι : Type*} [Fintype ι] {F : Type*}\n [DecidableEq F] (C : Set (ι → F)) [Nonempty C] (u : ι → F) :\n Δ₀(u, C) = Δ₀(u, pickClosestCodeword_of_Nonempty_Code C u) := by\n have h_exists :... | [
{
"name": "closeToCode_iff_closeToCodeword_of_minDist",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 45,
"n_chars": 2144,
"n_subproofs": 4,
"n_tactics": 29,
"cyclomatic": 4,
"n_automation": 3,
"n_rewrites": 4,
"n_structural": 11,
"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.Fin.Basic
import ArkLib.Data.CodingTheory.Prelim... | /-
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.Fin.Basic
import ArkLib.Data.CodingTheory.Prelim... | @@ -224,6 +224,14 @@
have h_M_spec := Classical.choose_spec h_exists
exact ⟨M_val, h_M_spec.1⟩
+lemma distFromPickClosestCodeword_of_Nonempty_Code {ι : Type*} [Fintype ι] {F : Type*}
+ [DecidableEq F] (C : Set (ι → F)) [Nonempty C] (u : ι → F) :
+ Δ₀(u, C) = Δ₀(u, pickClosestCodeword_of_Nonempty_Code C u)... | {
"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_a4ee404a88fd_0 | ec3a1a1f418e301b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Galois/Automorphism.lean | Automorphism | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "galoisAutₛ_toQuotient",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Rq.toQuotient, quotientHom_apply, galoisAutₛ_mk]",
"n_chars": 60,
"n_subproofs": 0,
"n_tactics": 2,
... | [
{
"name": "galoisAutₛ_mk",
"text": "/-- The semantic automorphism on a quotient class: `galoisAutₛ (mk p) = mk (aeval (X^i) p)`. -/\ntheorem galoisAutₛ_mk (α i : ℕ) (hi : Odd i) (p : Polynomial R) :\n galoisAutₛ α i hi (Ideal.Quotient.mk _ p)\n = Ideal.Quotient.mk _ (Polynomial.aeval (Polynomial.X ^... | [
{
"name": "galoisAutₛ_toQuotient",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 504,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"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.PowTwo
import ArkLib.ToMathlib.Polynomial.AevalXPow
/-!
# Galois Automorphisms `σ_i : X ↦ X^i` of the Cyclotomi... | /-
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.PowTwo
import ArkLib.ToMathlib.Polynomial.AevalXPow
/-!
# Galois Automorphisms `σ_i : X ↦ X^i` of the Cyclotomi... | @@ -147,12 +147,20 @@
exact (Ideal.Quotient.eq_zero_iff_mem).mpr (powTwo_galoisAeval_mem α i hi hp))
omit [DecidableEq R] in
+/-- The semantic automorphism on a quotient class: `galoisAutₛ (mk p) = mk (aeval (X^i) p)`. -/
+theorem galoisAutₛ_mk (α i : ℕ) (hi : Odd i) (p : Polynomial R) :
+ galoisAutₛ α i 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_a4ee404a88fd_1 | c849d40d0a583a11 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Galois/Automorphism.lean | Automorphism | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "mk_X_pow_periodic",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n nth_rewrite 1 [← Nat.div_add_mod n (2 ^ (α + 1))]\n rw [pow_add, pow_mul, map_mul, map_pow, mk_X_pow_conductor_eq_one, o... | [
{
"name": "mk_X_pow_conductor_eq_one",
"text": "/-- **(C-1)** `X^{2^{α+1}} ≡ 1` in the quotient, since `X^{2d} - 1 = (X^d - 1)(X^d + 1)`. -/\ntheorem mk_X_pow_conductor_eq_one (α : ℕ) :\n Ideal.Quotient.mk (powTwoCyclotomic (R := R) α).modIdeal (Polynomial.X ^ 2 ^ (α + 1)) = 1 := by\n have hmem : (Polyn... | [
{
"name": "mk_X_pow_periodic",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 429,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 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.PowTwo
import ArkLib.ToMathlib.Polynomial.AevalXPow
/-!
# Galois Automorphisms `σ_i : X ↦ X^i` of the Cyclotomi... | /-
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.PowTwo
import ArkLib.ToMathlib.Polynomial.AevalXPow
/-!
# Galois Automorphisms `σ_i : X ↦ X^i` of the Cyclotomi... | @@ -204,10 +204,26 @@
-- TODO this is not the right place for this.
omit [DecidableEq R] in
+/-- **(C-1)** `X^{2^{α+1}} ≡ 1` in the quotient, since `X^{2d} - 1 = (X^d - 1)(X^d + 1)`. -/
+theorem mk_X_pow_conductor_eq_one (α : ℕ) :
+ Ideal.Quotient.mk (powTwoCyclotomic (R := R) α).modIdeal (Polynomial.X ^ 2 ^ (α ... | {
"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_a4ee404a88fd_2 | e708e8ff07c97460 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Galois/Automorphism.lean | Automorphism | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "mk_X_pow_periodic",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n nth_rewrite 1 [← Nat.div_add_mod n (2 ^ (α + 1))]\n rw [pow_add, pow_mul, map_mul, map_pow, mk_X_pow_conductor_eq_one, o... | [
{
"name": "mk_X_pow_conductor_eq_one",
"text": "/-- **(C-1)** `X^{2^{α+1}} ≡ 1` in the quotient, since `X^{2d} - 1 = (X^d - 1)(X^d + 1)`. -/\ntheorem mk_X_pow_conductor_eq_one (α : ℕ) :\n Ideal.Quotient.mk (powTwoCyclotomic (R := R) α).modIdeal (Polynomial.X ^ 2 ^ (α + 1)) = 1 := by\n have hmem : (Polyn... | [
{
"name": "mk_aeval_X_pow_periodic",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 18,
"n_chars": 867,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"m... | 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.PowTwo
import ArkLib.ToMathlib.Polynomial.AevalXPow
/-!
# Galois Automorphisms `σ_i : X ↦ X^i` of the Cyclotomi... | /-
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.PowTwo
import ArkLib.ToMathlib.Polynomial.AevalXPow
/-!
# Galois Automorphisms `σ_i : X ↦ X^i` of the Cyclotomi... | @@ -204,10 +204,26 @@
-- TODO this is not the right place for this.
omit [DecidableEq R] in
+/-- **(C-1)** `X^{2^{α+1}} ≡ 1` in the quotient, since `X^{2d} - 1 = (X^d - 1)(X^d + 1)`. -/
+theorem mk_X_pow_conductor_eq_one (α : ℕ) :
+ Ideal.Quotient.mk (powTwoCyclotomic (R := R) α).modIdeal (Polynomial.X ^ 2 ^ (α ... | {
"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_a4ee404a88fd_4 | 22052d3011b5311c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Galois/Automorphism.lean | Automorphism | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "galoisAut_toQuotient",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [galoisAut, Rq.toQuotient_mk, galoisAutₛ_toQuotient α i hi, quotientHom_apply]\n exact congrArg (Ideal.Quotient.mk... | [
{
"name": "galoisAut_sum_toPoly_eq_aeval",
"text": "/-- **(S5)** The core polynomial identity behind soundness: the monomial-remapped sum (before\nreduction) equals `aeval (X^i)` of the underlying polynomial. Both sides are\n`∑_{k<d} X^{ki}·a_k`. -/\ntheorem galoisAut_sum_toPoly_eq_aeval (α i : ℕ) (a : Rq (... | [
{
"name": "galoisAut_periodic",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 10,
"n_chars": 486,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nes... | 5 | /-
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.PowTwo
import ArkLib.ToMathlib.Polynomial.AevalXPow
/-!
# Galois Automorphisms `σ_i : X ↦ X^i` of the Cyclotomi... | /-
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.PowTwo
import ArkLib.ToMathlib.Polynomial.AevalXPow
/-!
# Galois Automorphisms `σ_i : X ↦ X^i` of the Cyclotomi... | @@ -164,11 +164,28 @@
/-! ## Soundness bridge -/
+/-- **(S5)** The core polynomial identity behind soundness: the monomial-remapped sum (before
+reduction) equals `aeval (X^i)` of the underlying polynomial. Both sides are
+`∑_{k<d} X^{ki}·a_k`. -/
+theorem galoisAut_sum_toPoly_eq_aeval (α i : ℕ) (a : Rq (powTwoCyc... | {
"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_8f6651273f88_0 | 732a78ea18bafd4e | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/CosetFftDomain/ToFftDomain.lean | ToFftDomain | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "card_toFinset_eq_card_toFftDomain_toFinset",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n aesop (add simp [toFinset_image_toFftDomain_eq_toFinset])",
"n_chars": 63,
"n_subproofs"... | [
{
"name": "toFinset_image_toFftDomain_eq_toFinset",
"text": "/-- Scaling the normalized FFT-domain image by `ω 0` recovers\n the original coset FFT-domain image. -/\n@[simp]\nlemma toFinset_image_toFftDomain_eq_toFinset [Fintype ι] [DecidableEq F] {ω : D} :\n Finset.image (fun (w : F) ↦ ω 0 * w) (toFftDom... | [
{
"name": "card_toFinset_eq_card_toFftDomain_toFinset",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 327,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_onl... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -89,10 +89,31 @@
field_simp
rfl
+/-- Scaling the normalized FFT-domain image by `ω 0` recovers
+ the original coset FFT-domain image. -/
+@[simp]
+lemma toFinset_image_toFftDomain_eq_toFinset [Fintype ι] [DecidableEq F] {ω : D} :
+ Finset.image (fun (w : F) ↦ ω 0 * w) (toFftDomain ω).toFinset =
+ CosetF... | {
"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_8fdb66e35cc4_0 | fb8a381b8252d42e | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/TraceInnerProduct.lean | TraceInnerProduct | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "traceH_smul_fixed",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold traceH traceOver\n rw [Finset.mul_sum]\n refine Finset.sum_congr rfl (fun m hm => ?_)\n rw [galoisAut_mul α m (... | [
{
"name": "galoisAut_fixed_of_mem",
"text": "/-- Every `σ_m` with `m ∈ Hexp` fixes `R_q^H`: modulo `2d`, `m` is `±(4k+1)^a`, and the two\ngenerators `σ_{4k+1}`, `σ_{-1}` fix `R_q^H` (so does any composite). -/\ntheorem galoisAut_fixed_of_mem (α k : ℕ) {c : Rq (powTwoCyclotomic (R := R) α)}\n (hc : c ∈ fi... | [
{
"name": "traceH_smul_fixed",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 561,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
"max_nest... | 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.Packing
import ArkLib.Data.Lattices.CyclotomicRing.Subfield.TraceVanishing
/-!
# The Trace Formula `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.Subfield.Packing
import ArkLib.Data.Lattices.CyclotomicRing.Subfield.TraceVanishing
/-!
# The Trace Formula `Tr... | @@ -40,11 +40,62 @@
/-! ## `Tr_H` is `R_q^H`-linear -/
+/-- Every `σ_m` with `m ∈ Hexp` fixes `R_q^H`: modulo `2d`, `m` is `±(4k+1)^a`, and the two
+generators `σ_{4k+1}`, `σ_{-1}` fix `R_q^H` (so does any composite). -/
+theorem galoisAut_fixed_of_mem (α k : ℕ) {c : Rq (powTwoCyclotomic (R := R) α)}
+ (hc : c ... | {
"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_8fdb66e35cc4_1 | 60a91d225e65fb9c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/TraceInnerProduct.lean | TraceInnerProduct | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "traceH_psi_mul_conj",
"depth": 1,
"n_commands": 0,
"n_lines": 28,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨κ, rfl⟩ := hk2pow\n have hκ : κ + 1 ≤ α := succ_le_of_two_mul_two_pow_dvd hk\n -- `σ_{-1}(ψ(b)) = Σ_q ↑(b q)... | [
{
"name": "traceH_sum",
"text": "/-- `Tr_H` distributes over finite sums (it is additive). -/\ntheorem traceH_sum (α k : ℕ) {ι : Type*} (s : Finset ι)\n (f : ι → Rq (powTwoCyclotomic (R := R) α)) :\n traceH α k (∑ j ∈ s, f j) = ∑ j ∈ s, traceH α k (f j) := by\n classical\n induction s using Finset.i... | [
{
"name": "traceH_psi_mul_conj",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 41,
"n_chars": 2153,
"n_subproofs": 3,
"n_tactics": 24,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 11,
"n_structural": 2,
"automation_only": false,
"max... | 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 ArkLib.Data.Lattices.CyclotomicRing.Subfield.Packing
import ArkLib.Data.Lattices.CyclotomicRing.Subfield.TraceVanishing
/-!
# The Trace Formula `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.Subfield.Packing
import ArkLib.Data.Lattices.CyclotomicRing.Subfield.TraceVanishing
/-!
# The Trace Formula `Tr... | @@ -209,6 +209,19 @@
/-! ## The Theorem 2 trace formula -/
+/-- `Tr_H` distributes over finite sums (it is additive). -/
+theorem traceH_sum (α k : ℕ) {ι : Type*} (s : Finset ι)
+ (f : ι → Rq (powTwoCyclotomic (R := R) α)) :
+ traceH α k (∑ j ∈ s, f j) = ∑ j ∈ s, traceH α k (f j) := by
+ classical
+ induct... | {
"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_8fdb66e35cc4_2 | 5ada6e6bbc3fb656 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/TraceInnerProduct.lean | TraceInnerProduct | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "psi_injective",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨κ, rfl⟩ := hk2pow\n have hκ : κ ≤ α := Nat.le_of_succ_le (succ_le_of_two_mul_two_pow_dvd hk)\n have hunit : IsUnit... | [
{
"name": "traceH_psi_mul_conj",
"text": "/-- **Hachi [NOZ26, §3, Theorem 2]**: `Tr_H(ψ(a)·σ_{-1}(ψ(b))) = (d/k)·⟨a,b⟩`, where\n`⟨a,b⟩ = Σ_i a_i b_i` is the inner product over `R_q^H`. Expand the product as a double sum,\npull the `R_q^H`-coefficients out of `Tr_H` (`traceH_smul_fixed`), evaluate the monomi... | [
{
"name": "psi_injective",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 24,
"n_chars": 1308,
"n_subproofs": 7,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 3,
"n_structural": 5,
"automation_only": false,
"max_nestin... | 5 | /-
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.Packing
import ArkLib.Data.Lattices.CyclotomicRing.Subfield.TraceVanishing
/-!
# The Trace Formula `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.Subfield.Packing
import ArkLib.Data.Lattices.CyclotomicRing.Subfield.TraceVanishing
/-!
# The Trace Formula `Tr... | @@ -222,12 +222,68 @@
traceOver_add _ _ _ _,
ih, Finset.sum_insert ha]
+/-- **Hachi [NOZ26, §3, Theorem 2]**: `Tr_H(ψ(a)·σ_{-1}(ψ(b))) = (d/k)·⟨a,b⟩`, where
+`⟨a,b⟩ = Σ_i a_i b_i` is the inner product over `R_q^H`. Expand the product as a double sum,
+pull the `R_q^H`-coefficients out of `Tr_H` (`trac... | {
"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_5be96d160261_0 | 1f1f57ea16ba3b1a | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Bivariate.lean | Bivariate | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "natDeg_sum_eq_of_unique",
"depth": 1,
"n_commands": 0,
"n_lines": 41,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n intro hmxdeg others\n by_cases hdeg0 : deg = 0\n · have hothers0 : ∀ y ∈ s, y ≠ mx → f y = 0 := by\... | [
{
"name": "natDegree_sum_lt_of_forall_lt",
"text": "theorem natDegree_sum_lt_of_forall_lt {F : Type} [Semiring F]\n {α : Type} {s : Finset α} {g : α → F[X]} {deg : ℕ} :\n 0 < deg → (∀ x ∈ s, (g x).natDegree < deg) → (∑ x ∈ s, g x).natDegree < deg := by\n intro deg_pos h\n have hle : (∑ x ∈ s, g x).nat... | [
{
"name": "natDeg_sum_eq_of_unique",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 48,
"n_chars": 1913,
"n_subproofs": 11,
"n_tactics": 41,
"cyclomatic": 3,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 14,
"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, Ilia Vlasov
-/
import CompPoly.ToMathlib.Polynomial.BivariateWeightedDegree
import CompPoly.ToMathlib.Polynomial.Biv... | /-
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, Ilia Vlasov
-/
import CompPoly.ToMathlib.Polynomial.BivariateWeightedDegree
import CompPoly.ToMathlib.Polynomial.Biv... | @@ -51,6 +51,16 @@
attribute [local grind =] natDegree_mul natDegree_add_eq_right_of_degree_lt
natDegree_zero
+theorem natDegree_sum_lt_of_forall_lt {F : Type} [Semiring F]
+ {α : Type} {s : Finset α} {g : α → F[X]} {deg : ℕ} :
+ 0 < deg → (∀ x ∈ s, (g x).natDegree < deg) → (∑ x ∈ s, 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_5be96d160261_2 | 7a0357a967989de6 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Bivariate.lean | Bivariate | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "coeff_totalDegree_le'",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hn : n ∈ f.support\n · exact Or.inl (coeff_totalDegree_le f hn)\n · exact Or.inr (Polynomial.notMem_suppor... | [
{
"name": "coeff_totalDegree_le",
"text": "/-- Each coefficient's total-degree contribution is bounded by `totalDegree` when in support. -/\ntheorem coeff_totalDegree_le (f : F[X][Y]) {n : ℕ} (hn : n ∈ f.support) :\n (f.coeff n).natDegree + n ≤ totalDegree f := by\n classical\n unfold totalDegree\n ex... | [
{
"name": "coeff_totalDegree_le'",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 263,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"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, Ilia Vlasov
-/
import CompPoly.ToMathlib.Polynomial.BivariateWeightedDegree
import CompPoly.ToMathlib.Polynomial.Biv... | /-
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, Ilia Vlasov
-/
import CompPoly.ToMathlib.Polynomial.BivariateWeightedDegree
import CompPoly.ToMathlib.Polynomial.Biv... | @@ -97,10 +97,17 @@
lemma degreeY_le_degreeY_sub_degreeY [IsDomain F] {f q : F[X][Y]} (hf : f ≠ 0) (hg : q * f ≠ 0) :
natDegreeY q ≤ natDegreeY (q * f) - natDegreeY f := by grind
+/-- Each coefficient's total-degree contribution is bounded by `totalDegree` when in support. -/
+theorem coeff_totalDegree_le (f : 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_5be96d160261_3 | 08104e2efb2c2dca | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Bivariate.lean | Bivariate | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "totalDegree_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 100,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply le_antisymm (totalDegree_mul_le f g)\n classical\n rcases exists_max_index_totalDegree f hf with ⟨mmf, hmmf, hmmf... | [
{
"name": "coeff_totalDegree_le'",
"text": "theorem coeff_totalDegree_le' (f : F[X][Y]) (n : ℕ) :\n (f.coeff n).natDegree + n ≤ totalDegree f ∨ f.coeff n = 0 := by\n by_cases hn : n ∈ f.support\n · exact Or.inl (coeff_totalDegree_le f hn)\n · exact Or.inr (Polynomial.notMem_support_iff.mp hn)\n\n",
... | [
{
"name": "totalDegree_mul",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 106,
"n_chars": 5180,
"n_subproofs": 32,
"n_tactics": 98,
"cyclomatic": 10,
"n_automation": 19,
"n_rewrites": 7,
"n_structural": 27,
"automation_only": false,
"max... | 4 | /-
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, Ilia Vlasov
-/
import CompPoly.ToMathlib.Polynomial.BivariateWeightedDegree
import CompPoly.ToMathlib.Polynomial.Biv... | /-
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, Ilia Vlasov
-/
import CompPoly.ToMathlib.Polynomial.BivariateWeightedDegree
import CompPoly.ToMathlib.Polynomial.Biv... | @@ -104,6 +104,12 @@
unfold totalDegree
exact Finset.le_sup (f := fun m => (f.coeff m).natDegree + m) hn
+theorem coeff_totalDegree_le' (f : F[X][Y]) (n : ℕ) :
+ (f.coeff n).natDegree + n ≤ totalDegree f ∨ f.coeff n = 0 := by
+ by_cases hn : n ∈ f.support
+ · exact Or.inl (coeff_totalDegree_le f hn)
+ · e... | {
"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_cae0da9ef99c_0 | c2d46d74d55977f2 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Resultant.lean | Resultant | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "ps_resultant_dvd_pow_eval_x",
"depth": 1,
"n_commands": 0,
"n_lines": 83,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n set m := natDegreeY A with hm\n let p : F[X] := X - C x\n let M0 : Matrix (Fin (n + m)) (Fin (n... | [
{
"name": "ps_sylvester_mul_vec_eq_coeff_add",
"text": "/-- The Sylvester matrix–vector product gives coefficients of `A * P + B * Q`. -/\nlemma ps_sylvester_mul_vec_eq_coeff_add {R : Type} [CommRing R]\n (A B : R[X]) (m n : ℕ)\n (hm : A.natDegree ≤ m) (hn : B.natDegree ≤ n)\n (v : Fin (n + m) → R)... | [
{
"name": "ps_resultant_dvd_pow_eval_x",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 91,
"n_chars": 5083,
"n_subproofs": 20,
"n_tactics": 90,
"cyclomatic": 6,
"n_automation": 26,
"n_rewrites": 8,
"n_structural": 9,
"automation_only": false,... | 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.CodingTheory.PolishchukSpielman.Degrees
import Mathlib.Algebra.Polynomial.OfFn
/-!
# Resultants and Sylvester matrices for Poli... | /-
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.CodingTheory.PolishchukSpielman.Degrees
import Mathlib.Algebra.Polynomial.OfFn
/-!
# Resultants and Sylvester matrices for Poli... | @@ -52,6 +52,21 @@
by_cases h : ((j : ℕ) ≤ (i : ℕ) ∧ (i : ℕ) ≤ (j : ℕ) + n) <;>
simp [sylvester, of_apply, coeff_map, h]
+/-- The Sylvester matrix–vector product gives coefficients of `A * P + B * Q`. -/
+lemma ps_sylvester_mul_vec_eq_coeff_add {R : Type} [CommRing R]
+ (A B : R[X]) (m n : ℕ)
+ (hm ... | {
"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_cae0da9ef99c_1 | a2656db13decad12 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Resultant.lean | Resultant | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "ps_resultant_dvd_pow_eval_x",
"depth": 1,
"n_commands": 0,
"n_lines": 83,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n set m := natDegreeY A with hm\n let p : F[X] := X - C x\n let M0 : Matrix (Fin (n + m)) (Fin (n... | [
{
"name": "ps_sylvester_mul_vec_eq_coeff_add",
"text": "/-- The Sylvester matrix–vector product gives coefficients of `A * P + B * Q`. -/\nlemma ps_sylvester_mul_vec_eq_coeff_add {R : Type} [CommRing R]\n (A B : R[X]) (m n : ℕ)\n (hm : A.natDegree ≤ m) (hn : B.natDegree ≤ n)\n (v : Fin (n + m) → R)... | [
{
"name": "ps_resultant_dvd_pow_eval_y",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 17,
"n_chars": 728,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
... | 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.CodingTheory.PolishchukSpielman.Degrees
import Mathlib.Algebra.Polynomial.OfFn
/-!
# Resultants and Sylvester matrices for Poli... | /-
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.CodingTheory.PolishchukSpielman.Degrees
import Mathlib.Algebra.Polynomial.OfFn
/-!
# Resultants and Sylvester matrices for Poli... | @@ -52,6 +52,21 @@
by_cases h : ((j : ℕ) ≤ (i : ℕ) ∧ (i : ℕ) ≤ (j : ℕ) + n) <;>
simp [sylvester, of_apply, coeff_map, h]
+/-- The Sylvester matrix–vector product gives coefficients of `A * P + B * Q`. -/
+lemma ps_sylvester_mul_vec_eq_coeff_add {R : Type} [CommRing R]
+ (A B : R[X]) (m n : ℕ)
+ (hm ... | {
"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_cae0da9ef99c_2 | a5b1c21040b58eb5 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Resultant.lean | Resultant | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "ps_resultant_dvd_pow_eval_x",
"depth": 1,
"n_commands": 0,
"n_lines": 83,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n set m := natDegreeY A with hm\n let p : F[X] := X - C x\n let M0 : Matrix (Fin (n + m)) (Fin (n... | [
{
"name": "ps_sylvester_mul_vec_eq_coeff_add",
"text": "/-- The Sylvester matrix–vector product gives coefficients of `A * P + B * Q`. -/\nlemma ps_sylvester_mul_vec_eq_coeff_add {R : Type} [CommRing R]\n (A B : R[X]) (m n : ℕ)\n (hm : A.natDegree ≤ m) (hn : B.natDegree ≤ n)\n (v : Fin (n + m) → R)... | [
{
"name": "ps_resultant_ne_zero_of_is_rel_prime",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 70,
"n_chars": 3706,
"n_subproofs": 19,
"n_tactics": 75,
"cyclomatic": 4,
"n_automation": 33,
"n_rewrites": 11,
"n_structural": 16,
"automation_on... | 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.CodingTheory.PolishchukSpielman.Degrees
import Mathlib.Algebra.Polynomial.OfFn
/-!
# Resultants and Sylvester matrices for Poli... | /-
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.CodingTheory.PolishchukSpielman.Degrees
import Mathlib.Algebra.Polynomial.OfFn
/-!
# Resultants and Sylvester matrices for Poli... | @@ -30,9 +30,88 @@
open Polynomial.Bivariate Polynomial Matrix
open scoped BigOperators
+/-- The Sylvester matrix–vector product gives coefficients of `A * P + B * Q`. -/
+lemma ps_sylvester_mul_vec_eq_coeff_add {R : Type} [CommRing R]
+ (A B : R[X]) (m n : ℕ)
+ (hm : A.natDegree ≤ m) (hn : B.natDegree ≤ 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_b8f009bf4d5b_0 | 4802d9205c375e67 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/CosetFftDomain/Subdomain.lean | Subdomain | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "pow_mem_of_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 64,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨k, hk⟩ :\n ∃ k : Fin (2 ^ (n - j)), x =\n (mkSubgroupUnit ω (CosetFftDomainClass.subdomain_embed j k) : F) ... | [
{
"name": "mkSubgroupUnit_pow",
"text": "/-- Powers of normalized subgroup units correspond to additive multiples of their indices. -/\nprivate lemma mkSubgroupUnit_pow (ω : D) (a : Fin (2 ^ n)) (k : ℕ) :\n (mkSubgroupUnit ω a : F) ^ k = mkSubgroupUnit ω (k • a) := by\n induction k\n · aesop (add simp [p... | [
{
"name": "pow_mem_of_mem",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 69,
"n_chars": 2961,
"n_subproofs": 8,
"n_tactics": 65,
"cyclomatic": 2,
"n_automation": 22,
"n_rewrites": 5,
"n_structural": 5,
"automation_only": false,
"max_nest... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Tactic.CancelDenoms.Core
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Tactic.CancelDenoms.Core
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group... | @@ -148,6 +148,23 @@
mem_def,
CosetFftDomain.eval_coset_fft_domain_eq_eval_generator_mul_domain])
+/-- Powers of normalized subgroup units correspond to additive multiples of their indices. -/
+private lemma mkSubgroupUnit_pow (ω : D) (a : Fin (2 ^ n)) (k : ℕ) :
+ (mkSubgroupUnit ω a : 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_b8f009bf4d5b_1 | 24ffe949b0c64756 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/CosetFftDomain/Subdomain.lean | Subdomain | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "pow_mem_subdomain_of_mem_subdomain_0",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have key := pow_mem_of_mem (i := i) (j := 0) (h := h) (by omega)\n rw [mem_subdomain_of_eq_vals (j :=... | [
{
"name": "mem_subdomain_of_eq_vals",
"text": "/-- Membership in subdomains is invariant under equal subdomain indices. -/\nlemma mem_subdomain_of_eq_vals\n {i j : ℕ}\n (hij : i = j) :\n x ∈ subdomain ω i ↔ x ∈ subdomain ω j := by rw [hij]\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 203,
... | [
{
"name": "pow_mem_subdomain_of_mem_subdomain_0",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 9,
"n_chars": 360,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": fa... | 5 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Tactic.CancelDenoms.Core
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Tactic.CancelDenoms.Core
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group... | @@ -129,6 +129,12 @@
variable {ω : D} {x : F}
+/-- Membership in subdomains is invariant under equal subdomain indices. -/
+lemma mem_subdomain_of_eq_vals
+ {i j : ℕ}
+ (hij : i = j) :
+ x ∈ subdomain ω i ↔ x ∈ subdomain ω j := by rw [hij]
+
/-- The coset generator of the `i`th subdomain is `ω 0 ^ 2 ^ i`. -/
... | {
"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_b8f009bf4d5b_2 | 927eb60061efdd24 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/CosetFftDomain/Subdomain.lean | Subdomain | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "pow_mem_subdomain_of_mem_subdomain_0",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have key := pow_mem_of_mem (i := i) (j := 0) (h := h) (by omega)\n rw [mem_subdomain_of_eq_vals (j :=... | [
{
"name": "mem_subdomain_of_eq_vals",
"text": "/-- Membership in subdomains is invariant under equal subdomain indices. -/\nlemma mem_subdomain_of_eq_vals\n {i j : ℕ}\n (hij : i = j) :\n x ∈ subdomain ω i ↔ x ∈ subdomain ω j := by rw [hij]\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 203,
... | [
{
"name": "pow_mem_subdomain_of_mem_subdomain_0_toFinset",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 8,
"n_chars": 350,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_... | 6 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Tactic.CancelDenoms.Core
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Tactic.CancelDenoms.Core
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group... | @@ -129,6 +129,12 @@
variable {ω : D} {x : F}
+/-- Membership in subdomains is invariant under equal subdomain indices. -/
+lemma mem_subdomain_of_eq_vals
+ {i j : ℕ}
+ (hij : i = j) :
+ x ∈ subdomain ω i ↔ x ∈ subdomain ω j := by rw [hij]
+
/-- The coset generator of the `i`th subdomain is `ω 0 ^ 2 ^ i`. -/
... | {
"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_7da136b4e6a5_0 | 1fbc04d2194a2808 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Interface.lean | Interface | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "natDegree_polynomialOfCoeffs_deg_lt_deg",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n aesop (add simp polynomialOfCoeffs)\n (add safe apply natDegree_lt_of_lbounded_zero_coeff)",... | [
{
"name": "natDegree_lt_of_lbounded_zero_coeff",
"text": "lemma natDegree_lt_of_lbounded_zero_coeff {p : F[X]} [NeZero deg]\n (h : ∀ i, deg ≤ i → p.coeff i = 0) : p.natDegree < deg := by\n aesop (add unsafe [(by by_contra), (by specialize h p.natDegree)])\n\n",
"fan_in": 1,
"n_lines": 5,
"n_... | [
{
"name": "natDegree_polynomialOfCoeffs_deg_lt_deg",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 250,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only":... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: ArkLib Contributors
-/
import ArkLib.Data.Fin.Lift
import Mathlib.RingTheory.Polynomial.Basic
/-! # Polynomial Coefficient Interfaces -/
section PolynomialInterface
open P... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: ArkLib Contributors
-/
import ArkLib.Data.Fin.Lift
import Mathlib.RingTheory.Polynomial.Basic
/-! # Polynomial Coefficient Interfaces -/
section PolynomialInterface
open P... | @@ -14,6 +14,10 @@
variable {F : Type*} [Semiring F] {deg : ℕ} {coeffs : Fin deg → F}
+lemma natDegree_lt_of_lbounded_zero_coeff {p : F[X]} [NeZero deg]
+ (h : ∀ i, deg ≤ i → p.coeff i = 0) : p.natDegree < deg := by
+ aesop (add unsafe [(by by_contra), (by specialize h p.natDegree)])
+
def coeffsOfPolynomial ... | {
"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_7da136b4e6a5_1 | 923934c1a4a2b9ca | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Interface.lean | Interface | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "polynomialOfCoeffs_coeffsOfPolynomial",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext x; symm\n aesop (add simp [polynomialOfCoeffs, coeffsOfPolynomial, coeff_polynomialOfCoeffs_eq_c... | [
{
"name": "coeff_polynomialOfCoeffs_eq_coeffs'",
"text": "lemma coeff_polynomialOfCoeffs_eq_coeffs' :\n (polynomialOfCoeffs coeffs).coeff = fun x ↦ if h : x < deg then coeffs ⟨x, h⟩ else 0 := by\n aesop (add simp polynomialOfCoeffs)\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 184,
"n_sub... | [
{
"name": "polynomialOfCoeffs_coeffsOfPolynomial",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 351,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": f... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: ArkLib Contributors
-/
import ArkLib.Data.Fin.Lift
import Mathlib.RingTheory.Polynomial.Basic
/-! # Polynomial Coefficient Interfaces -/
section PolynomialInterface
open P... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: ArkLib Contributors
-/
import ArkLib.Data.Fin.Lift
import Mathlib.RingTheory.Polynomial.Basic
/-! # Polynomial Coefficient Interfaces -/
section PolynomialInterface
open P... | @@ -52,6 +52,10 @@
Fin.liftF' (polynomialOfCoeffs coeffs).coeff = coeffs := by
aesop (add simp [Fin.liftF', polynomialOfCoeffs])
+lemma coeff_polynomialOfCoeffs_eq_coeffs' :
+ (polynomialOfCoeffs coeffs).coeff = fun x ↦ if h : x < deg then coeffs ⟨x, h⟩ else 0 := by
+ aesop (add simp polynomialOfCoeffs)
+... | {
"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_7da136b4e6a5_2 | 359186269a00eba4 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/Interface.lean | Interface | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "polynomialOfCoeffs_coeffsOfPolynomial",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext x; symm\n aesop (add simp [polynomialOfCoeffs, coeffsOfPolynomial, coeff_polynomialOfCoeffs_eq_c... | [
{
"name": "coeff_polynomialOfCoeffs_eq_coeffs'",
"text": "lemma coeff_polynomialOfCoeffs_eq_coeffs' :\n (polynomialOfCoeffs coeffs).coeff = fun x ↦ if h : x < deg then coeffs ⟨x, h⟩ else 0 := by\n aesop (add simp polynomialOfCoeffs)\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 184,
"n_sub... | [
{
"name": "coeffsOfPolynomial_polynomialOfCoeffs",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 262,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": f... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: ArkLib Contributors
-/
import ArkLib.Data.Fin.Lift
import Mathlib.RingTheory.Polynomial.Basic
/-! # Polynomial Coefficient Interfaces -/
section PolynomialInterface
open P... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: ArkLib Contributors
-/
import ArkLib.Data.Fin.Lift
import Mathlib.RingTheory.Polynomial.Basic
/-! # Polynomial Coefficient Interfaces -/
section PolynomialInterface
open P... | @@ -52,6 +52,10 @@
Fin.liftF' (polynomialOfCoeffs coeffs).coeff = coeffs := by
aesop (add simp [Fin.liftF', polynomialOfCoeffs])
+lemma coeff_polynomialOfCoeffs_eq_coeffs' :
+ (polynomialOfCoeffs coeffs).coeff = fun x ↦ if h : x < deg then coeffs ⟨x, h⟩ else 0 := by
+ aesop (add simp polynomialOfCoeffs)
+... | {
"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_2152ec48008d_0 | de5ebbf48205915d | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "numVars_eq_of_gt_one",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n convert card_weigthBoundIndices_eq_sum D hk using 1\n have h_simp : ∑ j ∈ range (D / (k - 1) + 1), (D - (k -... | [
{
"name": "card_weigthBoundIndices_eq_sum",
"text": "/-- The number of variables is the sum over j of the number of valid i's. -/\nlemma card_weigthBoundIndices_eq_sum (D : ℕ) (hk : 1 < k) :\n (weigthBoundIndices k D).card = ∑ j ∈ range (D / (k - 1) + 1), (D - (k - 1) * j + 1) := by\n have h_split : (... | [
{
"name": "numVars_eq_of_gt_one",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 37,
"n_chars": 1916,
"n_subproofs": 2,
"n_tactics": 35,
"cyclomatic": 1,
"n_automation": 12,
"n_rewrites": 12,
"n_structural": 5,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -61,9 +61,76 @@
/-- The number of variables in the Guruswami-Sudan linear system. -/
def numVars (k D : ℕ) : ℕ := (weigthBoundIndices k D).card
+/-- The number of variables is the sum over j of the number of valid i's. -/
+lemma card_weigthBoundIndices_eq_sum (D : ℕ) (hk : 1 < k) :
+ (weigthBoundIndices k D).... | {
"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_2152ec48008d_1 | b64aa420ed630637 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "numVars_lower_bound_tight",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_numVars_def : numVars k D =\n ((D / (k - 1)) + 1) * (2 * D + 2 - (k - 1) * (D / (k - 1))) / ... | [
{
"name": "numVars_eq_of_gt_one",
"text": "/-- Closed form for the number of variables when k > 1. -/\nlemma numVars_eq_of_gt_one {D : ℕ} (hk : 1 < k) :\n numVars k D = let L := D / (k - 1); (L + 1) * (2 * D + 2 - (k - 1) * L) / 2 := by\n convert card_weigthBoundIndices_eq_sum D hk using 1\n ha... | [
{
"name": "numVars_lower_bound_tight",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 23,
"n_chars": 1030,
"n_subproofs": 1,
"n_tactics": 24,
"cyclomatic": 9,
"n_automation": 9,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -96,6 +96,42 @@
simp_all
exact h_split.trans (sum_congr rfl h_inner)
+/-- Closed form for the number of variables when k > 1. -/
+lemma numVars_eq_of_gt_one {D : ℕ} (hk : 1 < k) :
+ numVars k D = let L := D / (k - 1); (L + 1) * (2 * D + 2 - (k - 1) * L) / 2 := by
+ convert card_weigthBoundIndic... | {
"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_2152ec48008d_2 | f80e632d3945a533 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 2 | [
{
"theorem_name": "numVars_gt_numConstraints_of_gt_one",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n set D := proximity_gap_degree_bound k n m\n have hD : ((D + 1)^2 : ℝ) > ((m : ℝ) + 1 / 2)^2 *... | [
{
"name": "proximity_gap_degree_bound_sq_gt",
"text": "/-- Lower bound for the square of (D+1). Specifically, (D+1)^2 > (m+1/2)^2 * (k+1) * n. -/\nlemma proximity_gap_degree_bound_sq_gt (hn : n ≠ 0) :\n ((proximity_gap_degree_bound k n m : ℝ) + 1) ^ 2 >\n (m + 1 / 2) ^ 2 * (k + 1) * n := by\n s... | [
{
"name": "numVars_gt_numConstraints_of_gt_one",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 27,
"n_chars": 1536,
"n_subproofs": 5,
"n_tactics": 28,
"cyclomatic": 4,
"n_automation": 7,
"n_rewrites": 13,
"n_structural": 5,
"automation_only":... | 5 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -197,10 +197,30 @@
section numVars_gt_numConstraints
+/-- Lower bound for the square of (D+1). Specifically, (D+1)^2 > (m+1/2)^2 * (k+1) * n. -/
+lemma proximity_gap_degree_bound_sq_gt (hn : n ≠ 0) :
+ ((proximity_gap_degree_bound k n m : ℝ) + 1) ^ 2 >
+ (m + 1 / 2) ^ 2 * (k + 1) * n := by
+ set D ... | {
"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_2152ec48008d_3 | d301241c7a282aa9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "linearIndependent_monomials",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply _root_.linearIndependent_iff.mpr\n intro l hl\n ext ⟨i, j⟩\n simp only [Finsupp.coe_zero, Pi.z... | [
{
"name": "coeff_linearCombination_monomial",
"text": "/-- The coefficient of X^i Y^j in a linear combination of monomials is the coefficient\n of the combination. -/\nlemma coeff_linearCombination_monomial (c : ℕ × ℕ →₀ F) (i j : ℕ) :\n ((linearCombination F (fun p ↦ monomial (F := F) p.1 p.2) c).coe... | [
{
"name": "linearIndependent_monomials",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 421,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -380,9 +380,28 @@
section neZero
+/-- The coefficient of X^i Y^j in a linear combination of monomials is the coefficient
+ of the combination. -/
+lemma coeff_linearCombination_monomial (c : ℕ × ℕ →₀ F) (i j : ℕ) :
+ ((linearCombination F (fun p ↦ monomial (F := F) p.1 p.2) c).coeff j).coeff i = c (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_2152ec48008d_4 | f73e01445811585f | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "numVars_gt_numConstraints",
"depth": 1,
"n_commands": 0,
"n_lines": 59,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hk : k ≤ 1\n · interval_cases k <;> norm_num [numVars_eq_sq, numConstraints]\n · unfold proximity_g... | [
{
"name": "numVars_gt_numConstraints_of_gt_one",
"text": "lemma numVars_gt_numConstraints_of_gt_one (hn : n ≠ 0) (hk : 1 < k) (hm : 1 ≤ m) :\n numVars k (proximity_gap_degree_bound k n m) > numConstraints n m := by\n set D := proximity_gap_degree_bound k n m\n have hD : ((D + 1)^2 : ℝ) > ((m : ... | [
{
"name": "polySol_ne_zero",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 11,
"n_lines": 14,
"n_chars": 629,
"n_subproofs": 3,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nest... | 9 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -216,6 +216,32 @@
nlinarith [show 0 < (m + 1 / 2 : ℝ) * √((k + 1) * n) by
positivity, Real.mul_self_sqrt (show 0 ≤ (k + 1 : ℝ) * n by positivity)]
+lemma numVars_gt_numConstraints_of_gt_one (hn : n ≠ 0) (hk : 1 < k) (hm : 1 ≤ m) :
+ numVars k (proximity_gap_degree_bound k n m) > numConstraints 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_2152ec48008d_5 | ec925c43d0627f0f | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "natWeightedDegree_monomial_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n natWeightedDegree_monomial i j u v",
"n_chars": 39,
"n_subproofs": 0,
"n_tactics": 1,
"cycloma... | [
{
"name": "natWeightedDegree_monomial",
"text": "/-- The weighted degree of a monomial X^i Y^j is u*i + v*j. -/\nlemma natWeightedDegree_monomial (i j u v : ℕ) :\n natWeightedDegree (monomial (F := F) i j) u v = u * i + v * j := by\n classical\n simp only [natWeightedDegree, monomial]\n refine l... | [
{
"name": "natWeightedDegree_monomial_eq",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 226,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -385,8 +385,23 @@
section weightedDegree
/-- The weighted degree of a monomial X^i Y^j is u*i + v*j. -/
+lemma natWeightedDegree_monomial (i j u v : ℕ) :
+ natWeightedDegree (monomial (F := F) i j) u v = u * i + v * j := by
+ classical
+ simp only [natWeightedDegree, monomial]
+ refine le_antisymm ?_... | {
"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_2152ec48008d_6 | fb3d6f1d47dc4a59 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "natWeightedDegree_sum_le",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n induction s using Finset.induction with\n | empty =>\n simp only [sum_empty, sup_empty, Nat.bot_... | [
{
"name": "natWeightedDegree_add_le",
"text": "/-- The weighted degree of a sum is at most the maximum of the weighted degrees. -/\nlemma natWeightedDegree_add_le (p q : F[X][Y]) (u v : ℕ) :\n natWeightedDegree (p + q) u v ≤ max (natWeightedDegree p u v) (natWeightedDegree q u v) := by\n refine Finset.s... | [
{
"name": "natWeightedDegree_sum_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 694,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -384,6 +384,30 @@
section weightedDegree
+/-- The weighted degree of a sum is at most the maximum of the weighted degrees. -/
+lemma natWeightedDegree_add_le (p q : F[X][Y]) (u v : ℕ) :
+ natWeightedDegree (p + q) u v ≤ max (natWeightedDegree p u v) (natWeightedDegree q u v) := by
+ refine Finset.sup_le fun... | {
"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_2152ec48008d_7 | e4db6841fe97ea56 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "natWeightedDegree_coeffsToPoly_le",
"depth": 1,
"n_commands": 0,
"n_lines": 21,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_comb : ∃ (s : Finset (ℕ × ℕ)) (f : ℕ × ℕ → F), (coeffsToPoly k D c) =\n ∑ p ∈ s, f p • (mono... | [
{
"name": "natWeightedDegree_sum_le",
"text": "/-- The weighted degree of a sum is bounded by the supremum of the weighted degrees. -/\nlemma natWeightedDegree_sum_le {ι : Type*} (s : Finset ι) (f : ι → F[X][Y]) (u v : ℕ) :\n natWeightedDegree (∑ i ∈ s, f i) u v ≤ s.sup (fun i ↦ natWeightedDegree (f i) u... | [
{
"name": "natWeightedDegree_coeffsToPoly_le",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 25,
"n_chars": 1343,
"n_subproofs": 2,
"n_tactics": 24,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 4,
"n_structural": 6,
"automation_only": fa... | 5 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -427,6 +427,19 @@
· exact Or.inr <| Finset.le_sup (f := fun m ↦ u * natDegree (q.coeff m) + v * m) <| by aesop
· simp at hm
+/-- The weighted degree of a sum is bounded by the supremum of the weighted degrees. -/
+lemma natWeightedDegree_sum_le {ι : Type*} (s : Finset ι) (f : ι → F[X][Y]) (u v : ℕ) :
+ na... | {
"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_2152ec48008d_8 | 58f36b7f83a3b468 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "natWeightedDegree_sum_le",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n induction s using Finset.induction with\n | empty =>\n simp only [sum_empty, sup_empty, Nat.bot_... | [
{
"name": "natWeightedDegree_add_le",
"text": "/-- The weighted degree of a sum is at most the maximum of the weighted degrees. -/\nlemma natWeightedDegree_add_le (p q : F[X][Y]) (u v : ℕ) :\n natWeightedDegree (p + q) u v ≤ max (natWeightedDegree p u v) (natWeightedDegree q u v) := by\n refine Finset.s... | [
{
"name": "polySol_weightedDegree_le",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 15,
"n_lines": 10,
"n_chars": 446,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 13 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -403,6 +403,30 @@
natWeightedDegree (monomial (F := F) i j) u v = u * i + v * j :=
natWeightedDegree_monomial i j u v
+/-- The weighted degree of a sum is at most the maximum of the weighted degrees. -/
+lemma natWeightedDegree_add_le (p q : F[X][Y]) (u v : ℕ) :
+ natWeightedDegree (p + q) u v ≤ max (... | {
"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_2152ec48008d_9 | 6e18ef023532086f | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 2 | [
{
"theorem_name": "numVars_gt_numConstraints_of_gt_one",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n set D := proximity_gap_degree_bound k n m\n have hD : ((D + 1)^2 : ℝ) > ((m : ℝ) + 1 / 2)^2 *... | [
{
"name": "proximity_gap_degree_bound_sq_gt",
"text": "/-- Lower bound for the square of (D+1). Specifically, (D+1)^2 > (m+1/2)^2 * (k+1) * n. -/\nlemma proximity_gap_degree_bound_sq_gt (hn : n ≠ 0) :\n ((proximity_gap_degree_bound k n m : ℝ) + 1) ^ 2 >\n (m + 1 / 2) ^ 2 * (k + 1) * n := by\n s... | [
{
"name": "polySol_roots",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 10,
"n_lines": 9,
"n_chars": 532,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting"... | 8 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -197,10 +197,30 @@
section numVars_gt_numConstraints
+/-- Lower bound for the square of (D+1). Specifically, (D+1)^2 > (m+1/2)^2 * (k+1) * n. -/
+lemma proximity_gap_degree_bound_sq_gt (hn : n ≠ 0) :
+ ((proximity_gap_degree_bound k n m : ℝ) + 1) ^ 2 >
+ (m + 1 / 2) ^ 2 * (k + 1) * n := by
+ set D ... | {
"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_2152ec48008d_10 | 1506335cf17526e8 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "rootMultiplicity_ge_of_shift_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 60,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_contra h_contra\n cases h : rootMultiplicity f x y\n · simp_all only [ne_eq, Bivariate.rootMultipli... | [
{
"name": "shift_eq_zero_iff",
"text": "/-- Shifting a polynomial by (x, y) results in the zero polynomial if and only if the\n original polynomial was zero. -/\nlemma shift_eq_zero_iff {F : Type} [Field F] (f : F[X][Y]) (x y : F) : shift f x y = 0 ↔ f = 0 := by\n constructor <;> intro h <;> simp_all on... | [
{
"name": "rootMultiplicity_ge_of_shift_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 66,
"n_chars": 3721,
"n_subproofs": 6,
"n_tactics": 63,
"cyclomatic": 3,
"n_automation": 16,
"n_rewrites": 6,
"n_structural": 21,
"automation_only": ... | 1 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -392,6 +392,20 @@
section multiplicity
+/-- Shifting a polynomial by (x, y) results in the zero polynomial if and only if the
+ original polynomial was zero. -/
+lemma shift_eq_zero_iff {F : Type} [Field F] (f : F[X][Y]) (x y : F) : shift f x y = 0 ↔ f = 0 := by
+ constructor <;> intro h <;> simp_all only [... | {
"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_2152ec48008d_11 | 96c862626e22ef07 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "polySol_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have := Classical.choose_spec (exists_nonzero_solution k n m ωs f)\n have h_inj : Function.Injective (coeffsToPoly (F... | [
{
"name": "linearIndependent_monomials",
"text": "/-- The monomials are linearly independent. -/\nlemma linearIndependent_monomials :\n LinearIndependent F (fun p : ℕ × ℕ ↦ monomial (F := F) p.1 p.2) := by\n apply _root_.linearIndependent_iff.mpr\n intro l hl\n ext ⟨i, j⟩\n simp only [Finsupp... | [
{
"name": "polySol_multiplicity",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 14,
"n_lines": 13,
"n_chars": 593,
"n_subproofs": 2,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max... | 12 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -393,6 +393,16 @@
by_cases ha : a = i <;> by_cases hb : b = j <;> simp_all [coeff_monomial]
· exact fun h ↦ by left; exact Function.notMem_support.mp h
+/-- The monomials are linearly independent. -/
+lemma linearIndependent_monomials :
+ LinearIndependent F (fun p : ℕ × ℕ ↦ monomial (F := F) p.1 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_2152ec48008d_12 | c52796d838c6f5b0 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "orderAt_eval_ge",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n set Q_sh := (Q.comp (Y + C (C (P.eval x)))).map ((X + C x).compRingHom) with hQ_sh;\n set P_sh := P.comp (X + C x) - C (P... | [
{
"name": "eval_shifted_eq_shifted_eval",
"text": "/-- Evaluating the shifted bivariate polynomial at the shifted univariate polynomial\n is equivalent to shifting the result of the evaluation. -/\nlemma eval_shifted_eq_shifted_eval (Q : F[X][Y]) (P : F[X]) (x y : F) :\n let Q_sh := (Q.comp (Y + C (C ... | [
{
"name": "orderAt_eval_ge",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 22,
"n_chars": 1051,
"n_subproofs": 4,
"n_tactics": 22,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
"max_nest... | 2 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -420,6 +420,14 @@
if hi0 : (Q.coeff n).coeff i = 0 then by simp [hi0]
else h_div_term_all i n hi0
+/-- Evaluating the shifted bivariate polynomial at the shifted univariate polynomial
+ is equivalent to shifting the result of the evaluation. -/
+lemma eval_shifted_eq_shifted_eval (Q : F[X][Y]) (P : 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_2152ec48008d_13 | 9c8b917e2b3acc59 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "toPolynomial_degree_le",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [toPolynomial_def]\n obtain ⟨q, hq, hp⟩ := p.2\n have h_interpolate : (Lagrange.interpolate Finset.univ ... | [
{
"name": "interpolate_eq_of_degree_lt",
"text": "/-- If a polynomial `q` has degree less than `n`, then interpolating its values at `n`\n points recovers `q`. -/\nlemma interpolate_eq_of_degree_lt (q : F[X]) (hq : q.natDegree < n) :\n Lagrange.interpolate Finset.univ ωs (fun i ↦ q.eval (ωs i)) = q :=... | [
{
"name": "toPolynomial_degree_le",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 867,
"n_subproofs": 2,
"n_tactics": 13,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 4,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -402,12 +402,35 @@
def HasOrderAt (Q : F[X][Y]) (x y : F) (m : ℕ) : Prop :=
∀ i j, i + j < m → Bivariate.coeff (shift Q x y) i j = 0
+/-- If a polynomial `q` has degree less than `n`, then interpolating its values at `n`
+ points recovers `q`. -/
+lemma interpolate_eq_of_degree_lt (q : F[X]) (hq : q.natDegr... | {
"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_2152ec48008d_14 | 965f013df6cbaf97 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 2 | [
{
"theorem_name": "dvd_property",
"depth": 1,
"n_commands": 0,
"n_lines": 61,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n contrapose! h_dist with h_distots\n have hR_nonzero : (Q.eval (toPolynomial p)) ≠ 0 := by\n contrapose! h_distots\n... | [
{
"name": "toPolynomial_degree_le",
"text": "/-- The polynomial corresponding to a codeword has degree at most k-1. -/\nlemma toPolynomial_degree_le (hk : k + 1 ≤ n) (p : code ωs k) :\n (toPolynomial p).natDegree ≤ k - 1 := by\n rw [toPolynomial_def]\n obtain ⟨q, hq, hp⟩ := p.2\n have h_interpol... | [
{
"name": "dvd_property",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 8,
"n_lines": 72,
"n_chars": 3854,
"n_subproofs": 13,
"n_tactics": 66,
"cyclomatic": 2,
"n_automation": 12,
"n_rewrites": 5,
"n_structural": 17,
"automation_only": false,
"max_nest... | 8 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -530,6 +530,20 @@
norm_num
all_goals aesop
+/-- The polynomial corresponding to a codeword has degree at most k-1. -/
+lemma toPolynomial_degree_le (hk : k + 1 ≤ n) (p : code ωs k) :
+ (toPolynomial p).natDegree ≤ k - 1 := by
+ rw [toPolynomial_def]
+ obtain ⟨q, hq, hp⟩ := p.2
+ 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_2152ec48008d_15 | 0667b55fd11d4884 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 3 | [
{
"theorem_name": "numVars_gt_numConstraints_of_gt_one",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n set D := proximity_gap_degree_bound k n m\n have hD : ((D + 1)^2 : ℝ) > ((m : ℝ) + 1 / 2)^2 *... | [
{
"name": "card_constraintIndices",
"text": "/-- The indices of constraints are `m * (m + 1) / 2`. -/\nlemma card_constraintIndices (m : ℕ) : (constraintIndices m).card = m * (m + 1) / 2 := by\n rw [Nat.div_eq_of_eq_mul_left zero_lt_two]\n have h_eq : (constraintIndices m).card = ∑ s ∈ range m, (m - s) :=... | [
{
"name": "gs_numVars_gt_numConstraints_of_gt_one",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 28,
"n_chars": 1499,
"n_subproofs": 5,
"n_tactics": 28,
"cyclomatic": 4,
"n_automation": 8,
"n_rewrites": 13,
"n_structural": 5,
"automation_onl... | 5 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -175,6 +175,24 @@
/-- The number of constraints in the Guruswami-Sudan linear system. -/
def numConstraints (n m : ℕ) : ℕ := n * (constraintIndices m).card
+/-- The indices of constraints are `m * (m + 1) / 2`. -/
+lemma card_constraintIndices (m : ℕ) : (constraintIndices m).card = m * (m + 1) / 2 := by
+ rw [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_2152ec48008d_16 | b5cf5687b98e13d5 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/GuruswamiSudan/Basic.lean | Basic | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 2 | [
{
"theorem_name": "dvd_property",
"depth": 1,
"n_commands": 0,
"n_lines": 61,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n contrapose! h_dist with h_distots\n have hR_nonzero : (Q.eval (toPolynomial p)) ≠ 0 := by\n contrapose! h_distots\n... | [
{
"name": "toPolynomial_degree_le",
"text": "/-- The polynomial corresponding to a codeword has degree at most k-1. -/\nlemma toPolynomial_degree_le (hk : k + 1 ≤ n) (p : code ωs k) :\n (toPolynomial p).natDegree ≤ k - 1 := by\n rw [toPolynomial_def]\n obtain ⟨q, hq, hp⟩ := p.2\n have h_interpol... | [
{
"name": "gs_dvd_property",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 8,
"n_lines": 72,
"n_chars": 3786,
"n_subproofs": 13,
"n_tactics": 66,
"cyclomatic": 2,
"n_automation": 12,
"n_rewrites": 5,
"n_structural": 17,
"automation_only": false,
"max_n... | 8 | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | /-
Copyright (c) 2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Stefano Rocca
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Data.Real.Sqrt
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
imp... | @@ -530,6 +530,20 @@
norm_num
all_goals aesop
+/-- The polynomial corresponding to a codeword has degree at most k-1. -/
+lemma toPolynomial_degree_le (hk : k + 1 ≤ n) (p : code ωs k) :
+ (toPolynomial p).natDegree ≤ k - 1 := by
+ rw [toPolynomial_def]
+ obtain ⟨q, hq, hp⟩ := p.2
+ 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_58d76ae74dc2_0 | 8f60843977492259 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/Degrees.lean | Degrees | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "support_mul_C_le",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [mul_comm]\n exact support_C_mul_le p r",
"n_chars": 48,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic... | [
{
"name": "support_C_mul_le",
"text": "theorem support_C_mul_le (p : MvPolynomial σ R) (r : R) : (C r * p).support ⊆ p.support := by\n classical\n refine subset_trans (support_mul _ _) ?_\n rw [support_C]\n by_cases h : r = 0\n · simp [h]\n · simp [h, Finset.singleton_add, Finset.vadd_finset_def]\n\n"... | [
{
"name": "support_mul_C_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 143,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"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
-/
import Mathlib.Algebra.MvPolynomial.Degrees
import Mathlib.Algebra.MvPolynomial.Equiv
import Mathlib.Algebra.Group.Action.Pointwise.Finset
import ... | /-
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
-/
import Mathlib.Algebra.MvPolynomial.Degrees
import Mathlib.Algebra.MvPolynomial.Equiv
import Mathlib.Algebra.Group.Action.Pointwise.Finset
import ... | @@ -39,8 +39,18 @@
section Support
-theorem support_mul_C_le (p : MvPolynomial σ R) (r : R) : (p * C r).support ⊆ p.support := sorry
+theorem support_C_mul_le (p : MvPolynomial σ R) (r : R) : (C r * p).support ⊆ p.support := by
+ classical
+ refine subset_trans (support_mul _ _) ?_
+ rw [support_C]
+ by_cases ... | {
"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_58d76ae74dc2_1 | 5febdc9f77ed332e | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/Degrees.lean | Degrees | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "support_mul_C_le",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [mul_comm]\n exact support_C_mul_le p r",
"n_chars": 48,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic... | [
{
"name": "support_C_mul_le",
"text": "theorem support_C_mul_le (p : MvPolynomial σ R) (r : R) : (C r * p).support ⊆ p.support := by\n classical\n refine subset_trans (support_mul _ _) ?_\n rw [support_C]\n by_cases h : r = 0\n · simp [h]\n · simp [h, Finset.singleton_add, Finset.vadd_finset_def]\n\n"... | [
{
"name": "support_eval",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 407,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 4,
"n_structural": 3,
"automation_only": false,
"max_nesting"... | 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
-/
import Mathlib.Algebra.MvPolynomial.Degrees
import Mathlib.Algebra.MvPolynomial.Equiv
import Mathlib.Algebra.Group.Action.Pointwise.Finset
import ... | /-
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
-/
import Mathlib.Algebra.MvPolynomial.Degrees
import Mathlib.Algebra.MvPolynomial.Equiv
import Mathlib.Algebra.Group.Action.Pointwise.Finset
import ... | @@ -39,8 +39,18 @@
section Support
-theorem support_mul_C_le (p : MvPolynomial σ R) (r : R) : (p * C r).support ⊆ p.support := sorry
+theorem support_C_mul_le (p : MvPolynomial σ R) (r : R) : (C r * p).support ⊆ p.support := by
+ classical
+ refine subset_trans (support_mul _ _) ?_
+ rw [support_C]
+ by_cases ... | {
"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_58d76ae74dc2_2 | 35e4ae1b9658e967 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/Degrees.lean | Degrees | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "degrees_mul_C_le",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [mul_comm]\n exact degrees_C_mul_le p c",
"n_chars": 48,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic... | [
{
"name": "degrees_C_mul_le",
"text": "theorem degrees_C_mul_le (p : MvPolynomial σ R) (c : R) : (C c * p).degrees ≤ p.degrees := by\n refine le_trans degrees_mul_le ?_\n simp [degrees_C]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 153,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic... | [
{
"name": "degrees_mul_C_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 143,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"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
-/
import Mathlib.Algebra.MvPolynomial.Degrees
import Mathlib.Algebra.MvPolynomial.Equiv
import Mathlib.Algebra.Group.Action.Pointwise.Finset
import ... | /-
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
-/
import Mathlib.Algebra.MvPolynomial.Degrees
import Mathlib.Algebra.MvPolynomial.Equiv
import Mathlib.Algebra.Group.Action.Pointwise.Finset
import ... | @@ -47,8 +47,14 @@
section Degrees
-theorem degrees_mul_C_le (p : MvPolynomial σ R) (c : R) : (p * C c).degrees ≤ p.degrees := sorry
+theorem degrees_C_mul_le (p : MvPolynomial σ R) (c : R) : (C c * p).degrees ≤ p.degrees := by
+ refine le_trans degrees_mul_le ?_
+ simp [degrees_C]
+theorem degrees_mul_C_le (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_58d76ae74dc2_3 | 7e081a35cb6c4479 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/Degrees.lean | Degrees | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "degrees_mul_C_le",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [mul_comm]\n exact degrees_C_mul_le p c",
"n_chars": 48,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic... | [
{
"name": "degrees_C_mul_le",
"text": "theorem degrees_C_mul_le (p : MvPolynomial σ R) (c : R) : (C c * p).degrees ≤ p.degrees := by\n refine le_trans degrees_mul_le ?_\n simp [degrees_C]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 153,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic... | [
{
"name": "degrees_eval",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 409,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 4,
"n_structural": 3,
"automation_only": false,
"max_nesting"... | 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
-/
import Mathlib.Algebra.MvPolynomial.Degrees
import Mathlib.Algebra.MvPolynomial.Equiv
import Mathlib.Algebra.Group.Action.Pointwise.Finset
import ... | /-
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
-/
import Mathlib.Algebra.MvPolynomial.Degrees
import Mathlib.Algebra.MvPolynomial.Equiv
import Mathlib.Algebra.Group.Action.Pointwise.Finset
import ... | @@ -47,8 +47,14 @@
section Degrees
-theorem degrees_mul_C_le (p : MvPolynomial σ R) (c : R) : (p * C c).degrees ≤ p.degrees := sorry
+theorem degrees_C_mul_le (p : MvPolynomial σ R) (c : R) : (C c * p).degrees ≤ p.degrees := by
+ refine le_trans degrees_mul_le ?_
+ simp [degrees_C]
+theorem degrees_mul_C_le (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_d686f16365cb_0 | 48e75181d152af3e | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/ProofSystem/RingSwitching/General.lean | General | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "fullOracleReduction_perfectCompleteness",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply OracleReduction.append_perfectCompleteness (Oₛ₃:=by\n exact fun _ ↦ OracleInterface.instDe... | [
{
"name": "batchingCore_perfectCompleteness",
"text": "lemma batchingCore_perfectCompleteness :\n (batchingCoreReduction κ L K P ℓ ℓ' h_l mlIOPCS).perfectCompleteness\n (pSpec := pSpecLargeFieldReduction κ L K P ℓ')\n (relIn := BatchingPhase.batchingInputRelation κ L K P ℓ ℓ' h_l mlIOPCS.toAbstractOStmtI... | [
{
"name": "fullOracleReduction_perfectCompleteness",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 542,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 4,
"automation_only"... | 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.ProofSystem.RingSwitching.Spec
import ArkLib.ProofSystem.RingSwitching.BatchingPhase
import ArkLib.ProofSystem.RingSwitching.Sumchec... | /-
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.ProofSystem.RingSwitching.Spec
import ArkLib.ProofSystem.RingSwitching.BatchingPhase
import ArkLib.ProofSystem.RingSwitching.Sumchec... | @@ -103,6 +103,19 @@
variable {σ : Type} (init : ProbComp σ) {impl : QueryImpl []ₒ (StateT σ ProbComp)}
omit [(i : mlIOPCS.pSpec.ChallengeIdx) → SampleableType (mlIOPCS.pSpec.Challenge i)] in
+lemma batchingCore_perfectCompleteness :
+ (batchingCoreReduction κ L K P ℓ ℓ' h_l mlIOPCS).perfectCompleteness
+ (pSpec ... | {
"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_50add42ac415_0 | 6f6f2c0fd340862e | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/CosetFftDomain/Mem.lean | Mem | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 4 | [
{
"theorem_name": "mem_self",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by simp [mem_def]",
"n_chars": 18,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewr... | [
{
"name": "mem_def",
"text": "/-- Unfold membership in a class-level coset FFT domain. -/\nlemma mem_def : x ∈ ω ↔ ∃ i, ω i = x := by rfl\n\n",
"fan_in": 4,
"n_lines": 4,
"n_chars": 116,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
... | [
{
"name": "mem_self",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 140,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 1
}... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.TypeTags.Basic
import Mathlib.Algebra.G... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.TypeTags.Basic
import Mathlib.Algebra.G... | @@ -62,21 +62,29 @@
variable {D : Type} [FunLike D ι F] [CosetFftDomainClass D ι F] {ω : D}
variable {x : F}
+/-- Unfold membership in a class-level coset FFT domain. -/
+lemma mem_def : x ∈ ω ↔ ∃ i, ω i = x := by rfl
+
/-- Every value of a coset FFT domain belongs to that domain. -/
@[simp high]
lemma mem_self ... | {
"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_50add42ac415_1 | 4c61c185c6c87bdb | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/CosetFftDomain/Mem.lean | Mem | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "mem_toFinset_iff_exists_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [mem_iff_exists_mul]",
"n_chars": 31,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
... | [
{
"name": "mem_iff_exists_mul",
"text": "/-- Membership in a concrete coset FFT domain means\n being a coset generator times some subgroup element. -/\nlemma mem_iff_exists_mul :\n x ∈ ω ↔ ∃ i, x = ω.cosetGenerator * ω.subgroupDomain i := by\n aesop (add simp [Membership.mem])\n\n",
"fan_in": 1,
... | [
{
"name": "mem_toFinset_iff_exists_mul",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 311,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.TypeTags.Basic
import Mathlib.Algebra.G... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.TypeTags.Basic
import Mathlib.Algebra.G... | @@ -116,10 +116,17 @@
variable {ω : CosetFftDomain ι F} {x : F}
+/-- Membership in a concrete coset FFT domain means
+ being a coset generator times some subgroup element. -/
+lemma mem_iff_exists_mul :
+ x ∈ ω ↔ ∃ i, x = ω.cosetGenerator * ω.subgroupDomain i := by
+ aesop (add simp [Membership.mem])
+
/-- Mem... | {
"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_48b630c37be5_0 | 71a8ddbd1741a2f7 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Core/Modulus.lean | Modulus | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "powTwoCyclotomic_natDegree",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CompPoly.CPolynomial.natDegree_toPoly, powTwoCyclotomic_toPoly,\n show (Polynomial.X ^ 2 ^ α + 1 : Polyno... | [
{
"name": "powTwoCyclotomic_toPoly",
"text": "/-- The power-of-two modulus, as a Mathlib polynomial, is `X^{2^α} + 1`. -/\ntheorem powTwoCyclotomic_toPoly (α : ℕ) :\n (powTwoCyclotomic (R := R) α).φ.toPoly = Polynomial.X ^ (2 ^ α) + 1 := by\n change (CPolynomial.X ^ (2 ^ α) + 1 : CPolynomial R).toPoly =... | [
{
"name": "powTwoCyclotomic_natDegree",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 417,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"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: Tobias Rothmann
-/
import ArkLib.ToCompPoly.Univariate.Basic
import Mathlib.RingTheory.Polynomial.Cyclotomic.Basic
/-!
# Cyclotomic Moduli over `CPolynomial`
This file defi... | /-
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.ToCompPoly.Univariate.Basic
import Mathlib.RingTheory.Polynomial.Cyclotomic.Basic
/-!
# Cyclotomic Moduli over `CPolynomial`
This file defi... | @@ -119,9 +119,18 @@
rw [hX, cyclotomic_prime_pow_eq_geom_sum (R := R) (p := 2) (n := α) Nat.prime_two]
rw [Finset.sum_range_succ, Finset.sum_range_one, pow_zero, pow_one, _root_.add_comm]
+/-- The power-of-two modulus, as a Mathlib polynomial, is `X^{2^α} + 1`. -/
+theorem powTwoCyclotomic_toPoly (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_4d12810c234e_0 | e150d9d2793fa4f4 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 2 | [
{
"theorem_name": "galoisAut_Xpow",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hi' : i < (powTwoCyclotomic (R := R) α).φ.natDegree := by\n rwa [powTwoCyclotomic_natDegree]\n have key : (∑ kk ∈ ... | [
{
"name": "Xpow_coeff_of_lt",
"text": "/-- For `i < 2^α` (below the modulus degree), `X^i` is already reduced, so its `j`-th coefficient\nis the Kronecker delta `[j = i]`. -/\ntheorem Xpow_coeff_of_lt (α : ℕ) {i : ℕ} (hi : i < 2 ^ α) (j : ℕ) :\n (Xpow (powTwoCyclotomic (R := R) α) i).1.coeff j = if j = i... | [
{
"name": "galoisAut_Xpow",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 27,
"n_chars": 1583,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -44,6 +44,22 @@
def Xpow (Φ : CyclotomicModulus R) [IsCyclotomic Φ] (i : ℕ) : Rq Φ :=
Rq.mk Φ (CompPoly.CPolynomial.monomial i 1)
+/-- For `i < 2^α` (below the modulus degree), `X^i` is already reduced, so its `j`-th coefficient
+is the Kronecker delta `[j = i]`. -/
+theorem Xpow_coeff_of_lt (α : ℕ) {i : ℕ} (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_4d12810c234e_1 | e4791b87fc72202c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 5 | [
{
"theorem_name": "Xpow_add",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Rq.toQuotient_injective Φ\n have hmul : (Xpow Φ a * Xpow Φ b).toQuotient\n = (Xpow Φ a).toQuotient * (Xpow Φ b).toQuot... | [
{
"name": "Xpow_toQuotient",
"text": "/-- `X^n` lifts to the class of `X^n` in the semantic quotient. -/\ntheorem Xpow_toQuotient (Φ : CyclotomicModulus R) [IsCyclotomic Φ] (n : ℕ) :\n (Xpow Φ n).toQuotient = Ideal.Quotient.mk Φ.modIdeal (Polynomial.X ^ n) := by\n rw [Xpow, Rq.toQuotient_mk, quotientHom... | [
{
"name": "Xpow_add",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 413,
"n_subproofs": 1,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nesting": 6
... | 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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -44,24 +44,59 @@
def Xpow (Φ : CyclotomicModulus R) [IsCyclotomic Φ] (i : ℕ) : Rq Φ :=
Rq.mk Φ (CompPoly.CPolynomial.monomial i 1)
+/-- `X^n` lifts to the class of `X^n` in the semantic quotient. -/
+theorem Xpow_toQuotient (Φ : CyclotomicModulus R) [IsCyclotomic Φ] (n : ℕ) :
+ (Xpow Φ n).toQuotient = Ideal... | {
"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_4d12810c234e_2 | 0642e1547832f3b9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 2 | [
{
"theorem_name": "Xpow_fold",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv_lhs => rw [← Nat.div_add_mod n (2 ^ α)]\n rw [Xpow_add, Xpow_mul, Xpow_natDegree]",
"n_chars": 95,
"n_subproofs": 0... | [
{
"name": "Xpow_natDegree",
"text": "/-- **The key relation `X^{2^α} = -1`** (`X^d = -1`), proven via the quotient: `X^d + 1` is the\nmodulus, so it vanishes in the quotient. -/\ntheorem Xpow_natDegree (α : ℕ) : Xpow (powTwoCyclotomic (R := R) α) (2 ^ α) = -1 := by\n apply Rq.toQuotient_injective (powTwoCy... | [
{
"name": "Xpow_fold",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 11,
"n_chars": 474,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 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 ArkLib.Data.Lattices.CyclotomicRing.Galois.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -71,11 +71,30 @@
simp only [Xpow_toQuotient]
rw [← map_pow, ← pow_mul]
+/-- **The key relation `X^{2^α} = -1`** (`X^d = -1`), proven via the quotient: `X^d + 1` is the
+modulus, so it vanishes in the quotient. -/
+theorem Xpow_natDegree (α : ℕ) : Xpow (powTwoCyclotomic (R := R) α) (2 ^ α) = -1 := by
+ apply... | {
"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_4d12810c234e_3 | 726faadc6e4d003c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 5 | [
{
"theorem_name": "Xpow_add",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Rq.toQuotient_injective Φ\n have hmul : (Xpow Φ a * Xpow Φ b).toQuotient\n = (Xpow Φ a).toQuotient * (Xpow Φ b).toQuot... | [
{
"name": "Xpow_toQuotient",
"text": "/-- `X^n` lifts to the class of `X^n` in the semantic quotient. -/\ntheorem Xpow_toQuotient (Φ : CyclotomicModulus R) [IsCyclotomic Φ] (n : ℕ) :\n (Xpow Φ n).toQuotient = Ideal.Quotient.mk Φ.modIdeal (Polynomial.X ^ n) := by\n rw [Xpow, Rq.toQuotient_mk, quotientHom... | [
{
"name": "mk_monomial_eq",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 694,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -44,29 +44,70 @@
def Xpow (Φ : CyclotomicModulus R) [IsCyclotomic Φ] (i : ℕ) : Rq Φ :=
Rq.mk Φ (CompPoly.CPolynomial.monomial i 1)
+/-- `X^n` lifts to the class of `X^n` in the semantic quotient. -/
+theorem Xpow_toQuotient (Φ : CyclotomicModulus R) [IsCyclotomic Φ] (n : ℕ) :
+ (Xpow Φ n).toQuotient = Ideal... | {
"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_4d12810c234e_4 | 45e57354abc9466f | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "mk_monomial_fold",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [mk_monomial_eq, mk_monomial_eq, Xpow_fold]\n ring",
"n_chars": 59,
"n_subproofs": 0,
"n_tactics": 3,
... | [
{
"name": "mk_monomial_eq",
"text": "/-- The scaled monomial `c·X^j ∈ Rq Φ` factors as `(constant c)·X^j`. -/\ntheorem mk_monomial_eq (Φ : CyclotomicModulus R) [IsCyclotomic Φ] (j : ℕ) (c : R) :\n Rq.mk Φ (CompPoly.CPolynomial.monomial j c)\n = Rq.mk Φ (CompPoly.CPolynomial.C c) * Xpow Φ j := by\n ... | [
{
"name": "mk_monomial_fold",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 10,
"n_chars": 493,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 6 | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -98,12 +98,25 @@
/-! ## The coefficient action of `σ_m` -/
+/-- The scaled monomial `c·X^j ∈ Rq Φ` factors as `(constant c)·X^j`. -/
+theorem mk_monomial_eq (Φ : CyclotomicModulus R) [IsCyclotomic Φ] (j : ℕ) (c : R) :
+ Rq.mk Φ (CompPoly.CPolynomial.monomial j c)
+ = Rq.mk Φ (CompPoly.CPolynomial.C c) *... | {
"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_4d12810c234e_5 | 7d1c0f25cdb4e727 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 2 | [
{
"theorem_name": "Xpow_fold",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv_lhs => rw [← Nat.div_add_mod n (2 ^ α)]\n rw [Xpow_add, Xpow_mul, Xpow_natDegree]",
"n_chars": 95,
"n_subproofs": 0... | [
{
"name": "Xpow_natDegree",
"text": "/-- **The key relation `X^{2^α} = -1`** (`X^d = -1`), proven via the quotient: `X^d + 1` is the\nmodulus, so it vanishes in the quotient. -/\ntheorem Xpow_natDegree (α : ℕ) : Xpow (powTwoCyclotomic (R := R) α) (2 ^ α) = -1 := by\n apply Rq.toQuotient_injective (powTwoCy... | [
{
"name": "Xpow_conductor",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 255,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"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 ArkLib.Data.Lattices.CyclotomicRing.Galois.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -71,6 +71,23 @@
simp only [Xpow_toQuotient]
rw [← map_pow, ← pow_mul]
+/-- **The key relation `X^{2^α} = -1`** (`X^d = -1`), proven via the quotient: `X^d + 1` is the
+modulus, so it vanishes in the quotient. -/
+theorem Xpow_natDegree (α : ℕ) : Xpow (powTwoCyclotomic (R := R) α) (2 ^ α) = -1 := by
+ apply ... | {
"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_4d12810c234e_6 | 7bd30ef7b1d5490e | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 2 | [
{
"theorem_name": "Xpow_periodic",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv_lhs => rw [← Nat.div_add_mod n (2 ^ (α + 1))]\n rw [Xpow_add, Xpow_mul, Xpow_conductor, one_pow, _root_.one_mul]",
... | [
{
"name": "Xpow_conductor",
"text": "/-- `X^{2^{α+1}} = 1` (the conductor `2d = 2^{α+1}` is the order of `X`): `X^{2d} = (X^d)^2 = 1`. -/\ntheorem Xpow_conductor (α : ℕ) : Xpow (powTwoCyclotomic (R := R) α) (2 ^ (α + 1)) = 1 := by\n rw [pow_succ, Xpow_mul, Xpow_natDegree, neg_one_sq]\n\n",
"fan_in": 2,... | [
{
"name": "Xpow_periodic",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 8,
"n_chars": 367,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting":... | 5 | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -98,10 +98,16 @@
rw [galoisAut_toQuotient α m hm, Xpow_toQuotient, galoisAutₛ_mk, Xpow_toQuotient,
map_pow, Polynomial.aeval_X, ← pow_mul, Nat.mul_comm]
+/-- `X^{2^{α+1}} = 1` (the conductor `2d = 2^{α+1}` is the order of `X`): `X^{2d} = (X^d)^2 = 1`. -/
+theorem Xpow_conductor (α : ℕ) : Xpow (powTwoCyclot... | {
"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_4d12810c234e_7 | ad093620075267a9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "Xpow_congr_mod",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Xpow_periodic α a, Xpow_periodic α b, h]",
"n_chars": 52,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic"... | [
{
"name": "Xpow_periodic",
"text": "/-- **Conductor periodicity**: `X^n = X^{n mod 2^{α+1}}` (no sign — `X` has order `2d`). -/\ntheorem Xpow_periodic (α n : ℕ) :\n Xpow (powTwoCyclotomic (R := R) α) n\n = Xpow (powTwoCyclotomic (R := R) α) (n % 2 ^ (α + 1)) := by\n conv_lhs => rw [← Nat.div_add_mo... | [
{
"name": "Xpow_congr_mod",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 6,
"n_chars": 282,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting"... | 6 | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -102,9 +102,17 @@
theorem Xpow_conductor (α : ℕ) : Xpow (powTwoCyclotomic (R := R) α) (2 ^ (α + 1)) = 1 := by
rw [pow_succ, Xpow_mul, Xpow_natDegree, neg_one_sq]
+/-- **Conductor periodicity**: `X^n = X^{n mod 2^{α+1}}` (no sign — `X` has order `2d`). -/
+theorem Xpow_periodic (α n : ℕ) :
+ Xpow (powTwoCycl... | {
"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_4d12810c234e_8 | 531d37e791a4538b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 2 | [
{
"theorem_name": "Xpow_periodic",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv_lhs => rw [← Nat.div_add_mod n (2 ^ (α + 1))]\n rw [Xpow_add, Xpow_mul, Xpow_conductor, one_pow, _root_.one_mul]",
... | [
{
"name": "Xpow_conductor",
"text": "/-- `X^{2^{α+1}} = 1` (the conductor `2d = 2^{α+1}` is the order of `X`): `X^{2d} = (X^d)^2 = 1`. -/\ntheorem Xpow_conductor (α : ℕ) : Xpow (powTwoCyclotomic (R := R) α) (2 ^ (α + 1)) = 1 := by\n rw [pow_succ, Xpow_mul, Xpow_natDegree, neg_one_sq]\n\n",
"fan_in": 2,... | [
{
"name": "Xpow_mul_conjExp",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 26,
"n_chars": 1366,
"n_subproofs": 5,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false,
"max_nes... | 5 | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -98,10 +98,16 @@
rw [galoisAut_toQuotient α m hm, Xpow_toQuotient, galoisAutₛ_mk, Xpow_toQuotient,
map_pow, Polynomial.aeval_X, ← pow_mul, Nat.mul_comm]
+/-- `X^{2^{α+1}} = 1` (the conductor `2d = 2^{α+1}` is the order of `X`): `X^{2d} = (X^d)^2 = 1`. -/
+theorem Xpow_conductor (α : ℕ) : Xpow (powTwoCyclot... | {
"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_4d12810c234e_9 | 5a4f967e9073dfb6 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "Xpow_sub_one_isUnit",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hz : (Xpow (powTwoCyclotomic (R := R) α) c) ^ (2 ^ t) = -1 := by rw [← Xpow_mul]; exact ht\n have hmul : (∑ j ∈ ... | [
{
"name": "isUnit_two",
"text": "/-- `2` is a unit in `Rq Φ` when it is a unit in `R` (e.g. `R = ZMod q`, `q` odd). Transferred\nfrom `R` through the algebra map into the semantic quotient and back across `equivQuotient`. -/\ntheorem isUnit_two (Φ : CyclotomicModulus R) [IsCyclotomic Φ] (h2 : (2 : R) ≠ 0) :... | [
{
"name": "Xpow_sub_one_isUnit",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 20,
"n_chars": 1121,
"n_subproofs": 3,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 3,
"automation_only": false,
"max_... | 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.Galois.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -114,6 +114,17 @@
Xpow (powTwoCyclotomic (R := R) α) a = Xpow (powTwoCyclotomic (R := R) α) b := by
rw [Xpow_periodic α a, Xpow_periodic α b, h]
+/-- `2` is a unit in `Rq Φ` when it is a unit in `R` (e.g. `R = ZMod q`, `q` odd). Transferred
+from `R` through the algebra map into the semantic quotient and b... | {
"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_4d12810c234e_10 | 496e739c8af6fb21 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 2 | [
{
"theorem_name": "conjAut_Xpow",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [conjAut, galoisRingHom_apply, galoisAut_Xpow' α (conjExp α) e (conjExp_odd α)]",
"n_chars": 91,
"n_subproofs": 0,
... | [
{
"name": "galoisAut_Xpow'",
"text": "/-- **`σ_m (X^j) = X^{j·m}` for any exponent `j`** (`m` odd, so `σ_m` is a genuine automorphism).\nUnlike `galoisAut_Xpow`, no `j < d` bound: routes through the semantic side, where `σ_m` is\n`aeval (X^m)` and `X^j ↦ (X^m)^j = X^{jm}`. -/\ntheorem galoisAut_Xpow' (α m j... | [
{
"name": "conjAut_Xpow",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 287,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"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 ArkLib.Data.Lattices.CyclotomicRing.Galois.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -88,6 +88,16 @@
rw [Xpow_toQuotient, hneg]
exact eq_neg_of_add_eq_zero_left hzero
+/-- **`σ_m (X^j) = X^{j·m}` for any exponent `j`** (`m` odd, so `σ_m` is a genuine automorphism).
+Unlike `galoisAut_Xpow`, no `j < d` bound: routes through the semantic side, where `σ_m` is
+`aeval (X^m)` and `X^j ↦ (X^m)^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_4d12810c234e_11 | 4031408ebe621d39 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 3 | [
{
"theorem_name": "mem_fixed_symm",
"depth": 1,
"n_commands": 0,
"n_lines": 39,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hgenX : ∀ f, genAut α (2 ^ κ) (Xpow (powTwoCyclotomic (R := R) α) f)\n = Xpow (powTwoCyclotomic α) (f * genExp (2... | [
{
"name": "conjAut_Xpow",
"text": "/-- `σ_{-1}(X^e) = X^{e·conjExp}`. -/\ntheorem conjAut_Xpow (α e : ℕ) :\n conjAut α (Xpow (powTwoCyclotomic (R := R) α) e)\n = Xpow (powTwoCyclotomic (R := R) α) (e * conjExp α) := by\n rw [conjAut, galoisRingHom_apply, galoisAut_Xpow' α (conjExp α) e (conjExp_odd... | [
{
"name": "mem_fixed_symm",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 9,
"n_lines": 47,
"n_chars": 2836,
"n_subproofs": 13,
"n_tactics": 44,
"cyclomatic": 1,
"n_automation": 13,
"n_rewrites": 16,
"n_structural": 8,
"automation_only": false,
"max_ne... | 9 | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -160,11 +160,55 @@
/-! ## Explicit `H`-fixed elements `X^e + σ_{-1}(X^e)` -/
+/-- `σ_{-1}(X^e) = X^{e·conjExp}`. -/
+theorem conjAut_Xpow (α e : ℕ) :
+ conjAut α (Xpow (powTwoCyclotomic (R := R) α) e)
+ = Xpow (powTwoCyclotomic (R := R) α) (e * conjExp α) := by
+ rw [conjAut, galoisRingHom_apply, galoi... | {
"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_4d12810c234e_12 | 8a90ac9582571f26 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "Xpow_coeff_eq_zero_of_ne",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hmod : f % 2 ^ α < 2 ^ α := Nat.mod_lt _ (by positivity)\n rw [Xpow, mk_monomial_fold]\n rcases Nat.even_or... | [
{
"name": "mk_monomial_coeff_lt",
"text": "/-- The `j`-th coefficient of the reduced `c·X^i` (for `i < d`) is `c·[j = i]`. -/\ntheorem mk_monomial_coeff_lt (α : ℕ) {i : ℕ} (hi : i < 2 ^ α) (c : R) (j : ℕ) :\n (Rq.mk (powTwoCyclotomic α) (CompPoly.CPolynomial.monomial i c)).1.coeff j\n = if j = i the... | [
{
"name": "Xpow_coeff_eq_zero_of_ne",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 13,
"n_chars": 779,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
"m... | 8 | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -242,6 +242,20 @@
/-! ## Coefficients of monomials and conjugates -/
+/-- The `j`-th coefficient of the reduced `c·X^i` (for `i < d`) is `c·[j = i]`. -/
+theorem mk_monomial_coeff_lt (α : ℕ) {i : ℕ} (hi : i < 2 ^ α) (c : R) (j : ℕ) :
+ (Rq.mk (powTwoCyclotomic α) (CompPoly.CPolynomial.monomial i c)).1.coeff ... | {
"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_4d12810c234e_13 | 88baa40580319a5c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "conjAut_Xpow_coeff_low",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hhalf : (2 : ℕ) ^ α = 2 * 2 ^ (α - 1) := by rw [← pow_succ']; congr 1; omega\n rw [conjAut_Xpow]\n refine Xpo... | [
{
"name": "Xpow_coeff_eq_zero_of_ne",
"text": "/-- **`X^f` has no coefficient off its folded position**: `(X^f).coeff p = 0` for `p < d` with\n`p ≠ f mod d`. Proved by folding `X^f = (-1)^{f/d}·X^{f mod d}` and casing on the parity of `f/d`\n(so the sign is literally `±1`), avoiding any product-coefficient ... | [
{
"name": "conjAut_Xpow_coeff_low",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 13,
"n_lines": 14,
"n_chars": 675,
"n_subproofs": 1,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false,
"ma... | 12 | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -256,6 +256,18 @@
change ((powTwoCyclotomic (R := R) α).reduce (CompPoly.CPolynomial.monomial i c)).coeff j = _
rw [hself, CPolynomial.coeff_monomial]
+/-- **`X^f` has no coefficient off its folded position**: `(X^f).coeff p = 0` for `p < d` with
+`p ≠ f mod d`. Proved by folding `X^f = (-1)^{f/d}·X^{f mod d... | {
"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_4d12810c234e_14 | 5ddbc6bee786ae35 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/Basis.lean | Basis | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "vElt_coeff",
"depth": 1,
"n_commands": 0,
"n_lines": 34,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hα : 1 ≤ α := by omega\n have hhalf : (2 : ℕ) ^ (α - 1) = 2 ^ (α - κ - 1) * 2 ^ κ := by rw [← pow_add]; congr 1; omega\n ... | [
{
"name": "conjAut_Xpow_coeff_low",
"text": "/-- **`σ_{-1}(X^e)` has no low-degree coefficient**: for `0 < e < d/2` and `p < d/2`,\n`(σ_{-1}(X^e)).coeff p = 0` (its only coefficient sits at `d - e > d/2`). -/\ntheorem conjAut_Xpow_coeff_low (α : ℕ) (hα : 1 ≤ α) {e p : ℕ} (he0 : 0 < e)\n (he : e < 2 ^ (α ... | [
{
"name": "vElt_coeff",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 16,
"n_lines": 42,
"n_chars": 2504,
"n_subproofs": 10,
"n_tactics": 41,
"cyclomatic": 1,
"n_automation": 11,
"n_rewrites": 22,
"n_structural": 3,
"automation_only": false,
"max_nesti... | 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.Data.Lattices.CyclotomicRing.Galois.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | /-
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.FixedSubring
/-!
# Monomials and the `Z_q`-Basis of the Fixed Subring `R_q^H` (Hachi §3, Eq. 7)
This fi... | @@ -300,6 +300,19 @@
rw [Nat.ModEq] at hmod
rw [hmod, Nat.mod_eq_of_lt (by omega)]
+/-- **`σ_{-1}(X^e)` has no low-degree coefficient**: for `0 < e < d/2` and `p < d/2`,
+`(σ_{-1}(X^e)).coeff p = 0` (its only coefficient sits at `d - e > d/2`). -/
+theorem conjAut_Xpow_coeff_low (α : ℕ) (hα : 1 ≤ α) {e p : 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_ba6009742fe5_0 | 809e43c64836ccf0 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/ElocPoly.lean | ElocPoly | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "errors_are_roots_of_elocPolyF",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [←liftF_eval (f := ωs)]\n aesop (config := {warnOnNonterminal := false})\n rw [BerlekampWelch.errors_are... | [
{
"name": "errors_are_roots_of_elocPoly",
"text": "protected lemma errors_are_roots_of_elocPoly {i : ℕ}\n (hi : i < n) (h : f i ≠ p.eval (ωs i)) : (ElocPoly n ωs f p).eval (ωs i) = 0 := by\n induction n with\n | zero => aesop\n | succ n ih =>\n by_cases i = n\n · aesop\n · have : i < n := by ... | [
{
"name": "errors_are_roots_of_elocPolyF",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 343,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 0,
"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: František Silváši, Ilia Vlasov
-/
import Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | /-
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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | @@ -83,6 +83,16 @@
aesop (add safe [(by existsi i), (by omega)])
· aesop (add safe (by use n))
+protected lemma errors_are_roots_of_elocPoly {i : ℕ}
+ (hi : i < n) (h : f i ≠ p.eval (ωs i)) : (ElocPoly n ωs f p).eval (ωs i) = 0 := by
+ induction n with
+ | zero => aesop
+ | succ n ih =>
+ by_case... | {
"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_802759abfb78_7 | f0d001a9e0aad903 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/KZG/FunctionBinding/DegreeConflict.lean | DegreeConflict | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "function_binding_interpolation_branch_maps_to_arsdh",
"depth": 1,
"n_commands": 0,
"n_lines": 39,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [interpolationArsdhOutput, FunctionBindingArsdhOutput.toTuple,\n Groups.a... | [
{
"name": "find_s_card",
"text": "/-- A successful `findS` result has cardinality `n + 1`. -/\nlemma find_s_card\n {L : ℕ} (n : ℕ) (c : G₁) (A S : Finset (Fin L))\n (srs : Vector G₁ (n + 1) × Vector G₂ 2) (query : Fin L → ZMod p)\n (response : Fin L → ZMod p) (hres : some (S) = findS n A c srs quer... | [
{
"name": "function_binding_interpolation_branch_maps_to_arsdh",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 8,
"n_lines": 63,
"n_chars": 3354,
"n_subproofs": 10,
"n_tactics": 40,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 13,
"... | 8 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.KZG.FunctionBinding.Support
/-!
# Degree-Conflict Branch for KZG Function Binding
Branch-specific interpolation search a... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.KZG.FunctionBinding.Support
/-!
# Degree-Conflict Branch for KZG Function Binding
Branch-specific interpolation search a... | @@ -119,6 +119,22 @@
candidates.find? fun s =>
commit srs.1 ((CLagrange.interpolate s query response).val.coeff ∘ Fin.val) ≠ c
+/-- A successful `findS` result has cardinality `n + 1`. -/
+lemma find_s_card
+ {L : ℕ} (n : ℕ) (c : G₁) (A S : Finset (Fin L))
+ (srs : Vector G₁ (n + 1) × Vector G₂ 2) (quer... | {
"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_a98152497f69_0 | 17f8d9481483f385 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/OracleReduction/Security/TranscriptTree/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "exists_of_mem_fullTranscripts",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [fullTranscript, ChallengeTree.fullTranscripts] using\n (exists_of_mem_transcripts (T := T) (pre := ... | [
{
"name": "exists_of_mem_transcripts",
"text": "/-- Every transcript listed by a tree is selected by some leaf path. -/\ntheorem exists_of_mem_transcripts :\n {m : Fin (n + 1)} → {T : ChallengeTree pSpec arity m} →\n {pre : Transcript m pSpec} → {tr : FullTranscript pSpec} →\n tr ∈ T.transcri... | [
{
"name": "exists_of_mem_fullTranscripts",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 414,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"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: Tobias Rothmann
-/
import ArkLib.OracleReduction.Security.Basic
/-!
# Trees of transcripts — core definitions
This file defines `ChallengeTree`, the *tree 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.Basic
/-!
# Trees of transcripts — core definitions
This file defines `ChallengeTree`, the *tree of transcrip... | @@ -203,10 +203,30 @@
simp only [transcript, transcripts, List.mem_flatMap, List.mem_finRange]
exact ⟨j, trivial, mem_transcripts path (pre.concat (chals j))⟩
+/-- Every transcript listed by a tree is selected by some leaf path. -/
+theorem exists_of_mem_transcripts :
+ {m : Fin (n + 1)} → {T : 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_e5abdcc76fc4_0 | 4c0a2b93b11f2966 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Condition.lean | Condition | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "eval_solutionToQ",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases e with _ | e\n · simp [eval_solutionToQ_cast]\n · rw [Polynomial.eval_eq_sum_range'\n (n := (e + 1) + k... | [
{
"name": "eval_solutionToQ_cast",
"text": "lemma eval_solutionToQ_cast {x : F} (h : e = 0) :\n eval x (solutionToQ e k v) = ∑ i ∈ Finset.range k, liftF v i * x ^ i := by\n subst h\n simp only [solutionToQ, Nat.mul_zero, zero_add, ne_eq]\n rw [eval_eq_sum, sum_def]\n simp only [support_ofFinsupp, coe... | [
{
"name": "eval_solutionToQ",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 16,
"n_chars": 574,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_nest... | 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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | /-
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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | @@ -237,12 +237,22 @@
rw [WithBot.unbotD_le_iff] <;>
aesop (add safe (by omega))
+lemma eval_solutionToQ_cast {x : F} (h : e = 0) :
+ eval x (solutionToQ e k v) = ∑ i ∈ Finset.range k, liftF v i * x ^ i := by
+ subst h
+ simp only [solutionToQ, Nat.mul_zero, zero_add, ne_eq]
+ rw [eval_eq_sum, sum_def]
+ ... | {
"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_e5abdcc76fc4_1 | 63d9bce65d35198b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Condition.lean | Condition | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "eval_solutionToQ",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases e with _ | e\n · simp [eval_solutionToQ_cast]\n · rw [Polynomial.eval_eq_sum_range'\n (n := (e + 1) + k... | [
{
"name": "eval_solutionToQ_cast",
"text": "lemma eval_solutionToQ_cast {x : F} (h : e = 0) :\n eval x (solutionToQ e k v) = ∑ i ∈ Finset.range k, liftF v i * x ^ i := by\n subst h\n simp only [solutionToQ, Nat.mul_zero, zero_add, ne_eq]\n rw [eval_eq_sum, sum_def]\n simp only [support_ofFinsupp, coe... | [
{
"name": "solution_to_BerlekampWelch_condition",
"fan_in": 3,
"n_deps_direct": 6,
"n_deps_transitive": 8,
"n_lines": 67,
"n_chars": 2599,
"n_subproofs": 1,
"n_tactics": 65,
"cyclomatic": 2,
"n_automation": 30,
"n_rewrites": 3,
"n_structural": 22,
"automation_only... | 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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | /-
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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | @@ -243,12 +243,22 @@
rw [WithBot.unbotD_le_iff] <;>
aesop (add safe (by omega))
+lemma eval_solutionToQ_cast {x : F} (h : e = 0) :
+ eval x (solutionToQ e k v) = ∑ i ∈ Finset.range k, liftF v i * x ^ i := by
+ subst h
+ simp only [solutionToQ, Nat.mul_zero, zero_add, ne_eq]
+ rw [eval_eq_sum, sum_def]
+ ... | {
"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_e5abdcc76fc4_2 | 6ed3651288dfb591 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Condition.lean | Condition | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 3 | [
{
"theorem_name": "BerlekampWelchCondition_iff_Solution",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨solution_to_BerlekampWelch_condition, BerlekampWelchCondition_to_Solution'⟩",
"n_chars": 83,
"n_... | [
{
"name": "solution_to_BerlekampWelch_condition",
"text": "private lemma solution_to_BerlekampWelch_condition {e k : ℕ}\n [NeZero n]\n {ωs f : Fin n → F}\n {v : Fin (2 * e + k) → F}\n (h_sol : IsBerlekampWelchSolution e k ωs f v) :\n BerlekampWelchCondition e k ωs f (solutionToE e k v) (solutionToQ e k... | [
{
"name": "BerlekampWelchCondition_iff_Solution",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 12,
"n_lines": 8,
"n_chars": 334,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": f... | 4 | /-
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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | /-
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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | @@ -309,11 +309,78 @@
IsBerlekampWelchSolution 0 0 ωs f v ↔ f = 0 := by
simp [IsBerlekampWelchSolution]
+private lemma solution_to_BerlekampWelch_condition {e k : ℕ}
+ [NeZero n]
+ {ωs f : Fin n → F}
+ {v : Fin (2 * e + k) → F}
+ (h_sol : IsBerlekampWelchSolution e k ωs f v) :
+ BerlekampWelchCondition e... | {
"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_e5abdcc76fc4_3 | ccf41d5269cb3cb8 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Condition.lean | Condition | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 3 | [
{
"theorem_name": "BerlekampWelchCondition_iff_Solution",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨solution_to_BerlekampWelch_condition, BerlekampWelchCondition_to_Solution'⟩",
"n_chars": 83,
"n_... | [
{
"name": "solution_to_BerlekampWelch_condition",
"text": "private lemma solution_to_BerlekampWelch_condition {e k : ℕ}\n [NeZero n]\n {ωs f : Fin n → F}\n {v : Fin (2 * e + k) → F}\n (h_sol : IsBerlekampWelchSolution e k ωs f v) :\n BerlekampWelchCondition e k ωs f (solutionToE e k v) (solutionToQ e k... | [
{
"name": "linsolve_to_BerlekampWelch_condition",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 10,
"n_lines": 9,
"n_chars": 367,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": f... | 4 | /-
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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | /-
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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | @@ -296,12 +296,79 @@
IsBerlekampWelchSolution 0 0 ωs f v ↔ f = 0 := by
simp [IsBerlekampWelchSolution]
+private lemma solution_to_BerlekampWelch_condition {e k : ℕ}
+ [NeZero n]
+ {ωs f : Fin n → F}
+ {v : Fin (2 * e + k) → F}
+ (h_sol : IsBerlekampWelchSolution e k ωs f v) :
+ BerlekampWelchCondition e... | {
"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_e5abdcc76fc4_4 | 53e151bcb42e188b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Condition.lean | Condition | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 2 | [
{
"theorem_name": "BerlekampWelch_Q_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " fun contr ↦\n have h_cond := h_bw.cond\n let S : Finset (Fin n) := {i | ¬f i = 0}\n by replace h_dist : e < S.card :... | [
{
"name": "BerlekampWelch_E_ne_zero",
"text": "lemma BerlekampWelch_E_ne_zero {e k : ℕ}\n {ωs f : Fin n → F}\n {E Q : Polynomial F}\n (h_cond : BerlekampWelchCondition e k ωs f E Q) : E ≠ 0 := by\n have h_deg := h_cond.E_natDegree\n have h_leadCoeff := h_cond.E_leadingCoeff\n aesop\n\n",
"fan_in... | [
{
"name": "BerlekampWelch_Q_ne_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 781,
"n_subproofs": 3,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 1,
"n_structural": 2,
"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: František Silváši, Ilia Vlasov
-/
import Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | /-
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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | @@ -287,6 +287,14 @@
end
+lemma BerlekampWelch_E_ne_zero {e k : ℕ}
+ {ωs f : Fin n → F}
+ {E Q : Polynomial F}
+ (h_cond : BerlekampWelchCondition e k ωs f E Q) : E ≠ 0 := by
+ have h_deg := h_cond.E_natDegree
+ have h_leadCoeff := h_cond.E_leadingCoeff
+ aesop
+
section
open Polynomial
@@ -299,7 +307,... | {
"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_e5abdcc76fc4_5 | a0ae7fcfac5414a2 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Condition.lean | Condition | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 2 | [
{
"theorem_name": "BerlekampWelch_Q_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " fun contr ↦\n have h_cond := h_bw.cond\n let S : Finset (Fin n) := {i | ¬f i = 0}\n by replace h_dist : e < S.card :... | [
{
"name": "BerlekampWelch_E_ne_zero",
"text": "lemma BerlekampWelch_E_ne_zero {e k : ℕ}\n {ωs f : Fin n → F}\n {E Q : Polynomial F}\n (h_cond : BerlekampWelchCondition e k ωs f E Q) : E ≠ 0 := by\n have h_deg := h_cond.E_natDegree\n have h_leadCoeff := h_cond.E_leadingCoeff\n aesop\n\n",
"fan_in... | [
{
"name": "solutionToQ_ne_zero",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 11,
"n_lines": 14,
"n_chars": 379,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_n... | 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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | /-
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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | @@ -359,6 +359,14 @@
end
+lemma BerlekampWelch_E_ne_zero {e k : ℕ}
+ {ωs f : Fin n → F}
+ {E Q : Polynomial F}
+ (h_cond : BerlekampWelchCondition e k ωs f E Q) : E ≠ 0 := by
+ have h_deg := h_cond.E_natDegree
+ have h_leadCoeff := h_cond.E_leadingCoeff
+ aesop
+
section
open Polynomial
@@ -371,7 +379,... | {
"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_e5abdcc76fc4_6 | 536aefcf1651c85f | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/Condition.lean | Condition | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 2 | [
{
"theorem_name": "BerlekampWelch_Q_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " fun contr ↦\n have h_cond := h_bw.cond\n let S : Finset (Fin n) := {i | ¬f i = 0}\n by replace h_dist : e < S.card :... | [
{
"name": "BerlekampWelch_E_ne_zero",
"text": "lemma BerlekampWelch_E_ne_zero {e k : ℕ}\n {ωs f : Fin n → F}\n {E Q : Polynomial F}\n (h_cond : BerlekampWelchCondition e k ωs f E Q) : E ≠ 0 := by\n have h_deg := h_cond.E_natDegree\n have h_leadCoeff := h_cond.E_leadingCoeff\n aesop\n\n",
"fan_in... | [
{
"name": "E_and_Q_unique",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 38,
"n_chars": 1355,
"n_subproofs": 3,
"n_tactics": 29,
"cyclomatic": 7,
"n_automation": 11,
"n_rewrites": 2,
"n_structural": 6,
"automation_only": false,
"max_nest... | 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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | /-
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 Init.Data.List.FinRange
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Algebra.Polynomial.... | @@ -287,6 +287,14 @@
end
+lemma BerlekampWelch_E_ne_zero {e k : ℕ}
+ {ωs f : Fin n → F}
+ {E Q : Polynomial F}
+ (h_cond : BerlekampWelchCondition e k ωs f E Q) : E ≠ 0 := by
+ have h_deg := h_cond.E_natDegree
+ have h_leadCoeff := h_cond.E_leadingCoeff
+ aesop
+
section
open Polynomial
@@ -307,7 +315,... | {
"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_7eeeb86a5165_0 | ffe527e5e755853c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ProximityGap/MCAGenerator.lean | MCAGenerator | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "generatorSubset",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro U γ\n exact le_trans (Pr_le_Pr_of_implies ($ᵖ S) _ _\n fun x h => isMCA_projectedGenerator_of_isMCA LC G κ ... | [
{
"name": "isMCA_projectedGenerator_of_isMCA",
"text": "/-- If the MCA condition `IsMCA` holds for a projected generator, then `IsMCA` holds for the\noriginal generator `G` with the zero-extension defined above. -/\nlemma isMCA_projectedGenerator_of_isMCA (LC : LinearCode ι F) [Nonempty S] (G : Generator S ... | [
{
"name": "generatorSubset",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 610,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"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: Katerina Hristova
-/
import ArkLib.Data.CodingTheory.ProximityGap.ProximityGenerators
import ArkLib.Data.Matrix.Basic
import ArkLib.Data.Probability.Instances
/-!
## Main R... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova
-/
import ArkLib.Data.CodingTheory.ProximityGap.ProximityGenerators
import ArkLib.Data.Matrix.Basic
import ArkLib.Data.Probability.Instances
/-!
## Main R... | @@ -57,12 +57,36 @@
noncomputable def zeroExtend (κ : Set ℓ) (U : κ → (ι → F)) : ℓ → (ι → F) :=
fun i => if h : i ∈ κ then U ⟨i, h⟩ else 0
+/-- If the MCA condition `IsMCA` holds for a projected generator, then `IsMCA` holds for the
+original generator `G` with the zero-extension defined above. -/
+lemma isMCA_proj... | {
"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_1ce24689ab29_1 | bf0ca80fafcb1965 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/Gadget.lean | Gadget | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "gadgetMul_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [gadgetMul, matVecMul_apply, dot_eq_sum]\n simp only [gadgetMatrix]\n rw [← Equiv.sum_comp finProdFinEquiv (fun j => ... | [
{
"name": "gadgetEntry_finProdFinEquiv",
"text": "/-- The gadget entry at the flattened index `finProdFinEquiv (i', e)` is `constRq (base^e)`\non the diagonal block and `0` elsewhere. -/\ntheorem gadgetEntry_finProdFinEquiv (base : R) {rows digits : Nat} (hd : 0 < digits)\n (i i' : Fin rows) (e : Fin dig... | [
{
"name": "gadgetMul_apply",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 30,
"n_chars": 1366,
"n_subproofs": 0,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 5,
"n_structural": 7,
"automation_only": false,
"max_nest... | 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.ModuleSIS
import Mathlib.Data.Nat.Digits.Lemmas
import Mathlib.Data.ZMod.Basic
import Mathlib.Algebra.Field.ZMod
/-!
# Ajtai G... | /-
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.ModuleSIS
import Mathlib.Data.Nat.Digits.Lemmas
import Mathlib.Data.ZMod.Basic
import Mathlib.Algebra.Field.ZMod
/-!
# Ajtai G... | @@ -139,6 +139,22 @@
/-! ## The gadget product as a block digit-sum -/
omit [DecidableEq R] in
+/-- The gadget entry at the flattened index `finProdFinEquiv (i', e)` is `constRq (base^e)`
+on the diagonal block and `0` elsewhere. -/
+theorem gadgetEntry_finProdFinEquiv (base : R) {rows digits : Nat} (hd : 0 < digit... | {
"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_1ce24689ab29_2 | 709ed893fb058c27 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/Gadget.lean | Gadget | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "gadgetDecompose_lawful",
"depth": 1,
"n_commands": 0,
"n_lines": 29,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro x\n funext i\n rw [gadgetMul_apply Φ base hd]\n simp_rw [gadgetDecompose_apply Φ dd x i]\n apply Subtype.... | [
{
"name": "gadgetDecompose_apply",
"text": "/-- Value of `gadgetDecompose` at the flattened index `finProdFinEquiv (i, e)`. -/\ntheorem gadgetDecompose_apply {rows digits : Nat} (dd : DigitDecomposition base digits)\n (x : PolyVec (Rq Φ) rows) (i : Fin rows) (e : Fin digits) :\n gadgetDecompose Φ dd x... | [
{
"name": "gadgetDecompose_lawful",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 34,
"n_chars": 1550,
"n_subproofs": 2,
"n_tactics": 29,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 5,
"n_structural": 7,
"automation_only": false,
"m... | 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.ModuleSIS
import Mathlib.Data.Nat.Digits.Lemmas
import Mathlib.Data.ZMod.Basic
import Mathlib.Algebra.Field.ZMod
/-!
# Ajtai G... | /-
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.ModuleSIS
import Mathlib.Data.Nat.Digits.Lemmas
import Mathlib.Data.ZMod.Basic
import Mathlib.Algebra.Field.ZMod
/-!
# Ajtai G... | @@ -192,10 +192,46 @@
fun j => Rq.ofFinCoeff Φ Φ.φ.natDegree
(fun k => dd.digit ((x (finProdFinEquiv.symm j).1).1.coeff k) (finProdFinEquiv.symm j).2)
+/-- Value of `gadgetDecompose` at the flattened index `finProdFinEquiv (i, e)`. -/
+theorem gadgetDecompose_apply {rows digits : Nat} (dd : DigitDecomposition... | {
"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_913d27efc10a_0 | a1fd5b37d8b7b0e2 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ProximityGap/AHIV22.lean | AHIV22 | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "e_le_dist_over_3",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hline :\n (∀ x ∈ Affine.affineLineAtOrigin (F := F) u v, Δ₀(x, ReedSolomon.code α deg) ≤ e)\n ... | [
{
"name": "e_le_dist_over_3_strong",
"text": "/-- **Lemma 4.4, [AHIV22] (strong form).**\n\nEither all points on the affine line are `e`-close to the Reed–Solomon code, or at most\n`‖RS‖₀` points are.\n-/\nlemma e_le_dist_over_3_strong\n {deg : ℕ}\n {α : ι ↪ F} {e : ℕ} {u v : ι → F}\n (he : (e : ℚ≥... | [
{
"name": "e_le_dist_over_3",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 33,
"n_chars": 1373,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nes... | 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, Chung Thai Nguyen, Elias Judin,
Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.ProximityGap.AHIV22Support
/-!
## Main Defin... | /-
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.ProximityGap.AHIV22Support
/-!
## Main Defin... | @@ -35,6 +35,472 @@
-- We first prove the distance-bound form `e_le_dist_over_3_strong` and then derive the
-- mutual-exclusion corollary `e_le_dist_over_3` from it.
+/-- **Lemma 4.4, [AHIV22] (strong form).**
+
+Either all points on the affine line are `e`-close to the Reed–Solomon code, or at most
+`‖RS‖₀` points... | {
"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_913d27efc10a_1 | 8c3e8013bd62cabf | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ProximityGap/AHIV22.lean | AHIV22 | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "e_le_dist_over_3",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hline :\n (∀ x ∈ Affine.affineLineAtOrigin (F := F) u v, Δ₀(x, ReedSolomon.code α deg) ≤ e)\n ... | [
{
"name": "e_le_dist_over_3_strong",
"text": "/-- **Lemma 4.4, [AHIV22] (strong form).**\n\nEither all points on the affine line are `e`-close to the Reed–Solomon code, or at most\n`‖RS‖₀` points are.\n-/\nlemma e_le_dist_over_3_strong\n {deg : ℕ}\n {α : ι ↪ F} {e : ℕ} {u v : ι → F}\n (he : (e : ℚ≥... | [
{
"name": "prob_of_bad_pts",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 380,
"n_chars": 18764,
"n_subproofs": 89,
"n_tactics": 345,
"cyclomatic": 8,
"n_automation": 49,
"n_rewrites": 5,
"n_structural": 82,
"automation_only": false,
"ma... | 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, Chung Thai Nguyen, Elias Judin,
Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.ProximityGap.AHIV22Support
/-!
## Main Defin... | /-
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.ProximityGap.AHIV22Support
/-!
## Main Defin... | @@ -35,6 +35,472 @@
-- We first prove the distance-bound form `e_le_dist_over_3_strong` and then derive the
-- mutual-exclusion corollary `e_le_dist_over_3` from it.
+/-- **Lemma 4.4, [AHIV22] (strong form).**
+
+Either all points on the affine line are `e`-close to the Reed–Solomon code, or at most
+`‖RS‖₀` points... | {
"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_5f51ee93fb2a_0 | 80c3aaf8e508abda | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/KZG/FunctionBinding/Support.lean | Support | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "response_eq_of_find_conflict_none",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_contra hresp\n exact (find_conflict_unsuccessful query response hfc) ⟨i, j, by simp [hquery, hresp]⟩"... | [
{
"name": "find_conflict_unsuccessful",
"text": "/-- If `findConflict` returns `none`, no pair of indices has equal query and unequal response. -/\nlemma find_conflict_unsuccessful {L : ℕ} (query : Fin L → ZMod p) (response : Fin L → ZMod p)\n (hfc : findConflict query response = none) :\n ¬(∃ i : Fin... | [
{
"name": "response_eq_of_find_conflict_none",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 410,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"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: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.KZG.Correctness
import ArkLib.Commitments.Functional.KZG.HardnessAssumptions
import ArkLib.ToCompPoly.Univariate.Lagrange
... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.KZG.Correctness
import ArkLib.Commitments.Functional.KZG.HardnessAssumptions
import ArkLib.ToCompPoly.Univariate.Lagrange
... | @@ -68,11 +68,27 @@
if query i == query j && response i != response j then some (i, j) else none
omit [Fact (Nat.Prime p)] [DecidableEq G₁] [Group G₁] in
+/-- If `findConflict` returns `none`, no pair of indices has equal query and unequal response. -/
+lemma find_conflict_unsuccessful {L : ℕ} (query : Fin L ... | {
"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_a766d00cfaa5_0 | 0c1621ab1ea78556 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Ordinary/Ajtai/Simple/Security.lean | Security | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "bindingAdvantage_le_moduleSIS_of_shortClosure",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold bindingAdvantage CommitmentScheme.bindingExp ModuleSIS.advantage\n SIS.advantage S... | [
{
"name": "probOutput_pure_bool_le",
"text": "/-- Boolean monotonicity of `pure` outcome probability. -/\nprivate theorem probOutput_pure_bool_le (b₁ b₂ : Bool) (h : b₁ = true → b₂ = true) :\n Pr[= true | (pure b₁ : ProbComp Bool)] ≤ Pr[= true | (pure b₂ : ProbComp Bool)] := by\n cases b₁ <;> cases b₂ <... | [
{
"name": "bindingAdvantage_le_moduleSIS_of_shortClosure",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 27,
"n_chars": 1732,
"n_subproofs": 4,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 5,
"automati... | 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.Commitments.Ordinary.Ajtai.Simple.Correctness
import ArkLib.Data.Lattices.CyclotomicRing.NormBounds
/-!
# Binding Security of the Simple Ajt... | /-
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.Commitments.Ordinary.Ajtai.Simple.Correctness
import ArkLib.Data.Lattices.CyclotomicRing.NormBounds
/-!
# Binding Security of the Simple Ajt... | @@ -31,6 +31,11 @@
variable {R : Type} [Field R] [BEq R] [LawfulBEq R] (Φ : CyclotomicModulus R) [IsCyclotomic Φ]
+/-- Boolean monotonicity of `pure` outcome probability. -/
+private theorem probOutput_pure_bool_le (b₁ b₂ : Bool) (h : b₁ = true → b₂ = true) :
+ Pr[= true | (pure b₁ : ProbComp Bool)] ≤ Pr[= true... | {
"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_a766d00cfaa5_1 | 22b58387c9a6788d | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Ordinary/Ajtai/Simple/Security.lean | Security | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "bindingAdvantage_le_moduleSIS_of_shortClosure",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold bindingAdvantage CommitmentScheme.bindingExp ModuleSIS.advantage\n SIS.advantage S... | [
{
"name": "probOutput_pure_bool_le",
"text": "/-- Boolean monotonicity of `pure` outcome probability. -/\nprivate theorem probOutput_pure_bool_le (b₁ b₂ : Bool) (h : b₁ = true → b₂ = true) :\n Pr[= true | (pure b₁ : ProbComp Bool)] ≤ Pr[= true | (pure b₂ : ProbComp Bool)] := by\n cases b₁ <;> cases b₂ <... | [
{
"name": "bindingAdvantage_le_moduleSIS",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 21,
"n_chars": 1171,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 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.Commitments.Ordinary.Ajtai.Simple.Correctness
import ArkLib.Data.Lattices.CyclotomicRing.NormBounds
/-!
# Binding Security of the Simple Ajt... | /-
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.Commitments.Ordinary.Ajtai.Simple.Correctness
import ArkLib.Data.Lattices.CyclotomicRing.NormBounds
/-!
# Binding Security of the Simple Ajt... | @@ -31,6 +31,11 @@
variable {R : Type} [Field R] [BEq R] [LawfulBEq R] (Φ : CyclotomicModulus R) [IsCyclotomic Φ]
+/-- Boolean monotonicity of `pure` outcome probability. -/
+private theorem probOutput_pure_bool_le (b₁ b₂ : Bool) (h : b₁ = true → b₂ = true) :
+ Pr[= true | (pure b₁ : ProbComp Bool)] ≤ Pr[= true... | {
"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_c783500d055a_0 | 14c19df0dd2028a5 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/ToVCVio/OracleComp/SimSemantics/SimulateQ.lean | SimulateQ | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "StateT.run'_simulateQ_bind_map_eq_of_body",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← StateT.run'_map_comm f]\n exact congrArg (fun mx : StateT σ ProbComp β => mx.run' s)\n ... | [
{
"name": "simulateQ_bind_map_eq_of_body",
"text": "lemma simulateQ_bind_map_eq_of_body\n {ι σ α β γ : Type} {spec : OracleSpec ι}\n (impl : QueryImpl spec (StateT σ ProbComp))\n (oa : OracleComp spec α) (body₁ : α → OracleComp spec β)\n (body₂ : α → OracleComp spec γ) (f : γ → β)\n (hBody : ... | [
{
"name": "StateT.run'_simulateQ_bind_map_eq_of_body",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 639,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_onl... | 1 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
-/
import ArkLib.ToVCVio.EvalDist.Instances.OptionT
import ArkLib.ToVCVio.OracleComp.Coercions.SubSpec
import ArkLib.ToVCVio.ToMathlib.Control.StateT
import VCVio.EvalDist.Defs.NeverFails... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
-/
import ArkLib.ToVCVio.EvalDist.Instances.OptionT
import ArkLib.ToVCVio.OracleComp.Coercions.SubSpec
import ArkLib.ToVCVio.ToMathlib.Control.StateT
import VCVio.EvalDist.Defs.NeverFails... | @@ -24,6 +24,20 @@
end StateT
+lemma simulateQ_bind_map_eq_of_body
+ {ι σ α β γ : Type} {spec : OracleSpec ι}
+ (impl : QueryImpl spec (StateT σ ProbComp))
+ (oa : OracleComp spec α) (body₁ : α → OracleComp spec β)
+ (body₂ : α → OracleComp spec γ) (f : γ → β)
+ (hBody : ∀ a, simulateQ impl (body₁ a... | {
"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_49ba969e6235_0 | 463eafad99fbc05f | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/Mem.lean | Mem | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "mem_iff_mem_toCosetFftDomain",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [mem_iff_exists, mem_iff_exists_mul, ω.cosetGenerator_one]",
"n_chars": 70,
"n_subproofs": 0,
... | [
{
"name": "mem_iff_exists",
"text": "/-- Membership in a concrete FFT domain means\n being one of the values of its subgroup parametrization. -/\nlemma mem_iff_exists :\n x ∈ ω ↔ ∃ i, x = ω.subgroupDomain i := by\n aesop (add simp [Membership.mem])\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": ... | [
{
"name": "mem_iff_mem_toCosetFftDomain",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 264,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.TypeTags.Basic
import Mathlib.Algebra.G... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.TypeTags.Basic
import Mathlib.Algebra.G... | @@ -54,10 +54,17 @@
variable {ω : FftDomain ι F} {x : F}
+/-- Membership in a concrete FFT domain means
+ being one of the values of its subgroup parametrization. -/
+lemma mem_iff_exists :
+ x ∈ ω ↔ ∃ i, x = ω.subgroupDomain i := by
+ aesop (add simp [Membership.mem])
+
/-- Membership in an FFT domain is the ... | {
"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_49ba969e6235_1 | c5a83c154d6f9a8d | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/Mem.lean | Mem | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "mem_iff_mem_toCosetFftDomain",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [mem_iff_exists, mem_iff_exists_mul, ω.cosetGenerator_one]",
"n_chars": 70,
"n_subproofs": 0,
... | [
{
"name": "mem_iff_exists",
"text": "/-- Membership in a concrete FFT domain means\n being one of the values of its subgroup parametrization. -/\nlemma mem_iff_exists :\n x ∈ ω ↔ ∃ i, x = ω.subgroupDomain i := by\n aesop (add simp [Membership.mem])\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": ... | [
{
"name": "mem_toFinset_iff_exists",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 10,
"n_chars": 351,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.TypeTags.Basic
import Mathlib.Algebra.G... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.TypeTags.Basic
import Mathlib.Algebra.G... | @@ -54,10 +54,17 @@
variable {ω : FftDomain ι F} {x : F}
+/-- Membership in a concrete FFT domain means
+ being one of the values of its subgroup parametrization. -/
+lemma mem_iff_exists :
+ x ∈ ω ↔ ∃ i, x = ω.subgroupDomain i := by
+ aesop (add simp [Membership.mem])
+
/-- Membership in an FFT domain is the ... | {
"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_65be46bd304c_0 | c2c2fe46170adce1 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Existence.lean | Existence | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "ps_exists_p_nonzero",
"depth": 1,
"n_commands": 0,
"n_lines": 89,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n rcases ps_gcd_decompose (A := A) (B := B) hA0 hB0 with ⟨G, A1, B1, hA, hB, hrel, hA1, hB1⟩\n have hG0 : ... | [
{
"name": "ps_coprime_case_constant",
"text": "/-- If `A` and `B` are coprime and agree on sufficiently many lines, then `A` is constant. -/\nlemma ps_coprime_case_constant {F : Type} [Field F]\n (a_x a_y b_x b_y : ℕ) (n_x n_y : ℕ+)\n (h_bx_ge_ax : b_x ≥ a_x) (h_by_ge_ay : b_y ≥ a_y)\n (A B : F[X][... | [
{
"name": "ps_exists_p_nonzero",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 106,
"n_chars": 6282,
"n_subproofs": 34,
"n_tactics": 99,
"cyclomatic": 3,
"n_automation": 36,
"n_rewrites": 15,
"n_structural": 5,
"automation_only": false,
"... | 2 | /-
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.CodingTheory.PolishchukSpielman.Resultant
/-!
# Existence of polynomials for Polishchuk-Spielman
This file contains the core e... | /-
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.CodingTheory.PolishchukSpielman.Resultant
/-!
# Existence of polynomials for Polishchuk-Spielman
This file contains the core e... | @@ -40,6 +40,94 @@
subst ha; simp_all only [map_eq_zero]
exact ⟨B * C (C a⁻¹), by ext n m : 2; simp [coeff_mul_C, inv_mul_cancel_right₀ hA0]⟩
+/-- If `A` and `B` are coprime and agree on sufficiently many lines, then `A` is constant. -/
+lemma ps_coprime_case_constant {F : Type} [Field F]
+ (a_x a_y b_x b_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_65be46bd304c_1 | 09c79fb36b2c7e07 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/PolishchukSpielman/Existence.lean | Existence | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "ps_exists_p",
"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 · exact ⟨0, by simp [hB0]⟩\n by_cases hA0 :... | [
{
"name": "ps_exists_p_nonzero",
"text": "/-- Existence of `P` with `B = P * A` when both `A` and `B` are nonzero. -/\nlemma ps_exists_p_nonzero {F : Type} [Field F]\n (a_x a_y b_x b_y : ℕ) (n_x n_y : ℕ+)\n (h_bx_ge_ax : b_x ≥ a_x) (h_by_ge_ay : b_y ≥ a_y)\n (A B : F[X][Y]) (hA0 : A ≠ 0) (hB0 : B ≠... | [
{
"name": "ps_exists_p",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 31,
"n_chars": 1599,
"n_subproofs": 3,
"n_tactics": 16,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 2,
"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: Alexander Hicks, Aleph
-/
import ArkLib.Data.CodingTheory.PolishchukSpielman.Resultant
/-!
# Existence of polynomials for Polishchuk-Spielman
This file contains the core e... | /-
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.CodingTheory.PolishchukSpielman.Resultant
/-!
# Existence of polynomials for Polishchuk-Spielman
This file contains the core e... | @@ -128,6 +128,111 @@
linarith [mul_lt_mul_of_pos_left (show (b_x : ℚ) / n_x + b_y / n_y < 1 by linarith)
(show 0 < D by positivity)]
+/-- Existence of `P` with `B = P * A` when both `A` and `B` are nonzero. -/
+lemma ps_exists_p_nonzero {F : Type} [Field F]
+ (a_x a_y b_x b_y : ℕ) (n_x n_y : ℕ+)
+ (h_b... | {
"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_388712b88e50_0 | 9c84062acf997796 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/ToVCVio/ToMathlib/Data/Vector/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "Vector.mapM_id_option_map_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Vector.mapM_map]\n exact Vector.mapM_map_postcomp v (id : Option α → Option α) g",
"n_chars": 94,
... | [
{
"name": "Vector.mapM_map_postcomp",
"text": "/-- `Vector.mapM` commutes with post-composition by a pure map:\n mapping `g` after each monadic action is the same as mapping `g` over the collected vector. -/\nlemma Vector.mapM_map_postcomp {m : Type → Type} {α β γ : Type} {n : ℕ}\n [Monad m] [LawfulMo... | [
{
"name": "Vector.mapM_id_option_map_comm",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 481,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
-/
import Mathlib.Data.Vector.Basic
import VCVio.EvalDist.Monad.Basic
/-!
# Additions to VCV-io's `ToMathlib.Data.Vector.Basic`
-/
/-- `Option.map` distributes through `Vector.mapM id` ... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
-/
import Mathlib.Data.Vector.Basic
import VCVio.EvalDist.Monad.Basic
/-!
# Additions to VCV-io's `ToMathlib.Data.Vector.Basic`
-/
/-- `Vector.mapM` commutes with post-composition by a ... | @@ -10,11 +10,34 @@
# Additions to VCV-io's `ToMathlib.Data.Vector.Basic`
-/
+/-- `Vector.mapM` commutes with post-composition by a pure map:
+ mapping `g` after each monadic action is the same as mapping `g` over the collected vector. -/
+lemma Vector.mapM_map_postcomp {m : Type → Type} {α β γ : Type} {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_388712b88e50_1 | 69074578885bb284 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/ToVCVio/ToMathlib/Data/Vector/Basic.lean | Basic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "Vector.mapM_id_option_map_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Vector.mapM_map]\n exact Vector.mapM_map_postcomp v (id : Option α → Option α) g",
"n_chars": 94,
... | [
{
"name": "Vector.mapM_map_postcomp",
"text": "/-- `Vector.mapM` commutes with post-composition by a pure map:\n mapping `g` after each monadic action is the same as mapping `g` over the collected vector. -/\nlemma Vector.mapM_map_postcomp {m : Type → Type} {α β γ : Type} {n : ℕ}\n [Monad m] [LawfulMo... | [
{
"name": "Vector.mapM_bind_map_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 21,
"n_chars": 842,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 5,
"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.
-/
import Mathlib.Data.Vector.Basic
import VCVio.EvalDist.Monad.Basic
/-!
# Additions to VCV-io's `ToMathlib.Data.Vector.Basic`
-/
/-- Two `Vector.mapM` calls with pointwise-related mon... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
-/
import Mathlib.Data.Vector.Basic
import VCVio.EvalDist.Monad.Basic
/-!
# Additions to VCV-io's `ToMathlib.Data.Vector.Basic`
-/
/-- `Vector.mapM` commutes with post-composition by a ... | @@ -10,6 +10,27 @@
# Additions to VCV-io's `ToMathlib.Data.Vector.Basic`
-/
+/-- `Vector.mapM` commutes with post-composition by a pure map:
+ mapping `g` after each monadic action is the same as mapping `g` over the collected vector. -/
+lemma Vector.mapM_map_postcomp {m : Type → Type} {α β γ : Type} {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_47f6f81a1071_0 | 2b3441067214b5f5 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/TraceVanishing.lean | TraceVanishing | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "four_pow_i_geom_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply geom_sum_eq_zero_of_isUnit\n · rw [← Xpow_mul]\n have he : 4 * 2 ^ κ * i * 2 ^ (α - κ - 1) = 2 ^ (α + 1) * ... | [
{
"name": "geom_sum_eq_zero_of_isUnit",
"text": "/-- **Geometric sum vanishes when `r-1` is a unit**: if `r^n = 1` and `r - 1` is a unit (no\ndomain needed), then `∑_{i<n} r^i = 0`. Follows from `(∑ r^i)(r-1) = r^n - 1 = 0` and cancelling\nthe unit `r - 1`. This is what closes Claim 2 once `X^{4ki} - 1` is ... | [
{
"name": "four_pow_i_geom_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 34,
"n_chars": 2007,
"n_subproofs": 7,
"n_tactics": 32,
"cyclomatic": 3,
"n_automation": 9,
"n_rewrites": 16,
"n_structural": 11,
"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: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Subfield.Basis
/-!
# Trace of a Monomial: the Off-Diagonal Vanishing (Hachi §3, Claims 2 & 3)
The trace-of-mon... | /-
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.Basis
/-!
# Trace of a Monomial: the Off-Diagonal Vanishing (Hachi §3, Claims 2 & 3)
The trace-of-mon... | @@ -33,13 +33,46 @@
/-! ## Reducing the trace to a monomial sum -/
+/-- **Geometric sum vanishes when `r-1` is a unit**: if `r^n = 1` and `r - 1` is a unit (no
+domain needed), then `∑_{i<n} r^i = 0`. Follows from `(∑ r^i)(r-1) = r^n - 1 = 0` and cancelling
+the unit `r - 1`. This is what closes Claim 2 once `X^{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_47f6f81a1071_1 | 119e30e736e1512f | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/TraceVanishing.lean | TraceVanishing | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "traceH_Xpow_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 68,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨κ, rfl⟩ := hk2pow\n have hκ : κ + 1 ≤ α := succ_le_of_two_mul_two_pow_dvd hk\n have hrange : 2 ^ α / (2 * 2 ... | [
{
"name": "traceH_Xpow'",
"text": "/-- **`Tr_H(X^j) = Σ_{m∈H} X^{j·m}` for any exponent `j`** (no `j < d` bound), via the general\n`galoisAut_Xpow'` and oddness of the `Hexp` exponents. Needed for the Theorem 2 kernel, where the\nexponents `e_p + e_q·σ_{-1}` are large. -/\ntheorem traceH_Xpow' (α k j : ℕ) :... | [
{
"name": "traceH_Xpow_eq_zero",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 76,
"n_chars": 4514,
"n_subproofs": 28,
"n_tactics": 83,
"cyclomatic": 5,
"n_automation": 22,
"n_rewrites": 22,
"n_structural": 12,
"automation_only": false,
"... | 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 ArkLib.Data.Lattices.CyclotomicRing.Subfield.Basis
/-!
# Trace of a Monomial: the Off-Diagonal Vanishing (Hachi §3, Claims 2 & 3)
The trace-of-mon... | /-
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.Basis
/-!
# Trace of a Monomial: the Off-Diagonal Vanishing (Hachi §3, Claims 2 & 3)
The trace-of-mon... | @@ -33,6 +33,15 @@
/-! ## Reducing the trace to a monomial sum -/
+/-- **`Tr_H(X^j) = Σ_{m∈H} X^{j·m}` for any exponent `j`** (no `j < d` bound), via the general
+`galoisAut_Xpow'` and oddness of the `Hexp` exponents. Needed for the Theorem 2 kernel, where the
+exponents `e_p + e_q·σ_{-1}` are large. -/
+theorem 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_47f6f81a1071_2 | a63076be19aa70fc | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/TraceVanishing.lean | TraceVanishing | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "traceH_Xpow_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 68,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨κ, rfl⟩ := hk2pow\n have hκ : κ + 1 ≤ α := succ_le_of_two_mul_two_pow_dvd hk\n have hrange : 2 ^ α / (2 * 2 ... | [
{
"name": "traceH_Xpow'",
"text": "/-- **`Tr_H(X^j) = Σ_{m∈H} X^{j·m}` for any exponent `j`** (no `j < d` bound), via the general\n`galoisAut_Xpow'` and oddness of the `Hexp` exponents. Needed for the Theorem 2 kernel, where the\nexponents `e_p + e_q·σ_{-1}` are large. -/\ntheorem traceH_Xpow' (α k j : ℕ) :... | [
{
"name": "traceH_Xpow_neg_one_sq",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 83,
"n_chars": 4475,
"n_subproofs": 28,
"n_tactics": 79,
"cyclomatic": 3,
"n_automation": 24,
"n_rewrites": 17,
"n_structural": 22,
"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 ArkLib.Data.Lattices.CyclotomicRing.Subfield.Basis
/-!
# Trace of a Monomial: the Off-Diagonal Vanishing (Hachi §3, Claims 2 & 3)
The trace-of-mon... | /-
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.Basis
/-!
# Trace of a Monomial: the Off-Diagonal Vanishing (Hachi §3, Claims 2 & 3)
The trace-of-mon... | @@ -33,13 +33,96 @@
/-! ## Reducing the trace to a monomial sum -/
+/-- **`Tr_H(X^j) = Σ_{m∈H} X^{j·m}` for any exponent `j`** (no `j < d` bound), via the general
+`galoisAut_Xpow'` and oddness of the `Hexp` exponents. Needed for the Theorem 2 kernel, where the
+exponents `e_p + e_q·σ_{-1}` are large. -/
+theorem ... | {
"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_47f6f81a1071_3 | c1802510870c6b59 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Subfield/TraceVanishing.lean | TraceVanishing | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "traceH_Xpow_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 68,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨κ, rfl⟩ := hk2pow\n have hκ : κ + 1 ≤ α := succ_le_of_two_mul_two_pow_dvd hk\n have hrange : 2 ^ α / (2 * 2 ... | [
{
"name": "traceH_Xpow'",
"text": "/-- **`Tr_H(X^j) = Σ_{m∈H} X^{j·m}` for any exponent `j`** (no `j < d` bound), via the general\n`galoisAut_Xpow'` and oddness of the `Hexp` exponents. Needed for the Theorem 2 kernel, where the\nexponents `e_p + e_q·σ_{-1}` are large. -/\ntheorem traceH_Xpow' (α k j : ℕ) :... | [
{
"name": "traceH_Xpow_half",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 575,
"n_subproofs": 3,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
"max_nesti... | 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.Subfield.Basis
/-!
# Trace of a Monomial: the Off-Diagonal Vanishing (Hachi §3, Claims 2 & 3)
The trace-of-mon... | /-
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.Basis
/-!
# Trace of a Monomial: the Off-Diagonal Vanishing (Hachi §3, Claims 2 & 3)
The trace-of-mon... | @@ -33,13 +33,96 @@
/-! ## Reducing the trace to a monomial sum -/
+/-- **`Tr_H(X^j) = Σ_{m∈H} X^{j·m}` for any exponent `j`** (no `j < d` bound), via the general
+`galoisAut_Xpow'` and oddness of the `Hexp` exponents. Needed for the Theorem 2 kernel, where the
+exponents `e_p + e_q·σ_{-1}` are large. -/
+theorem ... | {
"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_7f09cab7c7aa_0 | 15530436f7daf504 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/Subdomain.lean | Subdomain | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "mem_subdomain_of_mem_subdomain_of_le",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n aesop\n (add simp [mem_fft_subdomain_iff_mem_coset_subdomain])\n (add unsafe forward [mem_subdom... | [
{
"name": "mem_fft_subdomain_iff_mem_coset_subdomain",
"text": "/-- Membership in an FFT subdomain is the same as membership in\n the corresponding coset subdomain. -/\nlemma mem_fft_subdomain_iff_mem_coset_subdomain {i : ℕ} :\n x ∈ subdomain ω i ↔ x ∈ CosetFftDomainClass.subdomain ω i := by\n simp [subd... | [
{
"name": "mem_subdomain_of_mem_subdomain_of_le",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 364,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": tr... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -60,10 +60,19 @@
def subdomain (ω : D) (i : ℕ) : SmoothFftDomain (n - i) F :=
(CosetFftDomainClass.subdomain ω i).toFftDomain
+/-- Membership in an FFT subdomain is the same as membership in
+ the corresponding coset subdomain. -/
+lemma mem_fft_subdomain_iff_mem_coset_subdomain {i : ℕ} :
+ x ∈ subdomain ω i... | {
"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_7f09cab7c7aa_1 | fe9d644937b331a3 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/Subdomain.lean | Subdomain | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 3 | [
{
"theorem_name": "subdomain_toFinset_subset_subdomain_toFinset_of_le",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " fun x hx ↦ by\n aesop (add unsafe [mem_subdomain_of_mem_subdomain_of_le])",
"n_chars": 76... | [
{
"name": "mem_subdomain_of_mem_subdomain_of_le",
"text": "/-- If `x` is a member of `subdomain ω i` it is a member of\n any `subdomain ω j` with `j ≤ i`. -/\nlemma mem_subdomain_of_mem_subdomain_of_le {i j : ℕ} (h : x ∈ subdomain ω i) (hji : j ≤ i) :\n x ∈ subdomain ω j := by\n aesop\n (add simp [mem... | [
{
"name": "subdomain_toFinset_subset_subdomain_toFinset_of_le",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 388,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automa... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -66,11 +66,20 @@
x ∈ subdomain ω i ↔ x ∈ CosetFftDomainClass.subdomain ω i := by
simp [subdomain, mem_toFftDomain_iff_mul_mem, CosetFftDomain.map_0_eq_coset_generator]
+/-- If `x` is a member of `subdomain ω i` it is a member of
+ any `subdomain ω j` with `j ≤ i`. -/
+lemma mem_subdomain_of_mem_subdomain_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... |
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