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_f34241427335_11 | 3087e6d14a911f4b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ToPoly/Impl.lean | Impl | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 6 | [
{
"theorem_name": "monomial_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext i\n simp only [CPolynomial.toPoly, monomial]\n rw [Polynomial.coeff_monomial, coeff_toPoly, CPolynomial.Raw.coeff_mon... | [
{
"name": "coeff_toPoly",
"text": "/-- CPolynomial.coeff is correct wrt the Mathlib spec. -/\ntheorem coeff_toPoly [BEq R] [LawfulBEq R] (p : CPolynomial R) (i : ℕ) :\n p.coeff i = p.toPoly.coeff i := by\n unfold toPoly coeff\n simp [Raw.coeff_toPoly]\n\n",
"fan_in": 6,
"n_lines": 7,
"n_cha... | [
{
"name": "C_mul_X_pow_toPoly",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 299,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | @@ -27,8 +27,17 @@
/-- CPolynomial.monomial is correct wrt the Mathlib spec. -/
theorem monomial_toPoly [DecidableEq R] [LawfulBEq R] (n : ℕ) (c : R) :
- (monomial n c).toPoly = Polynomial.monomial n c := sorry
+ (monomial n c).toPoly = Polynomial.monomial n c := by
+ ext i
+ simp only [CPolynomial.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_f34241427335_12 | acf6645009bb1835 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ToPoly/Impl.lean | Impl | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 6 | [
{
"theorem_name": "monomial_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext i\n simp only [CPolynomial.toPoly, monomial]\n rw [Polynomial.coeff_monomial, coeff_toPoly, CPolynomial.Raw.coeff_mon... | [
{
"name": "coeff_toPoly",
"text": "/-- CPolynomial.coeff is correct wrt the Mathlib spec. -/\ntheorem coeff_toPoly [BEq R] [LawfulBEq R] (p : CPolynomial R) (i : ℕ) :\n p.coeff i = p.toPoly.coeff i := by\n unfold toPoly coeff\n simp [Raw.coeff_toPoly]\n\n",
"fan_in": 6,
"n_lines": 7,
"n_cha... | [
{
"name": "lcoeff_toPoly",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 262,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": ... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | @@ -25,9 +25,16 @@
variable {R : Type*} [Semiring R]
+/-- CPolynomial.coeff is correct wrt the Mathlib spec. -/
+theorem coeff_toPoly [BEq R] [LawfulBEq R] (p : CPolynomial R) (i : ℕ) :
+ p.coeff i = p.toPoly.coeff i := by
+ unfold toPoly coeff
+ simp [Raw.coeff_toPoly]
+
/-- CPolynomial.lcoeff is correct wr... | {
"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_f34241427335_13 | 202df8fec145118c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ToPoly/Impl.lean | Impl | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 3 | [
{
"theorem_name": "degree_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hp : p = 0\n · subst hp\n rw [toPoly_zero, CPolynomial.degree]\n rfl\n · have hsize := size_eq_toPoly_natDe... | [
{
"name": "size_eq_toPoly_natDegree_succ",
"text": "/-- lemma: size = natDegree's succ -/\nprivate lemma size_eq_toPoly_natDegree_succ [BEq R] [LawfulBEq R]\n (p : CPolynomial R) (hp : p ≠ 0) :\n p.val.size = p.toPoly.natDegree + 1 := by\n have htoPoly : p.toPoly ≠ 0 := (toPoly_eq_zero_iff p).not.mpr... | [
{
"name": "degreeLE_toPoly",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 8,
"n_chars": 327,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | @@ -32,6 +32,16 @@
· exact (hq hzero).elim
· simp [himpl]
+/-- lemma: size = natDegree's succ -/
+private lemma size_eq_toPoly_natDegree_succ [BEq R] [LawfulBEq R]
+ (p : CPolynomial R) (hp : p ≠ 0) :
+ p.val.size = p.toPoly.natDegree + 1 := by
+ have htoPoly : p.toPoly ≠ 0 := (toPoly_eq_zero_iff p).not.... | {
"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_f34241427335_14 | f3cf9b65c69fbeda | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ToPoly/Impl.lean | Impl | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 3 | [
{
"theorem_name": "degree_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hp : p = 0\n · subst hp\n rw [toPoly_zero, CPolynomial.degree]\n rfl\n · have hsize := size_eq_toPoly_natDe... | [
{
"name": "size_eq_toPoly_natDegree_succ",
"text": "/-- lemma: size = natDegree's succ -/\nprivate lemma size_eq_toPoly_natDegree_succ [BEq R] [LawfulBEq R]\n (p : CPolynomial R) (hp : p ≠ 0) :\n p.val.size = p.toPoly.natDegree + 1 := by\n have htoPoly : p.toPoly ≠ 0 := (toPoly_eq_zero_iff p).not.mpr... | [
{
"name": "degreeLT_toPoly",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 8,
"n_chars": 315,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | @@ -32,6 +32,16 @@
· exact (hq hzero).elim
· simp [himpl]
+/-- lemma: size = natDegree's succ -/
+private lemma size_eq_toPoly_natDegree_succ [BEq R] [LawfulBEq R]
+ (p : CPolynomial R) (hp : p ≠ 0) :
+ p.val.size = p.toPoly.natDegree + 1 := by
+ have htoPoly : p.toPoly ≠ 0 := (toPoly_eq_zero_iff p).not.... | {
"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_f34241427335_15 | 8d9c3739ef9abe84 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ToPoly/Impl.lean | Impl | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 7 | [
{
"theorem_name": "eval_C",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CPolynomial.eval_toPoly, CPolynomial.C_toPoly, Polynomial.eval_C]",
"n_chars": 75,
"n_subproofs": 0,
"n_tactics": 2,... | [
{
"name": "eval_toPoly",
"text": "/-- CPolynomial.eval is correct wrt the Mathlib spec. -/\ntheorem eval_toPoly [BEq R] [LawfulBEq R] (x : R) (p : CPolynomial R) :\n eval x p = p.toPoly.eval x := by\n change Raw.eval x p.val = p.val.toPoly.eval x\n exact (Raw.eval_toPoly_eq_eval x p.val).symm\n\n",
... | [
{
"name": "eval_mul",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 270,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | @@ -25,6 +25,12 @@
variable {R : Type*} [Semiring R]
+/-- CPolynomial.eval is correct wrt the Mathlib spec. -/
+theorem eval_toPoly [BEq R] [LawfulBEq R] (x : R) (p : CPolynomial R) :
+ eval x p = p.toPoly.eval x := by
+ change Raw.eval x p.val = p.val.toPoly.eval x
+ exact (Raw.eval_toPoly_eq_eval x p.val).s... | {
"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_f34241427335_16 | 475df0bbb61b75c5 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ToPoly/Impl.lean | Impl | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 3 | [
{
"theorem_name": "degree_toPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hp : p = 0\n · subst hp\n rw [toPoly_zero, CPolynomial.degree]\n rfl\n · have hsize := size_eq_toPoly_natDe... | [
{
"name": "size_eq_toPoly_natDegree_succ",
"text": "/-- lemma: size = natDegree's succ -/\nprivate lemma size_eq_toPoly_natDegree_succ [BEq R] [LawfulBEq R]\n (p : CPolynomial R) (hp : p ≠ 0) :\n p.val.size = p.toPoly.natDegree + 1 := by\n have htoPoly : p.toPoly ≠ 0 := (toPoly_eq_zero_iff p).not.mpr... | [
{
"name": "eval_ext",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 37,
"n_chars": 1454,
"n_subproofs": 6,
"n_tactics": 22,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 4,
"automation_only": false,
"max_nesting": 6... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | @@ -38,6 +38,16 @@
· exact (hq hzero).elim
· simp [himpl]
+/-- lemma: size = natDegree's succ -/
+private lemma size_eq_toPoly_natDegree_succ [BEq R] [LawfulBEq R]
+ (p : CPolynomial R) (hp : p ≠ 0) :
+ p.val.size = p.toPoly.natDegree + 1 := by
+ have htoPoly : p.toPoly ≠ 0 := (toPoly_eq_zero_iff p).not.... | {
"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_f34241427335_17 | ad9257acccccb865 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ToPoly/Impl.lean | Impl | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 7 | [
{
"theorem_name": "eval_C",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CPolynomial.eval_toPoly, CPolynomial.C_toPoly, Polynomial.eval_C]",
"n_chars": 75,
"n_subproofs": 0,
"n_tactics": 2,... | [
{
"name": "eval_toPoly",
"text": "/-- CPolynomial.eval is correct wrt the Mathlib spec. -/\ntheorem eval_toPoly [BEq R] [LawfulBEq R] (x : R) (p : CPolynomial R) :\n eval x p = p.toPoly.eval x := by\n change Raw.eval x p.val = p.val.toPoly.eval x\n exact (Raw.eval_toPoly_eq_eval x p.val).symm\n\n",
... | [
{
"name": "eval_sub",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 347,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting": 4
... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | @@ -25,6 +25,12 @@
variable {R : Type*} [Semiring R]
+/-- CPolynomial.eval is correct wrt the Mathlib spec. -/
+theorem eval_toPoly [BEq R] [LawfulBEq R] (x : R) (p : CPolynomial R) :
+ eval x p = p.toPoly.eval x := by
+ change Raw.eval x p.val = p.val.toPoly.eval x
+ exact (Raw.eval_toPoly_eq_eval x p.val).s... | {
"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_f34241427335_18 | d0a185a88adde6b0 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ToPoly/Impl.lean | Impl | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 7 | [
{
"theorem_name": "eval_C",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CPolynomial.eval_toPoly, CPolynomial.C_toPoly, Polynomial.eval_C]",
"n_chars": 75,
"n_subproofs": 0,
"n_tactics": 2,... | [
{
"name": "eval_toPoly",
"text": "/-- CPolynomial.eval is correct wrt the Mathlib spec. -/\ntheorem eval_toPoly [BEq R] [LawfulBEq R] (x : R) (p : CPolynomial R) :\n eval x p = p.toPoly.eval x := by\n change Raw.eval x p.val = p.val.toPoly.eval x\n exact (Raw.eval_toPoly_eq_eval x p.val).symm\n\n",
... | [
{
"name": "eval_one",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 268,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | @@ -25,6 +25,12 @@
variable {R : Type*} [Semiring R]
+/-- CPolynomial.eval is correct wrt the Mathlib spec. -/
+theorem eval_toPoly [BEq R] [LawfulBEq R] (x : R) (p : CPolynomial R) :
+ eval x p = p.toPoly.eval x := by
+ change Raw.eval x p.val = p.val.toPoly.eval x
+ exact (Raw.eval_toPoly_eq_eval x p.val).s... | {
"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_f34241427335_19 | bacaab9a7941e5f0 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ToPoly/Impl.lean | Impl | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 7 | [
{
"theorem_name": "eval_C",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CPolynomial.eval_toPoly, CPolynomial.C_toPoly, Polynomial.eval_C]",
"n_chars": 75,
"n_subproofs": 0,
"n_tactics": 2,... | [
{
"name": "eval_toPoly",
"text": "/-- CPolynomial.eval is correct wrt the Mathlib spec. -/\ntheorem eval_toPoly [BEq R] [LawfulBEq R] (x : R) (p : CPolynomial R) :\n eval x p = p.toPoly.eval x := by\n change Raw.eval x p.val = p.val.toPoly.eval x\n exact (Raw.eval_toPoly_eq_eval x p.val).symm\n\n",
... | [
{
"name": "eval_divX_eq_zero_of_ne_zero_root",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 5,
"n_lines": 21,
"n_chars": 921,
"n_subproofs": 2,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 4,
"automation_only": fal... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | @@ -37,9 +37,16 @@
change (CPolynomial.Raw.X : CPolynomial.Raw R).toPoly = Polynomial.X
exact CPolynomial.Raw.toPoly_X (R := R)
+/-- CPolynomial.eval is correct wrt the Mathlib spec. -/
+theorem eval_toPoly [BEq R] [LawfulBEq R] (x : R) (p : CPolynomial R) :
+ eval x p = p.toPoly.eval x := by
+ change Raw.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_f34241427335_20 | 352e7d402feeb38f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ToPoly/Impl.lean | Impl | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "eval_divX_eq_zero_of_ne_zero_root",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hdecomp := CPolynomial.X_mul_divX_add (p := p)\n have hroot' :\n CPolynomial.eval a (CPolynom... | [
{
"name": "eval_C",
"text": "/-- Evaluation of a constant computable polynomial. -/\ntheorem eval_C [BEq R] [LawfulBEq R] (a c : R) :\n CPolynomial.eval a (CPolynomial.C c) = c := by\n rw [CPolynomial.eval_toPoly, CPolynomial.C_toPoly, Polynomial.eval_C]\n\n",
"fan_in": 2,
"n_lines": 6,
"n_c... | [
{
"name": "eval_sub_C_mul_X_pow_trim_eq_self_of_eval_eq_zero",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 12,
"n_chars": 545,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 0,
"automa... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | @@ -37,6 +37,11 @@
change Raw.eval x p.val = p.val.toPoly.eval x
exact (Raw.eval_toPoly_eq_eval x p.val).symm
+/-- Evaluation of a constant computable polynomial. -/
+theorem eval_C [BEq R] [LawfulBEq R] (a c : R) :
+ CPolynomial.eval a (CPolynomial.C c) = c := by
+ rw [CPolynomial.eval_toPoly, CPolynomial.... | {
"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_f34241427335_21 | a9464213de4021d4 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ToPoly/Impl.lean | Impl | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "eval_divX_eq_zero_of_ne_zero_root",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hdecomp := CPolynomial.X_mul_divX_add (p := p)\n have hroot' :\n CPolynomial.eval a (CPolynom... | [
{
"name": "eval_C",
"text": "/-- Evaluation of a constant computable polynomial. -/\ntheorem eval_C [BEq R] [LawfulBEq R] (a c : R) :\n CPolynomial.eval a (CPolynomial.C c) = c := by\n rw [CPolynomial.eval_toPoly, CPolynomial.C_toPoly, Polynomial.eval_C]\n\n",
"fan_in": 2,
"n_lines": 6,
"n_c... | [
{
"name": "eval_divModByMonicAux_go_snd_eq_self_of_eval_eq_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 21,
"n_chars": 698,
"n_subproofs": 0,
"n_tactics": 16,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 6,
"au... | 6 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | @@ -37,6 +37,11 @@
change Raw.eval x p.val = p.val.toPoly.eval x
exact (Raw.eval_toPoly_eq_eval x p.val).symm
+/-- Evaluation of a constant computable polynomial. -/
+theorem eval_C [BEq R] [LawfulBEq R] (a c : R) :
+ CPolynomial.eval a (CPolynomial.C c) = c := by
+ rw [CPolynomial.eval_toPoly, CPolynomial.... | {
"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_f34241427335_22 | cc61ec8e25719b3c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ToPoly/Impl.lean | Impl | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "eval_divX_eq_zero_of_ne_zero_root",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hdecomp := CPolynomial.X_mul_divX_add (p := p)\n have hroot' :\n CPolynomial.eval a (CPolynom... | [
{
"name": "eval_C",
"text": "/-- Evaluation of a constant computable polynomial. -/\ntheorem eval_C [BEq R] [LawfulBEq R] (a c : R) :\n CPolynomial.eval a (CPolynomial.C c) = c := by\n rw [CPolynomial.eval_toPoly, CPolynomial.C_toPoly, Polynomial.eval_C]\n\n",
"fan_in": 2,
"n_lines": 6,
"n_c... | [
{
"name": "eval_modByMonic_eq_self_of_eval_eq_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 8,
"n_chars": 338,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import CompPoly.Univariate.ToPoly.Equiv
import Mathlib.Algebra.Polynomial.Roots
/-!
# Proofs of Correctness for CPolynomial Operations, wr... | @@ -37,6 +37,11 @@
change Raw.eval x p.val = p.val.toPoly.eval x
exact (Raw.eval_toPoly_eq_eval x p.val).symm
+/-- Evaluation of a constant computable polynomial. -/
+theorem eval_C [BEq R] [LawfulBEq R] (a c : R) :
+ CPolynomial.eval a (CPolynomial.C c) = c := by
+ rw [CPolynomial.eval_toPoly, CPolynomial.... | {
"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_d2fec450be47_0 | 51a264dbb39ae427 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/XPowTwoPowGcdCertificate.lean | XPowTwoPowGcdCertificate | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 66 | 1 | [
{
"theorem_name": "gcd_start_reduction",
"depth": 1,
"n_commands": 0,
"n_lines": 23,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- 1. Swap order: gcd(A, B) = gcd(B, A)\n rw [ZMod2Poly.euclidean_gcd_comm]\n -- 2. Reduce LHS mod RHS: gcd(B, A) = ... | [
{
"name": "toPoly_gcd_b_0_val_mod_ghashPoly_eq_gcd_b_0_val",
"text": "lemma toPoly_gcd_b_0_val_mod_ghashPoly_eq_gcd_b_0_val :\n (toPoly gcd_b_0_val) % ghashPoly = toPoly gcd_b_0_val := by\n rw [Polynomial.mod_eq_self_iff (hq0 := by exact ghashPoly_ne_zero)]\n rw [toPoly]; simp_rw [BitVec.getLsb]\n hav... | [
{
"name": "gcd_start_reduction",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 28,
"n_chars": 1173,
"n_subproofs": 2,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 9,
"n_structural": 1,
"automation_only": false,
"max_... | 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.XPowTwoPowModCertificate
/-!
# XPowTwoPow Gcd Certificate
Certificates for gcd conditions in the B... | /-
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.XPowTwoPowModCertificate
/-!
# XPowTwoPow Gcd Certificate
Certificates for gcd conditions in the B... | @@ -22,9 +22,64 @@
@[reducible]
def gcd_b_0_val : B256 := BitVec.ofNat 256 129460184901158119860735353079755610612
+lemma toPoly_gcd_b_0_val_mod_ghashPoly_eq_gcd_b_0_val :
+ (toPoly gcd_b_0_val) % ghashPoly = toPoly gcd_b_0_val := by
+ rw [Polynomial.mod_eq_self_iff (hq0 := by exact ghashPoly_ne_zero)]
+ rw [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_d2fec450be47_1 | b880d6f707c4d1fb | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/XPowTwoPowGcdCertificate.lean | XPowTwoPowGcdCertificate | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 66 | 1 | [
{
"theorem_name": "rabin_gcd_condition_gHashPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 137,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [gcd_start_reduction]\n change EuclideanDomain.gcd (ghashPoly) (toPoly gcd_b_1_val) = 1\n have h_ghash... | [
{
"name": "gcd_step_44",
"text": "lemma gcd_step_44 : toPoly gcd_a_44_val\n = (toPoly gcd_q_44_val) * (toPoly gcd_b_44_val) + (toPoly gcd_r_44_val) := by\n apply verify_div_step_bounded gcd_a_44_val gcd_q_44_val gcd_b_44_val gcd_r_44_val\n (hq := by simp only [BitVec.toNat_ofNat, Nat.reducePow, Nat.r... | [
{
"name": "rabin_gcd_condition_gHashPoly",
"fan_in": 0,
"n_deps_direct": 65,
"n_deps_transitive": 66,
"n_lines": 139,
"n_chars": 8808,
"n_subproofs": 1,
"n_tactics": 136,
"cyclomatic": 1,
"n_automation": 66,
"n_rewrites": 133,
"n_structural": 1,
"automation_only":... | 66 | /-
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.XPowTwoPowModCertificate
/-!
# XPowTwoPow Gcd Certificate
Certificates for gcd conditions in the B... | /-
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.XPowTwoPowModCertificate
/-!
# XPowTwoPow Gcd Certificate
Certificates for gcd conditions in the B... | @@ -602,6 +602,14 @@
@[reducible] def gcd_b_44_val : B256 := BitVec.ofNat 256 7520384504995
@[reducible] def gcd_q_44_val : B256 := BitVec.ofNat 256 15
@[reducible] def gcd_r_44_val : B256 := BitVec.ofNat 256 1678400792017
+lemma gcd_step_44 : toPoly gcd_a_44_val
+ = (toPoly gcd_q_44_val) * (toPoly gcd_b_44_val) ... | {
"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_144cf04b0eff_0 | 69fe2dba79c8e496 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/FilterCorrectness.lean | FilterCorrectness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "gsFilteredCore_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases (mem_gsFilteredCore_iff\n (interpContext := interpContext) (rootContext := rootContext)\n (params := ... | [
{
"name": "passesCandidateDistance_iff",
"text": "/-- Boolean distance filtering agrees with the executable mismatch count. -/\ntheorem passesCandidateDistance_iff {F : Type*} [Semiring F] [BEq F]\n {points : Array (Prod F F)} {radius : Nat} {p : CPolynomial F} :\n passesCandidateDistance points radiu... | [
{
"name": "gsFilteredCore_sound",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 25,
"n_chars": 1168,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 3,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_... | 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.CoreCorrectness
/-!
# Guruswami-Sudan Candidate Filter Correctness
Correctness and completeness lemmas for generic ... | /-
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.CoreCorrectness
/-!
# Guruswami-Sudan Candidate Filter Correctness
Correctness and completeness lemmas for generic ... | @@ -17,6 +17,14 @@
namespace GuruswamiSudan
+/-- Boolean distance filtering agrees with the executable mismatch count. -/
+theorem passesCandidateDistance_iff {F : Type*} [Semiring F] [BEq F]
+ {points : Array (Prod F F)} {radius : Nat} {p : CPolynomial F} :
+ passesCandidateDistance points radius p = true ↔... | {
"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_144cf04b0eff_1 | fc8e4fe0132287dc | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/FilterCorrectness.lean | FilterCorrectness | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 3 | [
{
"theorem_name": "gsFilteredCore_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases (mem_gsFilteredCore_iff\n (interpContext := interpContext) (rootContext := rootContext)\n (params := ... | [
{
"name": "mem_gsFilteredCore_iff",
"text": "/-- Membership in `gsFilteredCore` is membership in `gsCore` plus the packed\ndistance predicate. -/\ntheorem mem_gsFilteredCore_iff {F : Type*}\n [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]\n {points : Array (Prod F F)}\n {interpContext : GSInterpCo... | [
{
"name": "gsFilteredCore_complete_of_roots_all_valid_witnesses",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 1035,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"au... | 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.CoreCorrectness
/-!
# Guruswami-Sudan Candidate Filter Correctness
Correctness and completeness lemmas for generic ... | /-
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.CoreCorrectness
/-!
# Guruswami-Sudan Candidate Filter Correctness
Correctness and completeness lemmas for generic ... | @@ -17,6 +17,20 @@
namespace GuruswamiSudan
+/-- Membership in `gsFilteredCore` is membership in `gsCore` plus the packed
+distance predicate. -/
+theorem mem_gsFilteredCore_iff {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]
+ {points : Array (Prod F F)}
+ {interpContext : GSInterpContext 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_144cf04b0eff_2 | 841e98a9a85e079c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/FilterCorrectness.lean | FilterCorrectness | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 3 | [
{
"theorem_name": "gsFilteredCore_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases (mem_gsFilteredCore_iff\n (interpContext := interpContext) (rootContext := rootContext)\n (params := ... | [
{
"name": "mem_gsFilteredCore_iff",
"text": "/-- Membership in `gsFilteredCore` is membership in `gsCore` plus the packed\ndistance predicate. -/\ntheorem mem_gsFilteredCore_iff {F : Type*}\n [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]\n {points : Array (Prod F F)}\n {interpContext : GSInterpCo... | [
{
"name": "gsFilteredCore_complete_of_enough_matches",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 939,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_onl... | 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.CoreCorrectness
/-!
# Guruswami-Sudan Candidate Filter Correctness
Correctness and completeness lemmas for generic ... | /-
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.CoreCorrectness
/-!
# Guruswami-Sudan Candidate Filter Correctness
Correctness and completeness lemmas for generic ... | @@ -17,6 +17,20 @@
namespace GuruswamiSudan
+/-- Membership in `gsFilteredCore` is membership in `gsCore` plus the packed
+distance predicate. -/
+theorem mem_gsFilteredCore_iff {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]
+ {points : Array (Prod F F)}
+ {interpContext : GSInterpContext 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_76463c98025e_2 | 59bf8500f11c8d29 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/PolynomialMatrix/MuldersStorjohannCorrectness/Combinations.lean | Combinations | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "rowLinearCombination_eq_zeroRow_of_forall_zero_or_row_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [rowLinearCombination] using\n rowLinearCombination_range_eq_zeroRow_of... | [
{
"name": "rowLinearCombination_range_eq_zeroRow_of_forall_zero_or_row_zero",
"text": "theorem rowLinearCombination_range_eq_zeroRow_of_forall_zero_or_row_zero\n {M : PolynomialMatrix F} (hM : WellFormed M)\n (coeffs : Array (CPolynomial F))\n (hzero : ∀ i, i < M.size →\n coeffs.getD i 0 = 0 ∨... | [
{
"name": "rowLinearCombination_eq_zeroRow_of_forall_zero_or_row_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 478,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
... | 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.PolynomialMatrix.MuldersStorjohannCorrectness.Measure
/-!
# Mulders-Storjohann Correctness Row Combination Helpers
Row-linear-... | /-
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.PolynomialMatrix.MuldersStorjohannCorrectness.Measure
/-!
# Mulders-Storjohann Correctness Row Combination Helpers
Row-linear-... | @@ -38,12 +38,48 @@
(rowShiftedLeadingPosition? (M.getD i #[]) shift).getD 0
omit [DecidableEq F] in
+theorem rowLinearCombination_range_eq_zeroRow_of_forall_zero_or_row_zero
+ {M : PolynomialMatrix F} (hM : WellFormed M)
+ (coeffs : Array (CPolynomial F))
+ (hzero : ∀ i, i < M.size →
+ coeffs.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_76463c98025e_3 | 78d78b9c1d76306a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/PolynomialMatrix/MuldersStorjohannCorrectness/Combinations.lean | Combinations | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "rowLinearCombination_eq_zeroRow_of_forall_zero_or_row_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [rowLinearCombination] using\n rowLinearCombination_range_eq_zeroRow_of... | [
{
"name": "rowLinearCombination_range_eq_zeroRow_of_forall_zero_or_row_zero",
"text": "theorem rowLinearCombination_range_eq_zeroRow_of_forall_zero_or_row_zero\n {M : PolynomialMatrix F} (hM : WellFormed M)\n (coeffs : Array (CPolynomial F))\n (hzero : ∀ i, i < M.size →\n coeffs.getD i 0 = 0 ∨... | [
{
"name": "rowCombinationTermSupport_nonempty_of_combination_degree_some",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 33,
"n_chars": 1395,
"n_subproofs": 5,
"n_tactics": 27,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": ... | 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.PolynomialMatrix.MuldersStorjohannCorrectness.Measure
/-!
# Mulders-Storjohann Correctness Row Combination Helpers
Row-linear-... | /-
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.PolynomialMatrix.MuldersStorjohannCorrectness.Measure
/-!
# Mulders-Storjohann Correctness Row Combination Helpers
Row-linear-... | @@ -38,12 +38,48 @@
(rowShiftedLeadingPosition? (M.getD i #[]) shift).getD 0
omit [DecidableEq F] in
+theorem rowLinearCombination_range_eq_zeroRow_of_forall_zero_or_row_zero
+ {M : PolynomialMatrix F} (hM : WellFormed M)
+ (coeffs : Array (CPolynomial F))
+ (hzero : ∀ i, i < M.size →
+ coeffs.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_9e044d7d92b6_0 | 8d0912cb39408c55 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/DefiningPoly.lean | DefiningPoly | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "degree_s_smul_X_add_1",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [degree_add_eq_left_of_degree_lt]\n · exact degree_s_smul_X s\n · rw [degree_one]; rw [degree_s_smul_X]; norm_nu... | [
{
"name": "degree_s_smul_X",
"text": "lemma degree_s_smul_X {F : Type*} [Field F] [Fintype F] (s : F) [NeZero s] :\n (C s * (X : (F)[X])).degree = 1 := by\n apply degree_C_mul_X (a:=s)\n exact NeZero.ne s\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 170,
"n_subproofs": 0,
"n_tactics"... | [
{
"name": "degree_s_smul_X_add_1",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 251,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import CompPoly.Fields.Binary.Tower.Support.LinearIndependentFin2
/-!
# Binary Tower Defining Polynomials
Defining polynomials and basic de... | /-
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.LinearIndependentFin2
/-!
# Binary Tower Defining Polynomials
Defining polynomials and basic de... | @@ -21,11 +21,16 @@
noncomputable def definingPoly {F : Type*} [instField : Field F] (s : F) :=
X ^ 2 + C s * X + 1
+lemma degree_s_smul_X {F : Type*} [Field F] [Fintype F] (s : F) [NeZero s] :
+ (C s * (X : (F)[X])).degree = 1 := by
+ apply degree_C_mul_X (a:=s)
+ exact NeZero.ne s
+
lemma degree_s_smul_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_9e044d7d92b6_1 | d245597feed97198 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/DefiningPoly.lean | DefiningPoly | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "definingPoly_is_monic",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [definingPoly]\n -- Goal : ⊢ (X ^ 2 + (t1 * X + 1)).Monic\n have leadingCoeffIs1 : (definingPoly s).leadingCoef... | [
{
"name": "degree_s_smul_X_add_1",
"text": "lemma degree_s_smul_X_add_1 {F : Type*} [Field F] [Fintype F] (s : F) [NeZero s] :\n (C s * (X : (F)[X]) + 1).degree = 1 := by\n rw [degree_add_eq_left_of_degree_lt]\n · exact degree_s_smul_X s\n · rw [degree_one]; rw [degree_s_smul_X]; norm_num\n\n",
"f... | [
{
"name": "definingPoly_is_monic",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 18,
"n_chars": 624,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 5,
"n_structural": 2,
"automation_only": false,
"max... | 2 | /-
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.LinearIndependentFin2
/-!
# Binary Tower Defining Polynomials
Defining polynomials and basic de... | /-
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.LinearIndependentFin2
/-!
# Binary Tower Defining Polynomials
Defining polynomials and basic de... | @@ -26,11 +26,27 @@
apply degree_C_mul_X (a:=s)
exact NeZero.ne s
+lemma degree_s_smul_X_add_1 {F : Type*} [Field F] [Fintype F] (s : F) [NeZero s] :
+ (C s * (X : (F)[X]) + 1).degree = 1 := by
+ rw [degree_add_eq_left_of_degree_lt]
+ · exact degree_s_smul_X s
+ · rw [degree_one]; rw [degree_s_smul_X]; no... | {
"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_9e044d7d92b6_2 | 8ddff879b0ded68a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/DefiningPoly.lean | DefiningPoly | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "definingPoly_is_monic",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [definingPoly]\n -- Goal : ⊢ (X ^ 2 + (t1 * X + 1)).Monic\n have leadingCoeffIs1 : (definingPoly s).leadingCoef... | [
{
"name": "degree_s_smul_X_add_1",
"text": "lemma degree_s_smul_X_add_1 {F : Type*} [Field F] [Fintype F] (s : F) [NeZero s] :\n (C s * (X : (F)[X]) + 1).degree = 1 := by\n rw [degree_add_eq_left_of_degree_lt]\n · exact degree_s_smul_X s\n · rw [degree_one]; rw [degree_s_smul_X]; norm_num\n\n",
"f... | [
{
"name": "degree_definingPoly",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 12,
"n_chars": 389,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 5,
"n_structural": 0,
"automation_only": false,
"max_n... | 2 | /-
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.LinearIndependentFin2
/-!
# Binary Tower Defining Polynomials
Defining polynomials and basic de... | /-
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.LinearIndependentFin2
/-!
# Binary Tower Defining Polynomials
Defining polynomials and basic de... | @@ -26,13 +26,22 @@
apply degree_C_mul_X (a:=s)
exact NeZero.ne s
+lemma degree_s_smul_X_add_1 {F : Type*} [Field F] [Fintype F] (s : F) [NeZero s] :
+ (C s * (X : (F)[X]) + 1).degree = 1 := by
+ rw [degree_add_eq_left_of_degree_lt]
+ · exact degree_s_smul_X s
+ · rw [degree_one]; rw [degree_s_smul_X]; no... | {
"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_9e044d7d92b6_3 | a1148f8646b7b9d9 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/DefiningPoly.lean | DefiningPoly | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "definingPoly_is_monic",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [definingPoly]\n -- Goal : ⊢ (X ^ 2 + (t1 * X + 1)).Monic\n have leadingCoeffIs1 : (definingPoly s).leadingCoef... | [
{
"name": "degree_s_smul_X_add_1",
"text": "lemma degree_s_smul_X_add_1 {F : Type*} [Field F] [Fintype F] (s : F) [NeZero s] :\n (C s * (X : (F)[X]) + 1).degree = 1 := by\n rw [degree_add_eq_left_of_degree_lt]\n · exact degree_s_smul_X s\n · rw [degree_one]; rw [degree_s_smul_X]; norm_num\n\n",
"f... | [
{
"name": "natDegree_definingPoly",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 4,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_... | 3 | /-
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.LinearIndependentFin2
/-!
# Binary Tower Defining Polynomials
Defining polynomials and basic de... | /-
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.LinearIndependentFin2
/-!
# Binary Tower Defining Polynomials
Defining polynomials and basic de... | @@ -26,13 +26,22 @@
apply degree_C_mul_X (a:=s)
exact NeZero.ne s
+lemma degree_s_smul_X_add_1 {F : Type*} [Field F] [Fintype F] (s : F) [NeZero s] :
+ (C s * (X : (F)[X]) + 1).degree = 1 := by
+ rw [degree_add_eq_left_of_degree_lt]
+ · exact degree_s_smul_X s
+ · rw [degree_one]; rw [degree_s_smul_X]; no... | {
"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_9e044d7d92b6_4 | 22f94ea2571a701d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/DefiningPoly.lean | DefiningPoly | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "definingPoly_is_monic",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [definingPoly]\n -- Goal : ⊢ (X ^ 2 + (t1 * X + 1)).Monic\n have leadingCoeffIs1 : (definingPoly s).leadingCoef... | [
{
"name": "degree_s_smul_X_add_1",
"text": "lemma degree_s_smul_X_add_1 {F : Type*} [Field F] [Fintype F] (s : F) [NeZero s] :\n (C s * (X : (F)[X]) + 1).degree = 1 := by\n rw [degree_add_eq_left_of_degree_lt]\n · exact degree_s_smul_X s\n · rw [degree_one]; rw [degree_s_smul_X]; norm_num\n\n",
"f... | [
{
"name": "definingPoly_ne_zero",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 214,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_ne... | 3 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import CompPoly.Fields.Binary.Tower.Support.LinearIndependentFin2
/-!
# Binary Tower Defining Polynomials
Defining polynomials and basic de... | /-
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.LinearIndependentFin2
/-!
# Binary Tower Defining Polynomials
Defining polynomials and basic de... | @@ -26,11 +26,27 @@
apply degree_C_mul_X (a:=s)
exact NeZero.ne s
+lemma degree_s_smul_X_add_1 {F : Type*} [Field F] [Fintype F] (s : F) [NeZero s] :
+ (C s * (X : (F)[X]) + 1).degree = 1 := by
+ rw [degree_add_eq_left_of_degree_lt]
+ · exact degree_s_smul_X s
+ · rw [degree_one]; rw [degree_s_smul_X]; no... | {
"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_9e044d7d92b6_5 | 5b4935090c82d489 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/DefiningPoly.lean | DefiningPoly | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "definingPoly_is_monic",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [definingPoly]\n -- Goal : ⊢ (X ^ 2 + (t1 * X + 1)).Monic\n have leadingCoeffIs1 : (definingPoly s).leadingCoef... | [
{
"name": "degree_s_smul_X_add_1",
"text": "lemma degree_s_smul_X_add_1 {F : Type*} [Field F] [Fintype F] (s : F) [NeZero s] :\n (C s * (X : (F)[X]) + 1).degree = 1 := by\n rw [degree_add_eq_left_of_degree_lt]\n · exact degree_s_smul_X s\n · rw [degree_one]; rw [degree_s_smul_X]; norm_num\n\n",
"f... | [
{
"name": "definingPoly_is_not_unit",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 13,
"n_chars": 417,
"n_subproofs": 3,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"m... | 3 | /-
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.LinearIndependentFin2
/-!
# Binary Tower Defining Polynomials
Defining polynomials and basic de... | /-
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.LinearIndependentFin2
/-!
# Binary Tower Defining Polynomials
Defining polynomials and basic de... | @@ -26,13 +26,22 @@
apply degree_C_mul_X (a:=s)
exact NeZero.ne s
+lemma degree_s_smul_X_add_1 {F : Type*} [Field F] [Fintype F] (s : F) [NeZero s] :
+ (C s * (X : (F)[X]) + 1).degree = 1 := by
+ rw [degree_add_eq_left_of_degree_lt]
+ · exact degree_s_smul_X s
+ · rw [degree_one]; rw [degree_s_smul_X]; no... | {
"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_2e71bd970873_0 | 9752e6433a70c77d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 1 | [
{
"theorem_name": "eval_horner_eq_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [eval, evalHorner, eval₂, eval₂Horner] using\n (eval₂_horner_eq_eval₂ (f := RingHom.id R) (x := x) (p := p))",... | [
{
"name": "eval₂_horner_eq_eval₂",
"text": "/-- Horner evaluation agrees with the sum-of-powers evaluation. -/\ntheorem eval₂_horner_eq_eval₂ {S : Type*} [Semiring R] [Semiring S]\n (f : R →+* S) (x : S) (p : CPolynomial R) :\n eval₂Horner f x p = eval₂ f x p :=\n CPolynomial.Raw.eval₂Horner_eq_eval₂... | [
{
"name": "eval_horner_eq_eval",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 302,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nest... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -249,8 +249,16 @@
p.eval₂Horner (RingHom.id R) x
/-- Horner evaluation agrees with the sum-of-powers evaluation. -/
+theorem eval₂_horner_eq_eval₂ {S : Type*} [Semiring R] [Semiring S]
+ (f : R →+* S) (x : S) (p : CPolynomial R) :
+ eval₂Horner f x p = eval₂ f x p :=
+ CPolynomial.Raw.eval₂Horner_eq_eva... | {
"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_2e71bd970873_1 | 6c330ec2f94afff6 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 8 | [
{
"theorem_name": "monomial_add",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (eq_iff_coeff).2\n intro i\n rw [coeff_monomial, coeff_add, coeff_monomial, coeff_monomial]\n split_ifs <;> simp_all"... | [
{
"name": "coeff_add",
"text": "/-- Coefficient of a sum. -/\nlemma coeff_add [Semiring R] [BEq R] [LawfulBEq R]\n (p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by\n unfold coeff; exact Raw.add_coeff_trimmed p.val q.val i\n\n",
"fan_in": 8,
"n_lines": 6,
"n_chars... | [
{
"name": "monomial_add",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 10,
"n_chars": 335,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -306,6 +306,11 @@
change Raw.coeff (1 : CPolynomial.Raw R) i = if i = 0 then 1 else 0
exact Raw.coeff_one (R := R) i
+/-- Coefficient of a sum. -/
+lemma coeff_add [Semiring R] [BEq R] [LawfulBEq R]
+ (p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by
+ unfold coeff; exact Raw.... | {
"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_2e71bd970873_2 | 587046f7d70ed2de | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 5 | [
{
"theorem_name": "eq_zero_iff_coeff_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff_coeff]; simp only [coeff_zero]",
"n_chars": 47,
"n_subproofs": 0,
"n_tactics": 3,
"cyclom... | [
{
"name": "coeff_zero",
"text": "/-- Coefficient of the zero polynomial. -/\n@[simp]\nlemma coeff_zero [Zero R] (i : ℕ) : coeff (0 : CPolynomial R) i = 0 := by\n change (#[].getD i 0) = 0\n simp\n\n",
"fan_in": 5,
"n_lines": 7,
"n_chars": 163,
"n_subproofs": 0,
"n_tactics": 3,
"cyc... | [
{
"name": "eq_zero_iff_coeff_zero",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 6,
"n_chars": 239,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -294,6 +294,12 @@
unfold Raw.C Raw.coeff
split_ifs with h <;> simp [h]
+/-- Coefficient of the zero polynomial. -/
+@[simp]
+lemma coeff_zero [Zero R] (i : ℕ) : coeff (0 : CPolynomial R) i = 0 := by
+ change (#[].getD i 0) = 0
+ simp
+
/-- Coefficient of the constant polynomial `1`. -/
lemma coeff_one [S... | {
"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_2e71bd970873_3 | 5733860335bfda9a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 5 | [
{
"theorem_name": "monomial_add",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (eq_iff_coeff).2\n intro i\n rw [coeff_monomial, coeff_add, coeff_monomial, coeff_monomial]\n split_ifs <;> simp_all"... | [
{
"name": "coeff_monomial",
"text": "/-- Coefficient of a monomial. -/\nlemma coeff_monomial [Semiring R] [BEq R] [LawfulBEq R] [DecidableEq R]\n (n i : ℕ) (c : R) :\n coeff (monomial n c) i = if i = n then c else 0 := by\n unfold coeff monomial; rw [Raw.coeff_monomial]; simp only [eq_comm]\n\n",
... | [
{
"name": "coeff_monomial_mul",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 16,
"n_chars": 644,
"n_subproofs": 1,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 3,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -311,6 +311,12 @@
(p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by
unfold coeff; exact Raw.add_coeff_trimmed p.val q.val i
+/-- Coefficient of a monomial. -/
+lemma coeff_monomial [Semiring R] [BEq R] [LawfulBEq R] [DecidableEq R]
+ (n i : ℕ) (c : R) :
+ coeff (monomial 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_2e71bd970873_4 | 233db8483ae517ca | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 5 | [
{
"theorem_name": "eq_zero_iff_coeff_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff_coeff]; simp only [coeff_zero]",
"n_chars": 47,
"n_subproofs": 0,
"n_tactics": 3,
"cyclom... | [
{
"name": "coeff_zero",
"text": "/-- Coefficient of the zero polynomial. -/\n@[simp]\nlemma coeff_zero [Zero R] (i : ℕ) : coeff (0 : CPolynomial R) i = 0 := by\n change (#[].getD i 0) = 0\n simp\n\n",
"fan_in": 5,
"n_lines": 7,
"n_chars": 163,
"n_subproofs": 0,
"n_tactics": 3,
"cyc... | [
{
"name": "support_empty_iff",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 9,
"n_chars": 370,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,
"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, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -294,6 +294,12 @@
unfold Raw.C Raw.coeff
split_ifs with h <;> simp [h]
+/-- Coefficient of the zero polynomial. -/
+@[simp]
+lemma coeff_zero [Zero R] (i : ℕ) : coeff (0 : CPolynomial R) i = 0 := by
+ change (#[].getD i 0) = 0
+ simp
+
/-- Coefficient of the constant polynomial `1`. -/
lemma coeff_one [S... | {
"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_2e71bd970873_5 | fac74ea60133e7e6 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 6 | [
{
"theorem_name": "C_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_zero_iff_coeff_zero]; intro i; rw [coeff_C]; simp",
"n_chars": 62,
"n_subproofs": 0,
"n_tactics": 5,
"cycloma... | [
{
"name": "coeff_C",
"text": "/-- Coefficient of the constant polynomial `C r`. -/\nlemma coeff_C [Zero R] [BEq R] [LawfulBEq R] (r : R) (i : ℕ) :\n coeff (C r) i = if i = 0 then r else 0 := by\n unfold coeff C\n rw [Trim.coeff_eq_coeff]\n unfold Raw.C Raw.coeff\n split_ifs with h <;> simp [h]\n\n",
... | [
{
"name": "C_zero",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 6,
"n_chars": 202,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
}
... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -286,6 +286,14 @@
rw [h_last_eq]
exact p.property hp_pos⟩
+/-- Coefficient of the constant polynomial `C r`. -/
+lemma coeff_C [Zero R] [BEq R] [LawfulBEq R] (r : R) (i : ℕ) :
+ coeff (C r) i = if i = 0 then r else 0 := by
+ unfold coeff C
+ rw [Trim.coeff_eq_coeff]
+ unfold Raw.C Raw.coeff
+ spli... | {
"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_2e71bd970873_6 | 1b97b684b5424e90 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 6 | [
{
"theorem_name": "C_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_zero_iff_coeff_zero]; intro i; rw [coeff_C]; simp",
"n_chars": 62,
"n_subproofs": 0,
"n_tactics": 5,
"cycloma... | [
{
"name": "coeff_C",
"text": "/-- Coefficient of the constant polynomial `C r`. -/\nlemma coeff_C [Zero R] [BEq R] [LawfulBEq R] (r : R) (i : ℕ) :\n coeff (C r) i = if i = 0 then r else 0 := by\n unfold coeff C\n rw [Trim.coeff_eq_coeff]\n unfold Raw.C Raw.coeff\n split_ifs with h <;> simp [h]\n\n",
... | [
{
"name": "natDegree_C",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 11,
"n_chars": 358,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 5,
"n_structural": 0,
"automation_only": false,
"max_nesting": ... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -286,6 +286,14 @@
rw [h_last_eq]
exact p.property hp_pos⟩
+/-- Coefficient of the constant polynomial `C r`. -/
+lemma coeff_C [Zero R] [BEq R] [LawfulBEq R] (r : R) (i : ℕ) :
+ coeff (C r) i = if i = 0 then r else 0 := by
+ unfold coeff C
+ rw [Trim.coeff_eq_coeff]
+ unfold Raw.C Raw.coeff
+ spli... | {
"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_2e71bd970873_7 | d21595d12c35ebc6 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 6 | [
{
"theorem_name": "C_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_zero_iff_coeff_zero]; intro i; rw [coeff_C]; simp",
"n_chars": 62,
"n_subproofs": 0,
"n_tactics": 5,
"cycloma... | [
{
"name": "coeff_C",
"text": "/-- Coefficient of the constant polynomial `C r`. -/\nlemma coeff_C [Zero R] [BEq R] [LawfulBEq R] (r : R) (i : ℕ) :\n coeff (C r) i = if i = 0 then r else 0 := by\n unfold coeff C\n rw [Trim.coeff_eq_coeff]\n unfold Raw.C Raw.coeff\n split_ifs with h <;> simp [h]\n\n",
... | [
{
"name": "support_C",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 8,
"n_chars": 245,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting": 4
... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -286,6 +286,14 @@
rw [h_last_eq]
exact p.property hp_pos⟩
+/-- Coefficient of the constant polynomial `C r`. -/
+lemma coeff_C [Zero R] [BEq R] [LawfulBEq R] (r : R) (i : ℕ) :
+ coeff (C r) i = if i = 0 then r else 0 := by
+ unfold coeff C
+ rw [Trim.coeff_eq_coeff]
+ unfold Raw.C Raw.coeff
+ spli... | {
"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_2e71bd970873_8 | 78ec922f17862bc5 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 5 | [
{
"theorem_name": "monomial_add",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (eq_iff_coeff).2\n intro i\n rw [coeff_monomial, coeff_add, coeff_monomial, coeff_monomial]\n split_ifs <;> simp_all"... | [
{
"name": "coeff_monomial",
"text": "/-- Coefficient of a monomial. -/\nlemma coeff_monomial [Semiring R] [BEq R] [LawfulBEq R] [DecidableEq R]\n (n i : ℕ) (c : R) :\n coeff (monomial n c) i = if i = n then c else 0 := by\n unfold coeff monomial; rw [Raw.coeff_monomial]; simp only [eq_comm]\n\n",
... | [
{
"name": "support_monomial",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 297,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -311,6 +311,12 @@
(p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by
unfold coeff; exact Raw.add_coeff_trimmed p.val q.val i
+/-- Coefficient of a monomial. -/
+lemma coeff_monomial [Semiring R] [BEq R] [LawfulBEq R] [DecidableEq R]
+ (n i : ℕ) (c : R) :
+ coeff (monomial 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_2e71bd970873_9 | 36840e622043b558 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 8 | [
{
"theorem_name": "monomial_add",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (eq_iff_coeff).2\n intro i\n rw [coeff_monomial, coeff_add, coeff_monomial, coeff_monomial]\n split_ifs <;> simp_all"... | [
{
"name": "coeff_add",
"text": "/-- Coefficient of a sum. -/\nlemma coeff_add [Semiring R] [BEq R] [LawfulBEq R]\n (p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by\n unfold coeff; exact Raw.add_coeff_trimmed p.val q.val i\n\n",
"fan_in": 8,
"n_lines": 6,
"n_chars... | [
{
"name": "support_add_subset",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 437,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 2,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -306,6 +306,11 @@
change Raw.coeff (1 : CPolynomial.Raw R) i = if i = 0 then 1 else 0
exact Raw.coeff_one (R := R) i
+/-- Coefficient of a sum. -/
+lemma coeff_add [Semiring R] [BEq R] [LawfulBEq R]
+ (p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by
+ unfold coeff; exact Raw.... | {
"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_2e71bd970873_10 | 265982ae2aa5cdf0 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 6 | [
{
"theorem_name": "C_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_zero_iff_coeff_zero]; intro i; rw [coeff_C]; simp",
"n_chars": 62,
"n_subproofs": 0,
"n_tactics": 5,
"cycloma... | [
{
"name": "coeff_C",
"text": "/-- Coefficient of the constant polynomial `C r`. -/\nlemma coeff_C [Zero R] [BEq R] [LawfulBEq R] (r : R) (i : ℕ) :\n coeff (C r) i = if i = 0 then r else 0 := by\n unfold coeff C\n rw [Trim.coeff_eq_coeff]\n unfold Raw.C Raw.coeff\n split_ifs with h <;> simp [h]\n\n",
... | [
{
"name": "coeff_C_mul",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 11,
"n_chars": 365,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 3,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -286,6 +286,14 @@
rw [h_last_eq]
exact p.property hp_pos⟩
+/-- Coefficient of the constant polynomial `C r`. -/
+lemma coeff_C [Zero R] [BEq R] [LawfulBEq R] (r : R) (i : ℕ) :
+ coeff (C r) i = if i = 0 then r else 0 := by
+ unfold coeff C
+ rw [Trim.coeff_eq_coeff]
+ unfold Raw.C Raw.coeff
+ spli... | {
"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_2e71bd970873_11 | bb5974b14a3b05be | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 2 | [
{
"theorem_name": "coeff_X_mul_succ",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold coeff\n change ((X.val * p.val).coeff (n + 1) = p.val.coeff n)\n rw [Raw.mul_coeff]\n simp only [X]\n have hme... | [
{
"name": "coeff_X",
"text": "/-- Coefficient of the variable `X`. -/\nlemma coeff_X [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] (i : ℕ) :\n coeff X i = if i = 1 then 1 else 0 := by\n unfold coeff X Raw.X Raw.coeff\n rcases i with (_ | _ | i) <;> rfl\n\n",
"fan_in": 2,
"n_lines": 7,
"... | [
{
"name": "coeff_X_mul_succ",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 755,
"n_subproofs": 3,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 6,
"n_structural": 2,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -294,6 +294,12 @@
unfold Raw.C Raw.coeff
split_ifs with h <;> simp [h]
+/-- Coefficient of the variable `X`. -/
+lemma coeff_X [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] (i : ℕ) :
+ coeff X i = if i = 1 then 1 else 0 := by
+ unfold coeff X Raw.X Raw.coeff
+ rcases i with (_ | _ | i) <;> rfl
+
/-... | {
"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_2e71bd970873_12 | d19c89ce670bea80 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 2 | [
{
"theorem_name": "coeff_X_mul_succ",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold coeff\n change ((X.val * p.val).coeff (n + 1) = p.val.coeff n)\n rw [Raw.mul_coeff]\n simp only [X]\n have hme... | [
{
"name": "coeff_X",
"text": "/-- Coefficient of the variable `X`. -/\nlemma coeff_X [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] (i : ℕ) :\n coeff X i = if i = 1 then 1 else 0 := by\n unfold coeff X Raw.X Raw.coeff\n rcases i with (_ | _ | i) <;> rfl\n\n",
"fan_in": 2,
"n_lines": 7,
"... | [
{
"name": "coeff_mul_X_succ",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 28,
"n_chars": 842,
"n_subproofs": 5,
"n_tactics": 24,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 6,
"n_structural": 4,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -294,6 +294,12 @@
unfold Raw.C Raw.coeff
split_ifs with h <;> simp [h]
+/-- Coefficient of the variable `X`. -/
+lemma coeff_X [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] (i : ℕ) :
+ coeff X i = if i = 1 then 1 else 0 := by
+ unfold coeff X Raw.X Raw.coeff
+ rcases i with (_ | _ | i) <;> rfl
+
/-... | {
"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_2e71bd970873_13 | e5dfe6c97d33f3c1 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 3 | [
{
"theorem_name": "coeff_monomial_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [coeff_mul]\n have hsummand : ∀ j ∈ Finset.range (i + 1),\n coeff (monomial n c) j * coeff p (i - j) =\n ... | [
{
"name": "coeff_mul",
"text": "/-- Coefficient of a product (convolution sum). -/\nlemma coeff_mul [Semiring R] [BEq R] [LawfulBEq R]\n (p q : CPolynomial R) (k : ℕ) :\n coeff (p * q) k = (Finset.range (k + 1)).sum (fun i => coeff p i * coeff q (k - i)) := by\n unfold coeff; exact Raw.mul_coeff p.va... | [
{
"name": "coeff_mul_X_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 163,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -311,6 +311,12 @@
(p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by
unfold coeff; exact Raw.add_coeff_trimmed p.val q.val i
+/-- Coefficient of a product (convolution sum). -/
+lemma coeff_mul [Semiring R] [BEq R] [LawfulBEq R]
+ (p q : CPolynomial R) (k : ℕ) :
+ coeff (p ... | {
"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_2e71bd970873_14 | a1a15c4b76e62a99 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 1 | [
{
"theorem_name": "coeff_divX",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n coeff_extract_succ (a := (↑p : CPolynomial.Raw R)) (i := i)",
"n_chars": 64,
"n_subproofs": 0,
"n_tactics": 1,
"cyc... | [
{
"name": "coeff_extract_succ",
"text": "lemma coeff_extract_succ [Zero R] (a : CPolynomial.Raw R) (i : ℕ) :\n Raw.coeff (a.extract 1 a.size) i = Raw.coeff a (i + 1) := by\n simp [Raw.coeff, Array.getElem?_extract]\n by_cases h : i < a.size - 1\n · have h1 : 1 + i = i + 1 := by omega\n simp [h, h1]... | [
{
"name": "coeff_divX",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 165,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -328,8 +328,18 @@
(C (0 : R) : CPolynomial R) = 0 := by
rw [eq_zero_iff_coeff_zero]; intro i; rw [coeff_C]; simp
+lemma coeff_extract_succ [Zero R] (a : CPolynomial.Raw R) (i : ℕ) :
+ Raw.coeff (a.extract 1 a.size) i = Raw.coeff a (i + 1) := by
+ simp [Raw.coeff, Array.getElem?_extract]
+ by_cases 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_2e71bd970873_15 | f5ae1e1f3af15b49 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 6 | [
{
"theorem_name": "C_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_zero_iff_coeff_zero]; intro i; rw [coeff_C]; simp",
"n_chars": 62,
"n_subproofs": 0,
"n_tactics": 5,
"cycloma... | [
{
"name": "coeff_C",
"text": "/-- Coefficient of the constant polynomial `C r`. -/\nlemma coeff_C [Zero R] [BEq R] [LawfulBEq R] (r : R) (i : ℕ) :\n coeff (C r) i = if i = 0 then r else 0 := by\n unfold coeff C\n rw [Trim.coeff_eq_coeff]\n unfold Raw.C Raw.coeff\n split_ifs with h <;> simp [h]\n\n",
... | [
{
"name": "X_mul_divX_add",
"fan_in": 1,
"n_deps_direct": 9,
"n_deps_transitive": 12,
"n_lines": 32,
"n_chars": 1395,
"n_subproofs": 5,
"n_tactics": 29,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 8,
"n_structural": 6,
"automation_only": false,
"max_nest... | 7 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -286,6 +286,14 @@
rw [h_last_eq]
exact p.property hp_pos⟩
+/-- Coefficient of the constant polynomial `C r`. -/
+lemma coeff_C [Zero R] [BEq R] [LawfulBEq R] (r : R) (i : ℕ) :
+ coeff (C r) i = if i = 0 then r else 0 := by
+ unfold coeff C
+ rw [Trim.coeff_eq_coeff]
+ unfold Raw.C Raw.coeff
+ spli... | {
"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_2e71bd970873_16 | 36067c6034b8660e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 2 | [
{
"theorem_name": "coeff_X_mul_succ",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold coeff\n change ((X.val * p.val).coeff (n + 1) = p.val.coeff n)\n rw [Raw.mul_coeff]\n simp only [X]\n have hme... | [
{
"name": "coeff_X",
"text": "/-- Coefficient of the variable `X`. -/\nlemma coeff_X [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] (i : ℕ) :\n coeff X i = if i = 1 then 1 else 0 := by\n unfold coeff X Raw.X Raw.coeff\n rcases i with (_ | _ | i) <;> rfl\n\n",
"fan_in": 2,
"n_lines": 7,
"... | [
{
"name": "divX_mul_X_add",
"fan_in": 0,
"n_deps_direct": 7,
"n_deps_transitive": 12,
"n_lines": 23,
"n_chars": 835,
"n_subproofs": 1,
"n_tactics": 20,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 8,
"n_structural": 3,
"automation_only": false,
"max_nesti... | 9 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -294,6 +294,12 @@
unfold Raw.C Raw.coeff
split_ifs with h <;> simp [h]
+/-- Coefficient of the variable `X`. -/
+lemma coeff_X [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] (i : ℕ) :
+ coeff X i = if i = 1 then 1 else 0 := by
+ unfold coeff X Raw.X Raw.coeff
+ rcases i with (_ | _ | i) <;> rfl
+
/-... | {
"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_2e71bd970873_17 | aab04134424c3e30 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 6 | [
{
"theorem_name": "C_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_zero_iff_coeff_zero]; intro i; rw [coeff_C]; simp",
"n_chars": 62,
"n_subproofs": 0,
"n_tactics": 5,
"cycloma... | [
{
"name": "coeff_C",
"text": "/-- Coefficient of the constant polynomial `C r`. -/\nlemma coeff_C [Zero R] [BEq R] [LawfulBEq R] (r : R) (i : ℕ) :\n coeff (C r) i = if i = 0 then r else 0 := by\n unfold coeff C\n rw [Trim.coeff_eq_coeff]\n unfold Raw.C Raw.coeff\n split_ifs with h <;> simp [h]\n\n",
... | [
{
"name": "induction_on",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 14,
"n_lines": 36,
"n_chars": 1565,
"n_subproofs": 9,
"n_tactics": 27,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 2,
"n_structural": 7,
"automation_only": false,
"max_nestin... | 9 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -286,6 +286,14 @@
rw [h_last_eq]
exact p.property hp_pos⟩
+/-- Coefficient of the constant polynomial `C r`. -/
+lemma coeff_C [Zero R] [BEq R] [LawfulBEq R] (r : R) (i : ℕ) :
+ coeff (C r) i = if i = 0 then r else 0 := by
+ unfold coeff C
+ rw [Trim.coeff_eq_coeff]
+ unfold Raw.C Raw.coeff
+ spli... | {
"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_2e71bd970873_18 | cf0521a2f3556da4 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 1 | [
{
"theorem_name": "degree_eq_support_max",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n obtain ⟨k, hk⟩ := degree_eq_support_max_aux_lastNonzero (p := p) hp\n refine ⟨k.val, ?_⟩\n constructor\n · exact d... | [
{
"name": "degree_eq_support_max_aux_degree",
"text": "/-- Lemma for `degree_eq_support_max`: degree in terms of `lastNonzero`. -/\nlemma degree_eq_support_max_aux_degree [Zero R] [BEq R] [LawfulBEq R]\n (p : CPolynomial R) {k : Fin p.val.size}\n (hk : p.val.lastNonzero = some k) : p.degree = k.val :=... | [
{
"name": "degree_eq_support_max",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 12,
"n_chars": 538,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 5,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -328,6 +328,23 @@
(C (0 : R) : CPolynomial R) = 0 := by
rw [eq_zero_iff_coeff_zero]; intro i; rw [coeff_C]; simp
+/-- Lemma for `degree_eq_support_max`: degree in terms of `lastNonzero`. -/
+lemma degree_eq_support_max_aux_degree [Zero R] [BEq R] [LawfulBEq R]
+ (p : CPolynomial R) {k : Fin p.val.size}
... | {
"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_2e71bd970873_19 | eba8b850f94f3851 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 6 | [
{
"theorem_name": "support_empty_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_zero_iff_coeff_zero, Finset.eq_empty_iff_forall_notMem]\n constructor\n · intro h i; by_contra hne; exact h i ((... | [
{
"name": "mem_support_iff",
"text": "/-- An index is in the support iff the coefficient there is nonzero. -/\nlemma mem_support_iff [Zero R] [BEq R] [LawfulBEq R] (p : CPolynomial R) (i : ℕ) :\n i ∈ p.support ↔ coeff p i ≠ 0 := by\n unfold support coeff\n rw [Finset.mem_filter]\n constructor\n · int... | [
{
"name": "natDegree_eq_support_sup",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 37,
"n_chars": 1717,
"n_subproofs": 13,
"n_tactics": 33,
"cyclomatic": 2,
"n_automation": 7,
"n_rewrites": 2,
"n_structural": 7,
"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, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -323,6 +323,21 @@
p = 0 ↔ ∀ i, coeff p i = 0 := by
rw [eq_iff_coeff]; simp only [coeff_zero]
+/-- An index is in the support iff the coefficient there is nonzero. -/
+lemma mem_support_iff [Zero R] [BEq R] [LawfulBEq R] (p : CPolynomial R) (i : ℕ) :
+ i ∈ p.support ↔ coeff p i ≠ 0 := by
+ unfold suppor... | {
"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_2e71bd970873_20 | c10581c0106022d8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 6 | [
{
"theorem_name": "support_empty_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_zero_iff_coeff_zero, Finset.eq_empty_iff_forall_notMem]\n constructor\n · intro h i; by_contra hne; exact h i ((... | [
{
"name": "mem_support_iff",
"text": "/-- An index is in the support iff the coefficient there is nonzero. -/\nlemma mem_support_iff [Zero R] [BEq R] [LawfulBEq R] (p : CPolynomial R) (i : ℕ) :\n i ∈ p.support ↔ coeff p i ≠ 0 := by\n unfold support coeff\n rw [Finset.mem_filter]\n constructor\n · int... | [
{
"name": "le_natDegree_of_ne_zero",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 8,
"n_chars": 306,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -323,6 +323,21 @@
p = 0 ↔ ∀ i, coeff p i = 0 := by
rw [eq_iff_coeff]; simp only [coeff_zero]
+/-- An index is in the support iff the coefficient there is nonzero. -/
+lemma mem_support_iff [Zero R] [BEq R] [LawfulBEq R] (p : CPolynomial R) (i : ℕ) :
+ i ∈ p.support ↔ coeff p i ≠ 0 := by
+ unfold suppor... | {
"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_2e71bd970873_21 | 2b043fba673dcf88 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 8 | [
{
"theorem_name": "monomial_add",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (eq_iff_coeff).2\n intro i\n rw [coeff_monomial, coeff_add, coeff_monomial, coeff_monomial]\n split_ifs <;> simp_all"... | [
{
"name": "coeff_add",
"text": "/-- Coefficient of a sum. -/\nlemma coeff_add [Semiring R] [BEq R] [LawfulBEq R]\n (p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by\n unfold coeff; exact Raw.add_coeff_trimmed p.val q.val i\n\n",
"fan_in": 8,
"n_lines": 6,
"n_chars... | [
{
"name": "natDegree_add_le",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 9,
"n_chars": 404,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -306,6 +306,11 @@
change Raw.coeff (1 : CPolynomial.Raw R) i = if i = 0 then 1 else 0
exact Raw.coeff_one (R := R) i
+/-- Coefficient of a sum. -/
+lemma coeff_add [Semiring R] [BEq R] [LawfulBEq R]
+ (p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by
+ unfold coeff; exact Raw.... | {
"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_2e71bd970873_22 | 0a2878f7d80f65ca | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 1 | [
{
"theorem_name": "C_mul_X_pow_eq_monomial",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Subtype.ext\n -- Reduce to Raw-level equality via val_pow\n have hval : (C r * X ^ n : CPolynomial R).val ... | [
{
"name": "val_pow",
"text": "/-- The underlying `Raw` value of `p ^ n` equals `p.val ^ n`\n(using the Raw `Pow` instance). This bridges the optimized\n`powBySq` used in the `Semiring` instance with the spec\n`pow`. -/\nlemma val_pow [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (p : CPolynomial R)... | [
{
"name": "C_mul_X_pow_eq_monomial",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 22,
"n_chars": 909,
"n_subproofs": 1,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 9,
"n_structural": 2,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -535,6 +535,14 @@
simp only [coeff_add, coeff_C, coeff_one]
split_ifs <;> simp_all
+/-- The underlying `Raw` value of `p ^ n` equals `p.val ^ n`
+(using the Raw `Pow` instance). This bridges the optimized
+`powBySq` used in the `Semiring` instance with the spec
+`pow`. -/
+lemma val_pow [Semiring R] [BEq... | {
"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_2e71bd970873_23 | a8c30f15fed0cb96 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 23 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 5 | [
{
"theorem_name": "eq_zero_iff_coeff_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff_coeff]; simp only [coeff_zero]",
"n_chars": 47,
"n_subproofs": 0,
"n_tactics": 3,
"cyclom... | [
{
"name": "coeff_zero",
"text": "/-- Coefficient of the zero polynomial. -/\n@[simp]\nlemma coeff_zero [Zero R] (i : ℕ) : coeff (0 : CPolynomial R) i = 0 := by\n change (#[].getD i 0) = 0\n simp\n\n",
"fan_in": 5,
"n_lines": 7,
"n_chars": 163,
"n_subproofs": 0,
"n_tactics": 3,
"cyc... | [
{
"name": "coeff_finset_sum",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 454,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -294,6 +294,12 @@
unfold Raw.C Raw.coeff
split_ifs with h <;> simp [h]
+/-- Coefficient of the zero polynomial. -/
+@[simp]
+lemma coeff_zero [Zero R] (i : ℕ) : coeff (0 : CPolynomial R) i = 0 := by
+ change (#[].getD i 0) = 0
+ simp
+
/-- Coefficient of the constant polynomial `1`. -/
lemma coeff_one [S... | {
"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_2e71bd970873_24 | 2194ecf0314f6e06 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 24 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 8 | [
{
"theorem_name": "monomial_add",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (eq_iff_coeff).2\n intro i\n rw [coeff_monomial, coeff_add, coeff_monomial, coeff_monomial]\n split_ifs <;> simp_all"... | [
{
"name": "coeff_add",
"text": "/-- Coefficient of a sum. -/\nlemma coeff_add [Semiring R] [BEq R] [LawfulBEq R]\n (p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by\n unfold coeff; exact Raw.add_coeff_trimmed p.val q.val i\n\n",
"fan_in": 8,
"n_lines": 6,
"n_chars... | [
{
"name": "monomial_add_erase",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 6,
"n_lines": 15,
"n_chars": 500,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
"max_ne... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -306,6 +306,11 @@
change Raw.coeff (1 : CPolynomial.Raw R) i = if i = 0 then 1 else 0
exact Raw.coeff_one (R := R) i
+/-- Coefficient of a sum. -/
+lemma coeff_add [Semiring R] [BEq R] [LawfulBEq R]
+ (p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by
+ unfold coeff; exact Raw.... | {
"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_2e71bd970873_25 | bec76cba9a2280e0 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 25 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 5 | [
{
"theorem_name": "eq_zero_iff_coeff_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff_coeff]; simp only [coeff_zero]",
"n_chars": 47,
"n_subproofs": 0,
"n_tactics": 3,
"cyclom... | [
{
"name": "coeff_zero",
"text": "/-- Coefficient of the zero polynomial. -/\n@[simp]\nlemma coeff_zero [Zero R] (i : ℕ) : coeff (0 : CPolynomial R) i = 0 := by\n change (#[].getD i 0) = 0\n simp\n\n",
"fan_in": 5,
"n_lines": 7,
"n_chars": 163,
"n_subproofs": 0,
"n_tactics": 3,
"cyc... | [
{
"name": "subMulMonomial_eq",
"fan_in": 0,
"n_deps_direct": 6,
"n_deps_transitive": 9,
"n_lines": 38,
"n_chars": 1463,
"n_subproofs": 4,
"n_tactics": 33,
"cyclomatic": 2,
"n_automation": 9,
"n_rewrites": 11,
"n_structural": 4,
"automation_only": false,
"max_n... | 8 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -301,6 +301,12 @@
unfold Raw.C Raw.coeff
split_ifs with h <;> simp [h]
+/-- Coefficient of the zero polynomial. -/
+@[simp]
+lemma coeff_zero [Zero R] (i : ℕ) : coeff (0 : CPolynomial R) i = 0 := by
+ change (#[].getD i 0) = 0
+ simp
+
/-- Coefficient of the constant polynomial `1`. -/
lemma coeff_one [S... | {
"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_2e71bd970873_26 | 6a2f4030bba5ad88 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 26 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 5 | [
{
"theorem_name": "monomial_add",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (eq_iff_coeff).2\n intro i\n rw [coeff_monomial, coeff_add, coeff_monomial, coeff_monomial]\n split_ifs <;> simp_all"... | [
{
"name": "coeff_monomial",
"text": "/-- Coefficient of a monomial. -/\nlemma coeff_monomial [Semiring R] [BEq R] [LawfulBEq R] [DecidableEq R]\n (n i : ℕ) (c : R) :\n coeff (monomial n c) i = if i = n then c else 0 := by\n unfold coeff monomial; rw [Raw.coeff_monomial]; simp only [eq_comm]\n\n",
... | [
{
"name": "erase_correct",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 5,
"n_lines": 13,
"n_chars": 444,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 2,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -311,6 +311,12 @@
(p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by
unfold coeff; exact Raw.add_coeff_trimmed p.val q.val i
+/-- Coefficient of a monomial. -/
+lemma coeff_monomial [Semiring R] [BEq R] [LawfulBEq R] [DecidableEq R]
+ (n i : ℕ) (c : R) :
+ coeff (monomial 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_2e71bd970873_27 | caf5f153b6798d54 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 27 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 2 | [
{
"theorem_name": "smul_add",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply smul_eq_of_coeff_eq; intro i\n show (Raw.smul r (p.val + q.val)).trim.coeff i =\n ((Raw.smul r p.val).trim + (Raw.smul r... | [
{
"name": "smul_eq_of_coeff_eq",
"text": "/-- Helper lemma: Two CPolynomials are equal if\n the underlying Raw CPolynomials are trim equivalent. -/\nlemma smul_eq_of_coeff_eq [Zero R] [BEq R] [LawfulBEq R] {p q : CPolynomial R}\n (h : Trim.equiv p.val q.val) : p = q := by\n apply CPolynomial.ext\n e... | [
{
"name": "smul_add",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 543,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 3,
"automation_only": false,
"max_nesting": 6
... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -658,10 +658,24 @@
rw [eq_iff_coeff]; intro i
rw [coeff_smul, coeff_zero]; simp
+/-- Helper lemma: Two CPolynomials are equal if
+ the underlying Raw CPolynomials are trim equivalent. -/
+lemma smul_eq_of_coeff_eq [Zero R] [BEq R] [LawfulBEq R] {p q : CPolynomial R}
+ (h : Trim.equiv p.val q.val) : p =... | {
"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_2e71bd970873_28 | 5200b29bf0ca4e42 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 28 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 8 | [
{
"theorem_name": "monomial_add",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (eq_iff_coeff).2\n intro i\n rw [coeff_monomial, coeff_add, coeff_monomial, coeff_monomial]\n split_ifs <;> simp_all"... | [
{
"name": "coeff_add",
"text": "/-- Coefficient of a sum. -/\nlemma coeff_add [Semiring R] [BEq R] [LawfulBEq R]\n (p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by\n unfold coeff; exact Raw.add_coeff_trimmed p.val q.val i\n\n",
"fan_in": 8,
"n_lines": 6,
"n_chars... | [
{
"name": "add_smul",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 8,
"n_chars": 285,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -306,6 +306,11 @@
change Raw.coeff (1 : CPolynomial.Raw R) i = if i = 0 then 1 else 0
exact Raw.coeff_one (R := R) i
+/-- Coefficient of a sum. -/
+lemma coeff_add [Semiring R] [BEq R] [LawfulBEq R]
+ (p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by
+ unfold coeff; exact Raw.... | {
"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_2e71bd970873_29 | bf584ca634fb1b8d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Basic.lean | Basic | 29 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 11 | [
{
"theorem_name": "monomial_add",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (eq_iff_coeff).2\n intro i\n rw [coeff_monomial, coeff_add, coeff_monomial, coeff_monomial]\n split_ifs <;> simp_all"... | [
{
"name": "eq_iff_coeff",
"text": "/-- Two polynomials are equal iff they have the same coefficients. -/\ntheorem eq_iff_coeff [Zero R] [BEq R] [LawfulBEq R] {p q : CPolynomial R} :\n p = q ↔ ∀ i, coeff p i = coeff q i := by\n constructor\n · intro h i; rw [h]\n · intro h; apply ext; exact Trim.isCano... | [
{
"name": "one_smul",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 6,
"n_chars": 208,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles, Valerii Huhnin
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.... | @@ -311,9 +311,17 @@
(p q : CPolynomial R) (i : ℕ) : coeff (p + q) i = coeff p i + coeff q i := by
unfold coeff; exact Raw.add_coeff_trimmed p.val q.val i
+/-- Two polynomials are equal iff they have the same coefficients. -/
+theorem eq_iff_coeff [Zero R] [BEq R] [LawfulBEq R] {p q : CPolynomial R} :
+ p ... | {
"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_762316194cc5_0 | b95bc6db2fcd13c4 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Equiv.lean | Equiv | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 3 | [
{
"theorem_name": "towerRingHomForwardMap_one",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction k with\n | zero =>\n unfold towerRingHomForwardMap\n simp only [RingEquiv.toEquiv_eq_coe, Equi... | [
{
"name": "towerRingHomForwardMap_zero",
"text": "lemma towerRingHomForwardMap_zero {k : ℕ} :\n (towerRingHomForwardMap k) 0 = 0 := by\n induction k with\n | zero =>\n unfold towerRingHomForwardMap\n simp only [RingEquiv.toEquiv_eq_coe, Equiv.toFun_as_coe, EquivLike.coe_coe, ↓reduceDIte,\n t... | [
{
"name": "towerRingHomForwardMap_one",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 18,
"n_chars": 648,
"n_subproofs": 0,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Fields.Binary.Tower.Concrete.Basis
/-!
# Binary Tower Equivalence
Equivalences between the abstract and concrete binary t... | /-
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.Tower.Concrete.Basis
/-!
# Binary Tower Equivalence
Equivalences between the abstract and concrete binary t... | @@ -91,6 +91,23 @@
unfold towerRingHomForwardMap
simp only [RingEquiv.toEquiv_eq_coe, Equiv.toFun_as_coe, EquivLike.coe_coe, ↓reduceDIte]
+lemma towerRingHomForwardMap_zero {k : ℕ} :
+ (towerRingHomForwardMap k) 0 = 0 := by
+ induction k with
+ | zero =>
+ unfold towerRingHomForwardMap
+ simp only [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_762316194cc5_1 | c7de34b7fd4633f2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Equiv.lean | Equiv | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "towerRingHomForwardMap_join",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n set x := 《 hi, lo 》\n have h_split : (hi, lo) = (split (k:=k) (h:=h_pos) x) := by\n apply split_of_join (k... | [
{
"name": "towerRingHomForwardMap_split_eq",
"text": "lemma towerRingHomForwardMap_split_eq (k : ℕ) (h_pos : k > 0) (x : ConcreteBTField k) :\n let p := split (k:=k) (h:=h_pos) x\n towerRingHomForwardMap (k:=k) (x) =\n BinaryTower.join_via_add_smul (k:=k) (h_pos:=h_pos)\n (hi_btf := towerRingHom... | [
{
"name": "towerRingHomForwardMap_join",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 691,
"n_subproofs": 3,
"n_tactics": 11,
"cyclomatic": 4,
"n_automation": 1,
"n_rewrites": 6,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Fields.Binary.Tower.Concrete.Basis
/-!
# Binary Tower Equivalence
Equivalences between the abstract and concrete binary t... | /-
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.Tower.Concrete.Basis
/-!
# Binary Tower Equivalence
Equivalences between the abstract and concrete binary t... | @@ -295,11 +295,37 @@
abel_nf
· rw [towerRingHomForwardMap_add_eq, ih, ih];
+lemma towerRingHomForwardMap_split_eq (k : ℕ) (h_pos : k > 0) (x : ConcreteBTField k) :
+ let p := split (k:=k) (h:=h_pos) x
+ towerRingHomForwardMap (k:=k) (x) =
+ BinaryTower.join_via_add_smul (k:=k) (h_pos:=h_pos)
+ ... | {
"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_762316194cc5_2 | a54d76c3e4e9f692 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Equiv.lean | Equiv | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "towerEquiv_commutes_left_succ",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro r\n -- Rewrite the tower equivalence maps to the explicit forward map\n rw [towerEquiv_ringEquiv_app... | [
{
"name": "towerRingHomForwardMap_join",
"text": "lemma towerRingHomForwardMap_join {k : ℕ} (h_pos : k > 0) (hi lo : ConcreteBTField (k - 1)) :\n towerRingHomForwardMap (k:=k) (《 hi, lo 》) =\n BinaryTower.join_via_add_smul (k:=k) (h_pos:=by omega)\n (hi_btf := towerRingHomForwardMap (k:=k-1) hi)\... | [
{
"name": "towerEquiv_commutes_left_diff",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 64,
"n_chars": 3894,
"n_subproofs": 5,
"n_tactics": 60,
"cyclomatic": 2,
"n_automation": 34,
"n_rewrites": 5,
"n_structural": 6,
"automation_only": false... | 7 | /-
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.Tower.Concrete.Basis
/-!
# Binary Tower Equivalence
Equivalences between the abstract and concrete binary t... | /-
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.Tower.Concrete.Basis
/-!
# Binary Tower Equivalence
Equivalences between the abstract and concrete binary t... | @@ -311,6 +311,22 @@
rw! [←hhi]
grind
+lemma towerRingHomForwardMap_join {k : ℕ} (h_pos : k > 0) (hi lo : ConcreteBTField (k - 1)) :
+ towerRingHomForwardMap (k:=k) (《 hi, lo 》) =
+ BinaryTower.join_via_add_smul (k:=k) (h_pos:=by omega)
+ (hi_btf := towerRingHomForwardMap (k:=k-1) hi)
+ (lo_btf ... | {
"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_bd04a2592009_0 | 0a72a564ddc1847f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Abstract/Algebra.lean | Algebra | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 4 | [
{
"theorem_name": "towerAlgebraMap_succ_1",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold towerAlgebraMap\n simp only [Nat.left_eq_add, one_ne_zero, ↓reduceDIte,\n Nat.add_one_sub_one, eq_mp_eq_c... | [
{
"name": "towerAlgebraMap_id",
"text": "lemma towerAlgebraMap_id (k : ℕ) : towerAlgebraMap (h_le:=by omega) = RingHom.id (BTField k) := by\n unfold towerAlgebraMap\n exact (Ne.dite_eq_left_iff fun h a ↦ h rfl).mpr rfl\n\n",
"fan_in": 4,
"n_lines": 5,
"n_chars": 183,
"n_subproofs": 0,
... | [
{
"name": "towerAlgebraMap_succ_1",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 300,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_... | 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.Abstract.Core
/-!
# Abstract Binary Tower Algebra
Algebra maps and tower embeddings for the abstract bi... | /-
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.Abstract.Core
/-!
# Abstract Binary Tower Algebra
Algebra maps and tower embeddings for the abstract bi... | @@ -74,8 +74,16 @@
exact Eq.mp ringHomEq.symm (canonicalEmbedding (r - 1))
exact next_embedding.comp map_to_r_sub_1
+lemma towerAlgebraMap_id (k : ℕ) : towerAlgebraMap (h_le:=by omega) = RingHom.id (BTField k) := by
+ unfold towerAlgebraMap
+ exact (Ne.dite_eq_left_iff fun h a ↦ h rfl).mpr rfl
+
lemma ... | {
"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_bd04a2592009_1 | 041b7e6509445464 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Abstract/Algebra.lean | Algebra | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 4 | [
{
"theorem_name": "towerAlgebraMap_succ_1",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold towerAlgebraMap\n simp only [Nat.left_eq_add, one_ne_zero, ↓reduceDIte,\n Nat.add_one_sub_one, eq_mp_eq_c... | [
{
"name": "towerAlgebraMap_id",
"text": "lemma towerAlgebraMap_id (k : ℕ) : towerAlgebraMap (h_le:=by omega) = RingHom.id (BTField k) := by\n unfold towerAlgebraMap\n exact (Ne.dite_eq_left_iff fun h a ↦ h rfl).mpr rfl\n\n",
"fan_in": 4,
"n_lines": 5,
"n_chars": 183,
"n_subproofs": 0,
... | [
{
"name": "towerAlgebraMap_succ_last",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 23,
"n_chars": 1104,
"n_subproofs": 2,
"n_tactics": 13,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
... | 3 | /-
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.Abstract.Core
/-!
# Abstract Binary Tower Algebra
Algebra maps and tower embeddings for the abstract bi... | /-
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.Abstract.Core
/-!
# Abstract Binary Tower Algebra
Algebra maps and tower embeddings for the abstract bi... | @@ -74,8 +74,16 @@
exact Eq.mp ringHomEq.symm (canonicalEmbedding (r - 1))
exact next_embedding.comp map_to_r_sub_1
+lemma towerAlgebraMap_id (k : ℕ) : towerAlgebraMap (h_le:=by omega) = RingHom.id (BTField k) := by
+ unfold towerAlgebraMap
+ exact (Ne.dite_eq_left_iff fun h a ↦ h rfl).mpr rfl
+
lemma ... | {
"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_bd04a2592009_2 | 70647c0459791c61 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Abstract/Algebra.lean | Algebra | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 4 | [
{
"theorem_name": "towerAlgebraMap_succ_1",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold towerAlgebraMap\n simp only [Nat.left_eq_add, one_ne_zero, ↓reduceDIte,\n Nat.add_one_sub_one, eq_mp_eq_c... | [
{
"name": "towerAlgebraMap_id",
"text": "lemma towerAlgebraMap_id (k : ℕ) : towerAlgebraMap (h_le:=by omega) = RingHom.id (BTField k) := by\n unfold towerAlgebraMap\n exact (Ne.dite_eq_left_iff fun h a ↦ h rfl).mpr rfl\n\n",
"fan_in": 4,
"n_lines": 5,
"n_chars": 183,
"n_subproofs": 0,
... | [
{
"name": "binaryTowerAlgebra_apply_assoc",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 13,
"n_chars": 597,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
... | 4 | /-
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.Abstract.Core
/-!
# Abstract Binary Tower Algebra
Algebra maps and tower embeddings for the abstract bi... | /-
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.Abstract.Core
/-!
# Abstract Binary Tower Algebra
Algebra maps and tower embeddings for the abstract bi... | @@ -74,8 +74,16 @@
exact Eq.mp ringHomEq.symm (canonicalEmbedding (r - 1))
exact next_embedding.comp map_to_r_sub_1
+lemma towerAlgebraMap_id (k : ℕ) : towerAlgebraMap (h_le:=by omega) = RingHom.id (BTField k) := by
+ unfold towerAlgebraMap
+ exact (Ne.dite_eq_left_iff fun h a ↦ h rfl).mpr rfl
+
lemma ... | {
"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_bd04a2592009_3 | bcf4e4665f83cc9b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Abstract/Algebra.lean | Algebra | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 4 | [
{
"theorem_name": "towerAlgebraMap_succ_1",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold towerAlgebraMap\n simp only [Nat.left_eq_add, one_ne_zero, ↓reduceDIte,\n Nat.add_one_sub_one, eq_mp_eq_c... | [
{
"name": "towerAlgebraMap_id",
"text": "lemma towerAlgebraMap_id (k : ℕ) : towerAlgebraMap (h_le:=by omega) = RingHom.id (BTField k) := by\n unfold towerAlgebraMap\n exact (Ne.dite_eq_left_iff fun h a ↦ h rfl).mpr rfl\n\n",
"fan_in": 4,
"n_lines": 5,
"n_chars": 183,
"n_subproofs": 0,
... | [
{
"name": "algebraMap_adjacent_tower_succ_eq_Adjoin_of",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 6,
"n_chars": 173,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_on... | 3 | /-
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.Abstract.Core
/-!
# Abstract Binary Tower Algebra
Algebra maps and tower embeddings for the abstract bi... | /-
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.Abstract.Core
/-!
# Abstract Binary Tower Algebra
Algebra maps and tower embeddings for the abstract bi... | @@ -74,8 +74,16 @@
exact Eq.mp ringHomEq.symm (canonicalEmbedding (r - 1))
exact next_embedding.comp map_to_r_sub_1
+lemma towerAlgebraMap_id (k : ℕ) : towerAlgebraMap (h_le:=by omega) = RingHom.id (BTField k) := by
+ unfold towerAlgebraMap
+ exact (Ne.dite_eq_left_iff fun h a ↦ h rfl).mpr rfl
+
lemma ... | {
"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_bd04a2592009_4 | 5c0215308e6932e2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Abstract/Algebra.lean | Algebra | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 4 | [
{
"theorem_name": "towerAlgebraMap_succ_1",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold towerAlgebraMap\n simp only [Nat.left_eq_add, one_ne_zero, ↓reduceDIte,\n Nat.add_one_sub_one, eq_mp_eq_c... | [
{
"name": "towerAlgebraMap_id",
"text": "lemma towerAlgebraMap_id (k : ℕ) : towerAlgebraMap (h_le:=by omega) = RingHom.id (BTField k) := by\n unfold towerAlgebraMap\n exact (Ne.dite_eq_left_iff fun h a ↦ h rfl).mpr rfl\n\n",
"fan_in": 4,
"n_lines": 5,
"n_chars": 183,
"n_subproofs": 0,
... | [
{
"name": "algebra_adjacent_tower_def",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 210,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 0,
"automation_only": false,
"... | 3 | /-
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.Abstract.Core
/-!
# Abstract Binary Tower Algebra
Algebra maps and tower embeddings for the abstract bi... | /-
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.Abstract.Core
/-!
# Abstract Binary Tower Algebra
Algebra maps and tower embeddings for the abstract bi... | @@ -74,8 +74,16 @@
exact Eq.mp ringHomEq.symm (canonicalEmbedding (r - 1))
exact next_embedding.comp map_to_r_sub_1
+lemma towerAlgebraMap_id (k : ℕ) : towerAlgebraMap (h_le:=by omega) = RingHom.id (BTField k) := by
+ unfold towerAlgebraMap
+ exact (Ne.dite_eq_left_iff fun h a ↦ h rfl).mpr rfl
+
lemma ... | {
"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_bd04a2592009_5 | daed8b69808951c1 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Abstract/Algebra.lean | Algebra | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 4 | [
{
"theorem_name": "towerAlgebraMap_succ_1",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold towerAlgebraMap\n simp only [Nat.left_eq_add, one_ne_zero, ↓reduceDIte,\n Nat.add_one_sub_one, eq_mp_eq_c... | [
{
"name": "towerAlgebraMap_id",
"text": "lemma towerAlgebraMap_id (k : ℕ) : towerAlgebraMap (h_le:=by omega) = RingHom.id (BTField k) := by\n unfold towerAlgebraMap\n exact (Ne.dite_eq_left_iff fun h a ↦ h rfl).mpr rfl\n\n",
"fan_in": 4,
"n_lines": 5,
"n_chars": 183,
"n_subproofs": 0,
... | [
{
"name": "algebra_adjacent_tower_eq_AdjoinRoot_algebra",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 10,
"n_chars": 367,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 1,
"automation_... | 4 | /-
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.Abstract.Core
/-!
# Abstract Binary Tower Algebra
Algebra maps and tower embeddings for the abstract bi... | /-
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.Abstract.Core
/-!
# Abstract Binary Tower Algebra
Algebra maps and tower embeddings for the abstract bi... | @@ -74,8 +74,16 @@
exact Eq.mp ringHomEq.symm (canonicalEmbedding (r - 1))
exact next_embedding.comp map_to_r_sub_1
+lemma towerAlgebraMap_id (k : ℕ) : towerAlgebraMap (h_le:=by omega) = RingHom.id (BTField k) := by
+ unfold towerAlgebraMap
+ exact (Ne.dite_eq_left_iff fun h a ↦ h rfl).mpr rfl
+
lemma ... | {
"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_4664c09e72dd_0 | 06b27072c70bef9d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/CoeffRows.lean | CoeffRows | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "rowShiftedDegree?_eq_natWeightedDegree_ofCoeffRow",
"depth": 1,
"n_commands": 0,
"n_lines": 77,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hshift :\n ∀ j, j < row.size → (weightedDegreeShift w row.size).getD j 0 = j *... | [
{
"name": "coeff_ofCoeffRow_of_size_le",
"text": "/-- Coefficients past the row width vanish after row-to-bivariate conversion. -/\ntheorem coeff_ofCoeffRow_of_size_le [Zero F] [BEq F] [LawfulBEq F]\n (row : PolynomialRow F) {i j : Nat} (hj : row.size ≤ j) :\n CBivariate.coeff (ofCoeffRow row) i j = 0... | [
{
"name": "rowShiftedDegree?_eq_natWeightedDegree_ofCoeffRow",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 85,
"n_chars": 3829,
"n_subproofs": 16,
"n_tactics": 77,
"cyclomatic": 1,
"n_automation": 11,
"n_rewrites": 10,
"n_structural": 13,
"... | 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.Basic
import CompPoly.LinearAlgebra.PolynomialMatrix.Shifted
/-!
# Coefficient Rows for Bivariate Polynomials
Conversions between ... | /-
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.Basic
import CompPoly.LinearAlgebra.PolynomialMatrix.Shifted
/-!
# Coefficient Rows for Bivariate Polynomials
Conversions between ... | @@ -33,6 +33,16 @@
def weightedDegreeShift (w width : Nat) : Array Nat :=
(List.range width).map (fun j ↦ j * w) |>.toArray
+/-- Coefficients past the row width vanish after row-to-bivariate conversion. -/
+theorem coeff_ofCoeffRow_of_size_le [Zero F] [BEq F] [LawfulBEq F]
+ (row : PolynomialRow F) {i j : Nat}... | {
"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_4664c09e72dd_1 | d2c22f4e4ce69e5b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/CoeffRows.lean | CoeffRows | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "natWeightedDegree_ofCoeffRow_le_of_rowShiftedDegree?_le",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [rowShiftedDegree?_eq_natWeightedDegree_ofCoeffRow row w d hdeg]\n exact hle",
... | [
{
"name": "rowShiftedDegree?_eq_natWeightedDegree_ofCoeffRow",
"text": "/-- Row shifted degree for the Lee shift matches weighted degree of the bivariate view. -/\ntheorem rowShiftedDegree?_eq_natWeightedDegree_ofCoeffRow\n [Field F] [BEq F] [LawfulBEq F]\n (row : PolynomialRow F) (w d : Nat)\n (hd... | [
{
"name": "natWeightedDegree_ofCoeffRow_le_of_rowShiftedDegree?_le",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 12,
"n_chars": 519,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"... | 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.Basic
import CompPoly.LinearAlgebra.PolynomialMatrix.Shifted
/-!
# Coefficient Rows for Bivariate Polynomials
Conversions between ... | /-
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.Basic
import CompPoly.LinearAlgebra.PolynomialMatrix.Shifted
/-!
# Coefficient Rows for Bivariate Polynomials
Conversions between ... | @@ -43,6 +43,90 @@
change CPolynomial.coeff (CPolynomial.Raw.coeff row j) i = 0
simpa [CPolynomial.Raw.coeff, hj] using CPolynomial.coeff_zero (R := F) i
+/-- Row shifted degree for the Lee shift matches weighted degree of the bivariate view. -/
+theorem rowShiftedDegree?_eq_natWeightedDegree_ofCoeffRow
+ [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_960a0a709958_1 | 59f954023976131d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Quotient/Core.lean | Core | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 3 | [
{
"theorem_name": "mulStep_equiv",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply_rules [ add_equiv, mulPowX_equiv, smul_equiv ]",
"n_chars": 58,
"n_subproofs": 0,
"n_tactics": 2,
"cycl... | [
{
"name": "mulPowX_equiv",
"text": "/-- Multiplication by `X^i` respects the equivalence relation. -/\nlemma mulPowX_equiv {R : Type*} [Zero R]\n (i : ℕ) (p q : CPolynomial.Raw R) (h : equiv p q) :\n equiv (mulPowX i p) (mulPowX i q) := by\n unfold equiv at *\n intro j\n by_cases hj : j < i <;> simp_... | [
{
"name": "mulStep_equiv",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 348,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | @@ -89,6 +89,18 @@
exact fun i => ⟨ add_coeff? p1 q1 i, add_coeff? p2 q2 i ⟩
simp_all [ equiv ]
+/-- Multiplication by `X^i` respects the equivalence relation. -/
+lemma mulPowX_equiv {R : Type*} [Zero R]
+ (i : ℕ) (p q : CPolynomial.Raw R) (h : equiv p q) :
+ equiv (mulPowX i p) (mulPowX i q) := by
+ un... | {
"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_960a0a709958_2 | 36023280ff0df887 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Quotient/Core.lean | Core | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "mulStep_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_mulStep : mulStep q acc (0, i) = acc.add ((smul 0 q).mulPowX i) := by exact rfl\n have h_mulPowX : mulPowX i (smul 0 q... | [
{
"name": "add_zero_equiv",
"text": "/-- Adding a polynomial equivalent to zero acts as the identity. -/\nlemma add_zero_equiv {R : Type*} [Semiring R] [BEq R] [LawfulBEq R]\n (p q : CPolynomial.Raw R) (hq : equiv q 0) :\n equiv (add p q) p := by\n intro x\n have := add_coeff? p q x\n have hq_zero : ... | [
{
"name": "mulStep_zero",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 10,
"n_chars": 534,
"n_subproofs": 2,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | @@ -101,6 +101,17 @@
· rw [ if_neg ( not_lt_of_ge hj ) ]
· rw [ if_neg ( not_lt_of_ge hj ) ]
+/-- Adding a polynomial equivalent to zero acts as the identity. -/
+lemma add_zero_equiv {R : Type*} [Semiring R] [BEq R] [LawfulBEq R]
+ (p q : CPolynomial.Raw R) (hq : equiv q 0) :
+ equiv (add p q) p := 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_960a0a709958_3 | eefed5814dd0f89a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Quotient/Core.lean | Core | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "mul_trim_equiv",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_zipIdx_split : ∃ l, a.zipIdx.toList = a.trim.zipIdx.toList ++ l ∧ ∀ x ∈ l, x.1 = 0 := by\n exact zipIdx_trim_appe... | [
{
"name": "foldl_mulStep_zeros",
"text": "/-- Folding `mulStep` over a list of zero coefficients preserves equivalence. -/\nlemma foldl_mulStep_zeros {R : Type*} [Semiring R] [BEq R] [LawfulBEq R]\n (q : CPolynomial.Raw R) (acc : CPolynomial.Raw R) (l : List (R × ℕ))\n (hl : ∀ x ∈ l, x.1 = 0) :\n equiv... | [
{
"name": "mul_trim_equiv",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 17,
"n_chars": 1034,
"n_subproofs": 6,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_nesti... | 6 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | @@ -126,6 +126,22 @@
rw [ h_mulStep, h_mulPowX ]
exact add_zero_equiv _ _ ( smul_zero_equiv _ )
+/-- Folding `mulStep` over a list of zero coefficients preserves equivalence. -/
+lemma foldl_mulStep_zeros {R : Type*} [Semiring R] [BEq R] [LawfulBEq R]
+ (q : CPolynomial.Raw R) (acc : CPolynomial.Raw R) (l : ... | {
"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_960a0a709958_4 | e0106388c6e3b3b4 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Quotient/Core.lean | Core | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "foldl_mulStep_zeros",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction' l using List.reverseRecOn with x xs ih generalizing acc\n · intro _; rfl\n · simp_all +decide [ List.fold... | [
{
"name": "mulStep_zero",
"text": "/-- The multiplication step with a zero coefficient acts as the identity modulo equivalence. -/\nlemma mulStep_zero {R : Type*} [Semiring R] [BEq R] [LawfulBEq R]\n (q : CPolynomial.Raw R) (acc : CPolynomial.Raw R) (i : ℕ) :\n equiv (mulStep q acc (0, i)) acc := by\n ... | [
{
"name": "mul_equiv",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 8,
"n_lines": 10,
"n_chars": 408,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nesting": 4
... | 8 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | @@ -117,6 +117,15 @@
(q : CPolynomial.Raw R) (acc : CPolynomial.Raw R) (x : R × ℕ) : CPolynomial.Raw R :=
acc.add ((smul x.1 q).mulPowX x.2)
+/-- The multiplication step with a zero coefficient acts as the identity modulo equivalence. -/
+lemma mulStep_zero {R : Type*} [Semiring R] [BEq R] [LawfulBEq 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_960a0a709958_5 | 36aa47b0bae6f67c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Quotient/Core.lean | Core | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 3 | [
{
"theorem_name": "mulStep_equiv",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply_rules [ add_equiv, mulPowX_equiv, smul_equiv ]",
"n_chars": 58,
"n_subproofs": 0,
"n_tactics": 2,
"cycl... | [
{
"name": "mulPowX_equiv",
"text": "/-- Multiplication by `X^i` respects the equivalence relation. -/\nlemma mulPowX_equiv {R : Type*} [Zero R]\n (i : ℕ) (p q : CPolynomial.Raw R) (h : equiv p q) :\n equiv (mulPowX i p) (mulPowX i q) := by\n unfold equiv at *\n intro j\n by_cases hj : j < i <;> simp_... | [
{
"name": "mul_equiv₂",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 24,
"n_chars": 1347,
"n_subproofs": 2,
"n_tactics": 21,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 7,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | @@ -89,6 +89,18 @@
exact fun i => ⟨ add_coeff? p1 q1 i, add_coeff? p2 q2 i ⟩
simp_all [ equiv ]
+/-- Multiplication by `X^i` respects the equivalence relation. -/
+lemma mulPowX_equiv {R : Type*} [Zero R]
+ (i : ℕ) (p q : CPolynomial.Raw R) (h : equiv p q) :
+ equiv (mulPowX i p) (mulPowX i q) := by
+ un... | {
"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_960a0a709958_7 | e0687eebfe321802 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Quotient/Core.lean | Core | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "mul_trim_equiv",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_zipIdx_split : ∃ l, a.zipIdx.toList = a.trim.zipIdx.toList ++ l ∧ ∀ x ∈ l, x.1 = 0 := by\n exact zipIdx_trim_appe... | [
{
"name": "zipIdx_trim_append",
"text": "/-- The `zipIdx` of a polynomial is the `zipIdx` of its trim followed by zero coefficients. -/\nlemma zipIdx_trim_append {R : Type*} [Zero R] [BEq R] [LawfulBEq R]\n (p : CPolynomial.Raw R) :\n ∃ l, p.zipIdx.toList = p.trim.zipIdx.toList ++ l ∧ ∀ x ∈ l, x.1 = 0... | [
{
"name": "mul_descends",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 12,
"n_lines": 10,
"n_chars": 404,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_nesting"... | 12 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | @@ -142,10 +142,42 @@
aesop
exact equiv_trans h_mulStep (ih acc)
+/-- The `zipIdx` of a polynomial is the `zipIdx` of its trim followed by zero coefficients. -/
+lemma zipIdx_trim_append {R : Type*} [Zero R] [BEq R] [LawfulBEq R]
+ (p : CPolynomial.Raw R) :
+ ∃ l, p.zipIdx.toList = p.trim.zipIdx.toL... | {
"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_960a0a709958_8 | 03a78d810439da49 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Quotient/Core.lean | Core | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 6 | [
{
"theorem_name": "add_assoc",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro a b c\n refine Quotient.inductionOn₃ a b c ?_\n intro p q r; clear a b c\n apply Quotient.sound\n apply eq_to_equiv\n ... | [
{
"name": "eq_to_equiv",
"text": "/-- Convert propositional equality to equivalence. -/\nlemma eq_to_equiv [Zero R] (p q : CPolynomial.Raw R) : p = q → p ≈ q := by\n intro h\n rw [h]\n\n",
"fan_in": 6,
"n_lines": 6,
"n_chars": 153,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,... | [
{
"name": "add_assoc",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 258,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 6,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | @@ -64,6 +64,11 @@
-- The operations on `CPolynomial.Raw` descend to `QuotientCPolynomial`
section EquivalenceLemmas
+/-- Convert propositional equality to equivalence. -/
+lemma eq_to_equiv [Zero R] (p q : CPolynomial.Raw R) : p = q → p ≈ q := by
+ intro h
+ rw [h]
+
/-- Scalar multiplication by 0 is equivalent... | {
"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_960a0a709958_9 | 13bc444c3b811a44 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Quotient/Core.lean | Core | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "commute_pow_self",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction' n with n ih generalizing x\n all_goals generalize_proofs at *\n · rw [show x.pow 0 = 1 from _]\n · simp +d... | [
{
"name": "pow_succ_left",
"text": "lemma pow_succ_left (n : ℕ) (x : QuotientCPolynomial R) :\n x.pow (n + 1) = x * x.pow n := by\n refine Quotient.inductionOn x ?_\n intro p\n apply Quotient.sound\n -- p.pow (n+1) = p * p.pow n is true by definition of pow for CPolynomial.Raw\n -- By definition of ... | [
{
"name": "commute_pow_self",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 5,
"n_lines": 10,
"n_chars": 329,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 1,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | @@ -618,6 +618,20 @@
/-
x^(n+1) = x * x^n for QuotientCPolynomial
-/
+lemma pow_succ_left (n : ℕ) (x : QuotientCPolynomial R) :
+ x.pow (n + 1) = x * x.pow n := by
+ refine Quotient.inductionOn x ?_
+ intro p
+ apply Quotient.sound
+ -- p.pow (n+1) = p * p.pow n is true by definition of pow for CPolynomial.Ra... | {
"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_960a0a709958_10 | ac37e042cdca9d0a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Quotient/Core.lean | Core | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "npow_succ",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro n x\n refine Quotient.inductionOn x ?_\n intro p; clear x\n apply Quotient.sound\n -- By definition of exponentiation,... | [
{
"name": "commute_pow_self",
"text": "lemma commute_pow_self (n : ℕ) (x : QuotientCPolynomial R) :\n x * x.pow n = x.pow n * x := by\n induction' n with n ih generalizing x\n all_goals generalize_proofs at *\n · rw [show x.pow 0 = 1 from _]\n · simp +decide [mul_one, one_mul]\n · exact npow_zer... | [
{
"name": "npow_succ",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 12,
"n_chars": 482,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 5,
"automation_only": false,
"max_nesting": 8... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
import CompPoly.Univaria... | @@ -632,8 +632,26 @@
/-
x commutes with x^n
-/
-lemma npow_succ : ∀ (n : ℕ) (x : QuotientCPolynomial R), x.pow (n + 1) = x.pow n * x := sorry
+lemma commute_pow_self (n : ℕ) (x : QuotientCPolynomial R) :
+ x * x.pow n = x.pow n * x := by
+ induction' n with n ih generalizing x
+ all_goals generalize_proofs at *... | {
"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_5a09a4e7213b_0 | 3b5719ba659f0791 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/CoefficientInterpolation.lean | CoefficientInterpolation | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "linearFactor_monic",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CPolynomial.monic_toPoly_iff]\n rw [linearFactor_toPoly]\n exact Polynomial.monic_X_sub_C x",
"n_chars": 101,
... | [
{
"name": "linearFactor_toPoly",
"text": "private theorem linearFactor_toPoly (x : F) :\n (CPolynomial.linearFactor x).toPoly =\n (Polynomial.X - Polynomial.C x : Polynomial F) := by\n rw [CPolynomial.linearFactor, CPolynomial.toPoly_add, CPolynomial.C_toPoly,\n CPolynomial.X_toPoly]\n rw [show... | [
{
"name": "linearFactor_monic",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 189,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nest... | 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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | /-
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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | @@ -22,8 +22,21 @@
variable {F : Type*} [Field F] [BEq F] [LawfulBEq F]
+private theorem linearFactor_toPoly (x : F) :
+ (CPolynomial.linearFactor x).toPoly =
+ (Polynomial.X - Polynomial.C x : Polynomial F) := by
+ rw [CPolynomial.linearFactor, CPolynomial.toPoly_add, CPolynomial.C_toPoly,
+ CPolynomi... | {
"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_5a09a4e7213b_1 | 5122206576c647a2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/CoefficientInterpolation.lean | CoefficientInterpolation | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "divByLinearFactor_fold_coeff_rec_aux",
"depth": 1,
"n_commands": 0,
"n_lines": 21,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n generalizing i state with\n | zero =>\n omega\n | succ n ih =>\n let nextCoef... | [
{
"name": "divByLinearFactor_fold_tail_of_le",
"text": "private theorem divByLinearFactor_fold_tail_of_le\n (p : CPolynomial F) (x : F) (n i : Nat) (state : F × List F)\n (hstate : state.2.getD 0 0 = state.1) (hi : n ≤ i) :\n ((List.range n).reverse.foldl\n (fun state j ↦\n let nextCoef... | [
{
"name": "divByLinearFactor_fold_coeff_rec_aux",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 35,
"n_chars": 1478,
"n_subproofs": 5,
"n_tactics": 20,
"cyclomatic": 2,
"n_automation": 8,
"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.Univariate.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | /-
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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | @@ -38,6 +38,32 @@
CPolynomial.ofArray coeffs.toArray
omit [BEq F] [LawfulBEq F] in
+private theorem divByLinearFactor_fold_tail_of_le
+ (p : CPolynomial F) (x : F) (n i : Nat) (state : F × List F)
+ (hstate : state.2.getD 0 0 = state.1) (hi : n ≤ i) :
+ ((List.range n).reverse.foldl
+ (fun state j ... | {
"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_5a09a4e7213b_2 | 14022a11fb94e5fa | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/CoefficientInterpolation.lean | CoefficientInterpolation | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "divByLinearFactor_fold_coeff_rec_aux",
"depth": 1,
"n_commands": 0,
"n_lines": 21,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n generalizing i state with\n | zero =>\n omega\n | succ n ih =>\n let nextCoef... | [
{
"name": "divByLinearFactor_fold_tail_of_le",
"text": "private theorem divByLinearFactor_fold_tail_of_le\n (p : CPolynomial F) (x : F) (n i : Nat) (state : F × List F)\n (hstate : state.2.getD 0 0 = state.1) (hi : n ≤ i) :\n ((List.range n).reverse.foldl\n (fun state j ↦\n let nextCoef... | [
{
"name": "divByLinearFactor_fold_coeff_rec",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 650,
"n_subproofs": 0,
"n_tactics": 2,
"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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | /-
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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | @@ -38,6 +38,32 @@
CPolynomial.ofArray coeffs.toArray
omit [BEq F] [LawfulBEq F] in
+private theorem divByLinearFactor_fold_tail_of_le
+ (p : CPolynomial F) (x : F) (n i : Nat) (state : F × List F)
+ (hstate : state.2.getD 0 0 = state.1) (hi : n ≤ i) :
+ ((List.range n).reverse.foldl
+ (fun state j ... | {
"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_5a09a4e7213b_3 | c7d7ecbd265522a3 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/CoefficientInterpolation.lean | CoefficientInterpolation | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "divByLinearFactor_fold_coeff_rec_aux",
"depth": 1,
"n_commands": 0,
"n_lines": 21,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n generalizing i state with\n | zero =>\n omega\n | succ n ih =>\n let nextCoef... | [
{
"name": "divByLinearFactor_fold_tail_of_le",
"text": "private theorem divByLinearFactor_fold_tail_of_le\n (p : CPolynomial F) (x : F) (n i : Nat) (state : F × List F)\n (hstate : state.2.getD 0 0 = state.1) (hi : n ≤ i) :\n ((List.range n).reverse.foldl\n (fun state j ↦\n let nextCoef... | [
{
"name": "divByLinearFactor_fold_coeff_eq_zero_of_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 400,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 0,
"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.Univariate.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | /-
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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | @@ -38,13 +38,41 @@
CPolynomial.ofArray coeffs.toArray
omit [BEq F] [LawfulBEq F] in
+private theorem divByLinearFactor_fold_tail_of_le
+ (p : CPolynomial F) (x : F) (n i : Nat) (state : F × List F)
+ (hstate : state.2.getD 0 0 = state.1) (hi : n ≤ i) :
+ ((List.range n).reverse.foldl
+ (fun state j... | {
"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_5a09a4e7213b_5 | f06fecfa88a39ddb | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/CoefficientInterpolation.lean | CoefficientInterpolation | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "divByLinearFactor_fold_coeff_rec_aux",
"depth": 1,
"n_commands": 0,
"n_lines": 21,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n generalizing i state with\n | zero =>\n omega\n | succ n ih =>\n let nextCoef... | [
{
"name": "divByLinearFactor_fold_tail_of_le",
"text": "private theorem divByLinearFactor_fold_tail_of_le\n (p : CPolynomial F) (x : F) (n i : Nat) (state : F × List F)\n (hstate : state.2.getD 0 0 = state.1) (hi : n ≤ i) :\n ((List.range n).reverse.foldl\n (fun state j ↦\n let nextCoef... | [
{
"name": "divByLinearFactor_coeff_eq_zero_of_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 316,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": f... | 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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | /-
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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | @@ -38,13 +38,41 @@
CPolynomial.ofArray coeffs.toArray
omit [BEq F] [LawfulBEq F] in
+private theorem divByLinearFactor_fold_tail_of_le
+ (p : CPolynomial F) (x : F) (n i : Nat) (state : F × List F)
+ (hstate : state.2.getD 0 0 = state.1) (hi : n ≤ i) :
+ ((List.range n).reverse.foldl
+ (fun state j... | {
"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_5a09a4e7213b_6 | 48334446fbc0711c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/CoefficientInterpolation.lean | CoefficientInterpolation | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 1 | [
{
"theorem_name": "divByLinearFactor_coeff_rec",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold divByLinearFactor\n rw [CPolynomial.coeff_ofArray]\n rw [CPolynomial.coeff_ofArray]\n simpa using div... | [
{
"name": "divByLinearFactor_fold_coeff_rec",
"text": "private theorem divByLinearFactor_fold_coeff_rec\n (p : CPolynomial F) (x : F) (n i : Nat) (hi : i < n) :\n ((List.range n).reverse.foldl\n (fun state j ↦\n let nextCoeff := p.coeff (j + 1) + x * state.1\n (nextCoeff, nextCoeff ... | [
{
"name": "divByLinearFactor_eq_divByMonic",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 9,
"n_lines": 52,
"n_chars": 2334,
"n_subproofs": 8,
"n_tactics": 48,
"cyclomatic": 2,
"n_automation": 7,
"n_rewrites": 17,
"n_structural": 8,
"automation_only": fal... | 9 | /-
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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | /-
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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | @@ -114,6 +114,22 @@
simpa using congrArg (fun t ↦ p.coeff (n + 1) + x * t) hstate.symm
omit [BEq F] [LawfulBEq F] in
+private theorem divByLinearFactor_fold_coeff_rec
+ (p : CPolynomial F) (x : F) (n i : Nat) (hi : i < n) :
+ ((List.range n).reverse.foldl
+ (fun state j ↦
+ let nextCoeff ... | {
"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_5a09a4e7213b_8 | 31cb5a2428b181a9 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/CoefficientInterpolation.lean | CoefficientInterpolation | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 1 | [
{
"theorem_name": "divByLinearFactor_eq_divByMonic",
"depth": 1,
"n_commands": 0,
"n_lines": 48,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (CPolynomial.eq_iff_coeff).2\n intro i\n rw [CPolynomial.coeff_toPoly]\n rw [CPolynomial.coeff_to... | [
{
"name": "divByLinearFactor_coeff_rec",
"text": "private theorem divByLinearFactor_coeff_rec\n (p : CPolynomial F) (x : F) {i : Nat} (hi : i < p.val.size - 1) :\n (divByLinearFactor p x).coeff i =\n p.coeff (i + 1) + x * (divByLinearFactor p x).coeff (i + 1) := by\n unfold divByLinearFactor\n ... | [
{
"name": "eval_divByLinearFactor_eq_zero_of_root_of_ne",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 11,
"n_lines": 24,
"n_chars": 1074,
"n_subproofs": 5,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 6,
"n_structural": 3,
"automati... | 11 | /-
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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | /-
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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | @@ -140,6 +140,15 @@
rw [divByLinearFactor_fold_tail_of_le p x n i (0, []) (by simp) hi]
simp
+private theorem divByLinearFactor_coeff_rec
+ (p : CPolynomial F) (x : F) {i : Nat} (hi : i < p.val.size - 1) :
+ (divByLinearFactor p x).coeff i =
+ p.coeff (i + 1) + x * (divByLinearFactor p x).coeff (i +... | {
"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_5a09a4e7213b_9 | 3a162a34d653ae05 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/CoefficientInterpolation.lean | CoefficientInterpolation | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 1 | [
{
"theorem_name": "divByLinearFactor_eq_divByMonic",
"depth": 1,
"n_commands": 0,
"n_lines": 48,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (CPolynomial.eq_iff_coeff).2\n intro i\n rw [CPolynomial.coeff_toPoly]\n rw [CPolynomial.coeff_to... | [
{
"name": "divByLinearFactor_coeff_rec",
"text": "private theorem divByLinearFactor_coeff_rec\n (p : CPolynomial F) (x : F) {i : Nat} (hi : i < p.val.size - 1) :\n (divByLinearFactor p x).coeff i =\n p.coeff (i + 1) + x * (divByLinearFactor p x).coeff (i + 1) := by\n unfold divByLinearFactor\n ... | [
{
"name": "eval_divByLinearFactor_self_eq_derivative",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 12,
"n_lines": 30,
"n_chars": 1483,
"n_subproofs": 4,
"n_tactics": 25,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 8,
"n_structural": 2,
"automation_... | 12 | /-
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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | /-
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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | @@ -146,6 +146,15 @@
rw [divByLinearFactor_fold_tail_of_le p x n i (0, []) (by simp) hi]
simp
+private theorem divByLinearFactor_coeff_rec
+ (p : CPolynomial F) (x : F) {i : Nat} (hi : i < p.val.size - 1) :
+ (divByLinearFactor p x).coeff i =
+ p.coeff (i + 1) + x * (divByLinearFactor p x).coeff (i +... | {
"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_5a09a4e7213b_14 | ba78742660d4f282 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/CoefficientInterpolation.lean | CoefficientInterpolation | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "eval_divByLinearFactor_eq_zero_of_root_of_ne",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have haRoot : p.toPoly.IsRoot a := by\n rw [Polynomial.IsRoot, ← CPolynomial.eval_toPoly]\... | [
{
"name": "divByLinearFactor_toPoly",
"text": "private theorem divByLinearFactor_toPoly (p : CPolynomial F) (x : F) :\n (divByLinearFactor p x).toPoly =\n p.toPoly /ₘ (Polynomial.X - Polynomial.C x) := by\n rw [divByLinearFactor_eq_divByMonic]\n rw [CPolynomial.divByMonic_toPoly_eq_divByMonic p\n ... | [
{
"name": "interpolateCoefficientForm_eval_point",
"fan_in": 0,
"n_deps_direct": 6,
"n_deps_transitive": 20,
"n_lines": 121,
"n_chars": 5467,
"n_subproofs": 26,
"n_tactics": 111,
"cyclomatic": 2,
"n_automation": 18,
"n_rewrites": 25,
"n_structural": 10,
"automatio... | 20 | /-
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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | /-
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.BatchEval.Context
import CompPoly.Univariate.Deriv
import CompPoly.Univariate.Vanishing
/-!
# Coefficient-Form Interpolation from ... | @@ -229,16 +229,70 @@
rw [← CPolynomial.coeff_toPoly]
exact hcoeff (p.val.size - 1 - i) i rfl
+private theorem divByLinearFactor_toPoly (p : CPolynomial F) (x : F) :
+ (divByLinearFactor p x).toPoly =
+ p.toPoly /ₘ (Polynomial.X - Polynomial.C x) := by
+ rw [divByLinearFactor_eq_divByMonic]
+ 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_a24ab9116a27_0 | fab5ee1991e86d33 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/Preliminaries.lean | Preliminaries | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "non_trivial_factors_of_non_trivial_poly_have_deg_ge_1",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_contra h_deg_a_not_nat\n have h_deg_a_ge_1_or_deg_b_ge_1 := not_and_or.mp h_deg_... | [
{
"name": "is_unit_iff_deg_0",
"text": "theorem is_unit_iff_deg_0 {R : Type*} [Field R] {p : R[X]} : p.degree = 0 ↔ IsUnit p := by\n constructor\n · -- (→) If degree = 0, then p is a unit\n intro h_deg_zero\n let a := coeff p 0\n have p_is_C : p = C a := eq_C_of_degree_eq_zero h_deg_zero\n -- ... | [
{
"name": "non_trivial_factors_of_non_trivial_poly_have_deg_ge_1",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 32,
"n_chars": 1327,
"n_subproofs": 5,
"n_tactics": 24,
"cyclomatic": 4,
"n_automation": 0,
"n_rewrites": 4,
"n_structural": 7,
"... | 2 | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | @@ -63,6 +63,36 @@
rfl
-- Field R
+theorem is_unit_iff_deg_0 {R : Type*} [Field R] {p : R[X]} : p.degree = 0 ↔ IsUnit p := by
+ constructor
+ · -- (→) If degree = 0, then p is a unit
+ intro h_deg_zero
+ let a := coeff p 0
+ have p_is_C : p = C a := eq_C_of_degree_eq_zero h_deg_zero
+ -- Show 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_a24ab9116a27_1 | bc59dcd5f338d8b8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/Preliminaries.lean | Preliminaries | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "unique_linear_sum_repr",
"depth": 1,
"n_commands": 0,
"n_lines": 83,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Get the coordinate representation of s in terms of the basis\n let repr := pb.basis.repr s\n have s_repr : s =... | [
{
"name": "unique_repr",
"text": "theorem unique_repr {R : Type*} [CommRing R] {S : Type*} [CommRing S] [Algebra R S]\n (pb : PowerBasis R S) (repr1 repr2 : Fin pb.dim →₀ R)\n (h : ∑ i : Fin pb.dim, repr1 i • pb.basis i = ∑ i : Fin pb.dim, repr2 i • pb.basis i) :\n repr1 = repr2 := by\n -- Use the... | [
{
"name": "unique_linear_sum_repr",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 87,
"n_chars": 3413,
"n_subproofs": 15,
"n_tactics": 76,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 39,
"n_structural": 9,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | @@ -57,6 +57,40 @@
-- if linear combination of two representations with the same PowerBasis are equal
-- then the representations are exactly the same
+theorem unique_repr {R : Type*} [CommRing R] {S : Type*} [CommRing S] [Algebra R S]
+ (pb : PowerBasis R S) (repr1 repr2 : Fin pb.dim →₀ R)
+ (h : ∑ i : Fin p... | {
"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_a24ab9116a27_2 | 5689aceef5e40ce2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/Preliminaries.lean | Preliminaries | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 3 | [
{
"theorem_name": "sum_square_char2",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction s using Finset.induction_on with\n | empty =>\n rw [Finset.sum_empty, zero_pow (by norm_num), Finset.sum_em... | [
{
"name": "sum_of_pow_exp_of_2",
"text": "theorem sum_of_pow_exp_of_2 {F : Type*} [Field F]\n (sumZeroIffEq : ∀ (x y : F), x + y = 0 ↔ x = y)\n (i : ℕ) : ∀ (a b c : F), a + b = c → a^(2^i) + b^(2^i) = c^(2^i) := by\n induction i with\n | zero =>\n simp [pow_zero] -- a^1 + b^1 = a + b = c = c^1\n ... | [
{
"name": "sum_square_char2",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 877,
"n_subproofs": 3,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 5,
"n_structural": 3,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | @@ -296,9 +296,67 @@
-------------------------------------------------------------------------------------------
+theorem sum_of_pow_exp_of_2 {F : Type*} [Field F]
+ (sumZeroIffEq : ∀ (x y : F), x + y = 0 ↔ x = y)
+ (i : ℕ) : ∀ (a b c : F), a + b = c → a^(2^i) + b^(2^i) = c^(2^i) := by
+ induction i 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_a24ab9116a27_3 | c78162c278547904 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/Preliminaries.lean | Preliminaries | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 5 | [
{
"theorem_name": "two_pow_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_contra hn\n have h_1_le_0 : 1 ≤ 0 := by\n calc 1 ≤ 2^n := by exact one_le_two_pow_n n\n _ = 0 := by rw [hn]\n ex... | [
{
"name": "one_le_two_pow_n",
"text": "theorem one_le_two_pow_n (n : ℕ) : 1 ≤ 2 ^ n := by\n calc\n 1 = 2^0 := by rw [Nat.pow_zero]\n _ ≤ 2 ^ n := Nat.pow_le_pow_right (by decide) (by exact Nat.zero_le n)\n\n",
"fan_in": 5,
"n_lines": 6,
"n_chars": 198,
"n_subproo... | [
{
"name": "two_pow_ne_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 222,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | @@ -296,9 +296,16 @@
-------------------------------------------------------------------------------------------
+theorem one_le_two_pow_n (n : ℕ) : 1 ≤ 2 ^ n := by
+ calc
+ 1 = 2^0 := by rw [Nat.pow_zero]
+ _ ≤ 2 ^ n := Nat.pow_le_pow_right (by decide) (by exact Nat.zero_le n)
+
theo... | {
"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_a24ab9116a27_4 | 571a3d2401a51cba | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/Preliminaries.lean | Preliminaries | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "pow_exp_of_2_repr_given_x_square_repr",
"depth": 1,
"n_commands": 0,
"n_lines": 194,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro i\n induction i with\n | zero =>\n -- # Base case (i = 0): When `i = 0`, the expression ... | [
{
"name": "two_le_two_pow_n_plus_1",
"text": "theorem two_le_two_pow_n_plus_1 (n : ℕ) : 2 ≤ 2 ^ (n + 1) := by\n calc\n 2 = 2 ^ 1 := by rw [Nat.pow_one]\n _ ≤ 2 ^ (n + 1) := Nat.pow_le_pow_right (by decide) (by exact Nat.zero_lt_succ n)\n\n",
"fan_in": 1,
"n_lines": 6,
... | [
{
"name": "pow_exp_of_2_repr_given_x_square_repr",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 5,
"n_lines": 201,
"n_chars": 11279,
"n_subproofs": 17,
"n_tactics": 138,
"cyclomatic": 4,
"n_automation": 30,
"n_rewrites": 38,
"n_structural": 30,
"automatio... | 5 | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | @@ -377,6 +377,11 @@
_ = ∑ j ∈ Finset.Icc (a + shift) (b + shift), f j := by
rw [Finset.Ico_add_one_right_eq_Icc]
+theorem two_le_two_pow_n_plus_1 (n : ℕ) : 2 ≤ 2 ^ (n + 1) := by
+ calc
+ 2 = 2 ^ 1 := by rw [Nat.pow_one]
+ _ ≤ 2 ^ (n + 1) := Nat.pow_le_pow_right (by decide) (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_a24ab9116a27_5 | 019e0ee3fec4ac3f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/Preliminaries.lean | Preliminaries | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "galois_eval_in_BTField",
"depth": 1,
"n_commands": 0,
"n_lines": 77,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n\n have u_pow_2_pow_k : u ^ 2 ^ 2 ^ k = u * t1 ^ (2 ^ 2 ^ k - 1)\n + ∑ j ∈ Finset.Icc 1 (2 ^ k), t1 ^ (2 ^ 2 ^ k ... | [
{
"name": "pow_exp_of_2_repr_given_x_square_repr",
"text": "/-- For any field element (x : F) where x^2 = x*z + 1, this theorem gives\n a closed form for x^(2^i). -/\ntheorem pow_exp_of_2_repr_given_x_square_repr {F : Type*} [instField : Field F]\n (sumZeroIffEq : ∀ (x y : F), x + y = 0 ↔ x = y) (x z ... | [
{
"name": "galois_eval_in_BTField",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 7,
"n_lines": 92,
"n_chars": 4619,
"n_subproofs": 8,
"n_tactics": 72,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 27,
"n_structural": 18,
"automation_only": false,
... | 7 | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | @@ -387,6 +387,206 @@
1 = 2^0 := by rw [Nat.pow_zero]
_ ≤ 2 ^ n := Nat.pow_le_pow_right (by decide) (by exact Nat.zero_le n)
+/-- For any field element (x : F) where x^2 = x*z + 1, this theorem gives
+ a closed form for x^(2^i). -/
+theorem pow_exp_of_2_repr_given_x_square_repr {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_a24ab9116a27_6 | 5267df8a959cd537 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/Preliminaries.lean | Preliminaries | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "galois_automorphism_power",
"depth": 1,
"n_commands": 0,
"n_lines": 53,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n\n have h_t1_pow_2_pow_2_pow_k : t1^(2^(2^k)) = t1 := by\n calc t1^(2^(2^k)) = t1^(2^(2^k) - 1 + 1) := by rw\... | [
{
"name": "galois_eval_in_BTField",
"text": "lemma galois_eval_in_BTField\n {curBTField : Type*} [Field curBTField]\n (u : curBTField) (t1 : curBTField) -- here t1 is already lifted to curBTField\n (k : ℕ)\n (sumZeroIffEq : ∀ (x y : curBTField), x + y = 0 ↔ x = y)\n (prevSpecialElementNeZero ... | [
{
"name": "galois_automorphism_power",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 8,
"n_lines": 67,
"n_chars": 3319,
"n_subproofs": 11,
"n_tactics": 54,
"cyclomatic": 4,
"n_automation": 4,
"n_rewrites": 16,
"n_structural": 13,
"automation_only": false,
... | 8 | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | @@ -594,6 +594,97 @@
f a * (∏ x ∈ s.erase a, f x) = ∏ x ∈ s, f x := by
rw [mul_comm]; exact Finset.prod_erase_mul s f h
+lemma galois_eval_in_BTField
+ {curBTField : Type*} [Field curBTField]
+ (u : curBTField) (t1 : curBTField) -- here t1 is already lifted to curBTField
+ (k : ℕ)
+ (sumZeroIffEq ... | {
"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_a24ab9116a27_7 | f533635b1297025d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/Preliminaries.lean | Preliminaries | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "lifted_trace_map_eval_at_roots_prev_BTField",
"depth": 1,
"n_commands": 0,
"n_lines": 92,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n\n calc\n ∑ i ∈ Finset.range (2 ^ (k+1)), u ^ (2 ^ i)\n = ∑ i ∈ Finset.Icc 0 (2^(k+1) -... | [
{
"name": "two_pow_ne_zero",
"text": "theorem two_pow_ne_zero (n : ℕ) : 2 ^ n ≠ 0 := by\n by_contra hn\n have h_1_le_0 : 1 ≤ 0 := by\n calc 1 ≤ 2^n := by exact one_le_two_pow_n n\n _ = 0 := by rw [hn]\n exact Nat.not_le_of_gt (by decide) h_1_le_0\n\n",
"fan_in": 1,
"n_lines": 8,
"n_char... | [
{
"name": "lifted_trace_map_eval_at_roots_prev_BTField",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 102,
"n_chars": 4658,
"n_subproofs": 5,
"n_tactics": 85,
"cyclomatic": 1,
"n_automation": 8,
"n_rewrites": 33,
"n_structural": 15,
"automat... | 3 | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | @@ -344,6 +344,13 @@
1 = 2^0 := by rw [Nat.pow_zero]
_ ≤ 2 ^ n := Nat.pow_le_pow_right (by decide) (by exact Nat.zero_le n)
+theorem two_pow_ne_zero (n : ℕ) : 2 ^ n ≠ 0 := by
+ by_contra hn
+ have h_1_le_0 : 1 ≤ 0 := by
+ calc 1 ≤ 2^n := by exact one_le_two_pow_n n
+ _ = 0 := 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_a24ab9116a27_8 | 20b31ad6916304a1 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/Preliminaries.lean | Preliminaries | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 5 | [
{
"theorem_name": "two_pow_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_contra hn\n have h_1_le_0 : 1 ≤ 0 := by\n calc 1 ≤ 2^n := by exact one_le_two_pow_n n\n _ = 0 := by rw [hn]\n ex... | [
{
"name": "one_le_two_pow_n",
"text": "theorem one_le_two_pow_n (n : ℕ) : 1 ≤ 2 ^ n := by\n calc\n 1 = 2^0 := by rw [Nat.pow_zero]\n _ ≤ 2 ^ n := Nat.pow_le_pow_right (by decide) (by exact Nat.zero_le n)\n\n",
"fan_in": 5,
"n_lines": 6,
"n_chars": 198,
"n_subproo... | [
{
"name": "rsum_eq_t1_square_aux",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 114,
"n_chars": 4773,
"n_subproofs": 12,
"n_tactics": 95,
"cyclomatic": 1,
"n_automation": 19,
"n_rewrites": 15,
"n_structural": 29,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | @@ -296,6 +296,11 @@
-------------------------------------------------------------------------------------------
+theorem one_le_two_pow_n (n : ℕ) : 1 ≤ 2 ^ n := by
+ calc
+ 1 = 2^0 := by rw [Nat.pow_zero]
+ _ ≤ 2 ^ n := Nat.pow_le_pow_right (by decide) (by exact Nat.zero_le 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_a24ab9116a27_9 | 02e4cc3c58cdc990 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Support/Preliminaries.lean | Preliminaries | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "charP_eq_2_of_add_self_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n have h_two : (2 : (F)) = 0 := by\n have h := sumZeroIffEq 1 1\n simp only at h\n exact two_eq_zero_in... | [
{
"name": "two_eq_zero_in_char2_field",
"text": "theorem two_eq_zero_in_char2_field {F : Type*} [Field F]\n (sumZeroIffEq : ∀ (x y : F), x + y = 0 ↔ x = y) :\n (2 : F) = 0 := by\n have char_two : (1 : F) + (1 : F) = 0 := by\n exact (sumZeroIffEq 1 1).mpr rfl\n have : (2 : F) = (1 : F) + (1 : F) :... | [
{
"name": "charP_eq_2_of_add_self_eq_zero",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 29,
"n_chars": 1024,
"n_subproofs": 7,
"n_tactics": 25,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 5,
"n_structural": 8,
"automation_only": false... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen
-/
import Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | /-
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 Mathlib.FieldTheory.Finite.GaloisField
import CompPoly.Data.Fin.BigOperators
import CompPoly.Data.Nat.Bitwise
import Mathlib.LinearAlg... | @@ -296,6 +296,15 @@
-------------------------------------------------------------------------------------------
+theorem two_eq_zero_in_char2_field {F : Type*} [Field F]
+ (sumZeroIffEq : ∀ (x y : F), x + y = 0 ↔ x = y) :
+ (2 : F) = 0 := by
+ have char_two : (1 : F) + (1 : F) = 0 := by
+ exact (sumZero... | {
"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_0f1b5a65164a_0 | 65b08c147a549d4c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/DivisionCorrectness.lean | DivisionCorrectness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 2 | [
{
"theorem_name": "toPoly_truncate_lowEq",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro i hi\n simp [toPoly_truncate_coeff, hi]",
"n_chars": 51,
"n_subproofs": 0,
"n_tactics": 3,
"cy... | [
{
"name": "toPoly_truncate_coeff",
"text": "private lemma toPoly_truncate_coeff (k : Nat) (p : Raw R) (i : Nat) :\n (truncate k p).toPoly.coeff i = if i < k then p.toPoly.coeff i else 0 := by\n rw [Raw.coeff_toPoly, Raw.truncate_coeff, Raw.coeff_toPoly]\n\nomit [BEq R] [LawfulBEq R] in\n",
"fan_in":... | [
{
"name": "toPoly_truncate_lowEq",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 158,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin, Juan Conejero
-/
import Mathlib.Algebra.Polynomial.Div
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.Algebra.Polynomial.Reverse
import Mathlib.Tactic.Ring
im... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin, Juan Conejero
-/
import Mathlib.Algebra.Polynomial.Div
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.Algebra.Polynomial.Reverse
import Mathlib.Tactic.Ring
im... | @@ -34,8 +34,15 @@
∀ i, i < k → p.coeff i = q.coeff i
omit [BEq R] [LawfulBEq R] in
+private lemma toPoly_truncate_coeff (k : Nat) (p : Raw R) (i : Nat) :
+ (truncate k p).toPoly.coeff i = if i < k then p.toPoly.coeff i else 0 := by
+ rw [Raw.coeff_toPoly, Raw.truncate_coeff, Raw.coeff_toPoly]
+
+omit [BEq 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_0f1b5a65164a_3 | 60dac43d256ad26b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/DivisionCorrectness.lean | DivisionCorrectness | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 4 | [
{
"theorem_name": "lowEq.mul_right",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro i hi\n calc\n (p * r).coeff i = (r * p).coeff i := by rw [_root_.mul_comm p r]\n _ = (r * q).coeff i := lowEq.... | [
{
"name": "lowEq.mul_left",
"text": "private lemma lowEq.mul_left {k : Nat} {p q : R[X]} (r : R[X])\n (h : lowEq k p q) : lowEq k (r * p) (r * q) := by\n intro i hi\n rw [Polynomial.coeff_mul, Polynomial.coeff_mul]\n apply Finset.sum_congr rfl\n intro x hx\n rcases x with ⟨a, b⟩\n have hab : a + b ... | [
{
"name": "lowEq.newton_step",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 36,
"n_chars": 1382,
"n_subproofs": 10,
"n_tactics": 28,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 3,
"n_structural": 6,
"automation_only": false,
"max_n... | 4 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin, Juan Conejero
-/
import Mathlib.Algebra.Polynomial.Div
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.Algebra.Polynomial.Reverse
import Mathlib.Tactic.Ring
im... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin, Juan Conejero
-/
import Mathlib.Algebra.Polynomial.Div
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.Algebra.Polynomial.Reverse
import Mathlib.Tactic.Ring
im... | @@ -52,6 +52,18 @@
simp [h i hi]
omit [BEq R] [LawfulBEq R] in
+private lemma lowEq.mul_left {k : Nat} {p q : R[X]} (r : R[X])
+ (h : lowEq k p q) : lowEq k (r * p) (r * q) := by
+ intro i hi
+ rw [Polynomial.coeff_mul, Polynomial.coeff_mul]
+ apply Finset.sum_congr rfl
+ intro x hx
+ rcases x with ⟨a, 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_0f1b5a65164a_7 | b6ce610930f0bbfa | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/DivisionCorrectness.lean | DivisionCorrectness | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 2 | [
{
"theorem_name": "toPoly_reverse_eq_reflect",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext i\n rw [toPoly_reverse_coeff, Polynomial.coeff_reflect]\n by_cases hi : i < n\n · have hle : i ≤ n - 1 :=... | [
{
"name": "toPoly_reverse_coeff",
"text": "private lemma toPoly_reverse_coeff (n : Nat) (p : Raw R) (i : Nat) :\n (reverse n p).toPoly.coeff i =\n if i < n then p.toPoly.coeff (n - 1 - i) else 0 := by\n rw [Raw.coeff_toPoly, Raw.reverse_coeff, Raw.coeff_toPoly]\n\n",
"fan_in": 2,
"n_lines":... | [
{
"name": "toPoly_reverse_natDegree_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 256,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 1,
"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, Juan Conejero
-/
import Mathlib.Algebra.Polynomial.Div
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.Algebra.Polynomial.Reverse
import Mathlib.Tactic.Ring
im... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin, Juan Conejero
-/
import Mathlib.Algebra.Polynomial.Div
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.Algebra.Polynomial.Reverse
import Mathlib.Tactic.Ring
im... | @@ -34,8 +34,18 @@
∀ i, i < k → p.coeff i = q.coeff i
omit [BEq R] [LawfulBEq R] in
+private lemma toPoly_reverse_coeff (n : Nat) (p : Raw R) (i : Nat) :
+ (reverse n p).toPoly.coeff i =
+ if i < n then p.toPoly.coeff (n - 1 - i) else 0 := by
+ rw [Raw.coeff_toPoly, Raw.reverse_coeff, Raw.coeff_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_0f1b5a65164a_22 | 0f0dd7dc906a297d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/DivisionCorrectness.lean | DivisionCorrectness | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 1 | [
{
"theorem_name": "inverseModX_go_lowEq",
"depth": 1,
"n_commands": 0,
"n_lines": 44,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro fuel\n induction fuel with\n | zero =>\n intro n g h\n unfold Raw.inverseModX.go\n have hg :\n... | [
{
"name": "min_mul_two_pow_le_min_min_mul",
"text": "private lemma min_mul_two_pow_le_min_min_mul (k n fuel : Nat) :\n Nat.min k (n * 2 ^ (fuel + 1)) ≤\n Nat.min k (Nat.min k (2 * n) * 2 ^ fuel) := by\n by_cases h : 2 * n < k\n · have hmin : Nat.min k (2 * n) = 2 * n := Nat.min_eq_right (le_of_lt ... | [
{
"name": "modByMonicByReversal_eq_modByMonic",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 27,
"n_lines": 91,
"n_chars": 4501,
"n_subproofs": 17,
"n_tactics": 87,
"cyclomatic": 2,
"n_automation": 9,
"n_rewrites": 20,
"n_structural": 11,
"automation_only... | 27 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin, Juan Conejero
-/
import Mathlib.Algebra.Polynomial.Div
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.Algebra.Polynomial.Reverse
import Mathlib.Tactic.Ring
im... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin, Juan Conejero
-/
import Mathlib.Algebra.Polynomial.Div
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.Algebra.Polynomial.Reverse
import Mathlib.Tactic.Ring
im... | @@ -163,6 +163,23 @@
simpa using h_e2.neg
exact hpg.trans (hpgcorrection.trans (lowEq.eq_one_of_sub hmain))
+private lemma min_mul_two_pow_le_min_min_mul (k n fuel : Nat) :
+ Nat.min k (n * 2 ^ (fuel + 1)) ≤
+ Nat.min k (Nat.min k (2 * n) * 2 ^ fuel) := by
+ by_cases h : 2 * n < k
+ · have hmin : Na... | {
"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_0 | 12614656e62c360e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 0 | 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": "toImpl_add",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 30,
"n_chars": 1428,
"n_subproofs": 5,
"n_tactics": 26,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 7,
"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... | @@ -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_1 | 38afa7bfe4bff980 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/ToPoly.lean | ToPoly | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 22 | 6 | [
{
"theorem_name": "toPoly_ofPoly",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply CPolynomial.eq_iff_coeff.mpr\n intro i\n -- Since `toPoly` is injective on canonical polynomials, coeffi... | [
{
"name": "toPoly_coeff",
"text": "/-- The outer coefficient of `toPoly p` is `CPolynomial.coeff p n` converted to `R[X]`. -/\ntheorem toPoly_coeff {R : Type*} [BEq R] [LawfulBEq R] [Semiring R]\n (p : CBivariate R) (n : ℕ) : (toPoly p).coeff n = (CPolynomial.coeff p n).toPoly := by\n rw [ CBivariat... | [
{
"name": "toPoly_ofPoly",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 731,
"n_subproofs": 3,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 5,
"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... | @@ -207,6 +207,14 @@
grind
· aesop
+/-- The outer coefficient of `toPoly p` is `CPolynomial.coeff p n` converted to `R[X]`. -/
+theorem toPoly_coeff {R : Type*} [BEq R] [LawfulBEq R] [Semiring R]
+ (p : CBivariate R) (n : ℕ) : (toPoly p).coeff n = (CPolynomial.coeff p n).toPoly := by
+ rw [ CB... | {
"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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