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_492f58bdb912_2 | 02baeba44992f786 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 4 | [
{
"theorem_name": "toImpl_add",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_add : (p.toImpl + q.toImpl).toPoly = (p + q).toImpl.toPoly := by\n have h_add : (p.toImpl + q.toImpl).toPoly ... | [
{
"name": "coeff_toPoly",
"text": "/-- `toPoly` preserves coefficients: coefficient of `X^i Y^j` matches. -/\ntheorem coeff_toPoly {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (f : CBivariate R) (i j : ℕ) :\n ((toPoly f).coeff j).coeff i = CBivariate.coeff (R := R) f i j := by\n rw... | [
{
"name": "ofPoly_one",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 9,
"n_chars": 309,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 7 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -138,7 +138,10 @@
have h_add_trim : ∀ p q : CPolynomial.Raw R,
p.toPoly = q.toPoly → p.trim = q.trim := by
intros p q h_eq
- have h_coeff : ∀ n, p.coeff n = q.coeff n := sorry
+ have h_coeff : ∀ n, p.coeff n = q.coeff n := by
+ intro n; exact (by
+ convert c... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_3 | cf7275bcceb9f7bb | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 4 | [
{
"theorem_name": "toImpl_add",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_add : (p.toImpl + q.toImpl).toPoly = (p + q).toImpl.toPoly := by\n have h_add : (p.toImpl + q.toImpl).toPoly ... | [
{
"name": "coeff_toPoly",
"text": "/-- `toPoly` preserves coefficients: coefficient of `X^i Y^j` matches. -/\ntheorem coeff_toPoly {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (f : CBivariate R) (i j : ℕ) :\n ((toPoly f).coeff j).coeff i = CBivariate.coeff (R := R) f i j := by\n rw... | [
{
"name": "ofPoly_mul",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 10,
"n_lines": 10,
"n_chars": 379,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 7 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -138,7 +138,10 @@
have h_add_trim : ∀ p q : CPolynomial.Raw R,
p.toPoly = q.toPoly → p.trim = q.trim := by
intros p q h_eq
- have h_coeff : ∀ n, p.coeff n = q.coeff n := sorry
+ have h_coeff : ∀ n, p.coeff n = q.coeff n := by
+ intro n; exact (by
+ convert c... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_4 | fd4f254c2b9fe2d2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 1 | [
{
"theorem_name": "toPoly_foldr_evalY_eq_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction l with\n | nil => simpa using CPolynomial.Raw.toPoly_zero\n | cons head tail ih =>\n show ((tai... | [
{
"name": "toPoly_zero",
"text": "/-- `toPoly` maps the zero bivariate polynomial to `0`. -/\nlemma toPoly_zero {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R] :\n toPoly (0 : CBivariate R) = 0 := by\n -- The sum over the empty set is zero.\n simp [CBivariate.toPoly]\n rw [ F... | [
{
"name": "toPoly_foldr_evalY_eq_sum",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 19,
"n_chars": 1029,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -286,6 +286,14 @@
map_mul' := by apply toPoly_mul
map_add' := by exact fun x y ↦ toPoly_add x y
+/-- `toPoly` maps the zero bivariate polynomial to `0`. -/
+lemma toPoly_zero {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R] :
+ toPoly (0 : CBivariate R) = 0 := by
+ -- The sum over the em... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_5 | 1772574a13a35ced | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 1 | [
{
"theorem_name": "evalY_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n show ((Array.foldr _ (CPolynomial.Raw.mk #[]) f.val).trim).toPoly = _\n rw [CPolynomial.Raw.toPoly_trim, ← Array.foldr_toLis... | [
{
"name": "toPoly_foldr_evalY_eq_sum",
"text": "/-- The deferred-trim raw Horner foldr commutes with `toPoly`: trimming the foldr\nand taking its `toPoly` image gives the sum-of-powers polynomial. -/\nprivate theorem toPoly_foldr_evalY_eq_sum {R : Type*} [BEq R] [LawfulBEq R]\n [Semiring R] (l : List (CP... | [
{
"name": "evalY_toPoly",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 22,
"n_chars": 900,
"n_subproofs": 0,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 8,
"n_rewrites": 6,
"n_structural": 1,
"automation_only": false,
"max_nesting"... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -315,6 +315,24 @@
The helper below bridges that raw fold's `toPoly` image with the `Finset.sum` form
of the polynomial evaluation. -/
+/-- The deferred-trim raw Horner foldr commutes with `toPoly`: trimming the foldr
+and taking its `toPoly` image gives the sum-of-powers polynomial. -/
+private theorem toPoly_fo... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_6 | 574aa14d34bdc447 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 4 | [
{
"theorem_name": "toImpl_add",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_add : (p.toImpl + q.toImpl).toPoly = (p + q).toImpl.toPoly := by\n have h_add : (p.toImpl + q.toImpl).toPoly ... | [
{
"name": "coeff_toPoly",
"text": "/-- `toPoly` preserves coefficients: coefficient of `X^i Y^j` matches. -/\ntheorem coeff_toPoly {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (f : CBivariate R) (i j : ℕ) :\n ((toPoly f).coeff j).coeff i = CBivariate.coeff (R := R) f i j := by\n rw... | [
{
"name": "eval_y_horner_eq_eval_y",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 29,
"n_chars": 1332,
"n_subproofs": 2,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 6,
"n_structural": 3,
"automation_only": false,
"... | 6 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -138,7 +138,10 @@
have h_add_trim : ∀ p q : CPolynomial.Raw R,
p.toPoly = q.toPoly → p.trim = q.trim := by
intros p q h_eq
- have h_coeff : ∀ n, p.coeff n = q.coeff n := sorry
+ have h_coeff : ∀ n, p.coeff n = q.coeff n := by
+ intro n; exact (by
+ convert c... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_7 | 7c9644678d1a52d4 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 4 | [
{
"theorem_name": "toImpl_add",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_add : (p.toImpl + q.toImpl).toPoly = (p + q).toImpl.toPoly := by\n have h_add : (p.toImpl + q.toImpl).toPoly ... | [
{
"name": "coeff_toPoly",
"text": "/-- `toPoly` preserves coefficients: coefficient of `X^i Y^j` matches. -/\ntheorem coeff_toPoly {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (f : CBivariate R) (i j : ℕ) :\n ((toPoly f).coeff j).coeff i = CBivariate.coeff (R := R) f i j := by\n rw... | [
{
"name": "eval_eval_horner_y_then_x_eq_eval_eval",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 9,
"n_chars": 391,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": ... | 7 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -138,7 +138,10 @@
have h_add_trim : ∀ p q : CPolynomial.Raw R,
p.toPoly = q.toPoly → p.trim = q.trim := by
intros p q h_eq
- have h_coeff : ∀ n, p.coeff n = q.coeff n := sorry
+ have h_coeff : ∀ n, p.coeff n = q.coeff n := by
+ intro n; exact (by
+ convert c... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_8 | 7aae414c2fa48cb9 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 3 | [
{
"theorem_name": "eval_y_horner_eq_eval_y",
"depth": 1,
"n_commands": 0,
"n_lines": 20,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_inj : Function.Injective (CPolynomial.toPoly (R := R)) := by\n intro p₁ p₂ h\n apply Subtype.ext\n ... | [
{
"name": "evalY_toPoly",
"text": "/--\n`evalY a` corresponds to outer evaluation at `Polynomial.C a`.\n-/\ntheorem evalY_toPoly {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (a : R) (f : CBivariate R) :\n (evalY (R := R) a f).toPoly = (toPoly f).eval (Polynomial.C a) := by\n show (... | [
{
"name": "evalEval_toPoly",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 8,
"n_chars": 400,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -336,10 +336,33 @@
/-! Correctness lemmas for evaluation, coefficients, support, and degrees. -/
section ImplementationCorrectness
+/--
+`evalY a` corresponds to outer evaluation at `Polynomial.C a`.
+-/
+theorem evalY_toPoly {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]
+ (a : R) (f : CBivari... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_9 | f92a0084d9111b1c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 4 | [
{
"theorem_name": "natDegreeY_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- The degree of the polynomial is the supremum of the exponents in its support.\n have h_deg : ∀ p : Polynomia... | [
{
"name": "support_toPoly_outer",
"text": "/-- The outer support of `toPoly f` equals the Y-support of `f`. -/\ntheorem support_toPoly_outer {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (f : CBivariate R) : (toPoly f).support = f.supportY := by\n ext x\n simp +decide [ CPolyn... | [
{
"name": "natDegreeY_toPoly",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 782,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -318,9 +318,30 @@
simpa [CBivariate.coeff] using
(CPolynomial.coeff_toPoly (p := CPolynomial.coeff f j) (i := i)).symm
+/-- The outer support of `toPoly f` equals the Y-support of `f`. -/
+theorem support_toPoly_outer {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]
+ (f : CBivariate R) : (... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_10 | c68617ea0c6a56fe | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 1 | [
{
"theorem_name": "natDegreeX_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [support_toPoly_outer, CBivariate.supportY, CBivariate.natDegreeX]\n refine Finset.sup_congr rfl ?_\n intro j hj\n ... | [
{
"name": "coeff_toPoly_Y",
"text": "/-- The outer `Y`-coefficient formula used for X-degree transport. -/\ntheorem coeff_toPoly_Y {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (f : CBivariate R) (j : ℕ) :\n (toPoly f).coeff j = CPolynomial.toPoly (f.val.coeff j) := by\n erw [ P... | [
{
"name": "natDegreeX_toPoly",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 491,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 3,
"automation_only": false,
"max_nest... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -328,10 +328,27 @@
rw [ CPolynomial.mem_support_iff, CPolynomial.toPoly_eq_zero_iff ]
aesop
+/-- The outer `Y`-coefficient formula used for X-degree transport. -/
+theorem coeff_toPoly_Y {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]
+ (f : CBivariate R) (j : ℕ) :
+ (toPoly f).co... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_11 | 37f72a5af265925e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 4 | [
{
"theorem_name": "toImpl_add",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_add : (p.toImpl + q.toImpl).toPoly = (p + q).toImpl.toPoly := by\n have h_add : (p.toImpl + q.toImpl).toPoly ... | [
{
"name": "coeff_toPoly",
"text": "/-- `toPoly` preserves coefficients: coefficient of `X^i Y^j` matches. -/\ntheorem coeff_toPoly {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (f : CBivariate R) (i j : ℕ) :\n ((toPoly f).coeff j).coeff i = CBivariate.coeff (R := R) f i j := by\n rw... | [
{
"name": "CC_toPoly",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 12,
"n_chars": 388,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -138,7 +138,10 @@
have h_add_trim : ∀ p q : CPolynomial.Raw R,
p.toPoly = q.toPoly → p.trim = q.trim := by
intros p q h_eq
- have h_coeff : ∀ n, p.coeff n = q.coeff n := sorry
+ have h_coeff : ∀ n, p.coeff n = q.coeff n := by
+ intro n; exact (by
+ convert c... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_12 | b624f72422ef9df2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 4 | [
{
"theorem_name": "toImpl_add",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_add : (p.toImpl + q.toImpl).toPoly = (p + q).toImpl.toPoly := by\n have h_add : (p.toImpl + q.toImpl).toPoly ... | [
{
"name": "coeff_toPoly",
"text": "/-- `toPoly` preserves coefficients: coefficient of `X^i Y^j` matches. -/\ntheorem coeff_toPoly {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (f : CBivariate R) (i j : ℕ) :\n ((toPoly f).coeff j).coeff i = CBivariate.coeff (R := R) f i j := by\n rw... | [
{
"name": "X_toPoly",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 11,
"n_chars": 386,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -138,7 +138,10 @@
have h_add_trim : ∀ p q : CPolynomial.Raw R,
p.toPoly = q.toPoly → p.trim = q.trim := by
intros p q h_eq
- have h_coeff : ∀ n, p.coeff n = q.coeff n := sorry
+ have h_coeff : ∀ n, p.coeff n = q.coeff n := by
+ intro n; exact (by
+ convert c... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_13 | 4091ca9123605f04 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 3 | [
{
"theorem_name": "ofPoly_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction p using Polynomial.induction_on'\n · rw [ ofPoly_add, toPoly_add,\n ‹(ofPoly _).toPoly = _›, ‹(of... | [
{
"name": "toPoly_monomial",
"text": "/-- `toPoly` sends a Y-monomial to the corresponding monomial in `R[X][Y]`. -/\nlemma toPoly_monomial {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n [DecidableEq R]\n (n : ℕ) (c : CPolynomial R) :\n toPoly (CPolynomial.monomial n c) = monomial ... | [
{
"name": "Y_toPoly",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 357,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -98,6 +98,21 @@
simp_all +decide [ CPolynomial.support ]
grind
+/-- `toPoly` sends a Y-monomial to the corresponding monomial in `R[X][Y]`. -/
+lemma toPoly_monomial {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]
+ [DecidableEq R]
+ (n : ℕ) (c : CPolynomial R) :
+ toPoly (... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_14 | 013aef5f04104cf4 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 3 | [
{
"theorem_name": "ofPoly_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction p using Polynomial.induction_on'\n · rw [ ofPoly_add, toPoly_add,\n ‹(ofPoly _).toPoly = _›, ‹(of... | [
{
"name": "toPoly_monomial",
"text": "/-- `toPoly` sends a Y-monomial to the corresponding monomial in `R[X][Y]`. -/\nlemma toPoly_monomial {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n [DecidableEq R]\n (n : ℕ) (c : CPolynomial R) :\n toPoly (CPolynomial.monomial n c) = monomial ... | [
{
"name": "monomialXY_toPoly",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 477,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -98,6 +98,21 @@
simp_all +decide [ CPolynomial.support ]
grind
+/-- `toPoly` sends a Y-monomial to the corresponding monomial in `R[X][Y]`. -/
+lemma toPoly_monomial {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]
+ [DecidableEq R]
+ (n : ℕ) (c : CPolynomial R) :
+ toPoly (... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_15 | 6d9701507af9d45f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 4 | [
{
"theorem_name": "natDegreeY_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- The degree of the polynomial is the supremum of the exponents in its support.\n have h_deg : ∀ p : Polynomia... | [
{
"name": "support_toPoly_outer",
"text": "/-- The outer support of `toPoly f` equals the Y-support of `f`. -/\ntheorem support_toPoly_outer {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (f : CBivariate R) : (toPoly f).support = f.supportY := by\n ext x\n simp +decide [ CPolyn... | [
{
"name": "supportX_toPoly",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 498,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_nestin... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -318,13 +318,28 @@
simpa [CBivariate.coeff] using
(CPolynomial.coeff_toPoly (p := CPolynomial.coeff f j) (i := i)).symm
+/-- The outer support of `toPoly f` equals the Y-support of `f`. -/
+theorem support_toPoly_outer {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]
+ (f : CBivariate R) : ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_16 | f5653a29690055bd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 4 | [
{
"theorem_name": "natDegreeY_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- The degree of the polynomial is the supremum of the exponents in its support.\n have h_deg : ∀ p : Polynomia... | [
{
"name": "support_toPoly_outer",
"text": "/-- The outer support of `toPoly f` equals the Y-support of `f`. -/\ntheorem support_toPoly_outer {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (f : CBivariate R) : (toPoly f).support = f.supportY := by\n ext x\n simp +decide [ CPolyn... | [
{
"name": "totalDegree_toPoly",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 15,
"n_chars": 554,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": false,
"max_nes... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -318,13 +318,29 @@
simpa [CBivariate.coeff] using
(CPolynomial.coeff_toPoly (p := CPolynomial.coeff f j) (i := i)).symm
+/-- The outer support of `toPoly f` equals the Y-support of `f`. -/
+theorem support_toPoly_outer {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]
+ (f : CBivariate R) : ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_17 | 491e83da4b7b94ed | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 3 | [
{
"theorem_name": "evalX_toPoly_eval_commute",
"depth": 1,
"n_commands": 0,
"n_lines": 34,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_lhs :\n (evalX (R := R) a f).toPoly.eval y =\n ∑ j ∈ (f.toPoly).support, ((f.toPoly).coeff j)... | [
{
"name": "evalX_toPoly_coeff",
"text": "/--\n`evalX a` evaluates each inner coefficient at `a`.\n-/\ntheorem evalX_toPoly_coeff {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n [DecidableEq R] (a : R) (f : CBivariate R) (j : ℕ) :\n ((evalX (R := R) a f).toPoly).coeff j = ((toPoly f).co... | [
{
"name": "evalX_toPoly_eval_commute",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 41,
"n_chars": 1863,
"n_subproofs": 3,
"n_tactics": 35,
"cyclomatic": 2,
"n_automation": 13,
"n_rewrites": 5,
"n_structural": 7,
"automation_only": false,
... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -319,6 +319,41 @@
(CPolynomial.coeff_toPoly (p := CPolynomial.coeff f j) (i := i)).symm
/--
+`evalX a` evaluates each inner coefficient at `a`.
+-/
+theorem evalX_toPoly_coeff {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]
+ [DecidableEq R] (a : R) (f : CBivariate R) (j : ℕ) :
+ ((evalX ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_18 | e3239dfb9fde3473 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 1 | [
{
"theorem_name": "evalX_toPoly_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa using\n (evalX_toPoly_eval_commute (R := R) (a := a) (y := y) (hc := Commute.all a y) (f := f))",
"n_chars":... | [
{
"name": "evalX_toPoly_eval_commute",
"text": "/--\n`evalX` is compatible with full bivariate evaluation when `a` and `y` commute.\n-/\ntheorem evalX_toPoly_eval_commute {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n [DecidableEq R] (a y : R) (hc : Commute a y) (f : CBivariate R) :\n ... | [
{
"name": "evalX_toPoly_eval",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 10,
"n_chars": 383,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesti... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -354,11 +354,53 @@
simp [Polynomial.coeff_monomial]
/--
+`evalX` is compatible with full bivariate evaluation when `a` and `y` commute.
+-/
+theorem evalX_toPoly_eval_commute {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]
+ [DecidableEq R] (a y : R) (hc : Commute a y) (f : CBivariate ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_19 | f89346e8fbc8c563 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 3 | [
{
"theorem_name": "evalX_toPoly_eval_commute",
"depth": 1,
"n_commands": 0,
"n_lines": 34,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_lhs :\n (evalX (R := R) a f).toPoly.eval y =\n ∑ j ∈ (f.toPoly).support, ((f.toPoly).coeff j)... | [
{
"name": "evalX_toPoly_coeff",
"text": "/--\n`evalX a` evaluates each inner coefficient at `a`.\n-/\ntheorem evalX_toPoly_coeff {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n [DecidableEq R] (a : R) (f : CBivariate R) (j : ℕ) :\n ((evalX (R := R) a f).toPoly).coeff j = ((toPoly f).co... | [
{
"name": "eval_eval_horner_x_then_y_eq_eval_eval",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 10,
"n_lines": 37,
"n_chars": 1774,
"n_subproofs": 2,
"n_tactics": 30,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 5,
"n_structural": 3,
"automation_onl... | 9 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -373,6 +373,41 @@
(CPolynomial.coeff_toPoly (p := CPolynomial.coeff f j) (i := i)).symm
/--
+`evalX a` evaluates each inner coefficient at `a`.
+-/
+theorem evalX_toPoly_coeff {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]
+ [DecidableEq R] (a : R) (f : CBivariate R) (j : ℕ) :
+ ((evalX ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_20 | 30b8c4ee8c395c43 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 3 | [
{
"theorem_name": "evalX_toPoly_eval_commute",
"depth": 1,
"n_commands": 0,
"n_lines": 34,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_lhs :\n (evalX (R := R) a f).toPoly.eval y =\n ∑ j ∈ (f.toPoly).support, ((f.toPoly).coeff j)... | [
{
"name": "evalX_toPoly_coeff",
"text": "/--\n`evalX a` evaluates each inner coefficient at `a`.\n-/\ntheorem evalX_toPoly_coeff {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n [DecidableEq R] (a : R) (f : CBivariate R) (j : ℕ) :\n ((evalX (R := R) a f).toPoly).coeff j = ((toPoly f).co... | [
{
"name": "evalX_toPoly_eval_commute_converse",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 29,
"n_chars": 1130,
"n_subproofs": 4,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 5,
"n_structural": 2,
"automation_only": f... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -330,6 +330,41 @@
(CPolynomial.monomial_toPoly (R := R) n c)
/--
+`evalX a` evaluates each inner coefficient at `a`.
+-/
+theorem evalX_toPoly_coeff {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]
+ [DecidableEq R] (a : R) (f : CBivariate R) (j : ℕ) :
+ ((evalX (R := R) a f).toPoly).coeff... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_21 | 3bd8d27fe5aa606b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 2 | [
{
"theorem_name": "eval_eval_horner_x_then_y_eq_eval_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 30,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let coeffEval : CPolynomial R →+* R :=\n (Polynomial.evalRingHom x).comp (CPolynomial.ringEquiv ... | [
{
"name": "evalX_toPoly_eval",
"text": "/--\n`evalX_toPoly_eval_commute` specialized to commutative rings.\n-/\ntheorem evalX_toPoly_eval {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [CommSemiring R]\n [DecidableEq R] (a y : R) (f : CBivariate R) :\n (evalX (R := R) a f).eval y = (toPoly f).evalEv... | [
{
"name": "eval_comm",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 7,
"n_lines": 12,
"n_chars": 487,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 6 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -441,6 +441,15 @@
· exact fun j hj => hc.pow_right j
/--
+`evalX_toPoly_eval_commute` specialized to commutative rings.
+-/
+theorem evalX_toPoly_eval {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [CommSemiring R]
+ [DecidableEq R] (a y : R) (f : CBivariate R) :
+ (evalX (R := R) a f).eval y = (toPo... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_22 | ad39ef8d21aa039c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 4 | [
{
"theorem_name": "natDegreeY_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- The degree of the polynomial is the supremum of the exponents in its support.\n have h_deg : ∀ p : Polynomia... | [
{
"name": "support_toPoly_outer",
"text": "/-- The outer support of `toPoly f` equals the Y-support of `f`. -/\ntheorem support_toPoly_outer {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (f : CBivariate R) : (toPoly f).support = f.supportY := by\n ext x\n simp +decide [ CPolyn... | [
{
"name": "leadingCoeffY_toPoly",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 17,
"n_chars": 680,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -318,9 +318,30 @@
simpa [CBivariate.coeff] using
(CPolynomial.coeff_toPoly (p := CPolynomial.coeff f j) (i := i)).symm
+/-- The outer support of `toPoly f` equals the Y-support of `f`. -/
+theorem support_toPoly_outer {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]
+ (f : CBivariate R) : (... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_23 | 784b33629b302b2a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 23 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 4 | [
{
"theorem_name": "toImpl_add",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_add : (p.toImpl + q.toImpl).toPoly = (p + q).toImpl.toPoly := by\n have h_add : (p.toImpl + q.toImpl).toPoly ... | [
{
"name": "coeff_toPoly",
"text": "/-- `toPoly` preserves coefficients: coefficient of `X^i Y^j` matches. -/\ntheorem coeff_toPoly {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (f : CBivariate R) (i j : ℕ) :\n ((toPoly f).coeff j).coeff i = CBivariate.coeff (R := R) f i j := by\n rw... | [
{
"name": "swap_toPoly_coeff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 108,
"n_chars": 4856,
"n_subproofs": 13,
"n_tactics": 101,
"cyclomatic": 3,
"n_automation": 16,
"n_rewrites": 20,
"n_structural": 18,
"automation_only": false,
"... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -138,7 +138,10 @@
have h_add_trim : ∀ p q : CPolynomial.Raw R,
p.toPoly = q.toPoly → p.trim = q.trim := by
intros p q h_eq
- have h_coeff : ∀ n, p.coeff n = q.coeff n := sorry
+ have h_coeff : ∀ n, p.coeff n = q.coeff n := by
+ intro n; exact (by
+ convert c... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_492f58bdb912_24 | 30799fac5da2b8ea | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 24 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 4 | [
{
"theorem_name": "natDegreeY_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- The degree of the polynomial is the supremum of the exponents in its support.\n have h_deg : ∀ p : Polynomia... | [
{
"name": "support_toPoly_outer",
"text": "/-- The outer support of `toPoly f` equals the Y-support of `f`. -/\ntheorem support_toPoly_outer {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]\n (f : CBivariate R) : (toPoly f).support = f.supportY := by\n ext x\n simp +decide [ CPolyn... | [
{
"name": "leadingCoeffX_toPoly",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 10,
"n_chars": 411,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_ne... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Derek Sorensen
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly.Impl
import Mathlib.Algebra.Polynomial.Bivariate
/-!
# Equivalence with Mathlib Bivariate Polynomials
T... | @@ -318,9 +318,30 @@
simpa [CBivariate.coeff] using
(CPolynomial.coeff_toPoly (p := CPolynomial.coeff f j) (i := i)).symm
+/-- The outer support of `toPoly f` equals the Y-support of `f`. -/
+theorem support_toPoly_outer {R : Type*} [BEq R] [LawfulBEq R] [Nontrivial R] [Semiring R]
+ (f : CBivariate R) : (... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_0 | 0b49b3a2ed302433 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "outerCoeff_partialDerivX",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n outerCoeff_support_monomial f CPolynomial.derivative CPolynomial.derivative_zero j",
"n_chars": 85,
"n_subpro... | [
{
"name": "outerCoeff_support_monomial",
"text": "/-- Outer coefficient of a `support`-sum of monomials whose `Y`-coefficients are mapped by a\nzero-preserving `g`: the `j`-th coefficient is `g` applied to the `j`-th `Y`-coefficient. -/\ntheorem outerCoeff_support_monomial [Semiring R] [BEq R] [LawfulBEq R]... | [
{
"name": "outerCoeff_partialDerivX",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 412,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -49,11 +49,29 @@
(f : CBivariate R) : CBivariate R :=
CPolynomial.derivative f
+/-- Outer coefficient of a `support`-sum of monomials whose `Y`-coefficients are mapped by a
+zero-preserving `g`: the `j`-th coefficient is `g` applied to the `j`-th `Y`-coefficient. -/
+theorem outerCoeff_support_monomial [Se... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_1 | e211b18b1abc677b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "coeff_partialDerivX",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [coeff_eq_coeff_coeff, outerCoeff_partialDerivX, CPolynomial.coeff_derivative]",
"n_chars": 94,
"n_su... | [
{
"name": "outerCoeff_partialDerivX",
"text": "/-- Outer coefficient of the X-partial derivative: differentiate the j-th Y-coefficient. -/\ntheorem outerCoeff_partialDerivX [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (f : CBivariate R) (j : ℕ) :\n CPolynomial.coeff (partialDeri... | [
{
"name": "coeff_partialDerivX",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 385,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nest... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -66,11 +66,19 @@
change g (CPolynomial.coeff f j) = 0
rw [hj]; exact hg
+/-- Outer coefficient of the X-partial derivative: differentiate the j-th Y-coefficient. -/
+theorem outerCoeff_partialDerivX [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]
+ (f : CBivariate R) (j : ℕ) :
+ C... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_2 | cba3d0615ead8568 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "partialDerivX_add",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold CBivariate\n rw [CPolynomial.eq_iff_coeff]\n intro j\n rw [CPolynomial.eq_iff_coeff]\n intro i\n simp only [... | [
{
"name": "coeff_partialDerivX",
"text": "/-- Coefficient formula for the X-partial derivative. -/\ntheorem coeff_partialDerivX [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (f : CBivariate R) (i j : ℕ) :\n CBivariate.coeff (partialDerivX f) i j =\n CBivariate.coeff f (i + 1... | [
{
"name": "partialDerivX_add",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 15,
"n_chars": 496,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 3,
"automation_only": false,
"max_nes... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -73,10 +73,26 @@
CPolynomial.derivative (CPolynomial.coeff f j) :=
outerCoeff_support_monomial f CPolynomial.derivative CPolynomial.derivative_zero j
+/-- Coefficient formula for the X-partial derivative. -/
+theorem coeff_partialDerivX [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_3 | 53af1d12107775cb | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "coeff_partialDerivX",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [coeff_eq_coeff_coeff, outerCoeff_partialDerivX, CPolynomial.coeff_derivative]",
"n_chars": 94,
"n_su... | [
{
"name": "outerCoeff_partialDerivX",
"text": "/-- Outer coefficient of the X-partial derivative: differentiate the j-th Y-coefficient. -/\ntheorem outerCoeff_partialDerivX [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (f : CBivariate R) (j : ℕ) :\n CPolynomial.coeff (partialDeri... | [
{
"name": "partialDerivX_toPoly",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 409,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_ne... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -66,11 +66,20 @@
change g (CPolynomial.coeff f j) = 0
rw [hj]; exact hg
+/-- Outer coefficient of the X-partial derivative: differentiate the j-th Y-coefficient. -/
+theorem outerCoeff_partialDerivX [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]
+ (f : CBivariate R) (j : ℕ) :
+ C... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_4 | 3a47f2e56561a333 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "partialDerivX_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply CBivariate.ringEquiv.injective\n show toPoly (partialDerivX (f * g)) = toPoly (partialDerivX f * g + f * partialD... | [
{
"name": "partialDerivX_toPoly",
"text": "/-- The X-partial derivative differentiates each Y-coefficient under `toPoly`. -/\ntheorem partialDerivX_toPoly [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (f : CBivariate R) (j : ℕ) :\n (toPoly (partialDerivX f)).coeff j =\n Poly... | [
{
"name": "partialDerivX_mul",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 15,
"n_chars": 744,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 4,
"automation_only": false,
"max_nes... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -73,10 +73,27 @@
CPolynomial.derivative (CPolynomial.coeff f j) :=
outerCoeff_support_monomial f CPolynomial.derivative CPolynomial.derivative_zero j
+/-- The X-partial derivative differentiates each Y-coefficient under `toPoly`. -/
+theorem partialDerivX_toPoly [Semiring R] [BEq R] [LawfulBEq R] [Nontri... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_5 | bbcf077bc47dfd3f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "partialDerivX_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply CBivariate.ringEquiv.injective\n show toPoly (partialDerivX (f * g)) = toPoly (partialDerivX f * g + f * partialD... | [
{
"name": "partialDerivX_toPoly",
"text": "/-- The X-partial derivative differentiates each Y-coefficient under `toPoly`. -/\ntheorem partialDerivX_toPoly [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (f : CBivariate R) (j : ℕ) :\n (toPoly (partialDerivX f)).coeff j =\n Poly... | [
{
"name": "iterPartialDerivX_toPoly",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 12,
"n_chars": 547,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"m... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -73,6 +73,14 @@
CPolynomial.derivative (CPolynomial.coeff f j) :=
outerCoeff_support_monomial f CPolynomial.derivative CPolynomial.derivative_zero j
+/-- The X-partial derivative differentiates each Y-coefficient under `toPoly`. -/
+theorem partialDerivX_toPoly [Semiring R] [BEq R] [LawfulBEq R] [Nontriv... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_6 | 7c5fa52728b272b9 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "iterPartialDerivY_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n generalizing f with\n | zero => rfl\n | succ n ih =>\n show toPoly (iterPartialDerivY n (partialD... | [
{
"name": "partialDerivY_toPoly",
"text": "/-- The Y-partial derivative corresponds to `Polynomial.derivative` under `toPoly`. -/\ntheorem partialDerivY_toPoly [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (f : CBivariate R) :\n toPoly (partialDerivY f) = Polynomial.derivative (t... | [
{
"name": "iterPartialDerivY_toPoly",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 510,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -49,6 +49,15 @@
(f : CBivariate R) : CBivariate R :=
CPolynomial.derivative f
+/-- The Y-partial derivative corresponds to `Polynomial.derivative` under `toPoly`. -/
+theorem partialDerivY_toPoly [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]
+ (f : CBivariate R) :
+ toPoly (partia... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_7 | 40b809cc715a580f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "partialDerivX_add",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold CBivariate\n rw [CPolynomial.eq_iff_coeff]\n intro j\n rw [CPolynomial.eq_iff_coeff]\n intro i\n simp only [... | [
{
"name": "coeff_partialDerivX",
"text": "/-- Coefficient formula for the X-partial derivative. -/\ntheorem coeff_partialDerivX [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (f : CBivariate R) (i j : ℕ) :\n CBivariate.coeff (partialDerivX f) i j =\n CBivariate.coeff f (i + 1... | [
{
"name": "partialDerivX_partialDerivY_comm",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 14,
"n_chars": 522,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 5,
"automation_only": false... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -73,6 +73,13 @@
CPolynomial.derivative (CPolynomial.coeff f j) :=
outerCoeff_support_monomial f CPolynomial.derivative CPolynomial.derivative_zero j
+/-- Coefficient formula for the X-partial derivative. -/
+theorem coeff_partialDerivX [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_8 | 1b6f961317a32ee2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "partialDerivX_partialDerivY_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply CPolynomial.eq_iff_coeff.mpr\n intro j\n apply CPolynomial.eq_iff_coeff.mpr\n intro i\n ... | [
{
"name": "coeff_partialDerivY",
"text": "/-- Coefficient formula for the Y-partial derivative. -/\ntheorem coeff_partialDerivY [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (f : CBivariate R) (i j : ℕ) :\n CBivariate.coeff (partialDerivY f) i j =\n CBivariate.coeff f i (j + 1) * (↑(j + 1) ... | [
{
"name": "mixedPartials_comm",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 9,
"n_chars": 378,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nest... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -80,6 +80,17 @@
CBivariate.coeff f (i + 1) j * (↑(i + 1) : R) := by
simp only [coeff_eq_coeff_coeff, outerCoeff_partialDerivX, CPolynomial.coeff_derivative]
+/-- Coefficient formula for the Y-partial derivative. -/
+theorem coeff_partialDerivY [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (f : C... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_9 | 9b82fce1604fdf69 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "outerCoeff_partialDerivX",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n outerCoeff_support_monomial f CPolynomial.derivative CPolynomial.derivative_zero j",
"n_chars": 85,
"n_subpro... | [
{
"name": "outerCoeff_support_monomial",
"text": "/-- Outer coefficient of a `support`-sum of monomials whose `Y`-coefficients are mapped by a\nzero-preserving `g`: the `j`-th coefficient is `g` applied to the `j`-th `Y`-coefficient. -/\ntheorem outerCoeff_support_monomial [Semiring R] [BEq R] [LawfulBEq R]... | [
{
"name": "outerCoeff_shiftX",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 390,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -49,6 +49,23 @@
(f : CBivariate R) : CBivariate R :=
CPolynomial.derivative f
+/-- Outer coefficient of a `support`-sum of monomials whose `Y`-coefficients are mapped by a
+zero-preserving `g`: the `j`-th coefficient is `g` applied to the `j`-th `Y`-coefficient. -/
+theorem outerCoeff_support_monomial [Sem... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_10 | 21185f9ddbc699cd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "shiftX_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Polynomial.ext\n intro j\n rw [toPoly_coeff, outerCoeff_shiftX, CPolynomial.taylor_toPoly, Polynomial.coeff_map,\n ... | [
{
"name": "outerCoeff_shiftX",
"text": "/-- Outer coefficient of the X-shift: Taylor-shift the j-th Y-coefficient. -/\ntheorem outerCoeff_shiftX [CommSemiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (a : R) (P : CBivariate R) (j : ℕ) :\n CPolynomial.coeff (shiftX a P) j = CPolynomial... | [
{
"name": "shiftX_toPoly",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 510,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nesting"... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -110,11 +110,21 @@
List.all (List.range (k + 1)) fun i ↦
CBivariate.coeff (shiftC a b Q) i (k - i) == 0
+/-- Outer coefficient of the X-shift: Taylor-shift the j-th Y-coefficient. -/
+theorem outerCoeff_shiftX [CommSemiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]
+ (a : R) (P : CBiva... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_11 | d5fb052857519534 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "shiftC_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold shiftC\n rw [shiftX_toPoly, shiftY_toPoly]\n rfl",
"n_chars": 61,
"n_subproofs": 0,
"n_tactics": 4,
... | [
{
"name": "shiftX_toPoly",
"text": "/-- The inner (X) shift corresponds to `X ↦ X + a` under `toPoly`. -/\ntheorem shiftX_toPoly [CommSemiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (a : R) (P : CBivariate R) :\n (shiftX a P).toPoly\n = (P.toPoly).map (Polynomial.compRingHom (P... | [
{
"name": "shiftC_toPoly",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 9,
"n_chars": 345,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting":... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -129,10 +129,23 @@
CPolynomial.coeff (shiftX a P) j = CPolynomial.taylor a (CPolynomial.coeff P j) :=
outerCoeff_support_monomial P (CPolynomial.taylor a) (CPolynomial.taylor_zero a) j
+/-- The inner (X) shift corresponds to `X ↦ X + a` under `toPoly`. -/
+theorem shiftX_toPoly [CommSemiring R] [BEq R] [La... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_12 | 7445fdcf1a041603 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "coeff_shiftC_zero_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [coeff_eq_coeff_coeff]\n unfold shiftC\n rw [outerCoeff_shiftX, CPolynomial.taylor_coeff_zero]\n unfold shiftY... | [
{
"name": "eval_C_eq_evalY",
"text": "/-- Evaluating the outer variable at the constant `C b` agrees with the Horner evaluator `evalY`. -/\ntheorem eval_C_eq_evalY [CommSemiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (b : R) (Q : CBivariate R) :\n CPolynomial.eval (CPolynomial.C b) Q = evalY b Q :=... | [
{
"name": "coeff_shiftC_zero_zero",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 13,
"n_chars": 464,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 7,
"n_structural": 0,
"automation_only": false,
"max... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -116,10 +116,27 @@
CPolynomial.coeff (shiftX a P) j = CPolynomial.taylor a (CPolynomial.coeff P j) :=
outerCoeff_support_monomial P (CPolynomial.taylor a) (CPolynomial.taylor_zero a) j
+/-- Evaluating the outer variable at the constant `C b` agrees with the Horner evaluator `evalY`. -/
+theorem eval_C_eq_e... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_13 | a2abff784d3fcb17 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "hasMultiplicity_one_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold hasMultiplicity\n constructor\n · intro h; have := h 0 0 (by omega); rwa [coeff_shiftC_zero_zero] at this\... | [
{
"name": "coeff_shiftC_zero_zero",
"text": "/-- The (0,0) coefficient of the shift is evaluation at the point. -/\ntheorem coeff_shiftC_zero_zero [CommSemiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (a b : R) (Q : CBivariate R) :\n CBivariate.coeff (shiftC a b Q) 0 0 = evalEval a b... | [
{
"name": "hasMultiplicity_one_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 12,
"n_chars": 509,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
"ma... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -126,14 +126,28 @@
exact (Polynomial.eval_map_apply (p := CPolynomial.toPoly Q)
(CPolynomial.ringEquiv (R := R)).toRingHom (CPolynomial.C b)).symm
+/-- The (0,0) coefficient of the shift is evaluation at the point. -/
+theorem coeff_shiftC_zero_zero [CommSemiring R] [BEq R] [LawfulBEq R] [Nontrivial ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_da28c7b694c4_14 | ed2864da7a2d4097 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Deriv.lean | Deriv | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "shiftC_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold shiftC\n rw [shiftX_toPoly, shiftY_toPoly]\n rfl",
"n_chars": 61,
"n_subproofs": 0,
"n_tactics": 4,
... | [
{
"name": "shiftX_toPoly",
"text": "/-- The inner (X) shift corresponds to `X ↦ X + a` under `toPoly`. -/\ntheorem shiftX_toPoly [CommSemiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (a : R) (P : CBivariate R) :\n (shiftX a P).toPoly\n = (P.toPoly).map (Polynomial.compRingHom (P... | [
{
"name": "hasMultiplicity_iff_rootMultiplicity",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 14,
"n_chars": 778,
"n_subproofs": 1,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": f... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Univariate.Deriv
import CompPoly.ToMathlib.Polynomial.BivariateMultiplicity
import Mathl... | @@ -129,10 +129,23 @@
CPolynomial.coeff (shiftX a P) j = CPolynomial.taylor a (CPolynomial.coeff P j) :=
outerCoeff_support_monomial P (CPolynomial.taylor a) (CPolynomial.taylor_zero a) j
+/-- The inner (X) shift corresponds to `X ↦ X + a` under `toPoly`. -/
+theorem shiftX_toPoly [CommSemiring R] [BEq R] [La... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_0 | 6f1647ba9e6c1623 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 1 | [
{
"theorem_name": "composeYCoeff_eq_fold_range_of_le",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold CBivariate.composeYCoeff\n have hsplit : List.range' 0 M =\n List.range' 0 Q.val.size ++ Li... | [
{
"name": "cpoly_mulPowCoeff_zero_left",
"text": "private theorem cpoly_mulPowCoeff_zero_left {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (P : CPolynomial F) (y n : Nat) :\n CPolynomial.mulPowCoeff (0 : CPolynomial F) P y n = 0 := by\n rw [cpoly_mulPowCoeff_eq_coeff_mul_pow, CPolynomial.zero_m... | [
{
"name": "composeYCoeff_eq_fold_range_of_le",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 24,
"n_chars": 997,
"n_subproofs": 4,
"n_tactics": 16,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 3,
"n_structural": 3,
"automation_only": fal... | 3 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -62,6 +62,13 @@
have hile : i ≤ n := Nat.lt_succ_iff.mp (Finset.mem_range.mp hi)
rw [hcoeff i hile]
+private theorem cpoly_mulPowCoeff_zero_left {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (P : CPolynomial F) (y n : Nat) :
+ CPolynomial.mulPowCoeff (0 : CPolynomial F) P y n = 0 := by
+ rw [cpol... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_1 | 2484d2966fb56934 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 1 | [
{
"theorem_name": "composeY_coeff_congr_of_coeff_eq_le",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← composeYCoeff_eq_composeY_coeff Q p n,\n ← composeYCoeff_eq_composeY_coeff R p n]\n let M :=... | [
{
"name": "cpoly_mul_coeff_congr_left_of_coeff_eq_le",
"text": "private theorem cpoly_mul_coeff_congr_left_of_coeff_eq_le {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n {P Q R : CPolynomial F} {n : Nat}\n (hcoeff : ∀ i, i ≤ n → P.coeff i = Q.coeff i) :\n (P * R).coeff n = (Q * R).coeff n := by\... | [
{
"name": "composeY_coeff_congr_of_coeff_eq_le",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 21,
"n_chars": 889,
"n_subproofs": 0,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 4,
"automation_only": f... | 5 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -51,6 +51,17 @@
_ = (n + 1) * d := by
rw [Nat.succ_mul, Nat.add_comm])
+private theorem cpoly_mul_coeff_congr_left_of_coeff_eq_le {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ {P Q R : CPolynomial F} {n : Nat}
+ (hcoeff : ∀ i, i ≤ n → P.coeff i = Q.coeff i) :
+ (P * R).coeff n... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_2 | 4ec8d71ef47331a1 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 1 | [
{
"theorem_name": "substituteYPolynomialPlusXPowerYTruncated_coeff_eq_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 88,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let lowEq : CBivariate F → CBivariate F → Prop :=\n fun A B ↦ ∀ x y, x < N → C... | [
{
"name": "cbivar_coeff_add",
"text": "private theorem cbivar_coeff_add {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (Q R : CBivariate F) (i j : Nat) :\n CBivariate.coeff (Q + R) i j = CBivariate.coeff Q i j + CBivariate.coeff R i j := by\n have houter :=\n congrArg (fun row : CPolynomial F ... | [
{
"name": "substituteYPolynomialPlusXPowerYTruncated_coeff_eq_of_lt",
"fan_in": 4,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 94,
"n_chars": 3702,
"n_subproofs": 5,
"n_tactics": 88,
"cyclomatic": 3,
"n_automation": 6,
"n_rewrites": 9,
"n_structural": 17,
... | 3 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -191,6 +191,17 @@
intro i hi
simpa [CBivariate.coeff] using hcoeff i y hi
+private theorem cbivar_coeff_add {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (Q R : CBivariate F) (i j : Nat) :
+ CBivariate.coeff (Q + R) i j = CBivariate.coeff Q i j + CBivariate.coeff R i j := by
+ have houter :=
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_3 | 4fff54ceef0580a1 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 1 | [
{
"theorem_name": "shiftedSubstitutionCoeffTerm_top_coeff",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold shiftedSubstitutionCoeffTerm\n rw [Nat.sub_self]\n simp only [Nat.choose_self, Nat.cast_one... | [
{
"name": "cpoly_coeff_mul_X_pow",
"text": "private theorem cpoly_coeff_mul_X_pow {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (q : CPolynomial F) (n x : Nat) :\n (q * CPolynomial.X ^ n).coeff (x + n) = q.coeff x := by\n rw [CPolynomial.coeff_toPoly]\n rw [CPolynomial.toPoly_mul, CPolynomial.t... | [
{
"name": "shiftedSubstitutionCoeffTerm_top_coeff",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 12,
"n_chars": 444,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 0,
"automation_only":... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -318,6 +318,16 @@
unfold substituteYPolynomialPlusXPowerYTruncated substituteYPolynomialPlusXPowerY
exact houter (List.range' 0 Q.val.size) 0 0 hzero i j hi
+private theorem cpoly_coeff_mul_X_pow {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (q : CPolynomial F) (n x : Nat) :
+ (q * CPolynomial.X ^... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_4 | 2c248e609543ce3e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 1 | [
{
"theorem_name": "shiftedSubstitutionCoeffTerm_coeff_zero_of_r_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold shiftedSubstitutionCoeffTerm\n have hpow : 0 < t * r := Nat.mul_pos ht hr\n simpa... | [
{
"name": "cpoly_coeff_mul_X_pow_zero",
"text": "private theorem cpoly_coeff_mul_X_pow_zero {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (q : CPolynomial F) {n : Nat} (hn : 0 < n) :\n (q * CPolynomial.X ^ n).coeff 0 = 0 := by\n rw [CPolynomial.coeff_toPoly]\n rw [CPolynomial.toPoly_mul, CPolyn... | [
{
"name": "shiftedSubstitutionCoeffTerm_coeff_zero_of_r_pos",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 470,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automat... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -328,6 +328,16 @@
rw [Polynomial.coeff_X_pow_mul]
rw [← CPolynomial.coeff_toPoly]
+private theorem cpoly_coeff_mul_X_pow_zero {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (q : CPolynomial F) {n : Nat} (hn : 0 < n) :
+ (q * CPolynomial.X ^ n).coeff 0 = 0 := by
+ rw [CPolynomial.coeff_toPoly]
+ r... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_5 | 33d33f765a83f85e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 2 | [
{
"theorem_name": "polynomialPrefix_add_shift_dropXPower",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CPolynomial.eq_iff_coeff]\n intro i\n rw [CPolynomial.coeff_add, shiftPolynomialByXPower_coeff... | [
{
"name": "shiftPolynomialByXPower_coeff",
"text": "private theorem shiftPolynomialByXPower_coeff {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (q : CPolynomial F) (t i : Nat) :\n (shiftPolynomialByXPower q t).coeff i = if t ≤ i then q.coeff (i - t) else 0 := by\n unfold shiftPolynomialByXPower\... | [
{
"name": "polynomialPrefix_add_shift_dropXPower",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 678,
"n_subproofs": 2,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 11,
"n_structural": 1,
"automation_only"... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -695,10 +695,41 @@
rw [htop] at hzeroCoeff
exact hcoeff_ne hzeroCoeff
+private theorem shiftPolynomialByXPower_coeff {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (q : CPolynomial F) (t i : Nat) :
+ (shiftPolynomialByXPower q t).coeff i = if t ≤ i then q.coeff (i - t) else 0 := by
+ unfold shiftP... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_6 | f8767a0c9cdaca40 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 1 | [
{
"theorem_name": "degreeLt_dropXPower_of_degreeLt_of_le",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply degreeLt_of_degreeLtBool\n rw [degreeLtBool]\n have hb := degreeLtBool_of_degreeLt hdegree\n ... | [
{
"name": "dropXPower_size_le",
"text": "private theorem dropXPower_size_le {F : Type*} [Zero F]\n (p : CPolynomial F) (t : Nat) :\n (CPolynomial.dropXPower p t).val.size ≤ p.val.size - t := by\n induction t generalizing p with\n | zero => simp [CPolynomial.dropXPower]\n | succ t ih =>\n rw [C... | [
{
"name": "degreeLt_dropXPower_of_degreeLt_of_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 401,
"n_subproofs": 2,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": ... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -756,6 +756,25 @@
| zero => simp
| succ i => simp
+private theorem dropXPower_size_le {F : Type*} [Zero F]
+ (p : CPolynomial F) (t : Nat) :
+ (CPolynomial.dropXPower p t).val.size ≤ p.val.size - t := by
+ induction t generalizing p with
+ | zero => simp [CPolynomial.dropXPower]
+ | succ t ih =>
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_7 | 86a42bffe44ffaac | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 1 | [
{
"theorem_name": "polynomialPrefix_rootPrefix_eq_of_degreeLt",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold MatchesRootPrefix MatchesPrefix at hmatch\n rw [← hmatch]\n rw [polynomialPrefix_prefix... | [
{
"name": "polynomialPrefix_prefix_of_le",
"text": "private theorem polynomialPrefix_prefix_of_le {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (p : CPolynomial F) {k t : Nat} (hkt : k ≤ t) :\n polynomialPrefix (polynomialPrefix p t) k = polynomialPrefix p k := by\n rw [CPolynomial.eq_iff_coeff]... | [
{
"name": "polynomialPrefix_rootPrefix_eq_of_degreeLt",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 510,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 1,
"automation_on... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -856,13 +856,33 @@
rw [polynomialPrefix_add_shift_prefix_dropXPower]
rw [houter, hsuffix]
+private theorem polynomialPrefix_prefix_of_le {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (p : CPolynomial F) {k t : Nat} (hkt : k ≤ t) :
+ polynomialPrefix (polynomialPrefix p t) k = polynomialPrefix p k ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_8 | c17bca99b92f4b04 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 3 | [
{
"theorem_name": "RootMod.normalizeAlekhnovichInput",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases normalizeAlekhnovichInput_eq_some hnorm with ⟨s, horder, hs, rfl, rfl⟩\n have hsum : s + (N - s) ... | [
{
"name": "normalizeAlekhnovichInput_eq_some",
"text": "private theorem normalizeAlekhnovichInput_eq_some {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n {Q Qnorm : CBivariate F} {N Nnorm : Nat}\n (hnorm : normalizeAlekhnovichInput Q N = some (Qnorm, Nnorm)) :\n ∃ s, CBivariate.xAdicOrder? Q = s... | [
{
"name": "RootMod.normalizeAlekhnovichInput",
"fan_in": 8,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 643,
"n_subproofs": 2,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": fals... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -1025,12 +1025,33 @@
rw [hroot]
exact CPolynomial.coeff_zero i
+private theorem normalizeAlekhnovichInput_eq_some {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ {Q Qnorm : CBivariate F} {N Nnorm : Nat}
+ (hnorm : normalizeAlekhnovichInput Q N = some (Qnorm, Nnorm)) :
+ ∃ s, CBivariate.xAdicOrder... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_9 | 98eaeb0e615e6447 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 2 | [
{
"theorem_name": "initialCoefficientPolynomial_exists_coeff_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let P := initialCoefficientPolynomial Q\n let y := P.natDegree\n have hcoeff : P.coeff... | [
{
"name": "initialCoefficientPolynomial_coeff_eq_zero_of_size_le",
"text": "private theorem initialCoefficientPolynomial_coeff_eq_zero_of_size_le {F : Type*}\n [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]\n (Q : CBivariate F) {j : Nat} (hj : Q.val.size ≤ j) :\n (initialCoefficientPolynomial Q).c... | [
{
"name": "initialCoefficientPolynomial_exists_coeff_ne_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 23,
"n_chars": 785,
"n_subproofs": 3,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 5,
"autom... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -1096,6 +1096,16 @@
exact hcoeff (by simpa using hcoeffInitial)
· simpa [CBivariate.stripXAdicFactor, horder] using hyStrip
+private theorem initialCoefficientPolynomial_coeff_eq_zero_of_size_le {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]
+ (Q : CBivariate F) {j : Nat} (hj :... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_10 | 105fda6b56f96c8a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 3 | [
{
"theorem_name": "alekhnovichRootPrefixesWithFuel_precision_pos_of_initial_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 64,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro fuel\n induction fuel with\n | zero =>\n intro Q N rootPrefi... | [
{
"name": "array_foldl_forall_of_forall_step_with_input",
"text": "private theorem array_foldl_forall_of_forall_step_with_input {α β : Type*}\n (P : β → Prop) (Q : α → Prop) (xs : Array α)\n (step : Array β → α → Array β) (init : Array β)\n (hinit : ∀ y, y ∈ init.toList → P y)\n (hxs : ∀ x, x ∈ ... | [
{
"name": "alekhnovichRootPrefixesWithFuel_precision_pos_of_initial_ne_zero",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 74,
"n_chars": 3240,
"n_subproofs": 6,
"n_tactics": 64,
"cyclomatic": 5,
"n_automation": 13,
"n_rewrites": 6,
"n_structura... | 5 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -123,6 +123,31 @@
exact Or.inr hxzs
simpa using haux data #[] (Or.inr hx)
+private theorem array_foldl_forall_of_forall_step_with_input {α β : Type*}
+ (P : β → Prop) (Q : α → Prop) (xs : Array α)
+ (step : Array β → α → Array β) (init : Array β)
+ (hinit : ∀ y, y ∈ init.toList →... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_11 | 538edba70ce050c4 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 1 | [
{
"theorem_name": "list_foldl_max_ge_of_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction xs generalizing acc with\n | nil =>\n simp at hx\n | cons y ys ih =>\n simp at hx\n ca... | [
{
"name": "list_foldl_max_ge_acc",
"text": "private theorem list_foldl_max_ge_acc {α : Type*} (f : α → Nat) :\n ∀ (xs : List α) (acc : Nat),\n acc ≤ xs.foldl (fun bound x ↦ Nat.max bound (f x)) acc := by\n intro xs\n induction xs with\n | nil =>\n intro acc\n simp\n | cons x xs ih =>\n... | [
{
"name": "list_foldl_max_ge_of_mem",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 528,
"n_subproofs": 0,
"n_tactics": 13,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -1559,6 +1559,19 @@
· simp [hzval, hz]
exact array_foldl_mem_of_mem_step prefixes step houterMem hstepOuter hpres
+private theorem list_foldl_max_ge_acc {α : Type*} (f : α → Nat) :
+ ∀ (xs : List α) (acc : Nat),
+ acc ≤ xs.foldl (fun bound x ↦ Nat.max bound (f x)... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_12 | 51d2865c51c7f4f9 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 1 | [
{
"theorem_name": "substituteYPolynomialPlusXPowerYTruncated_coeff_eq_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 88,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let lowEq : CBivariate F → CBivariate F → Prop :=\n fun A B ↦ ∀ x y, x < N → C... | [
{
"name": "cbivar_coeff_add",
"text": "private theorem cbivar_coeff_add {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (Q R : CBivariate F) (i j : Nat) :\n CBivariate.coeff (Q + R) i j = CBivariate.coeff Q i j + CBivariate.coeff R i j := by\n have houter :=\n congrArg (fun row : CPolynomial F ... | [
{
"name": "shiftedResidualUpTo_valuation_lt_alekhnovichPrecisionBound",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 14,
"n_lines": 11,
"n_chars": 443,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
... | 14 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -191,6 +191,17 @@
intro i hi
simpa [CBivariate.coeff] using hcoeff i y hi
+private theorem cbivar_coeff_add {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (Q R : CBivariate F) (i j : Nat) :
+ CBivariate.coeff (Q + R) i j = CBivariate.coeff Q i j + CBivariate.coeff R i j := by
+ have houter :=
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_13 | 74c684b23e6fad9c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 3 | [
{
"theorem_name": "initialCoefficientPolynomial_normalizeAlekhnovichInput_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases normalizeAlekhnovichInput_eq_some hnorm with ⟨s, horder, _hs, rfl, rf... | [
{
"name": "initialCoefficientPolynomial_stripXAdicFactor_ne_zero",
"text": "private theorem initialCoefficientPolynomial_stripXAdicFactor_ne_zero {F : Type*}\n [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]\n {Q : CBivariate F} (hQ : Q ≠ 0) :\n initialCoefficientPolynomial (CBivariate.stripXAdicFa... | [
{
"name": "shiftedResidualUpTo_initialCoefficientPolynomial_ne_zero_of_valuation_lt",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 24,
"n_chars": 1014,
"n_subproofs": 1,
"n_tactics": 17,
"cyclomatic": 3,
"n_automation": 4,
"n_rewrites": 2,
"n_st... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -1069,6 +1069,33 @@
rw [CBivariate.stripXAdicFactor, horder, cbivar_coeff_divXPower] at hcoeffStrip
exact hcoeff (by simpa using hcoeffStrip)
+private theorem initialCoefficientPolynomial_stripXAdicFactor_ne_zero {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]
+ {Q : CBivariate F}... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_14 | cc1f62d10f4b730c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 1 | [
{
"theorem_name": "alekhnovichPrecisionBound_divXPower_le_sub_xAdicOrder",
"depth": 1,
"n_commands": 0,
"n_lines": 113,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let M : Nat :=\n (List.range' 0 Q.val.size).foldl\n (fun bound y ↦ max boun... | [
{
"name": "cpoly_natDegree_dropXPower_add_le_of_ne_zero",
"text": "private theorem cpoly_natDegree_dropXPower_add_le_of_ne_zero {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (p : CPolynomial F) (t : Nat)\n (hdrop : CPolynomial.dropXPower p t ≠ 0) :\n (CPolynomial.dropXPower p t).natDegree + t ... | [
{
"name": "alekhnovichPrecisionBound_divXPower_le_sub_xAdicOrder",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 5,
"n_lines": 121,
"n_chars": 5358,
"n_subproofs": 32,
"n_tactics": 113,
"cyclomatic": 3,
"n_automation": 19,
"n_rewrites": 8,
"n_structural": 13,
... | 5 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -775,6 +775,20 @@
have h := ih (CPolynomial.divX p)
omega
+private theorem cpoly_natDegree_dropXPower_add_le_of_ne_zero {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (p : CPolynomial F) (t : Nat)
+ (hdrop : CPolynomial.dropXPower p t ≠ 0) :
+ (CPolynomial.dropXPower p t).natDegree +... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_15 | 767949f69ec2c7a8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 1 | [
{
"theorem_name": "composeYCoeff_eq_fold_range_of_le",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold CBivariate.composeYCoeff\n have hsplit : List.range' 0 M =\n List.range' 0 Q.val.size ++ Li... | [
{
"name": "cbivar_coeffY_eq_zero_of_y_size_le",
"text": "private theorem cbivar_coeffY_eq_zero_of_y_size_le {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (Q : CBivariate F) {y : Nat} (hy : Q.val.size ≤ y) :\n Q.val.coeff y = 0 := by\n rw [CPolynomial.eq_iff_coeff]\n intro i\n change CBivariate... | [
{
"name": "alekhnovichRootCandidatesWithFuel_complete",
"fan_in": 1,
"n_deps_direct": 7,
"n_deps_transitive": 75,
"n_lines": 84,
"n_chars": 3911,
"n_subproofs": 12,
"n_tactics": 72,
"cyclomatic": 4,
"n_automation": 11,
"n_rewrites": 0,
"n_structural": 13,
"automat... | 71 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -69,6 +69,15 @@
rw [cpoly_mulPowCoeff_eq_coeff_mul_pow, CPolynomial.zero_mul,
CPolynomial.coeff_zero]
+private theorem cbivar_coeffY_eq_zero_of_y_size_le {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (Q : CBivariate F) {y : Nat} (hy : Q.val.size ≤ y) :
+ Q.val.coeff y = 0 := by
+ rw [CPolynomia... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b55c19bb3f63_16 | 2158240459ada340 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Alekhnovich/Correctness.lean | Correctness | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 75 | 1 | [
{
"theorem_name": "composeY_eq_zero_of_rootMod_of_substitutionDegreeBound",
"depth": 1,
"n_commands": 0,
"n_lines": 37,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CPolynomial.eq_iff_coeff]\n intro i\n by_cases hi : i < N\n · exact hroot i ... | [
{
"name": "cpoly_natDegree_le_pred_of_degreeLt",
"text": "private theorem cpoly_natDegree_le_pred_of_degreeLt {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n {p : CPolynomial F} {k : Nat} (hp : degreeLt p k) :\n p.natDegree ≤ k - 1 := by\n rw [CPolynomial.natDegree_toPoly]\n unfold degreeLt at hp... | [
{
"name": "composeY_eq_zero_of_rootMod_of_substitutionDegreeBound",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 47,
"n_chars": 1931,
"n_subproofs": 8,
"n_tactics": 38,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 6,
"n_structural": 11,
... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Alekhnovich.Lemmas
import CompPoly.Bivariate.GuruswamiSudan.Root.RothRuckenstein.Lemmas
/-!
# Alekhnovich Root ... | @@ -51,6 +51,27 @@
_ = (n + 1) * d := by
rw [Nat.succ_mul, Nat.add_comm])
+private theorem cpoly_natDegree_le_pred_of_degreeLt {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ {p : CPolynomial F} {k : Nat} (hp : degreeLt p k) :
+ p.natDegree ≤ k - 1 := by
+ rw [CPolynomial.natDegree_t... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_6bce58c81ece_0 | df6876f438b133ba | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Pipeline.lean | Pipeline | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "forwardImpl_ofDomain_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [ofDomain] using forwardImpl_correct (P := ofDomain D) (ofDomain_wellFormed D) p",
"n_chars": 92,
... | [
{
"name": "forwardImpl_correct",
"text": "/-- A well-formed plan's forward transform computes the bit-reversed forward NTT. -/\ntheorem forwardImpl_correct (P : Plan R) (hP : WellFormed P) (p : CPolynomial.Raw R) :\n forwardImpl P p =\n NTT.Transform.bitRevPermute P.domain (NTT.Forward.forwardSpec P... | [
{
"name": "forwardImpl_ofDomain_correct",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 344,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | @@ -21,10 +21,18 @@
variable {R : Type*} [Field R]
namespace Plan
+/-- A well-formed plan's forward transform computes the bit-reversed forward NTT. -/
+theorem forwardImpl_correct (P : Plan R) (hP : WellFormed P) (p : CPolynomial.Raw R) :
+ forwardImpl P p =
+ NTT.Transform.bitRevPermute P.domain (NTT.Forw... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_6bce58c81ece_1 | 1be63468b793bc30 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Pipeline.lean | Pipeline | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "forwardPairImpl_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [forwardPairImpl_eq_pair P hP p q]\n simp [forwardImpl_correct P hP]",
"n_chars": 77,
"n_subproofs": 0,... | [
{
"name": "forwardPairImpl_eq_pair",
"text": "/-- The paired forward transform equals the pair of individual forward transforms. -/\ntheorem forwardPairImpl_eq_pair\n (P : Plan R) (hP : WellFormed P) (p q : CPolynomial.Raw R) :\n forwardPairImpl P p q = (forwardImpl P p, forwardImpl P q) := by\n rcas... | [
{
"name": "forwardPairImpl_correct",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 10,
"n_chars": 458,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"ma... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | @@ -28,12 +28,22 @@
rcases hP with ⟨_, _, htwiddles, _⟩
simp [forwardImpl, htwiddles, runStagesDIFRadix4WithTwiddles_correct]
+/-- The paired forward transform equals the pair of individual forward transforms. -/
+theorem forwardPairImpl_eq_pair
+ (P : Plan R) (hP : WellFormed P) (p q : CPolynomial.Raw R) :
... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_6bce58c81ece_2 | 529b7cf031771b82 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Pipeline.lean | Pipeline | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "inverseImpl_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hP with ⟨hinverseDomain, hnInv, htwiddles, hinverseTwiddles⟩\n rw [inverseImpl, hinverseDomain, hinverseTwiddl... | [
{
"name": "normalize_eq_ntt_normalize",
"text": "/-- Plan normalization agrees with `NTT.Inverse.normalize` for the same domain. -/\ntheorem normalize_eq_ntt_normalize (P : Plan R) (hP : WellFormed P) (a : Array R) :\n normalize P a = NTT.Inverse.normalize P.domain a := by\n rcases hP with ⟨_, hnInv, _⟩... | [
{
"name": "inverseImpl_correct",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 948,
"n_subproofs": 1,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 4,
"n_structural": 4,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | @@ -21,10 +21,30 @@
variable {R : Type*} [Field R]
namespace Plan
+/-- Plan normalization agrees with `NTT.Inverse.normalize` for the same domain. -/
+theorem normalize_eq_ntt_normalize (P : Plan R) (hP : WellFormed P) (a : Array R) :
+ normalize P a = NTT.Inverse.normalize P.domain a := by
+ rcases hP with ⟨_,... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_6bce58c81ece_3 | a50497691b55f808 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Pipeline.lean | Pipeline | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "inverseImpl_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hP with ⟨hinverseDomain, hnInv, htwiddles, hinverseTwiddles⟩\n rw [inverseImpl, hinverseDomain, hinverseTwiddl... | [
{
"name": "normalize_eq_ntt_normalize",
"text": "/-- Plan normalization agrees with `NTT.Inverse.normalize` for the same domain. -/\ntheorem normalize_eq_ntt_normalize (P : Plan R) (hP : WellFormed P) (a : Array R) :\n normalize P a = NTT.Inverse.normalize P.domain a := by\n rcases hP with ⟨_, hnInv, _⟩... | [
{
"name": "fastMulImpl_correct",
"fan_in": 7,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 11,
"n_chars": 463,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 0,
"automation_only": false,
"max_ne... | 6 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | @@ -45,10 +45,30 @@
rw [forwardPairImpl_eq_pair P hP p q]
simp [forwardImpl_correct P hP]
+/-- Plan normalization agrees with `NTT.Inverse.normalize` for the same domain. -/
+theorem normalize_eq_ntt_normalize (P : Plan R) (hP : WellFormed P) (a : Array R) :
+ normalize P a = NTT.Inverse.normalize P.domain a... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_6bce58c81ece_4 | 4f36ad6738e0e787 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Pipeline.lean | Pipeline | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "inverseImpl_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hP with ⟨hinverseDomain, hnInv, htwiddles, hinverseTwiddles⟩\n rw [inverseImpl, hinverseDomain, hinverseTwiddl... | [
{
"name": "normalize_eq_ntt_normalize",
"text": "/-- Plan normalization agrees with `NTT.Inverse.normalize` for the same domain. -/\ntheorem normalize_eq_ntt_normalize (P : Plan R) (hP : WellFormed P) (a : Array R) :\n normalize P a = NTT.Inverse.normalize P.domain a := by\n rcases hP with ⟨_, hnInv, _⟩... | [
{
"name": "fastMulImpl_trim_eq_mul",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 9,
"n_chars": 394,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max... | 6 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | @@ -45,10 +45,30 @@
rw [forwardPairImpl_eq_pair P hP p q]
simp [forwardImpl_correct P hP]
+/-- Plan normalization agrees with `NTT.Inverse.normalize` for the same domain. -/
+theorem normalize_eq_ntt_normalize (P : Plan R) (hP : WellFormed P) (a : Array R) :
+ normalize P a = NTT.Inverse.normalize P.domain a... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_6bce58c81ece_5 | a60192a440cd14d0 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Pipeline.lean | Pipeline | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "inverseImpl_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hP with ⟨hinverseDomain, hnInv, htwiddles, hinverseTwiddles⟩\n rw [inverseImpl, hinverseDomain, hinverseTwiddl... | [
{
"name": "normalize_eq_ntt_normalize",
"text": "/-- Plan normalization agrees with `NTT.Inverse.normalize` for the same domain. -/\ntheorem normalize_eq_ntt_normalize (P : Plan R) (hP : WellFormed P) (a : Array R) :\n normalize P a = NTT.Inverse.normalize P.domain a := by\n rcases hP with ⟨_, hnInv, _⟩... | [
{
"name": "fastMulImpl_eq_mul",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 9,
"n_chars": 376,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nest... | 6 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | @@ -45,10 +45,30 @@
rw [forwardPairImpl_eq_pair P hP p q]
simp [forwardImpl_correct P hP]
+/-- Plan normalization agrees with `NTT.Inverse.normalize` for the same domain. -/
+theorem normalize_eq_ntt_normalize (P : Plan R) (hP : WellFormed P) (a : Array R) :
+ normalize P a = NTT.Inverse.normalize P.domain a... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_6bce58c81ece_6 | cd53ecef82e4e238 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Pipeline.lean | Pipeline | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "inverseImpl_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hP with ⟨hinverseDomain, hnInv, htwiddles, hinverseTwiddles⟩\n rw [inverseImpl, hinverseDomain, hinverseTwiddl... | [
{
"name": "normalize_eq_ntt_normalize",
"text": "/-- Plan normalization agrees with `NTT.Inverse.normalize` for the same domain. -/\ntheorem normalize_eq_ntt_normalize (P : Plan R) (hP : WellFormed P) (a : Array R) :\n normalize P a = NTT.Inverse.normalize P.domain a := by\n rcases hP with ⟨_, hnInv, _⟩... | [
{
"name": "safeFastMul_eq_mul",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 8,
"n_lines": 8,
"n_chars": 289,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nest... | 6 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | @@ -45,10 +45,30 @@
rw [forwardPairImpl_eq_pair P hP p q]
simp [forwardImpl_correct P hP]
+/-- Plan normalization agrees with `NTT.Inverse.normalize` for the same domain. -/
+theorem normalize_eq_ntt_normalize (P : Plan R) (hP : WellFormed P) (a : Array R) :
+ normalize P a = NTT.Inverse.normalize P.domain a... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_6bce58c81ece_7 | 28b63d0e9f3cf0b8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Pipeline.lean | Pipeline | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "inverseImpl_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hP with ⟨hinverseDomain, hnInv, htwiddles, hinverseTwiddles⟩\n rw [inverseImpl, hinverseDomain, hinverseTwiddl... | [
{
"name": "normalize_eq_ntt_normalize",
"text": "/-- Plan normalization agrees with `NTT.Inverse.normalize` for the same domain. -/\ntheorem normalize_eq_ntt_normalize (P : Plan R) (hP : WellFormed P) (a : Array R) :\n normalize P a = NTT.Inverse.normalize P.domain a := by\n rcases hP with ⟨_, hnInv, _⟩... | [
{
"name": "withFallback_eq_mul",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 8,
"n_lines": 16,
"n_chars": 661,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 3,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_ne... | 6 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Pair
import CompPoly.Univariate.NTTFast.Correctness.Radix4DIT
/-!
# NTTFast multiplication correctness
Plan-le... | @@ -45,10 +45,30 @@
rw [forwardPairImpl_eq_pair P hP p q]
simp [forwardImpl_correct P hP]
+/-- Plan normalization agrees with `NTT.Inverse.normalize` for the same domain. -/
+theorem normalize_eq_ntt_normalize (P : Plan R) (hP : WellFormed P) (a : Array R) :
+ normalize P a = NTT.Inverse.normalize P.domain a... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_7a677566e322_1 | 655ffa5b4b3a872c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/LagrangeArray.lean | LagrangeArray | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "eval_interpolateArray_at_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases List.getElem_of_mem hpoint with ⟨idx, hidx, hget⟩\n let i : Fin points.size := ⟨idx, by simpa using h... | [
{
"name": "eval_interpolateArray_at_index",
"text": "/-- Evaluating the packed-array interpolant at one indexed node returns the indexed value. -/\ntheorem eval_interpolateArray_at_index\n (points : Array (F × F)) (hdistinct : DistinctPointNodes points)\n (i : Fin points.size) :\n CPolynomial.eval ... | [
{
"name": "eval_interpolateArray_at_mem",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 853,
"n_subproofs": 4,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Lagrange
/-!
# Array Wrappers for Computable Lagrange Interpolation
Finite-index adapters for `CPolynomial.CLagrange.interpolate`... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Lagrange
/-!
# Array Wrappers for Computable Lagrange Interpolation
Finite-index adapters for `CPolynomial.CLagrange.interpolate`... | @@ -72,11 +72,35 @@
(@List.getElem_inj F i.val j.val
(points.toList.map (fun point : F × F ↦ point.1)) hi hj hdistinct').mp hnodes
+/-- Evaluating the packed-array interpolant at one indexed node returns the indexed value. -/
+theorem eval_interpolateArray_at_index
+ (points : Array (F × F)) (hdistinct... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_4273a8ef4b5d_0 | b60f9a09678134bf | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Evaluation.lean | Evaluation | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "forwardSpec_eq_evalOnDomain",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Array.ext\n · simp [forwardSpec, evalOnDomain]\n · intro i hi₁ hi₂\n let k : D.Idx := ⟨i, by simpa [... | [
{
"name": "forwardSpec_eval_node_eq",
"text": "/-- Pointwise form: the forward NTT specification evaluates a raw polynomial at a domain node. -/\ntheorem forwardSpec_eval_node_eq (D : Domain R) (p : CPolynomial.Raw R)\n (hdeg : p.toPoly.natDegree < D.n) (k : D.Idx) :\n (forwardSpec D p)[k.1] = p.eval ... | [
{
"name": "forwardSpec_eq_evalOnDomain",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 462,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.BatchEval.Naive
import CompPoly.Univariate.NTT.Forward
import CompPoly.Univariate.ToPoly.Core
/-!
# NTT and Evaluation
Bridge definitions and t... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.BatchEval.Naive
import CompPoly.Univariate.NTT.Forward
import CompPoly.Univariate.ToPoly.Core
/-!
# NTT and Evaluation
Bridge definitions and t... | @@ -26,13 +26,37 @@
namespace Forward
+/-- Pointwise form: the forward NTT specification evaluates a raw polynomial at a domain node. -/
+theorem forwardSpec_eval_node_eq (D : Domain R) (p : CPolynomial.Raw R)
+ (hdeg : p.toPoly.natDegree < D.n) (k : D.Idx) :
+ (forwardSpec D p)[k.1] = p.eval (D.node k) := b... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_4273a8ef4b5d_1 | bd0dc5886bf7bc9d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Evaluation.lean | Evaluation | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "forwardSpec_eq_evalOnDomain",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Array.ext\n · simp [forwardSpec, evalOnDomain]\n · intro i hi₁ hi₂\n let k : D.Idx := ⟨i, by simpa [... | [
{
"name": "forwardSpec_eval_node_eq",
"text": "/-- Pointwise form: the forward NTT specification evaluates a raw polynomial at a domain node. -/\ntheorem forwardSpec_eval_node_eq (D : Domain R) (p : CPolynomial.Raw R)\n (hdeg : p.toPoly.natDegree < D.n) (k : D.Idx) :\n (forwardSpec D p)[k.1] = p.eval ... | [
{
"name": "forwardImpl_eval_node_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 416,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.BatchEval.Naive
import CompPoly.Univariate.NTT.Forward
import CompPoly.Univariate.ToPoly.Core
/-!
# NTT and Evaluation
Bridge definitions and t... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.BatchEval.Naive
import CompPoly.Univariate.NTT.Forward
import CompPoly.Univariate.ToPoly.Core
/-!
# NTT and Evaluation
Bridge definitions and t... | @@ -26,10 +26,35 @@
namespace Forward
+/-- Pointwise form: the forward NTT specification evaluates a raw polynomial at a domain node. -/
+theorem forwardSpec_eval_node_eq (D : Domain R) (p : CPolynomial.Raw R)
+ (hdeg : p.toPoly.natDegree < D.n) (k : D.Idx) :
+ (forwardSpec D p)[k.1] = p.eval (D.node k) := b... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_4273a8ef4b5d_2 | 492d7e6ce196bd79 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Evaluation.lean | Evaluation | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "forwardImpl_eq_evalOnDomain",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [forwardImpl_correct]\n exact forwardSpec_eq_evalOnDomain D p hdeg",
"n_chars": 75,
"n_subproofs": ... | [
{
"name": "forwardSpec_eq_evalOnDomain",
"text": "/-- The forward NTT specification evaluates a raw polynomial on all domain nodes. -/\ntheorem forwardSpec_eq_evalOnDomain (D : Domain R) (p : CPolynomial.Raw R)\n (hdeg : p.toPoly.natDegree < D.n) :\n forwardSpec D p = evalOnDomain D p := by\n apply A... | [
{
"name": "forwardImpl_eq_evalOnDomain",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 319,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.BatchEval.Naive
import CompPoly.Univariate.NTT.Forward
import CompPoly.Univariate.ToPoly.Core
/-!
# NTT and Evaluation
Bridge definitions and t... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.BatchEval.Naive
import CompPoly.Univariate.NTT.Forward
import CompPoly.Univariate.ToPoly.Core
/-!
# NTT and Evaluation
Bridge definitions and t... | @@ -48,10 +48,22 @@
_ = p.eval (D.node k) := by
exact CPolynomial.Raw.eval_toPoly_eq_eval (D.node k) p
+/-- The forward NTT specification evaluates a raw polynomial on all domain nodes. -/
+theorem forwardSpec_eq_evalOnDomain (D : Domain R) (p : CPolynomial.Raw R)
+ (hdeg : p.toPoly.natDegree < D... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9abf59d29bd0_0 | 8773f71c2730478d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Radix4DIT.lean | Radix4DIT | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "ditButterfly_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n change\n (let u := (ditButterfly v j0 j1 acc).getD i0 0\n let t := w * (ditButterfly v j0 j1 acc).getD i1 0\n ... | [
{
"name": "getD_ditButterfly_of_ne",
"text": "private theorem getD_ditButterfly_of_ne\n (w : R) (i0 i1 k : Nat) (acc : Array R) (hk0 : k ≠ i0) (hk1 : k ≠ i1) :\n (ditButterfly w i0 i1 acc).getD k 0 = acc.getD k 0 := by\n have h0 : i0 ≠ k := fun h ↦ hk0 h.symm\n have h1 : i1 ≠ k := fun h ↦ hk1 h.symm... | [
{
"name": "ditButterfly_comm",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 24,
"n_chars": 1107,
"n_subproofs": 0,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 10,
"n_structural": 0,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Basic
/-!
# Radix-4 DIT NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-time stage ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Basic
/-!
# Radix-4 DIT NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-time stage ... | @@ -26,11 +26,40 @@
let t := w * acc.getD i1 0
(acc.set! i0 (u + t)).set! i1 (u - t)
+private theorem getD_ditButterfly_of_ne
+ (w : R) (i0 i1 k : Nat) (acc : Array R) (hk0 : k ≠ i0) (hk1 : k ≠ i1) :
+ (ditButterfly w i0 i1 acc).getD k 0 = acc.getD k 0 := by
+ have h0 : i0 ≠ k := fun h ↦ hk0 h.symm
+ ha... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9abf59d29bd0_1 | 9ce8289de2c0f101 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Radix4DIT.lean | Radix4DIT | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "radix4Cell_eq_two_stage_cells",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold ditButterfly radix4Cell\n simp only [Array.set!, Array.getD_eq_getD_getElem?, Array.getElem?_setIfInB... | [
{
"name": "setIfInBounds_discard_four",
"text": "private theorem setIfInBounds_discard_four {α : Type*}\n (acc : Array α) (i0 i1 i2 i3 : Nat) (v0 v1 v2 v3 w0 w1 w2 w3 : α)\n (h01 : i0 ≠ i1) (h02 : i0 ≠ i2) (h03 : i0 ≠ i3)\n (h12 : i1 ≠ i2) (h13 : i1 ≠ i3) (h23 : i2 ≠ i3) :\n (((((((acc.setIfInBo... | [
{
"name": "radix4Cell_eq_two_stage_cells",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 19,
"n_chars": 882,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Basic
/-!
# Radix-4 DIT NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-time stage ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Basic
/-!
# Radix-4 DIT NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-time stage ... | @@ -194,6 +194,26 @@
(radix4Cell wLow wHigh0 wHigh1 i0 i1 i2 i3 acc).size = acc.size := by
simp [radix4Cell, Array.set!, Array.size_setIfInBounds]
+private theorem setIfInBounds_discard_four {α : Type*}
+ (acc : Array α) (i0 i1 i2 i3 : Nat) (v0 v1 v2 v3 w0 w1 w2 w3 : α)
+ (h01 : i0 ≠ i1) (h02 : i0 ≠ i2)... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9abf59d29bd0_2 | 446f4c859f069253 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Radix4DIT.lean | Radix4DIT | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "runStagesWithTwiddles_eq_ntt",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [runStagesWithTwiddles, NTT.Transform.runStages]\n rw [← List.range_eq_range']\n apply foldl_range_cong... | [
{
"name": "butterflyStageWithTwiddles_eq_ntt",
"text": "/-- A DIT butterfly stage with matching cached twiddles agrees with the `NTT` stage. -/\ntheorem butterflyStageWithTwiddles_eq_ntt\n (D : NTT.Domain R) (stage : Nat) (twiddles : Array R) (a : Array R)\n (htwiddles :\n ∀ j, j < 2 ^ stage →\n ... | [
{
"name": "runStagesWithTwiddles_eq_ntt",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 507,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Basic
/-!
# Radix-4 DIT NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-time stage ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Basic
/-!
# Radix-4 DIT NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-time stage ... | @@ -564,9 +564,40 @@
blocks 0 (butterflyDITBlocks twiddlesLow (2 * q) q (2 * blocks) 0 acc)
(by simp))
+/-- A DIT butterfly stage with matching cached twiddles agrees with the `NTT` stage. -/
+theorem butterflyStageWithTwiddles_eq_ntt
+ (D : NTT.Domain R) (stage : Nat) (twiddles : Arr... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9abf59d29bd0_3 | 0218f3d5a3d613fd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Radix4DIT.lean | Radix4DIT | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "runStagesRadix4WithTwiddles_eq_ntt",
"depth": 1,
"n_commands": 0,
"n_lines": 58,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← runStagesWithTwiddles_eq_ntt D a]\n let stageStep : Nat → Array R → Array R :=\n fun stage ac... | [
{
"name": "butterflyRadix4StageWithTwiddles_eq_two_stages",
"text": "private theorem butterflyRadix4StageWithTwiddles_eq_two_stages\n (D : NTT.Domain R) (lowStage : Nat) (twiddlesLow twiddlesHigh a : Array R)\n (ha : a.size = D.n) (hstage : lowStage + 1 < D.logN) :\n butterflyRadix4StageWithTwiddle... | [
{
"name": "runStagesRadix4WithTwiddles_eq_ntt",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 67,
"n_chars": 3269,
"n_subproofs": 5,
"n_tactics": 58,
"cyclomatic": 1,
"n_automation": 12,
"n_rewrites": 5,
"n_structural": 6,
"automation_only": ... | 3 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Basic
/-!
# Radix-4 DIT NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-time stage ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Basic
/-!
# Radix-4 DIT NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-time stage ... | @@ -564,6 +564,42 @@
blocks 0 (butterflyDITBlocks twiddlesLow (2 * q) q (2 * blocks) 0 acc)
(by simp))
+private theorem butterflyRadix4StageWithTwiddles_eq_two_stages
+ (D : NTT.Domain R) (lowStage : Nat) (twiddlesLow twiddlesHigh a : Array R)
+ (ha : a.size = D.n) (hstage : lowSta... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_393578abdafa_0 | 972af2cc81af5741 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "eval_horner_step_dot_product",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Vector.dotProduct_eq_root_dotProduct, Vector.dotProduct_eq_root_dotProduct]\n unfold _root_.dotProduct\n... | [
{
"name": "monomial_basis_even",
"text": "private lemma monomial_basis_even {n : ℕ} (x : Vector R (n + 1)) (j : Fin (2 ^ n)) :\n (monomialBasis x).get ⟨2 * j.val, by omega⟩ =\n (monomialBasis x.tail).get j := by\n unfold monomialBasis\n simp only [Vector.get_ofFn]\n simp only [BitVec.getLsb_eq_getE... | [
{
"name": "eval_horner_step_dot_product",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 38,
"n_chars": 1420,
"n_subproofs": 1,
"n_tactics": 33,
"cyclomatic": 1,
"n_automation": 14,
"n_rewrites": 11,
"n_structural": 8,
"automation_only": false... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | @@ -160,6 +160,21 @@
-- #eval monomialBasis #v[(1 : ℤ), 2, 3] (n := 3)
-- #eval Nat.digits 2 8
+private lemma monomial_basis_even {n : ℕ} (x : Vector R (n + 1)) (j : Fin (2 ^ n)) :
+ (monomialBasis x).get ⟨2 * j.val, by omega⟩ =
+ (monomialBasis x.tail).get j := by
+ unfold monomialBasis
+ simp only [Vector... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_393578abdafa_1 | cb9633c960d73881 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/Basic.lean | Basic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "eval_horner_step_dot_product",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Vector.dotProduct_eq_root_dotProduct, Vector.dotProduct_eq_root_dotProduct]\n unfold _root_.dotProduct\n... | [
{
"name": "monomial_basis_odd",
"text": "private lemma monomial_basis_odd {n : ℕ} (x : Vector R (n + 1)) (j : Fin (2 ^ n)) :\n (monomialBasis x).get ⟨2 * j.val + 1, by omega⟩ =\n x.head * (monomialBasis x.tail).get j := by\n unfold monomialBasis\n simp only [Vector.get_ofFn]\n simp only [BitVec.get... | [
{
"name": "eval_horner_eq_eval",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 15,
"n_chars": 571,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_n... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | @@ -175,6 +175,22 @@
rw [Nat.testBit_bit_succ]
simp [Vector.tail_eq_cast_extract, Nat.add_comm]
+private lemma monomial_basis_odd {n : ℕ} (x : Vector R (n + 1)) (j : Fin (2 ^ n)) :
+ (monomialBasis x).get ⟨2 * j.val + 1, by omega⟩ =
+ x.head * (monomialBasis x.tail).get j := by
+ unfold monomialBasis
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_393578abdafa_2 | 627b37a2427fc3dd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/Basic.lean | Basic | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "eval_horner_step_dot_product",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Vector.dotProduct_eq_root_dotProduct, Vector.dotProduct_eq_root_dotProduct]\n unfold _root_.dotProduct\n... | [
{
"name": "monomial_basis_odd",
"text": "private lemma monomial_basis_odd {n : ℕ} (x : Vector R (n + 1)) (j : Fin (2 ^ n)) :\n (monomialBasis x).get ⟨2 * j.val + 1, by omega⟩ =\n x.head * (monomialBasis x.tail).get j := by\n unfold monomialBasis\n simp only [Vector.get_ofFn]\n simp only [BitVec.get... | [
{
"name": "eval₂_horner_eq_eval₂",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 6,
"n_chars": 320,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_ne... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | @@ -175,6 +175,22 @@
rw [Nat.testBit_bit_succ]
simp [Vector.tail_eq_cast_extract, Nat.add_comm]
+private lemma monomial_basis_odd {n : ℕ} (x : Vector R (n + 1)) (j : Fin (2 ^ n)) :
+ (monomialBasis x).get ⟨2 * j.val + 1, by omega⟩ =
+ x.head * (monomialBasis x.tail).get j := by
+ unfold monomialBasis
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_393578abdafa_3 | 0b9b982103c7f939 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/Basic.lean | Basic | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "eval_mle_step_dot_product",
"depth": 1,
"n_commands": 0,
"n_lines": 35,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Vector.dotProduct_eq_root_dotProduct, Vector.dotProduct_eq_root_dotProduct]\n unfold _root_.dotProduct\n h... | [
{
"name": "lagrange_basis_even",
"text": "private lemma lagrange_basis_even {n : ℕ} (x : Vector R (n + 1)) (j : Fin (2 ^ n)) :\n (lagrangeBasis x).get ⟨2 * j.val, by omega⟩ =\n (1 - x.head) * (lagrangeBasis x.tail).get j := by\n unfold lagrangeBasis\n simp only [Vector.get_ofFn]\n simp only [BitVec... | [
{
"name": "eval_mle_step_dot_product",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 40,
"n_chars": 1543,
"n_subproofs": 1,
"n_tactics": 35,
"cyclomatic": 1,
"n_automation": 17,
"n_rewrites": 12,
"n_structural": 8,
"automation_only": false,
... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | @@ -313,6 +313,22 @@
-- #eval lagrangeBasis #v[(1 : ℤ), 2, 3] (n := 3)
-- #eval Nat.digits 2 8
+private lemma lagrange_basis_even {n : ℕ} (x : Vector R (n + 1)) (j : Fin (2 ^ n)) :
+ (lagrangeBasis x).get ⟨2 * j.val, by omega⟩ =
+ (1 - x.head) * (lagrangeBasis x.tail).get j := by
+ unfold lagrangeBasis
+ si... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_393578abdafa_4 | b0fd9f32102130c2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/Basic.lean | Basic | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "eval_mle_step_dot_product",
"depth": 1,
"n_commands": 0,
"n_lines": 35,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Vector.dotProduct_eq_root_dotProduct, Vector.dotProduct_eq_root_dotProduct]\n unfold _root_.dotProduct\n h... | [
{
"name": "lagrange_basis_odd",
"text": "private lemma lagrange_basis_odd {n : ℕ} (x : Vector R (n + 1)) (j : Fin (2 ^ n)) :\n (lagrangeBasis x).get ⟨2 * j.val + 1, by omega⟩ =\n x.head * (lagrangeBasis x.tail).get j := by\n unfold lagrangeBasis\n simp only [Vector.get_ofFn]\n simp only [BitVec.get... | [
{
"name": "eval_mle_eq_eval",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 15,
"n_chars": 569,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_nest... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | @@ -329,6 +329,22 @@
rw [Nat.testBit_bit_succ]
simp [Vector.tail_eq_cast_extract, Nat.add_comm]
+private lemma lagrange_basis_odd {n : ℕ} (x : Vector R (n + 1)) (j : Fin (2 ^ n)) :
+ (lagrangeBasis x).get ⟨2 * j.val + 1, by omega⟩ =
+ x.head * (lagrangeBasis x.tail).get j := by
+ unfold lagrangeBasis
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_393578abdafa_5 | c768e8f1aba77f30 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/Basic.lean | Basic | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "eval_mle_step_dot_product",
"depth": 1,
"n_commands": 0,
"n_lines": 35,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Vector.dotProduct_eq_root_dotProduct, Vector.dotProduct_eq_root_dotProduct]\n unfold _root_.dotProduct\n h... | [
{
"name": "lagrange_basis_odd",
"text": "private lemma lagrange_basis_odd {n : ℕ} (x : Vector R (n + 1)) (j : Fin (2 ^ n)) :\n (lagrangeBasis x).get ⟨2 * j.val + 1, by omega⟩ =\n x.head * (lagrangeBasis x.tail).get j := by\n unfold lagrangeBasis\n simp only [Vector.get_ofFn]\n simp only [BitVec.get... | [
{
"name": "eval₂_mle_eq_eval₂",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 8,
"n_chars": 331,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesti... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | @@ -329,6 +329,22 @@
rw [Nat.testBit_bit_succ]
simp [Vector.tail_eq_cast_extract, Nat.add_comm]
+private lemma lagrange_basis_odd {n : ℕ} (x : Vector R (n + 1)) (j : Fin (2 ^ n)) :
+ (lagrangeBasis x).get ⟨2 * j.val + 1, by omega⟩ =
+ x.head * (lagrangeBasis x.tail).get j := by
+ unfold lagrangeBasis
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_393578abdafa_6 | 9b42f6a2f93a381e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/Basic.lean | Basic | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 3 | [
{
"theorem_name": "forwardRange_dropLast",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply List.ext_getElem\n · rw [List.length_dropLast, forwardRange_length, forwardRange_length]\n simp only [add_... | [
{
"name": "forwardRange_length",
"text": "lemma forwardRange_length (n : ℕ) (r : Fin n) (l : Fin (r.val + 1)) :\n (forwardRange n r l).length = r.val - l.val + 1 := by\n unfold forwardRange\n simp only [List.length_ofFn]\n\n",
"fan_in": 3,
"n_lines": 6,
"n_chars": 184,
"n_subproofs": 0,... | [
{
"name": "forwardRange_dropLast",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 18,
"n_chars": 911,
"n_subproofs": 2,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 15,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"ma... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | @@ -533,6 +533,11 @@
⟨val, h_bound⟩
)
+lemma forwardRange_length (n : ℕ) (r : Fin n) (l : Fin (r.val + 1)) :
+ (forwardRange n r l).length = r.val - l.val + 1 := by
+ unfold forwardRange
+ simp only [List.length_ofFn]
+
lemma forwardRange_eq_of_r_eq (n : ℕ) (r1 r2 : Fin n) (h_r_eq : r1 = r2) (l : Fin (r... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_393578abdafa_7 | 7233e9c18db9d072 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/Basic.lean | Basic | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 3 | [
{
"theorem_name": "forwardRange_dropLast",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply List.ext_getElem\n · rw [List.length_dropLast, forwardRange_length, forwardRange_length]\n simp only [add_... | [
{
"name": "forwardRange_getElem",
"text": "lemma forwardRange_getElem (n : ℕ) (r : Fin n) (l : Fin (r.val + 1)) (k : Fin (r.val - l.val + 1)) :\n (forwardRange n r l).get ⟨k, by\n rw [forwardRange]; simp only [List.length_ofFn]; omega⟩ = ⟨l.val + k, by omega⟩ := by\n unfold forwardRange\n simp only ... | [
{
"name": "monoToLagrange_eq_monoToLagrangeSegment",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 10,
"n_chars": 432,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 2,
"automation_only"... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | @@ -543,6 +543,13 @@
subst h_r_eq
rfl
+lemma forwardRange_getElem (n : ℕ) (r : Fin n) (l : Fin (r.val + 1)) (k : Fin (r.val - l.val + 1)) :
+ (forwardRange n r l).get ⟨k, by
+ rw [forwardRange]; simp only [List.length_ofFn]; omega⟩ = ⟨l.val + k, by omega⟩ := by
+ unfold forwardRange
+ simp only [List.ge... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_393578abdafa_8 | 3ef58ca0a1c72afd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/Basic.lean | Basic | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 2 | [
{
"theorem_name": "lagrangeToMonoLevel_monoToLagrangeLevel_id",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold lagrangeToMonoLevel monoToLagrangeLevel\n simp only [Vector.getElem_ofFn]\n ext i1 i1_... | [
{
"name": "testBit_of_sub_two_pow_of_bit_1",
"text": "lemma testBit_of_sub_two_pow_of_bit_1 {n i : ℕ} (h_testBit_eq_1 : (n).testBit i = true) :\n (n - 2^i).testBit i = false := by\n have h := Nat.testBit_false_eq_getBit_eq_0 (n:=n - 2^i) (k:=i)\n rw [h]\n have h_getBit_eq_0: Nat.getBit i (n - 2^i) = 0... | [
{
"name": "lagrangeToMonoLevel_monoToLagrangeLevel_id",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 21,
"n_chars": 977,
"n_subproofs": 4,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 2,
"n_structural": 2,
"automation_o... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.RingTheory.MvPolynomial.Basic
import CompPoly.Data.List.Lemmas
import CompPoly.Data.Vector.Basic
import CompPoly.Data.Nat.Bitwise
/-!
# Mult... | @@ -659,11 +659,54 @@
congr
exact Eq.symm (forwardRange_0_eq_finRange n)
+lemma testBit_of_sub_two_pow_of_bit_1 {n i : ℕ} (h_testBit_eq_1 : (n).testBit i = true) :
+ (n - 2^i).testBit i = false := by
+ have h := Nat.testBit_false_eq_getBit_eq_0 (n:=n - 2^i) (k:=i)
+ rw [h]
+ have h_getBit_eq_0: Nat.getBit... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_6b60440e2833_0 | 4bb95a67a67fea0d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Abstract/Core.lean | Core | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "poly_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " (polyMonic n).ne_zero",
"n_chars": 22,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
... | [
{
"name": "polyMonic",
"text": "theorem polyMonic (n : ℕ) : Monic (poly n) := definingPoly_is_monic (Z n)\n\n",
"fan_in": 1,
"n_lines": 3,
"n_chars": 77,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automat... | [
{
"name": "poly_ne_zero",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 3,
"n_chars": 70,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 1... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import CompPoly.Fields.Binary.Tower.Support.IrreducibilityAndTraceMapProperty
import CompPoly.Data.RingTheory.AlgebraTower
import Mathlib.Tac... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import CompPoly.Fields.Binary.Tower.Support.IrreducibilityAndTraceMapProperty
import CompPoly.Data.RingTheory.AlgebraTower
import Mathlib.Tac... | @@ -505,8 +505,10 @@
instance polyIrreducibleFact (n : ℕ) : Fact (Irreducible (poly n)) := ⟨polyIrreducible n⟩
-lemma poly_ne_zero (n : ℕ) : poly n ≠ 0 := sorry
+theorem polyMonic (n : ℕ) : Monic (poly n) := definingPoly_is_monic (Z n)
+lemma poly_ne_zero (n : ℕ) : poly n ≠ 0 := (polyMonic n).ne_zero
+
end BTFi... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_0 | 5229667bff64d9bf | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "containsNat_eq_true_iff_exists",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h\n have hxList := containsNat_eq_true_iff.mp h\n rcases List.mem_iff_get.mp h... | [
{
"name": "containsNat_eq_true_iff",
"text": "private theorem containsNat_eq_true_iff {xs : Array Nat} {x : Nat} :\n containsNat xs x = true ↔ x ∈ xs.toList := by\n unfold containsNat\n rw [Array.any_eq_true']\n constructor\n · rintro ⟨y, hy, hbeq⟩\n have hyx : y = x := beq_iff_eq.mp hbeq\n sim... | [
{
"name": "containsNat_eq_true_iff_exists",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 18,
"n_chars": 665,
"n_subproofs": 1,
"n_tactics": 15,
"cyclomatic": 4,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 8,
"automation_only": false,... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -18,8 +18,34 @@
namespace DenseMatrix
+private theorem containsNat_eq_true_iff {xs : Array Nat} {x : Nat} :
+ containsNat xs x = true ↔ x ∈ xs.toList := by
+ unfold containsNat
+ rw [Array.any_eq_true']
+ constructor
+ · rintro ⟨y, hy, hbeq⟩
+ have hyx : y = x := beq_iff_eq.mp hbeq
+ simpa [hyx] us... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_1 | e9b6908c37be5bae | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "containsNat_eq_true_iff_exists",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h\n have hxList := containsNat_eq_true_iff.mp h\n rcases List.mem_iff_get.mp h... | [
{
"name": "containsNat_eq_true_iff",
"text": "private theorem containsNat_eq_true_iff {xs : Array Nat} {x : Nat} :\n containsNat xs x = true ↔ x ∈ xs.toList := by\n unfold containsNat\n rw [Array.any_eq_true']\n constructor\n · rintro ⟨y, hy, hbeq⟩\n have hyx : y = x := beq_iff_eq.mp hbeq\n sim... | [
{
"name": "containsNat_getD_ne",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 298,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nes... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -18,8 +18,34 @@
namespace DenseMatrix
+private theorem containsNat_eq_true_iff {xs : Array Nat} {x : Nat} :
+ containsNat xs x = true ↔ x ∈ xs.toList := by
+ unfold containsNat
+ rw [Array.any_eq_true']
+ constructor
+ · rintro ⟨y, hy, hbeq⟩
+ have hyx : y = x := beq_iff_eq.mp hbeq
+ simpa [hyx] us... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_2 | 7612990206f7201d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "containsNat_eq_true_iff_exists",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h\n have hxList := containsNat_eq_true_iff.mp h\n rcases List.mem_iff_get.mp h... | [
{
"name": "containsNat_eq_true_iff",
"text": "private theorem containsNat_eq_true_iff {xs : Array Nat} {x : Nat} :\n containsNat xs x = true ↔ x ∈ xs.toList := by\n unfold containsNat\n rw [Array.any_eq_true']\n constructor\n · rintro ⟨y, hy, hbeq⟩\n have hyx : y = x := beq_iff_eq.mp hbeq\n sim... | [
{
"name": "pivots_size_ge_cols_of_no_free_columns",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 16,
"n_chars": 689,
"n_subproofs": 7,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only"... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -18,6 +18,18 @@
namespace DenseMatrix
+private theorem containsNat_eq_true_iff {xs : Array Nat} {x : Nat} :
+ containsNat xs x = true ↔ x ∈ xs.toList := by
+ unfold containsNat
+ rw [Array.any_eq_true']
+ constructor
+ · rintro ⟨y, hy, hbeq⟩
+ have hyx : y = x := beq_iff_eq.mp hbeq
+ simpa [hyx] us... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_3 | 28bac77e87bf2685 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "containsNat_eq_true_iff_exists",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h\n have hxList := containsNat_eq_true_iff.mp h\n rcases List.mem_iff_get.mp h... | [
{
"name": "containsNat_eq_true_iff",
"text": "private theorem containsNat_eq_true_iff {xs : Array Nat} {x : Nat} :\n containsNat xs x = true ↔ x ∈ xs.toList := by\n unfold containsNat\n rw [Array.any_eq_true']\n constructor\n · rintro ⟨y, hy, hbeq⟩\n have hyx : y = x := beq_iff_eq.mp hbeq\n sim... | [
{
"name": "homogeneousWitness_exists_of_rows_lt_cols",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 16,
"n_chars": 680,
"n_subproofs": 4,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 2,
"automation_on... | 4 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -18,6 +18,18 @@
namespace DenseMatrix
+private theorem containsNat_eq_true_iff {xs : Array Nat} {x : Nat} :
+ containsNat xs x = true ↔ x ∈ xs.toList := by
+ unfold containsNat
+ rw [Array.any_eq_true']
+ constructor
+ · rintro ⟨y, hy, hbeq⟩
+ have hyx : y = x := beq_iff_eq.mp hbeq
+ simpa [hyx] us... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_4 | 01ddce0b922f3fc1 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "pivotRowOfColumn?_some_prop",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold pivotRowOfColumn? at h\n have hmem := list_find?_some_mem h\n have hpred := List.find?_some h\n exact... | [
{
"name": "list_find?_some_mem",
"text": "private theorem list_find?_some_mem {α : Type*} {p : α → Bool} {xs : List α} {x : α}\n (h : xs.find? p = some x) : x ∈ xs := by\n induction xs with\n | nil =>\n simp at h\n | cons y ys ih =>\n by_cases hp : p y = true\n · simp [List.find?, hp] a... | [
{
"name": "pivotRowOfColumn?_some_prop",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 351,
"n_subproofs": 2,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -18,9 +18,26 @@
namespace DenseMatrix
+private theorem list_find?_some_mem {α : Type*} {p : α → Bool} {xs : List α} {x : α}
+ (h : xs.find? p = some x) : x ∈ xs := by
+ induction xs with
+ | nil =>
+ simp at h
+ | cons y ys ih =>
+ by_cases hp : p y = true
+ · simp [List.find?, hp] at h
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_5 | 27f199e939fe088f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "pivotRowOfColumn?_some_prop",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold pivotRowOfColumn? at h\n have hmem := list_find?_some_mem h\n have hpred := List.find?_some h\n exact... | [
{
"name": "list_find?_some_mem",
"text": "private theorem list_find?_some_mem {α : Type*} {p : α → Bool} {xs : List α} {x : α}\n (h : xs.find? p = some x) : x ∈ xs := by\n induction xs with\n | nil =>\n simp at h\n | cons y ys ih =>\n by_cases hp : p y = true\n · simp [List.find?, hp] a... | [
{
"name": "pivotRowOfColumn?_eq_some_of_getD",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 28,
"n_chars": 1183,
"n_subproofs": 8,
"n_tactics": 24,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 3,
"n_structural": 5,
"automation_only": fa... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -18,9 +18,45 @@
namespace DenseMatrix
+private theorem list_find?_some_mem {α : Type*} {p : α → Bool} {xs : List α} {x : α}
+ (h : xs.find? p = some x) : x ∈ xs := by
+ induction xs with
+ | nil =>
+ simp at h
+ | cons y ys ih =>
+ by_cases hp : p y = true
+ · simp [List.find?, hp] at h
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_6 | 24438d67310fb7f2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 3 | [
{
"theorem_name": "containsNat_getD_ne",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro hget\n have htrue : containsNat xs x = true :=\n containsNat_eq_true_iff_exists.mpr ⟨i, hi, hget⟩\n simp [hc... | [
{
"name": "containsNat_eq_true_iff_exists",
"text": "private theorem containsNat_eq_true_iff_exists {xs : Array Nat} {x : Nat} :\n containsNat xs x = true ↔ ∃ i, i < xs.size ∧ xs.getD i 0 = x := by\n constructor\n · intro h\n have hxList := containsNat_eq_true_iff.mp h\n rcases List.mem_iff_get.m... | [
{
"name": "pivotRow_basisVectorForFreeColumn_term",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 80,
"n_chars": 3466,
"n_subproofs": 19,
"n_tactics": 72,
"cyclomatic": 2,
"n_automation": 13,
"n_rewrites": 15,
"n_structural": 19,
"automation_... | 6 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -30,11 +30,29 @@
refine ⟨x, Array.mem_def.mpr hx, ?_⟩
exact beq_iff_eq.mpr rfl
+private theorem containsNat_eq_true_iff_exists {xs : Array Nat} {x : Nat} :
+ containsNat xs x = true ↔ ∃ i, i < xs.size ∧ xs.getD i 0 = x := by
+ constructor
+ · intro h
+ have hxList := containsNat_eq_true_iff.mp h
... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_7 | b5c2303bb0187977 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 3 | [
{
"theorem_name": "containsNat_getD_ne",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro hget\n have htrue : containsNat xs x = true :=\n containsNat_eq_true_iff_exists.mpr ⟨i, hi, hget⟩\n simp [hc... | [
{
"name": "containsNat_eq_true_iff_exists",
"text": "private theorem containsNat_eq_true_iff_exists {xs : Array Nat} {x : Nat} :\n containsNat xs x = true ↔ ∃ i, i < xs.size ∧ xs.getD i 0 = x := by\n constructor\n · intro h\n have hxList := containsNat_eq_true_iff.mp h\n rcases List.mem_iff_get.m... | [
{
"name": "dotRow_basisVectorForFreeColumn_pivot",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 8,
"n_lines": 50,
"n_chars": 1793,
"n_subproofs": 6,
"n_tactics": 43,
"cyclomatic": 2,
"n_automation": 8,
"n_rewrites": 7,
"n_structural": 11,
"automation_only... | 8 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -30,11 +30,29 @@
refine ⟨x, Array.mem_def.mpr hx, ?_⟩
exact beq_iff_eq.mpr rfl
+private theorem containsNat_eq_true_iff_exists {xs : Array Nat} {x : Nat} :
+ containsNat xs x = true ↔ ∃ i, i < xs.size ∧ xs.getD i 0 = x := by
+ constructor
+ · intro h
+ have hxList := containsNat_eq_true_iff.mp h
... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_8 | ef4d0153be882c63 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "containsNat_eq_true_iff_exists",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h\n have hxList := containsNat_eq_true_iff.mp h\n rcases List.mem_iff_get.mp h... | [
{
"name": "containsNat_eq_true_iff",
"text": "private theorem containsNat_eq_true_iff {xs : Array Nat} {x : Nat} :\n containsNat xs x = true ↔ x ∈ xs.toList := by\n unfold containsNat\n rw [Array.any_eq_true']\n constructor\n · rintro ⟨y, hy, hbeq⟩\n have hyx : y = x := beq_iff_eq.mp hbeq\n sim... | [
{
"name": "dotRow_eq_getD_of_all_pivots",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 68,
"n_chars": 2513,
"n_subproofs": 12,
"n_tactics": 61,
"cyclomatic": 3,
"n_automation": 14,
"n_rewrites": 14,
"n_structural": 17,
"automation_only": fal... | 3 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -18,8 +18,34 @@
namespace DenseMatrix
+private theorem containsNat_eq_true_iff {xs : Array Nat} {x : Nat} :
+ containsNat xs x = true ↔ x ∈ xs.toList := by
+ unfold containsNat
+ rw [Array.any_eq_true']
+ constructor
+ · rintro ⟨y, hy, hbeq⟩
+ have hyx : y = x := beq_iff_eq.mp hbeq
+ simpa [hyx] us... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_9 | b6a1a91f9c63f28a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 3 | [
{
"theorem_name": "containsNat_getD_ne",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro hget\n have htrue : containsNat xs x = true :=\n containsNat_eq_true_iff_exists.mpr ⟨i, hi, hget⟩\n simp [hc... | [
{
"name": "containsNat_eq_true_iff_exists",
"text": "private theorem containsNat_eq_true_iff_exists {xs : Array Nat} {x : Nat} :\n containsNat xs x = true ↔ ∃ i, i < xs.size ∧ xs.getD i 0 = x := by\n constructor\n · intro h\n have hxList := containsNat_eq_true_iff.mp h\n rcases List.mem_iff_get.m... | [
{
"name": "basisVectorForFreeColumn_isHomogeneousSolution_rref",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 10,
"n_lines": 20,
"n_chars": 892,
"n_subproofs": 4,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 5,
"au... | 10 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -30,11 +30,29 @@
refine ⟨x, Array.mem_def.mpr hx, ?_⟩
exact beq_iff_eq.mpr rfl
+private theorem containsNat_eq_true_iff_exists {xs : Array Nat} {x : Nat} :
+ containsNat xs x = true ↔ ∃ i, i < xs.size ∧ xs.getD i 0 = x := by
+ constructor
+ · intro h
+ have hxList := containsNat_eq_true_iff.mp h
... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_10 | aced7b7e135c9475 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "homogeneousKernelBasis_getD_zero_size",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let R := rref M\n have hcols : R.matrix.cols = M.cols := by\n simpa [R] using rref_cols M\n cha... | [
{
"name": "basisVectorForFreeColumn_size",
"text": "private theorem basisVectorForFreeColumn_size [Field F] [BEq F]\n (A : DenseMatrix F) (pivots : Array Nat) (free : Nat) :\n (basisVectorForFreeColumn A pivots free).size = A.cols := by\n simp [basisVectorForFreeColumn]\n\n",
"fan_in": 1,
"n_... | [
{
"name": "homogeneousKernelBasis_getD_zero_size",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 775,
"n_subproofs": 1,
"n_tactics": 16,
"cyclomatic": 3,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 3,
"automation_only":... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -18,6 +18,11 @@
namespace DenseMatrix
+private theorem basisVectorForFreeColumn_size [Field F] [BEq F]
+ (A : DenseMatrix F) (pivots : Array Nat) (free : Nat) :
+ (basisVectorForFreeColumn A pivots free).size = A.cols := by
+ simp [basisVectorForFreeColumn]
+
private theorem homogeneousKernelBasis_getD_... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_11 | 2fdf6cd8cf3ed839 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "homogeneousKernelBasis_getD_zero_size",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let R := rref M\n have hcols : R.matrix.cols = M.cols := by\n simpa [R] using rref_cols M\n cha... | [
{
"name": "basisVectorForFreeColumn_size",
"text": "private theorem basisVectorForFreeColumn_size [Field F] [BEq F]\n (A : DenseMatrix F) (pivots : Array Nat) (free : Nat) :\n (basisVectorForFreeColumn A pivots free).size = A.cols := by\n simp [basisVectorForFreeColumn]\n\n",
"fan_in": 1,
"n_... | [
{
"name": "homogeneousWitness_width",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 382,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
"m... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -18,6 +18,11 @@
namespace DenseMatrix
+private theorem basisVectorForFreeColumn_size [Field F] [BEq F]
+ (A : DenseMatrix F) (pivots : Array Nat) (free : Nat) :
+ (basisVectorForFreeColumn A pivots free).size = A.cols := by
+ simp [basisVectorForFreeColumn]
+
private theorem homogeneousKernelBasis_getD_... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_12 | 7b6a6eb0fafbf64c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "homogeneousWitness_nonzero",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [homogeneousWitness] at h\n simp at h\n rw [← h.2]\n exact homogeneousKernelBasis_getD_zero_nonzero M h.1"... | [
{
"name": "homogeneousKernelBasis_getD_zero_nonzero",
"text": "private theorem homogeneousKernelBasis_getD_zero_nonzero [Field F] [BEq F]\n (M : DenseMatrix F) (h : ¬ homogeneousKernelBasis M = #[]) :\n NonzeroVector ((homogeneousKernelBasis M)[0]?.getD #[]) := by\n let R := rref M\n have hcols : R.... | [
{
"name": "homogeneousWitness_nonzero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 353,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -18,10 +18,43 @@
namespace DenseMatrix
+private theorem homogeneousKernelBasis_getD_zero_nonzero [Field F] [BEq F]
+ (M : DenseMatrix F) (h : ¬ homogeneousKernelBasis M = #[]) :
+ NonzeroVector ((homogeneousKernelBasis M)[0]?.getD #[]) := by
+ let R := rref M
+ have hcols : R.matrix.cols = M.cols := by
... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_13 | f7c4dcd41697b997 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "pivotRow_basisVectorForFreeColumn_term",
"depth": 1,
"n_commands": 0,
"n_lines": 71,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hrowA : row < A.rows := (hshape row hrow).1\n have hpivotCol : pivots.getD row 0 < A.cols := ... | [
{
"name": "containsNat_getD_ne",
"text": "private theorem containsNat_getD_ne {xs : Array Nat} {x i : Nat}\n (hcontains : containsNat xs x = false) (hi : i < xs.size) :\n xs.getD i 0 ≠ x := by\n intro hget\n have htrue : containsNat xs x = true :=\n containsNat_eq_true_iff_exists.mpr ⟨i, hi, hget... | [
{
"name": "homogeneousWitness_sound",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 18,
"n_lines": 38,
"n_chars": 1785,
"n_subproofs": 6,
"n_tactics": 32,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 9,
"n_structural": 6,
"automation_only": false,
... | 18 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -47,6 +47,14 @@
rw [← hgetD]
exact Array.getElem_mem (xs := xs) hi
+private theorem containsNat_getD_ne {xs : Array Nat} {x i : Nat}
+ (hcontains : containsNat xs x = false) (hi : i < xs.size) :
+ xs.getD i 0 ≠ x := by
+ intro hget
+ have htrue : containsNat xs x = true :=
+ containsNat_eq_tru... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_73b7f4b0d827_14 | 30dabdc7b214ed42 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelCorrectness.lean | KernelCorrectness | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 3 | [
{
"theorem_name": "containsNat_getD_ne",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro hget\n have htrue : containsNat xs x = true :=\n containsNat_eq_true_iff_exists.mpr ⟨i, hi, hget⟩\n simp [hc... | [
{
"name": "containsNat_eq_true_iff_exists",
"text": "private theorem containsNat_eq_true_iff_exists {xs : Array Nat} {x : Nat} :\n containsNat xs x = true ↔ ∃ i, i < xs.size ∧ xs.getD i 0 = x := by\n constructor\n · intro h\n have hxList := containsNat_eq_true_iff.mp h\n rcases List.mem_iff_get.m... | [
{
"name": "homogeneousWitness_none_complete",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 31,
"n_chars": 1469,
"n_subproofs": 11,
"n_tactics": 26,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 7,
"automation_only": fa... | 6 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.Kernel
import CompPoly.LinearAlgebra.Dense.RrefShape
import Mathlib.Data.Finset.Card
/-!
# Dense Homogeneous-Kernel Corre... | @@ -30,6 +30,23 @@
refine ⟨x, Array.mem_def.mpr hx, ?_⟩
exact beq_iff_eq.mpr rfl
+private theorem containsNat_eq_true_iff_exists {xs : Array Nat} {x : Nat} :
+ containsNat xs x = true ↔ ∃ i, i < xs.size ∧ xs.getD i 0 = x := by
+ constructor
+ · intro h
+ have hxList := containsNat_eq_true_iff.mp h
+... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_cca8eb9b4bf8_0 | 9c446a51d1136b2a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "ghashPoly_irreducible",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n letI : GCDMonoid (Polynomial (ZMod 2)) := by apply EuclideanDomain.gcdMonoid\n apply irreducible_of_rabin_128_passe... | [
{
"name": "irreducible_of_rabin_128_passed_over_GF2",
"text": "/--\n**Rabin's Irreducibility Test (Specialized for Degree 128)**\n\nThis lemma proves that if the two Rabin conditions hold for a degree 128 polynomial,\nit MUST be irreducible. It formalizes Lemma 1 from Rabin's paper.\n\nHypotheses:\n1. `h_de... | [
{
"name": "ghashPoly_irreducible",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 24,
"n_chars": 1283,
"n_subproofs": 2,
"n_tactics": 16,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 5,
"n_structural": 6,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Fields.Binary.BF128Ghash.XPowTwoPowGcdCertificate
/-!
# BinaryField128Ghash
Define `GF(2^128)` as a single field extension ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Fields.Binary.BF128Ghash.XPowTwoPowGcdCertificate
/-!
# BinaryField128Ghash
Define `GF(2^128)` as a single field extension ... | @@ -47,10 +47,109 @@
set_option maxRecDepth 1000
+/--
+**Rabin's Irreducibility Test (Specialized for Degree 128)**
+
+This lemma proves that if the two Rabin conditions hold for a degree 128 polynomial,
+it MUST be irreducible. It formalizes Lemma 1 from Rabin's paper.
+
+Hypotheses:
+1. `h_deg`: P has degree 128... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_cca8eb9b4bf8_1 | 164101b03239ac7c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Basic.lean | Basic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "ghashPoly_irreducible",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n letI : GCDMonoid (Polynomial (ZMod 2)) := by apply EuclideanDomain.gcdMonoid\n apply irreducible_of_rabin_128_passe... | [
{
"name": "irreducible_of_rabin_128_passed_over_GF2",
"text": "/--\n**Rabin's Irreducibility Test (Specialized for Degree 128)**\n\nThis lemma proves that if the two Rabin conditions hold for a degree 128 polynomial,\nit MUST be irreducible. It formalizes Lemma 1 from Rabin's paper.\n\nHypotheses:\n1. `h_de... | [
{
"name": "BF128Ghash_card",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 19,
"n_chars": 844,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Fields.Binary.BF128Ghash.XPowTwoPowGcdCertificate
/-!
# BinaryField128Ghash
Define `GF(2^128)` as a single field extension ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Fields.Binary.BF128Ghash.XPowTwoPowGcdCertificate
/-!
# BinaryField128Ghash
Define `GF(2^128)` as a single field extension ... | @@ -47,10 +47,109 @@
set_option maxRecDepth 1000
+/--
+**Rabin's Irreducibility Test (Specialized for Degree 128)**
+
+This lemma proves that if the two Rabin conditions hold for a degree 128 polynomial,
+it MUST be irreducible. It formalizes Lemma 1 from Rabin's paper.
+
+Hypotheses:
+1. `h_deg`: P has degree 128... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_abc5aacc676b_0 | 49f6c98d3b8bbbac | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/DIF.lean | DIF | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "omega_pow_add_domain_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [pow_add, omega_pow_domain_mul D k]\n simp",
"n_chars": 51,
"n_subproofs": 0,
"n_tactics": 3,
... | [
{
"name": "omega_pow_domain_mul",
"text": "private theorem omega_pow_domain_mul (D : NTT.Domain R) (k : Nat) :\n D.omega ^ (D.n * k) = 1 := by\n have h : D.omega ^ D.n = 1 := by\n simpa [NTT.Domain.n] using D.primitive.pow_eq_one\n rw [pow_mul, h, one_pow]\n\n",
"fan_in": 1,
"n_lines": 7,
... | [
{
"name": "omega_pow_add_domain_mul",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 171,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Basic
/-!
# DIF NTTFast correctness
Correctness proofs for the decimation-in-frequency stage loop used by `NTT... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Basic
/-!
# DIF NTTFast correctness
Correctness proofs for the decimation-in-frequency stage loop used by `NTT... | @@ -137,8 +137,16 @@
rw [pow_succ]
omega)
+private theorem omega_pow_domain_mul (D : NTT.Domain R) (k : Nat) :
+ D.omega ^ (D.n * k) = 1 := by
+ have h : D.omega ^ D.n = 1 := by
+ simpa [NTT.Domain.n] using D.primitive.pow_eq_one
+ rw [pow_mul, h, one_pow]
+
private theorem omega_pow_add_domain_mul... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_abc5aacc676b_1 | 86480fb429e23fb5 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/DIF.lean | DIF | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 4 | [
{
"theorem_name": "difMathPairsSpec_get_lower_current",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [difMathPairsSpec, dif_lower_div_block stage block j hj,\n dif_lower_mod_half stage block j hj]"... | [
{
"name": "dif_lower_div_block",
"text": "private theorem dif_lower_div_block (stage block j : Nat) (hj : j < 2 ^ stage) :\n (block * 2 ^ (stage + 1) + j) / 2 ^ (stage + 1) = block := by\n rw [Nat.mul_comm block (2 ^ (stage + 1))]\n rw [Nat.mul_add_div (Nat.two_pow_pos (stage + 1))]\n have hlt : j < 2... | [
{
"name": "difMathPairsSpec_get_lower_current",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 478,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Basic
/-!
# DIF NTTFast correctness
Correctness proofs for the decimation-in-frequency stage loop used by `NTT... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.Basic
/-!
# DIF NTTFast correctness
Correctness proofs for the decimation-in-frequency stage loop used by `NTT... | @@ -63,6 +63,15 @@
else
difMathValueAt D oldCompleted a i.1)
+private theorem dif_lower_div_block (stage block j : Nat) (hj : j < 2 ^ stage) :
+ (block * 2 ^ (stage + 1) + j) / 2 ^ (stage + 1) = block := by
+ rw [Nat.mul_comm block (2 ^ (stage + 1))]
+ rw [Nat.mul_add_div (Nat.two_pow_pos (stage ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
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