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_dbc8c0c74fd4_0 | fb1ac9f1f2bb81c4 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/ToMathlib/MvPolynomial/Equiv.lean | Equiv | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "finSuccEquivNth_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← finSuccEquivNth_eq, RingHom.coe_coe]",
"n_chars": 50,
"n_subproofs": 0,
"n_tactics": 2,
"cyclom... | [
{
"name": "finSuccEquivNth_eq",
"text": "theorem finSuccEquivNth_eq :\n (finSuccEquivNth R p : MvPolynomial (Fin (n + 1)) R →+* Polynomial (MvPolynomial (Fin n) R)) =\n eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))\n (Fin.insertNth p Polynomial.X (Polynomial.C ∘ X)) := by\n ... | [
{
"name": "finSuccEquivNth_apply",
"fan_in": 7,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 285,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | /-
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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | @@ -30,10 +30,21 @@
def finSuccEquivNth : MvPolynomial (Fin (n + 1)) R ≃ₐ[R] Polynomial (MvPolynomial (Fin n) R) :=
(renameEquiv R (_root_.finSuccEquiv' p)).trans (optionEquivLeft R (Fin n))
+theorem finSuccEquivNth_eq :
+ (finSuccEquivNth R p : MvPolynomial (Fin (n + 1)) R →+* Polynomial (MvPolynomial (Fin 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_dbc8c0c74fd4_1 | 9358710a568cfefa | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/ToMathlib/MvPolynomial/Equiv.lean | Equiv | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 7 | [
{
"theorem_name": "finSuccEquivNth_comp_C_eq_C",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine RingHom.ext fun x => ?_\n rw [RingHom.comp_apply]\n refine\n (finSuccEquivNth R p).injective\n ... | [
{
"name": "finSuccEquivNth_apply",
"text": "theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :\n finSuccEquivNth R p f =\n eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))\n (Fin.insertNth p Polynomial.X (Polynomial.C ∘ X)) f := by\n rw [← finSuccEquivNth_eq, R... | [
{
"name": "finSuccEquivNth_comp_C_eq_C",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 439,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | /-
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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | @@ -40,29 +40,63 @@
rfl
· refine Fin.succAboveCases p ?_ ?_ j <;> simp [finSuccEquivNth, optionEquivLeft]
+theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :
+ finSuccEquivNth R p f =
+ eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))
+ (Fin.insertNth p Polynomial... | {
"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_dbc8c0c74fd4_2 | 7daa5763234bc7e9 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/ToMathlib/MvPolynomial/Equiv.lean | Equiv | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 7 | [
{
"theorem_name": "finSuccEquivNth_comp_C_eq_C",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine RingHom.ext fun x => ?_\n rw [RingHom.comp_apply]\n refine\n (finSuccEquivNth R p).injective\n ... | [
{
"name": "finSuccEquivNth_apply",
"text": "theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :\n finSuccEquivNth R p f =\n eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))\n (Fin.insertNth p Polynomial.X (Polynomial.C ∘ X)) f := by\n rw [← finSuccEquivNth_eq, R... | [
{
"name": "finSuccEquivNth_X_same",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 120,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_n... | 2 | /-
Copyright (c) 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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | /-
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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | @@ -40,25 +40,53 @@
rfl
· refine Fin.succAboveCases p ?_ ?_ j <;> simp [finSuccEquivNth, optionEquivLeft]
+theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :
+ finSuccEquivNth R p f =
+ eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))
+ (Fin.insertNth p Polynomial... | {
"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_dbc8c0c74fd4_3 | 2c41a85c6ad2998e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/ToMathlib/MvPolynomial/Equiv.lean | Equiv | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 7 | [
{
"theorem_name": "finSuccEquivNth_comp_C_eq_C",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine RingHom.ext fun x => ?_\n rw [RingHom.comp_apply]\n refine\n (finSuccEquivNth R p).injective\n ... | [
{
"name": "finSuccEquivNth_apply",
"text": "theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :\n finSuccEquivNth R p f =\n eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))\n (Fin.insertNth p Polynomial.X (Polynomial.C ∘ X)) f := by\n rw [← finSuccEquivNth_eq, R... | [
{
"name": "eval_eq_eval_mv_eval_finSuccEquivNth",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 20,
"n_chars": 1082,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only":... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | /-
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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | @@ -40,25 +40,53 @@
rfl
· refine Fin.succAboveCases p ?_ ?_ j <;> simp [finSuccEquivNth, optionEquivLeft]
+theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :
+ finSuccEquivNth R p f =
+ eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))
+ (Fin.insertNth p Polynomial... | {
"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_dbc8c0c74fd4_4 | c55bf69d64b15e24 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/ToMathlib/MvPolynomial/Equiv.lean | Equiv | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 7 | [
{
"theorem_name": "finSuccEquivNth_comp_C_eq_C",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine RingHom.ext fun x => ?_\n rw [RingHom.comp_apply]\n refine\n (finSuccEquivNth R p).injective\n ... | [
{
"name": "finSuccEquivNth_apply",
"text": "theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :\n finSuccEquivNth R p f =\n eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))\n (Fin.insertNth p Polynomial.X (Polynomial.C ∘ X)) f := by\n rw [← finSuccEquivNth_eq, R... | [
{
"name": "totalDegree_coeff_finSuccEquivNth_add_le",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 19,
"n_chars": 1050,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_onl... | 3 | /-
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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | /-
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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | @@ -40,25 +40,53 @@
rfl
· refine Fin.succAboveCases p ?_ ?_ j <;> simp [finSuccEquivNth, optionEquivLeft]
+theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :
+ finSuccEquivNth R p f =
+ eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))
+ (Fin.insertNth p Polynomial... | {
"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_dbc8c0c74fd4_5 | f595fe278c3a474d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/ToMathlib/MvPolynomial/Equiv.lean | Equiv | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 7 | [
{
"theorem_name": "finSuccEquivNth_comp_C_eq_C",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine RingHom.ext fun x => ?_\n rw [RingHom.comp_apply]\n refine\n (finSuccEquivNth R p).injective\n ... | [
{
"name": "finSuccEquivNth_apply",
"text": "theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :\n finSuccEquivNth R p f =\n eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))\n (Fin.insertNth p Polynomial.X (Polynomial.C ∘ X)) f := by\n rw [← finSuccEquivNth_eq, R... | [
{
"name": "image_support_finSuccEquivNth",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 19,
"n_chars": 597,
"n_subproofs": 0,
"n_tactics": 15,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 5,
"n_structural": 7,
"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: Chung Thai Nguyen, Quang Dao
-/
import Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | /-
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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | @@ -40,25 +40,53 @@
rfl
· refine Fin.succAboveCases p ?_ ?_ j <;> simp [finSuccEquivNth, optionEquivLeft]
+theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :
+ finSuccEquivNth R p f =
+ eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))
+ (Fin.insertNth p Polynomial... | {
"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_dbc8c0c74fd4_6 | a758ba1868f37717 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/ToMathlib/MvPolynomial/Equiv.lean | Equiv | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 7 | [
{
"theorem_name": "finSuccEquivNth_comp_C_eq_C",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine RingHom.ext fun x => ?_\n rw [RingHom.comp_apply]\n refine\n (finSuccEquivNth R p).injective\n ... | [
{
"name": "finSuccEquivNth_apply",
"text": "theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :\n finSuccEquivNth R p f =\n eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))\n (Fin.insertNth p Polynomial.X (Polynomial.C ∘ X)) f := by\n rw [← finSuccEquivNth_eq, R... | [
{
"name": "mem_image_support_coeff_finSuccEquivNth",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 6,
"n_chars": 277,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only":... | 4 | /-
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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | /-
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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | @@ -40,25 +40,53 @@
rfl
· refine Fin.succAboveCases p ?_ ?_ j <;> simp [finSuccEquivNth, optionEquivLeft]
+theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :
+ finSuccEquivNth R p f =
+ eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))
+ (Fin.insertNth p Polynomial... | {
"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_dbc8c0c74fd4_7 | 7f727f2a0c6cde85 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/ToMathlib/MvPolynomial/Equiv.lean | Equiv | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 7 | [
{
"theorem_name": "finSuccEquivNth_comp_C_eq_C",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine RingHom.ext fun x => ?_\n rw [RingHom.comp_apply]\n refine\n (finSuccEquivNth R p).injective\n ... | [
{
"name": "finSuccEquivNth_apply",
"text": "theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :\n finSuccEquivNth R p f =\n eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))\n (Fin.insertNth p Polynomial.X (Polynomial.C ∘ X)) f := by\n rw [← finSuccEquivNth_eq, R... | [
{
"name": "mem_support_coeff_finSuccEquivNth",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 7,
"n_chars": 382,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"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: Chung Thai Nguyen, Quang Dao
-/
import Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | /-
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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | @@ -40,25 +40,53 @@
rfl
· refine Fin.succAboveCases p ?_ ?_ j <;> simp [finSuccEquivNth, optionEquivLeft]
+theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :
+ finSuccEquivNth R p f =
+ eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))
+ (Fin.insertNth p Polynomial... | {
"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_dbc8c0c74fd4_8 | b414556b78cb613b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/ToMathlib/MvPolynomial/Equiv.lean | Equiv | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "natDegree_finSuccEquivNth",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases c : f = 0\n · rw [c, map_zero, Polynomial.natDegree_zero, degreeOf_zero]\n · rw [Polynomial.natDegree,... | [
{
"name": "degree_finSuccEquivNth",
"text": "/-- The degree of `finSuccEquivNth R p f` equals the `p`-th degree of `f`. -/\ntheorem degree_finSuccEquivNth {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :\n (finSuccEquivNth R p f).degree = degreeOf p f := by\n have hCast : WithBot.some = Nat.cast := rfl\... | [
{
"name": "natDegree_finSuccEquivNth",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 422,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 0,
"automation_only": false,
"m... | 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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | /-
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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | @@ -114,12 +114,23 @@
rwa [← coeff, zero_apply, ← mem_support_iff, support_coeff_finSuccEquivNth,
insertNth_self_removeNth]
+/-- The degree of `finSuccEquivNth R p f` equals the `p`-th degree of `f`. -/
+theorem degree_finSuccEquivNth {f : MvPolynomial (Fin (n + 1)) R} (h : f ≠ 0) :
+ (finSuccEquivNth ... | {
"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_dbc8c0c74fd4_9 | 4de9a6f0829e7145 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/ToMathlib/MvPolynomial/Equiv.lean | Equiv | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 7 | [
{
"theorem_name": "finSuccEquivNth_comp_C_eq_C",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine RingHom.ext fun x => ?_\n rw [RingHom.comp_apply]\n refine\n (finSuccEquivNth R p).injective\n ... | [
{
"name": "finSuccEquivNth_apply",
"text": "theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :\n finSuccEquivNth R p f =\n eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))\n (Fin.insertNth p Polynomial.X (Polynomial.C ∘ X)) f := by\n rw [← finSuccEquivNth_eq, R... | [
{
"name": "degreeOf_coeff_finSuccEquivNth",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 11,
"n_chars": 567,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"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: Chung Thai Nguyen, Quang Dao
-/
import Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | /-
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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | @@ -40,25 +40,53 @@
rfl
· refine Fin.succAboveCases p ?_ ?_ j <;> simp [finSuccEquivNth, optionEquivLeft]
+theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :
+ finSuccEquivNth R p f =
+ eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))
+ (Fin.insertNth p Polynomial... | {
"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_dbc8c0c74fd4_10 | f655f8e4d2e9acc2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/ToMathlib/MvPolynomial/Equiv.lean | Equiv | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 7 | [
{
"theorem_name": "finSuccEquivNth_comp_C_eq_C",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine RingHom.ext fun x => ?_\n rw [RingHom.comp_apply]\n refine\n (finSuccEquivNth R p).injective\n ... | [
{
"name": "finSuccEquivNth_apply",
"text": "theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :\n finSuccEquivNth R p f =\n eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))\n (Fin.insertNth p Polynomial.X (Polynomial.C ∘ X)) f := by\n rw [← finSuccEquivNth_eq, R... | [
{
"name": "finSuccEquivNth_rename_finSuccEquivNth",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 22,
"n_chars": 1263,
"n_subproofs": 1,
"n_tactics": 9,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 3,
"automation_only"... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | /-
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 Mathlib.Algebra.MvPolynomial.Equiv
import CompPoly.ToMathlib.Finsupp.Fin
/-!
# MvPolynomial Equiv
Equivalences for multivariable pol... | @@ -40,25 +40,53 @@
rfl
· refine Fin.succAboveCases p ?_ ?_ j <;> simp [finSuccEquivNth, optionEquivLeft]
+theorem finSuccEquivNth_apply (f : MvPolynomial (Fin (n + 1)) R) :
+ finSuccEquivNth R p f =
+ eval₂Hom (Polynomial.C.comp (C : R →+* MvPolynomial (Fin n) R))
+ (Fin.insertNth p Polynomial... | {
"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_a45c72ecc959_0 | 256b36a421a84744 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "array_mem_of_mem_eraseDups",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold Array.eraseDups at h\n rcases xs with ⟨l⟩\n simp at h ⊢\n have hh := array_mem_eraseDups_fold a l #[] ... | [
{
"name": "array_mem_eraseDups_fold",
"text": "theorem array_mem_eraseDups_fold {α : Type*} [BEq α] [LawfulBEq α]\n (a : α) : ∀ (xs : List α) (out : Array α),\n a ∈ List.foldl (fun out x ↦ if x ∈ out then out else out.push x) out xs →\n a ∈ out ∨ a ∈ xs := by\n intro xs\n induction xs with\... | [
{
"name": "array_mem_of_mem_eraseDups",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 280,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -15,8 +15,39 @@
namespace CompPoly
+theorem array_mem_eraseDups_fold {α : Type*} [BEq α] [LawfulBEq α]
+ (a : α) : ∀ (xs : List α) (out : Array α),
+ a ∈ List.foldl (fun out x ↦ if x ∈ out then out else out.push x) out xs →
+ a ∈ out ∨ a ∈ xs := by
+ intro xs
+ induction xs with
+ | nil =>
+ ... | {
"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_a45c72ecc959_1 | 42e9397e9da0cbe2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 4 | [
{
"theorem_name": "cbivar_coeff_truncateX",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold CBivariate.coeff CBivariate.truncateX\n unfold CPolynomial.ofArray\n rw [CPolynomial.Raw.Trim.coeff_eq_coe... | [
{
"name": "cpoly_truncate_coeff",
"text": "theorem cpoly_truncate_coeff {R : Type*} [Zero R] [BEq R] [LawfulBEq R]\n (p : CPolynomial R) (n i : Nat) :\n (CPolynomial.truncate p n).coeff i = if i < n then p.coeff i else 0 := by\n unfold CPolynomial.truncate CPolynomial.ofArray CPolynomial.coeff\n rw ... | [
{
"name": "cbivar_coeff_truncateX",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 27,
"n_chars": 1193,
"n_subproofs": 2,
"n_tactics": 22,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 13,
"n_structural": 0,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -45,6 +45,19 @@
namespace GuruswamiSudan
+theorem cpoly_truncate_coeff {R : Type*} [Zero R] [BEq R] [LawfulBEq R]
+ (p : CPolynomial R) (n i : Nat) :
+ (CPolynomial.truncate p n).coeff i = if i < n then p.coeff i else 0 := by
+ unfold CPolynomial.truncate CPolynomial.ofArray CPolynomial.coeff
+ 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_a45c72ecc959_2 | 6180f91a0e0a1fc7 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 4 | [
{
"theorem_name": "cbivar_coeff_truncateX",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold CBivariate.coeff CBivariate.truncateX\n unfold CPolynomial.ofArray\n rw [CPolynomial.Raw.Trim.coeff_eq_coe... | [
{
"name": "cpoly_truncate_coeff",
"text": "theorem cpoly_truncate_coeff {R : Type*} [Zero R] [BEq R] [LawfulBEq R]\n (p : CPolynomial R) (n i : Nat) :\n (CPolynomial.truncate p n).coeff i = if i < n then p.coeff i else 0 := by\n unfold CPolynomial.truncate CPolynomial.ofArray CPolynomial.coeff\n rw ... | [
{
"name": "polynomialPrefix_zero",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 240,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -45,8 +45,27 @@
namespace GuruswamiSudan
+theorem cpoly_truncate_coeff {R : Type*} [Zero R] [BEq R] [LawfulBEq R]
+ (p : CPolynomial R) (n i : Nat) :
+ (CPolynomial.truncate p n).coeff i = if i < n then p.coeff i else 0 := by
+ unfold CPolynomial.truncate CPolynomial.ofArray CPolynomial.coeff
+ 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_a45c72ecc959_3 | 8fa912840477ad7f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 4 | [
{
"theorem_name": "cbivar_coeff_truncateX",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold CBivariate.coeff CBivariate.truncateX\n unfold CPolynomial.ofArray\n rw [CPolynomial.Raw.Trim.coeff_eq_coe... | [
{
"name": "cpoly_truncate_coeff",
"text": "theorem cpoly_truncate_coeff {R : Type*} [Zero R] [BEq R] [LawfulBEq R]\n (p : CPolynomial R) (n i : Nat) :\n (CPolynomial.truncate p n).coeff i = if i < n then p.coeff i else 0 := by\n unfold CPolynomial.truncate CPolynomial.ofArray CPolynomial.coeff\n rw ... | [
{
"name": "polynomialPrefix_succ",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 671,
"n_subproofs": 2,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -45,11 +45,37 @@
namespace GuruswamiSudan
+theorem cpoly_truncate_coeff {R : Type*} [Zero R] [BEq R] [LawfulBEq R]
+ (p : CPolynomial R) (n i : Nat) :
+ (CPolynomial.truncate p n).coeff i = if i < n then p.coeff i else 0 := by
+ unfold CPolynomial.truncate CPolynomial.ofArray CPolynomial.coeff
+ rw [CPo... | {
"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_a45c72ecc959_4 | 97f1b333af98c745 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 4 | [
{
"theorem_name": "cbivar_coeff_truncateX",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold CBivariate.coeff CBivariate.truncateX\n unfold CPolynomial.ofArray\n rw [CPolynomial.Raw.Trim.coeff_eq_coe... | [
{
"name": "cpoly_truncate_coeff",
"text": "theorem cpoly_truncate_coeff {R : Type*} [Zero R] [BEq R] [LawfulBEq R]\n (p : CPolynomial R) (n i : Nat) :\n (CPolynomial.truncate p n).coeff i = if i < n then p.coeff i else 0 := by\n unfold CPolynomial.truncate CPolynomial.ofArray CPolynomial.coeff\n rw ... | [
{
"name": "polynomialPrefix_eq_self_of_degreeLt",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 525,
"n_subproofs": 2,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 5,
"n_structural": 1,
"automation_only": ... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -58,10 +58,34 @@
simp
omega
+theorem cpoly_truncate_coeff {R : Type*} [Zero R] [BEq R] [LawfulBEq R]
+ (p : CPolynomial R) (n i : Nat) :
+ (CPolynomial.truncate p n).coeff i = if i < n then p.coeff i else 0 := by
+ unfold CPolynomial.truncate CPolynomial.ofArray CPolynomial.coeff
+ rw [CPolyn... | {
"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_a45c72ecc959_5 | d6707134d8e8deae | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 2 | [
{
"theorem_name": "composeY_add",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold CBivariate.composeY\n exact cpoly_eval_add P Q p",
"n_chars": 61,
"n_subproofs": 0,
"n_tactics": 3,
"c... | [
{
"name": "cpoly_eval_add",
"text": "theorem cpoly_eval_add {R : Type*}\n [Semiring R] [BEq R] [LawfulBEq R]\n (p q : CPolynomial R) (c : R) :\n CPolynomial.eval c (p + q) = CPolynomial.eval c p + CPolynomial.eval c q := by\n rw [CPolynomial.eval_toPoly, CPolynomial.toPoly_add, Polynomial.eval_add... | [
{
"name": "composeY_add",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 285,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -60,10 +60,19 @@
| n + 1 => by
rw [List.sum_range_succ, Finset.sum_range_succ, list_sum_map_range_eq_finset_sum f n]
+theorem cpoly_eval_add {R : Type*}
+ [Semiring R] [BEq R] [LawfulBEq R]
+ (p q : CPolynomial R) (c : R) :
+ CPolynomial.eval c (p + q) = CPolynomial.eval c p + CPolynomial.eval 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_a45c72ecc959_6 | bb2e3f608242ba0a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 2 | [
{
"theorem_name": "composeY_outer_monomial",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold CBivariate.composeY\n exact cpoly_eval_monomial y c p",
"n_chars": 66,
"n_subproofs": 0,
"n_tac... | [
{
"name": "cpoly_eval_monomial",
"text": "theorem cpoly_eval_monomial {R : Type*}\n [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (y : Nat) (a c : R) :\n (CPolynomial.monomial y a).eval c = a * c ^ y := by\n rw [CPolynomial.eval_toPoly]\n rw [show (CPolynomial.monomial y a :... | [
{
"name": "composeY_outer_monomial",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 302,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -60,10 +60,21 @@
| n + 1 => by
rw [List.sum_range_succ, Finset.sum_range_succ, list_sum_map_range_eq_finset_sum f n]
+theorem cpoly_eval_monomial {R : Type*}
+ [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]
+ (y : Nat) (a c : R) :
+ (CPolynomial.monomial y a).eval c = a * 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_a45c72ecc959_7 | 20fa660795d5e8c5 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "cpoly_mulPowCoeff_eq_coeff_mul_pow",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold CPolynomial.mulPowCoeff\n rw [list_foldl_add_eq_sum]\n rw [CPolynomial.coeff_mul]\n rw [list_s... | [
{
"name": "cpoly_powCoeff_eq_coeff_pow",
"text": "theorem cpoly_powCoeff_eq_coeff_pow {R : Type*}\n [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (p : CPolynomial R) (k n : Nat) :\n CPolynomial.powCoeff p k n = (p ^ k : CPolynomial R).coeff n := by\n induction k generalizing n with\n | zero... | [
{
"name": "cpoly_mulPowCoeff_eq_coeff_mul_pow",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 400,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 0,
"automation_only": fal... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -60,10 +60,31 @@
| n + 1 => by
rw [List.sum_range_succ, Finset.sum_range_succ, list_sum_map_range_eq_finset_sum f n]
+theorem cpoly_powCoeff_eq_coeff_pow {R : Type*}
+ [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (p : CPolynomial R) (k n : Nat) :
+ CPolynomial.powCoeff p k n = (p ^ k : CP... | {
"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_a45c72ecc959_8 | e7f89dda7445e124 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 2 | [
{
"theorem_name": "cpoly_coeff_zero_pow_monomial_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro n\n rw [cpoly_coeff_zero_pow]\n rw [CPolynomial.coeff_monomial]\n rfl",
"n_chars": 81,
... | [
{
"name": "cpoly_coeff_zero_pow",
"text": "theorem cpoly_coeff_zero_pow {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (p : CPolynomial F) :\n ∀ n : Nat, (p ^ n : CPolynomial F).coeff 0 = p.coeff 0 ^ n := by\n intro n\n induction n with\n | zero =>\n rw [pow_zero, pow_zero]\n rw [CPol... | [
{
"name": "cpoly_coeff_zero_pow_monomial_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 288,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": fal... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -60,10 +60,31 @@
| n + 1 => by
rw [List.sum_range_succ, Finset.sum_range_succ, list_sum_map_range_eq_finset_sum f n]
+theorem cpoly_coeff_zero_pow {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (p : CPolynomial F) :
+ ∀ n : Nat, (p ^ n : CPolynomial F).coeff 0 = p.coeff 0 ^ n := by
+ intro 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_a45c72ecc959_9 | eadced65e9bcf238 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 2 | [
{
"theorem_name": "cpoly_coeff_zero_pow_monomial_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro n\n rw [cpoly_coeff_zero_pow]\n rw [CPolynomial.coeff_monomial]\n rfl",
"n_chars": 81,
... | [
{
"name": "cpoly_coeff_zero_pow",
"text": "theorem cpoly_coeff_zero_pow {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (p : CPolynomial F) :\n ∀ n : Nat, (p ^ n : CPolynomial F).coeff 0 = p.coeff 0 ^ n := by\n intro n\n induction n with\n | zero =>\n rw [pow_zero, pow_zero]\n rw [CPol... | [
{
"name": "cpoly_mulPowCoeff_monomial_zero_depth_zero",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 12,
"n_chars": 496,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 7,
"n_structural": 0,
"automation_on... | 4 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -86,10 +86,31 @@
rw [list_sum_map_range_eq_finset_sum]
simp [cpoly_powCoeff_eq_coeff_pow]
+theorem cpoly_coeff_zero_pow {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (p : CPolynomial F) :
+ ∀ n : Nat, (p ^ n : CPolynomial F).coeff 0 = p.coeff 0 ^ n := by
+ intro n
+ induction n with
+ | zero =>... | {
"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_a45c72ecc959_10 | c6d242b80e56abfe | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 2 | [
{
"theorem_name": "cpoly_coeff_zero_pow_monomial_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro n\n rw [cpoly_coeff_zero_pow]\n rw [CPolynomial.coeff_monomial]\n rfl",
"n_chars": 81,
... | [
{
"name": "cpoly_coeff_zero_pow",
"text": "theorem cpoly_coeff_zero_pow {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (p : CPolynomial F) :\n ∀ n : Nat, (p ^ n : CPolynomial F).coeff 0 = p.coeff 0 ^ n := by\n intro n\n induction n with\n | zero =>\n rw [pow_zero, pow_zero]\n rw [CPol... | [
{
"name": "composeY_coeff_zero_zipIdx_eq_range_aux",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 33,
"n_chars": 1395,
"n_subproofs": 2,
"n_tactics": 23,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 5,
"n_structural": 2,
"automation_onl... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -69,6 +69,23 @@
rw [Finset.sum_range_succ]
rw [Finset.sum_range_zero, zero_add, tsub_zero]
+theorem cpoly_coeff_zero_pow {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (p : CPolynomial F) :
+ ∀ n : Nat, (p ^ n : CPolynomial F).coeff 0 = p.coeff 0 ^ n := by
+ intro n
+ induction n with
+ | zero =... | {
"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_a45c72ecc959_11 | 188e019b90ab3193 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 2 | [
{
"theorem_name": "cpoly_coeff_zero_pow_monomial_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro n\n rw [cpoly_coeff_zero_pow]\n rw [CPolynomial.coeff_monomial]\n rfl",
"n_chars": 81,
... | [
{
"name": "cpoly_coeff_zero_pow",
"text": "theorem cpoly_coeff_zero_pow {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (p : CPolynomial F) :\n ∀ n : Nat, (p ^ n : CPolynomial F).coeff 0 = p.coeff 0 ^ n := by\n intro n\n induction n with\n | zero =>\n rw [pow_zero, pow_zero]\n rw [CPol... | [
{
"name": "composeY_coeff_zero_fold_eq",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 12,
"n_chars": 537,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -69,6 +69,23 @@
rw [Finset.sum_range_succ]
rw [Finset.sum_range_zero, zero_add, tsub_zero]
+theorem cpoly_coeff_zero_pow {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (p : CPolynomial F) :
+ ∀ n : Nat, (p ^ n : CPolynomial F).coeff 0 = p.coeff 0 ^ n := by
+ intro n
+ induction n with
+ | zero =... | {
"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_a45c72ecc959_12 | 4b840dafc109d062 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "composeY_coeff_fold_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Array.foldl_zipIdx_eq_foldl_toList_zipIdx]\n simpa using\n (composeY_coeff_zipIdx_eq_range_aux coeffs.toList... | [
{
"name": "composeY_coeff_zipIdx_eq_range_aux",
"text": "theorem composeY_coeff_zipIdx_eq_range_aux {R : Type*}\n [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (xs : List (CPolynomial R)) (p accPoly : CPolynomial R) (accCoeff : R)\n (offset n : Nat) (hacc : accPoly.coeff n = accCoeff) :\n ... | [
{
"name": "composeY_coeff_fold_eq",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 551,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -60,12 +60,48 @@
| n + 1 => by
rw [List.sum_range_succ, Finset.sum_range_succ, list_sum_map_range_eq_finset_sum f n]
+theorem composeY_coeff_zipIdx_eq_range_aux {R : Type*}
+ [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (xs : List (CPolynomial R)) (p accPoly : CPolynomial R) (accCoeff : 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_a45c72ecc959_13 | 8cbf85cf743263d9 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 3 | [
{
"theorem_name": "cpoly_mulPowCoeff_monomial_zero_depth_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [cpoly_mulPowCoeff_eq_coeff_mul_pow]\n rw [CPolynomial.coeff_mul]\n rw [show Finset.range (... | [
{
"name": "cpoly_mulPowCoeff_eq_coeff_mul_pow",
"text": "theorem cpoly_mulPowCoeff_eq_coeff_mul_pow {R : Type*}\n [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (a p : CPolynomial R) (k n : Nat) :\n CPolynomial.mulPowCoeff a p k n = (a * (p ^ k : CPolynomial R)).coeff n := by\n unfold CPolyno... | [
{
"name": "composeYCoeff_eq_composeY_coeff",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 9,
"n_chars": 419,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
... | 4 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -76,6 +76,16 @@
rw [list_sum_map_range_eq_finset_sum]
simp [ih]
+theorem cpoly_mulPowCoeff_eq_coeff_mul_pow {R : Type*}
+ [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (a p : CPolynomial R) (k n : Nat) :
+ CPolynomial.mulPowCoeff a p k n = (a * (p ^ k : CPolynomial R)).coeff n := 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_a45c72ecc959_14 | 18934cbae742d163 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "composeY_coeff_fold_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Array.foldl_zipIdx_eq_foldl_toList_zipIdx]\n simpa using\n (composeY_coeff_zipIdx_eq_range_aux coeffs.toList... | [
{
"name": "composeY_coeff_zipIdx_eq_range_aux",
"text": "theorem composeY_coeff_zipIdx_eq_range_aux {R : Type*}\n [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (xs : List (CPolynomial R)) (p accPoly : CPolynomial R) (accCoeff : R)\n (offset n : Nat) (hacc : accPoly.coeff n = accCoeff) :\n ... | [
{
"name": "composeY_eq_range_fold",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 15,
"n_chars": 543,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false,
"max... | 6 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -86,12 +86,48 @@
rw [list_sum_map_range_eq_finset_sum]
simp [cpoly_powCoeff_eq_coeff_pow]
+theorem composeY_coeff_zipIdx_eq_range_aux {R : Type*}
+ [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (xs : List (CPolynomial R)) (p accPoly : CPolynomial R) (accCoeff : R)
+ (offset n : Nat) (hacc : ac... | {
"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_a45c72ecc959_15 | 7770e96174338b8a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "composeYCoeff_eq_composeY_coeff",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold CBivariate.composeYCoeff CBivariate.composeY CPolynomial.eval\n simp [cpoly_mulPowCoeff_eq_coeff_mu... | [
{
"name": "composeY_coeff_fold_eq",
"text": "theorem composeY_coeff_fold_eq {R : Type*}\n [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (coeffs : Array (CPolynomial R)) (p : CPolynomial R) (n : Nat) :\n List.foldl (fun acc y ↦ acc + ((coeffs.getD y 0) * p ^ y).coeff n) 0\n (List.range'... | [
{
"name": "composeY_zero",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 8,
"n_chars": 206,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting":... | 7 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -118,10 +118,24 @@
apply ih
rw [CPolynomial.coeff_add, hacc]
+theorem composeY_coeff_fold_eq {R : Type*}
+ [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (coeffs : Array (CPolynomial R)) (p : CPolynomial R) (n : Nat) :
+ List.foldl (fun acc y ↦ acc + ((coeffs.getD y 0) * p ^ y).coeff n)... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_a45c72ecc959_16 | 6ac7e2acf41b612c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 3 | [
{
"theorem_name": "cpoly_mulPowCoeff_monomial_zero_depth_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [cpoly_mulPowCoeff_eq_coeff_mul_pow]\n rw [CPolynomial.coeff_mul]\n rw [show Finset.range (... | [
{
"name": "cpoly_mulPowCoeff_eq_coeff_mul_pow",
"text": "theorem cpoly_mulPowCoeff_eq_coeff_mul_pow {R : Type*}\n [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (a p : CPolynomial R) (k n : Nat) :\n CPolynomial.mulPowCoeff a p k n = (a * (p ^ k : CPolynomial R)).coeff n := by\n unfold CPolyno... | [
{
"name": "initialCoefficientPolynomial_evalHorner_eq_composeYCoeff_monomial_zero",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 7,
"n_lines": 34,
"n_chars": 1486,
"n_subproofs": 1,
"n_tactics": 28,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 5,
"n_stru... | 7 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -92,6 +92,16 @@
rw [list_sum_map_range_eq_finset_sum]
simp [ih]
+theorem cpoly_mulPowCoeff_eq_coeff_mul_pow {R : Type*}
+ [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (a p : CPolynomial R) (k n : Nat) :
+ CPolynomial.mulPowCoeff a p k n = (a * (p ^ k : CPolynomial R)).coeff n := 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_a45c72ecc959_17 | babf7060dc1b4139 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "cpoly_mulPowCoeff_monomial_zero_depth_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [cpoly_mulPowCoeff_eq_coeff_mul_pow]\n rw [CPolynomial.coeff_mul]\n rw [show Finset.range (... | [
{
"name": "cpoly_coeff_zero_pow_monomial_zero",
"text": "theorem cpoly_coeff_zero_pow_monomial_zero {F : Type*}\n [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]\n (c : F) :\n ∀ n : Nat, ((CPolynomial.monomial 0 c) ^ n : CPolynomial F).coeff 0 = c ^ n := by\n intro n\n rw [cpoly_coeff_zero_pow]\n... | [
{
"name": "composeYCoeff_monomial_zero_eq_composeY_coeff_zero",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 8,
"n_lines": 10,
"n_chars": 462,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 0,
"autom... | 8 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -112,10 +112,25 @@
rw [Finset.sum_range_zero, zero_add, tsub_zero]
rw [ih]
+theorem cpoly_coeff_zero_pow_monomial_zero {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]
+ (c : F) :
+ ∀ n : Nat, ((CPolynomial.monomial 0 c) ^ n : CPolynomial F).coeff 0 = c ^ n := by
+ intro n
+ 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_a45c72ecc959_18 | b719889bbb6a5fbd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 2 | [
{
"theorem_name": "cpoly_coeff_zero_pow_monomial_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro n\n rw [cpoly_coeff_zero_pow]\n rw [CPolynomial.coeff_monomial]\n rfl",
"n_chars": 81,
... | [
{
"name": "cpoly_coeff_zero_pow",
"text": "theorem cpoly_coeff_zero_pow {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (p : CPolynomial F) :\n ∀ n : Nat, (p ^ n : CPolynomial F).coeff 0 = p.coeff 0 ^ n := by\n intro n\n induction n with\n | zero =>\n rw [pow_zero, pow_zero]\n rw [CPol... | [
{
"name": "initialCoefficientPolynomial_eval_eq_composeY_coeff_zero",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 12,
"n_lines": 10,
"n_chars": 473,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
... | 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.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -111,10 +111,31 @@
rw [Finset.sum_range_succ]
rw [Finset.sum_range_zero, zero_add, tsub_zero]
+theorem cpoly_coeff_zero_pow {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (p : CPolynomial F) :
+ ∀ n : Nat, (p ^ n : CPolynomial F).coeff 0 = p.coeff 0 ^ n := by
+ intro n
+ induction n with
+ | zer... | {
"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_a45c72ecc959_19 | 35a77f3410f5564b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 2 | [
{
"theorem_name": "polynomialPrefix_eq_self_of_degreeLt",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CPolynomial.eq_iff_coeff]\n intro i\n unfold polynomialPrefix\n rw [cpoly_truncate_coeff]\n b... | [
{
"name": "degreeLtBool_of_degreeLt",
"text": "theorem degreeLtBool_of_degreeLt {F : Type*} [Zero F]\n {p : CPolynomial F} {k : Nat} (h : degreeLt p k) : degreeLtBool p k = true := by\n rw [degreeLtBool]\n unfold degreeLt CPolynomial.degree at h\n cases hs : p.val.size with\n | zero =>\n simp\n ... | [
{
"name": "isRootYDegreeLtBool_of_root",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 10,
"n_chars": 368,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -45,6 +45,19 @@
namespace GuruswamiSudan
+theorem degreeLtBool_of_degreeLt {F : Type*} [Zero F]
+ {p : CPolynomial F} {k : Nat} (h : degreeLt p k) : degreeLtBool p k = true := by
+ rw [degreeLtBool]
+ unfold degreeLt CPolynomial.degree at h
+ cases hs : p.val.size with
+ | zero =>
+ simp
+ | succ 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_a45c72ecc959_20 | d757458847666460 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "rootsYDegreeLtFromCandidates_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold rootsYDegreeLtFromCandidates at h\n simp [isRootYDegreeLtBool] at h\n exact ⟨degreeLt_of_degree... | [
{
"name": "composeY_of_composeYHorner_eq_zero",
"text": "theorem composeY_of_composeYHorner_eq_zero {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n {Q : CBivariate F} {p : CPolynomial F}\n (h : CBivariate.composeYHorner Q p = 0) : CBivariate.composeY Q p = 0 := by\n simpa [CBivariate.composeY, CBi... | [
{
"name": "rootsYDegreeLtFromCandidates_sound",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 476,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": fal... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -71,12 +71,21 @@
| n + 1 => by
rw [List.sum_range_succ, Finset.sum_range_succ, list_sum_map_range_eq_finset_sum f n]
+theorem composeY_of_composeYHorner_eq_zero {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ {Q : CBivariate F} {p : CPolynomial F}
+ (h : CBivariate.composeYHorner Q p = 0) : CBiv... | {
"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_a45c72ecc959_21 | c9c848e38dbe91bd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "rootsYDegreeLtFromCandidates_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold rootsYDegreeLtFromCandidates at h\n simp [isRootYDegreeLtBool] at h\n exact ⟨degreeLt_of_degree... | [
{
"name": "degreeLt_of_degreeLtBool",
"text": "theorem degreeLt_of_degreeLtBool {F : Type*} [Zero F]\n {p : CPolynomial F} {k : Nat} (h : degreeLtBool p k = true) : degreeLt p k := by\n rw [degreeLtBool] at h\n simp at h\n unfold degreeLt CPolynomial.degree\n cases hs : p.val.size with\n | zero => s... | [
{
"name": "rootsYDegreeLtFromCandidates_eraseDups_sound",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 11,
"n_chars": 514,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_... | 5 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -79,6 +79,17 @@
namespace GuruswamiSudan
+theorem degreeLt_of_degreeLtBool {F : Type*} [Zero F]
+ {p : CPolynomial F} {k : Nat} (h : degreeLtBool p k = true) : degreeLt p k := by
+ rw [degreeLtBool] at h
+ simp at h
+ unfold degreeLt CPolynomial.degree
+ cases hs : p.val.size with
+ | zero => simp
+ | ... | {
"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_a45c72ecc959_22 | c6bb5ba364a9971a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "isRootYDegreeLtBool_of_root",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold isRootYDegreeLtBool\n rw [degreeLtBool_of_degreeLt hdegree, composeYHorner_eq_zero_of_composeY hroot]\n... | [
{
"name": "composeYHorner_eq_zero_of_composeY",
"text": "theorem composeYHorner_eq_zero_of_composeY {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n {Q : CBivariate F} {p : CPolynomial F}\n (h : CBivariate.composeY Q p = 0) : CBivariate.composeYHorner Q p = 0 := by\n simpa [CBivariate.composeY, CBi... | [
{
"name": "rootsYDegreeLtFromCandidates_complete_of_mem",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 11,
"n_chars": 466,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_... | 3 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -73,11 +73,20 @@
| n + 1 => by
rw [List.sum_range_succ, Finset.sum_range_succ, list_sum_map_range_eq_finset_sum f n]
+theorem composeYHorner_eq_zero_of_composeY {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ {Q : CBivariate F} {p : CPolynomial F}
+ (h : CBivariate.composeY Q p = 0) : CBivariate... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_a45c72ecc959_23 | 13ef13e8e9a441b6 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Root/Common/Lemmas.lean | Lemmas | 23 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "isRootYDegreeLtBool_of_root",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold isRootYDegreeLtBool\n rw [degreeLtBool_of_degreeLt hdegree, composeYHorner_eq_zero_of_composeY hroot]\n... | [
{
"name": "composeYHorner_eq_zero_of_composeY",
"text": "theorem composeYHorner_eq_zero_of_composeY {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n {Q : CBivariate F} {p : CPolynomial F}\n (h : CBivariate.composeY Q p = 0) : CBivariate.composeYHorner Q p = 0 := by\n simpa [CBivariate.composeY, CBi... | [
{
"name": "rootsYDegreeLtFromCandidates_eraseDups_complete_of_mem",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 18,
"n_chars": 806,
"n_subproofs": 3,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"... | 5 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Root.Common
import CompPoly.Bivariate.GuruswamiSudan.PolynomialCorrectness
/-!
# Common Guruswami-Sudan Root Helper ... | @@ -80,11 +80,20 @@
| n + 1 => by
rw [List.sum_range_succ, Finset.sum_range_succ, list_sum_map_range_eq_finset_sum f n]
+theorem composeYHorner_eq_zero_of_composeY {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ {Q : CBivariate F} {p : CPolynomial F}
+ (h : CBivariate.composeY Q p = 0) : CBivariate... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_17b6d6336bac_0 | 0b819a1e3fdd3ff2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ManyEval/Correctness.lean | Correctness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "size_le_foldl_max_size_of_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction polys generalizing acc with\n | nil => simp at hp\n | cons q polys ih =>\n simp only [List.... | [
{
"name": "le_foldl_max_size",
"text": "private lemma le_foldl_max_size [Zero R] (polys : List (CPolynomial R)) (acc : Nat) :\n acc ≤ polys.foldl (fun acc p ↦ Nat.max acc p.size) acc := by\n induction polys generalizing acc with\n | nil => simp\n | cons p polys ih =>\n exact (Nat.le_max_left acc ... | [
{
"name": "size_le_foldl_max_size_of_mem",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 566,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 3,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.ManyEval.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomia... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.ManyEval.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomia... | @@ -17,6 +17,13 @@
variable {R : Type*}
+private lemma le_foldl_max_size [Zero R] (polys : List (CPolynomial R)) (acc : Nat) :
+ acc ≤ polys.foldl (fun acc p ↦ Nat.max acc p.size) acc := by
+ induction polys generalizing acc with
+ | nil => simp
+ | cons p polys ih =>
+ exact (Nat.le_max_left acc p.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_17b6d6336bac_1 | c81b7c66817fb585 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ManyEval/Correctness.lean | Correctness | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "size_le_foldl_max_size_of_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction polys generalizing acc with\n | nil => simp at hp\n | cons q polys ih =>\n simp only [List.... | [
{
"name": "le_foldl_max_size",
"text": "private lemma le_foldl_max_size [Zero R] (polys : List (CPolynomial R)) (acc : Nat) :\n acc ≤ polys.foldl (fun acc p ↦ Nat.max acc p.size) acc := by\n induction polys generalizing acc with\n | nil => simp\n | cons p polys ih =>\n exact (Nat.le_max_left acc ... | [
{
"name": "size_le_maxCoeffSize_of_mem",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 314,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.ManyEval.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomia... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.ManyEval.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomia... | @@ -17,6 +17,13 @@
variable {R : Type*}
+private lemma le_foldl_max_size [Zero R] (polys : List (CPolynomial R)) (acc : Nat) :
+ acc ≤ polys.foldl (fun acc p ↦ Nat.max acc p.size) acc := by
+ induction polys generalizing acc with
+ | nil => simp
+ | cons p polys ih =>
+ exact (Nat.le_max_left acc p.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_17b6d6336bac_2 | 90e747fdc0ce7b0b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ManyEval/Correctness.lean | Correctness | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 2 | [
{
"theorem_name": "powerTable_size",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold ManyEval.powerTable\n rw [powerTableLoop_eq_foldl]\n simpa using foldl_push_size x (List.range' 0 limit) (#[] : Ar... | [
{
"name": "powerTableLoop_eq_foldl",
"text": "private lemma powerTableLoop_eq_foldl [Mul R] (x : R) (limit i : Nat) (pow : R)\n (acc : Array R) :\n ManyEval.powerTableLoop x limit i pow acc =\n (List.foldl (fun (b : Array R × R) (_ : Nat) ↦ (b.1.push b.2, b.2 * x))\n (acc, pow) (List.range... | [
{
"name": "powerTable_size",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 259,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.ManyEval.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomia... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.ManyEval.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomia... | @@ -55,8 +55,25 @@
exact _root_.mul_assoc base (x ^ offset) x
· simpa [Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hi
+private lemma powerTableLoop_eq_foldl [Mul R] (x : R) (limit i : Nat) (pow : R)
+ (acc : Array R) :
+ ManyEval.powerTableLoop x limit i pow acc =
+ (List.foldl (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_17b6d6336bac_3 | 81c93656f052d48b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ManyEval/Correctness.lean | Correctness | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 2 | [
{
"theorem_name": "powerTable_size",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold ManyEval.powerTable\n rw [powerTableLoop_eq_foldl]\n simpa using foldl_push_size x (List.range' 0 limit) (#[] : Ar... | [
{
"name": "powerTableLoop_eq_foldl",
"text": "private lemma powerTableLoop_eq_foldl [Mul R] (x : R) (limit i : Nat) (pow : R)\n (acc : Array R) :\n ManyEval.powerTableLoop x limit i pow acc =\n (List.foldl (fun (b : Array R × R) (_ : Nat) ↦ (b.1.push b.2, b.2 * x))\n (acc, pow) (List.range... | [
{
"name": "powerTable_getD_eq_pow",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 386,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.ManyEval.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomia... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.ManyEval.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomia... | @@ -55,9 +55,28 @@
exact _root_.mul_assoc base (x ^ offset) x
· simpa [Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hi
+private lemma powerTableLoop_eq_foldl [Mul R] (x : R) (limit i : Nat) (pow : R)
+ (acc : Array R) :
+ ManyEval.powerTableLoop x limit i pow acc =
+ (List.foldl (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_17b6d6336bac_4 | ee4a60c69269ca79 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ManyEval/Correctness.lean | Correctness | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "evalWithPowers_eq_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [ManyEval.evalWithPowers, Nat.min_eq_left hsize]\n rw [evalWithPowersLoop_eq_foldl_range]\n rw [Array.foldl_... | [
{
"name": "evalWithPowersLoop_eq_foldl_range",
"text": "private lemma evalWithPowersLoop_eq_foldl_range [Semiring R]\n (coeffs powers : Array R) (limit : Nat) (hcoeffs : limit ≤ coeffs.size)\n (hpowers : limit ≤ powers.size) (i : Nat) (acc : R) :\n ManyEval.evalWithPowersLoop coeffs powers limit hc... | [
{
"name": "evalWithPowers_eq_eval",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 18,
"n_chars": 685,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 5,
"n_structural": 3,
"automation_only": false,
"ma... | 3 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.ManyEval.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomia... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.ManyEval.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomia... | @@ -55,6 +55,30 @@
exact _root_.mul_assoc base (x ^ offset) x
· simpa [Nat.add_assoc, Nat.add_comm, Nat.add_left_comm] using hi
+private lemma evalWithPowersLoop_eq_foldl_range [Semiring R]
+ (coeffs powers : Array R) (limit : Nat) (hcoeffs : limit ≤ coeffs.size)
+ (hpowers : limit ≤ powers.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_17b6d6336bac_5 | e61f915005936ab0 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/ManyEval/Correctness.lean | Correctness | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "evalManySharedPowers_eq_map_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Array.toList_inj.mp\n simp only [evalManySharedPowers, evalManyWithPowersLoop_toList, Array.toList... | [
{
"name": "size_le_maxCoeffSize_of_mem",
"text": "private lemma size_le_maxCoeffSize_of_mem [Zero R]\n (polys : Array (CPolynomial R)) {p : CPolynomial R} (hp : p ∈ polys.toList) :\n p.size ≤ ManyEval.maxCoeffSize polys := by\n cases polys with\n | mk ps =>\n simpa [ManyEval.maxCoeffSize] using... | [
{
"name": "evalManySharedPowers_eq_map_eval",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 11,
"n_lines": 18,
"n_chars": 694,
"n_subproofs": 0,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 7,
"automation_only": fal... | 11 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.ManyEval.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomia... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.ManyEval.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomia... | @@ -38,6 +38,14 @@
(le_foldl_max_size polys (Nat.max acc q.size))
· exact ih (Nat.max acc q.size) hp
+private lemma size_le_maxCoeffSize_of_mem [Zero R]
+ (polys : Array (CPolynomial R)) {p : CPolynomial R} (hp : p ∈ polys.toList) :
+ p.size ≤ ManyEval.maxCoeffSize polys := by
+ cases polys w... | {
"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_12181c0117c9_0 | d69f57a6a01f901a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/PolynomialMatrix/Degree.lean | Degree | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "exists_nonzero_entry_of_rowIsZero_false",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hnot : ¬ RowIsZero row := by\n intro hz\n have htrue := (rowIsZero_iff (row := row)).2 ... | [
{
"name": "rowIsZero_iff",
"text": "/-- Boolean and propositional zero-row predicates agree. -/\ntheorem rowIsZero_iff [Zero F] [BEq F] [LawfulBEq F]\n {row : PolynomialRow F} :\n rowIsZero row = true ↔ RowIsZero row := by\n rw [rowIsZero]\n simp [RowIsZero]\n constructor\n · intro h p hp\n hav... | [
{
"name": "exists_nonzero_entry_of_rowIsZero_false",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 19,
"n_chars": 741,
"n_subproofs": 3,
"n_tactics": 14,
"cyclomatic": 3,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 4,
"automation_only... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.PolynomialMatrix.Basic
/-!
# Degree Helpers for Polynomial Rows
-/
namespace CompPoly
namespace PolynomialMatrix
variable {F... | /-
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.Basic
/-!
# Degree Helpers for Polynomial Rows
-/
namespace CompPoly
namespace PolynomialMatrix
variable {F... | @@ -28,10 +28,40 @@
def rowIsZero [Zero F] [BEq F] (row : PolynomialRow F) : Bool :=
row.all fun p ↦ p == 0
+/-- Boolean and propositional zero-row predicates agree. -/
+theorem rowIsZero_iff [Zero F] [BEq F] [LawfulBEq F]
+ {row : PolynomialRow F} :
+ rowIsZero row = true ↔ RowIsZero row := by
+ rw [rowIs... | {
"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_e6dfd169d3f9_0 | ae094bbf4cf3ecd8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Linear.lean | Linear | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 4 | [
{
"theorem_name": "zero_mem_degreeLT",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [mem_degreeLT_iff_size_le]\n exact Nat.zero_le n",
"n_chars": 57,
"n_subproofs": 0,
"n_tactics": 3,
"... | [
{
"name": "mem_degreeLT_iff_size_le",
"text": "/-- `degreeLT n` is exactly the bounded-size carrier storing at most `n` coefficients. -/\ntheorem mem_degreeLT_iff_size_le {n : ℕ} {p : CPolynomial R} :\n p ∈ degreeLT (R := R) n ↔ p.val.size ≤ n := by\n cases hs : p.val.size with\n | zero =>\n simp ... | [
{
"name": "zero_mem_degreeLT",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 207,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"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: Desmond Coles, Derek Sorensen
-/
import CompPoly.Univariate.Basic
/-!
# Linear Algebra API for Computable Univariate Polynomials
This file contains linear maps and instance-stable bounded-... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Desmond Coles, Derek Sorensen
-/
import CompPoly.Univariate.Basic
/-!
# Linear Algebra API for Computable Univariate Polynomials
This file contains linear maps and instance-stable bounded-... | @@ -41,8 +41,19 @@
def degreeLT (n : ℕ) : Set (CPolynomial R) :=
{ p | p.val.degreeBound < n }
+/-- `degreeLT n` is exactly the bounded-size carrier storing at most `n` coefficients. -/
+theorem mem_degreeLT_iff_size_le {n : ℕ} {p : CPolynomial R} :
+ p ∈ degreeLT (R := R) n ↔ p.val.size ≤ n := by
+ cases hs ... | {
"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_4ceb43656ca2_11 | 50a15e16875cee9e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/PolynomialMatrix/MuldersStorjohannCorrectness/Measure.lean | Measure | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "matrixShiftedDegreeSpecFold_row_le",
"depth": 1,
"n_commands": 0,
"n_lines": 32,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction xs generalizing acc with\n | nil =>\n cases hi\n | cons x xs ih =>\n rw [List.fol... | [
{
"name": "matrixShiftedDegreeSpecFold_acc_le",
"text": "theorem matrixShiftedDegreeSpecFold_acc_le\n {M : PolynomialMatrix F} {shift : Array Nat}\n (xs : List Nat) {acc : Option Nat} {a D : Nat}\n (hacc : acc = some a)\n (hfold : xs.foldl (matrixShiftedDegreeStep? M shift) acc = some D) :\n ... | [
{
"name": "shiftedMatrixMeasure_lt_muldersStorjohannFuel",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 12,
"n_lines": 19,
"n_chars": 713,
"n_subproofs": 3,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 3,
"automati... | 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.LinearAlgebra.PolynomialMatrix.MuldersStorjohannCorrectness.Leading
/-!
# Mulders-Storjohann Correctness Termination Measure Helpers
Measure... | /-
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.Leading
/-!
# Mulders-Storjohann Correctness Termination Measure Helpers
Measure... | @@ -60,6 +60,41 @@
rfl
omit [LawfulBEq F] [DecidableEq F] in
+theorem matrixShiftedDegreeSpecFold_acc_le
+ {M : PolynomialMatrix F} {shift : Array Nat}
+ (xs : List Nat) {acc : Option Nat} {a D : Nat}
+ (hacc : acc = some a)
+ (hfold : xs.foldl (matrixShiftedDegreeStep? M shift) acc = some D) :
+ 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_aac0e5ccd9d8_0 | 136045f7e89758b6 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multivariate/VarsDegrees.lean | VarsDegrees | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "degrees_one",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [degrees_equiv, map_one]",
"n_chars": 35,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automa... | [
{
"name": "degrees_equiv",
"text": "/-- `degrees` agrees with `MvPolynomial.degrees` via `fromCMvPolynomial`. -/\nlemma degrees_equiv [CommSemiring R] [BEq R] [LawfulBEq R]\n (p : CMvPolynomial n R) :\n p.degrees = (fromCMvPolynomial p).degrees := by\n ext i\n have hdeg : p.degreeOf i = (fromCMvPoly... | [
{
"name": "degrees_one",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 192,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fawad Haider
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import Mathlib.Algebra.MvPolynomial.Variables
/-!
# Lemmas for `CMvPolynomial.vars` and `CMvPolynomial.degrees`
Correctness le... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fawad Haider
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import Mathlib.Algebra.MvPolynomial.Variables
/-!
# Lemmas for `CMvPolynomial.vars` and `CMvPolynomial.degrees`
Correctness le... | @@ -27,6 +27,15 @@
i ∈ p.vars ↔ 0 < p.degreeOf i := by
simp [CMvPolynomial.vars]
+/-- `degrees` agrees with `MvPolynomial.degrees` via `fromCMvPolynomial`. -/
+lemma degrees_equiv [CommSemiring R] [BEq R] [LawfulBEq R]
+ (p : CMvPolynomial n R) :
+ p.degrees = (fromCMvPolynomial p).degrees := by
+ ext ... | {
"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_aac0e5ccd9d8_1 | 520ee38dea1f952d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multivariate/VarsDegrees.lean | VarsDegrees | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "vars_add_subset",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [vars_equiv (p := p + q), vars_equiv (p := p), vars_equiv (p := q)]\n simpa [map_add] using\n (MvPolynomial.vars_add... | [
{
"name": "vars_equiv",
"text": "/-- `vars` agrees with `MvPolynomial.vars` via `fromCMvPolynomial`. -/\nlemma vars_equiv [CommSemiring R] [BEq R] [LawfulBEq R]\n (p : CMvPolynomial n R) :\n p.vars = (fromCMvPolynomial p).vars := by\n ext i\n rw [mem_vars_iff_degreeOf_pos]\n have hdeg : p.degreeOf ... | [
{
"name": "vars_add_subset",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 360,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fawad Haider
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import Mathlib.Algebra.MvPolynomial.Variables
/-!
# Lemmas for `CMvPolynomial.vars` and `CMvPolynomial.degrees`
Correctness le... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Fawad Haider
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import Mathlib.Algebra.MvPolynomial.Variables
/-!
# Lemmas for `CMvPolynomial.vars` and `CMvPolynomial.degrees`
Correctness le... | @@ -36,6 +36,18 @@
congrFun (degreeOf_equiv (S := R) (p := p)) i
simpa [degreeOf_eq_count_degrees, MvPolynomial.degreeOf_def] using hdeg
+/-- `vars` agrees with `MvPolynomial.vars` via `fromCMvPolynomial`. -/
+lemma vars_equiv [CommSemiring R] [BEq R] [LawfulBEq R]
+ (p : CMvPolynomial n R) :
+ p.vars =... | {
"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_f6ddced5cb72_2 | 14be96d08e734f68 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/PolynomialMatrix/MuldersStorjohannCorrectness/RowOps.lean | RowOps | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 7 | [
{
"theorem_name": "rowGet_rowSub",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [rowSub, rowGet_rowAdd, rowGet_rowNeg, sub_eq_add_neg]",
"n_chars": 65,
"n_subproofs": 0,
"n_tactics": 2,
... | [
{
"name": "rowGet_rowAdd",
"text": "theorem rowGet_rowAdd (a b : PolynomialRow F) (j : Nat) :\n rowGet (rowAdd a b) j = rowGet a j + rowGet b j := by\n by_cases hj : j < (rowAdd a b).size\n · rw [rowGet, Array.getD_eq_getD_getElem?, Array.getElem?_eq_getElem hj]\n simp [rowAdd, rowGet] at hj ⊢\n · ... | [
{
"name": "rowGet_rowSub",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 179,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": ... | 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.MuldersStorjohann
import CompPoly.Univariate.ToPoly.Impl
/-!
# Mulders-Storjohann Correctness Row and Row-Span... | /-
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.MuldersStorjohann
import CompPoly.Univariate.ToPoly.Impl
/-!
# Mulders-Storjohann Correctness Row and Row-Span... | @@ -20,6 +20,20 @@
variable {F : Type*} [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]
omit [DecidableEq F] in
+theorem rowGet_rowAdd (a b : PolynomialRow F) (j : Nat) :
+ rowGet (rowAdd a b) j = rowGet a j + rowGet b j := by
+ by_cases hj : j < (rowAdd a b).size
+ · rw [rowGet, Array.getD_eq_getD_getElem?, 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_f6ddced5cb72_18 | cc4186d1678674e5 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/PolynomialMatrix/MuldersStorjohannCorrectness/RowOps.lean | RowOps | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 1 | [
{
"theorem_name": "rowScalePolynomial_rowLinearCombination_range",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro n\n induction n with\n | zero =>\n simp [rowScalePolynomial_zeroRow]\n | succ ... | [
{
"name": "rowScalePolynomial_zeroRow",
"text": "theorem rowScalePolynomial_zeroRow (c : CPolynomial F) (width : Nat) :\n rowScalePolynomial c (zeroRow (F := F) width) = zeroRow width := by\n apply Array.ext\n · simp [rowScalePolynomial, zeroRow]\n · intro j hj₁ hj₂\n simp [rowScalePolynomial, zero... | [
{
"name": "rowScalePolynomial_mem_rowSpan",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 9,
"n_chars": 347,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
... | 6 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.PolynomialMatrix.MuldersStorjohann
import CompPoly.Univariate.ToPoly.Impl
/-!
# Mulders-Storjohann Correctness Row and Row-Span... | /-
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.MuldersStorjohann
import CompPoly.Univariate.ToPoly.Impl
/-!
# Mulders-Storjohann Correctness Row and Row-Span... | @@ -20,6 +20,14 @@
variable {F : Type*} [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]
omit [DecidableEq F] in
+theorem rowScalePolynomial_zeroRow (c : CPolynomial F) (width : Nat) :
+ rowScalePolynomial c (zeroRow (F := F) width) = zeroRow width := by
+ apply Array.ext
+ · simp [rowScalePolynomial, zeroRow]
... | {
"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_f6ddced5cb72_22 | 96648e72f3f89b52 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/PolynomialMatrix/MuldersStorjohannCorrectness/RowOps.lean | RowOps | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 32 | 7 | [
{
"theorem_name": "rowGet_rowSub",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [rowSub, rowGet_rowAdd, rowGet_rowNeg, sub_eq_add_neg]",
"n_chars": 65,
"n_subproofs": 0,
"n_tactics": 2,
... | [
{
"name": "rowGet_rowAdd",
"text": "theorem rowGet_rowAdd (a b : PolynomialRow F) (j : Nat) :\n rowGet (rowAdd a b) j = rowGet a j + rowGet b j := by\n by_cases hj : j < (rowAdd a b).size\n · rw [rowGet, Array.getD_eq_getD_getElem?, Array.getElem?_eq_getElem hj]\n simp [rowAdd, rowGet] at hj ⊢\n · ... | [
{
"name": "cancelShiftedLeadingTerm_mem_rowSpan",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 22,
"n_lines": 12,
"n_chars": 474,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 10,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 2,
"automation_only"... | 22 | /-
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.MuldersStorjohann
import CompPoly.Univariate.ToPoly.Impl
/-!
# Mulders-Storjohann Correctness Row and Row-Span... | /-
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.MuldersStorjohann
import CompPoly.Univariate.ToPoly.Impl
/-!
# Mulders-Storjohann Correctness Row and Row-Span... | @@ -20,6 +20,20 @@
variable {F : Type*} [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]
omit [DecidableEq F] in
+theorem rowGet_rowAdd (a b : PolynomialRow F) (j : Nat) :
+ rowGet (rowAdd a b) j = rowGet a j + rowGet b j := by
+ by_cases hj : j < (rowAdd a b).size
+ · rw [rowGet, Array.getD_eq_getD_getElem?, 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_3a129ab4328d_0 | a68684a81a42b03f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/KoalaBear/Fast.lean | Fast | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 8 | [
{
"theorem_name": "montgomeryReduceNat_cast",
"depth": 1,
"n_commands": 0,
"n_lines": 44,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let m := x % UInt32.size * montgomeryNegInv.toNat % UInt32.size\n let u := (x + m * KoalaBear.fieldSize) / UInt3... | [
{
"name": "uint32Size_ne_zero_in_field",
"text": "private theorem uint32Size_ne_zero_in_field :\n (UInt32.size : KoalaBear.Field) ≠ 0 := by\n decide\n\n",
"fan_in": 8,
"n_lines": 5,
"n_chars": 104,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_r... | [
{
"name": "montgomeryReduceNat_cast",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 48,
"n_chars": 2037,
"n_subproofs": 7,
"n_tactics": 44,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 9,
"n_structural": 5,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | /-
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.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | @@ -84,6 +84,10 @@
(r2ModModulus.toNat : KoalaBear.Field) = (UInt32.size : KoalaBear.Field) ^ 2 := by
decide
+private theorem uint32Size_ne_zero_in_field :
+ (UInt32.size : KoalaBear.Field) ≠ 0 := by
+ decide
+
private theorem montgomery_sum_dvd (x : Nat) :
UInt32.size ∣
x + ((x % UInt32.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_3a129ab4328d_1 | 6cd6dd43b4fd7776 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/KoalaBear/Fast.lean | Fast | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 2 | [
{
"theorem_name": "montgomery_u_lt_two_fieldSize",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [montgomery_u_eq_nat x h]\n let mNat := x.toNat % UInt32.size * montgomeryNegInv.toNat % UInt32.size\n ... | [
{
"name": "montgomery_u_eq_nat",
"text": "private theorem montgomery_u_eq_nat (x : UInt64)\n (h : x.toNat < KoalaBear.fieldSize * UInt32.size) :\n (let m : UInt32 := x.toUInt32 * montgomeryNegInv\n (((x + m.toUInt64 * modulus64) >>> 32).toUInt32).toNat) =\n (x.toNat + ((x.toNat % UInt32.size ... | [
{
"name": "montgomery_u_lt_two_fieldSize",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 19,
"n_chars": 869,
"n_subproofs": 3,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | /-
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.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | @@ -195,11 +195,46 @@
rw [← hfield]
simpa only [m, u, hu, if_false] using hmr
+private theorem montgomery_u_eq_nat (x : UInt64)
+ (h : x.toNat < KoalaBear.fieldSize * UInt32.size) :
+ (let m : UInt32 := x.toUInt32 * montgomeryNegInv
+ (((x + m.toUInt64 * modulus64) >>> 32).toUInt32).toNat) =
+ ... | {
"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_3a129ab4328d_2 | 9401a3fc46c51b90 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/KoalaBear/Fast.lean | Fast | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "montgomeryQuotient_cast",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let m := x % UInt32.size * montgomeryNegInv.toNat % UInt32.size\n let u := (x + m * KoalaBear.fieldSize) / UInt32... | [
{
"name": "montgomeryReduceNat_cast",
"text": "private theorem montgomeryReduceNat_cast (x : Nat) :\n (montgomeryReduceNat x : KoalaBear.Field) =\n (x : KoalaBear.Field) * (UInt32.size : KoalaBear.Field)⁻¹ := by\n let m := x % UInt32.size * montgomeryNegInv.toNat % UInt32.size\n let u := (x + m * ... | [
{
"name": "toField_eq_raw_mul_inv",
"fan_in": 10,
"n_deps_direct": 2,
"n_deps_transitive": 11,
"n_lines": 15,
"n_chars": 709,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 6,
"n_structural": 0,
"automation_only": false,
"... | 8 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | /-
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.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | @@ -128,11 +128,72 @@
let u := (x + m * KoalaBear.fieldSize) / UInt32.size
if u < KoalaBear.fieldSize then u else u - KoalaBear.fieldSize
+private theorem montgomeryReduceNat_cast (x : Nat) :
+ (montgomeryReduceNat x : KoalaBear.Field) =
+ (x : KoalaBear.Field) * (UInt32.size : KoalaBear.Field)⁻¹ := 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_3a129ab4328d_3 | edf5c01c6d19ed58 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/KoalaBear/Fast.lean | Fast | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 2 | [
{
"theorem_name": "montgomeryReduceBoundedRaw_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold montgomeryReduceBoundedRaw\n exact reduceUInt32Lt2ModulusRaw_lt _\n (montgomery_u_lt_two_fieldSize... | [
{
"name": "montgomery_u_lt_two_fieldSize",
"text": "private theorem montgomery_u_lt_two_fieldSize (x : UInt64)\n (h : x.toNat < KoalaBear.fieldSize * UInt32.size) :\n (let m : UInt32 := x.toUInt32 * montgomeryNegInv\n (((x + m.toUInt64 * modulus64) >>> 32).toUInt32).toNat) <\n 2 * KoalaBear.f... | [
{
"name": "raw_cast_eq_toField_mul",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 12,
"n_lines": 9,
"n_chars": 264,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 4,
"n_structural": 0,
"automation_only": false,
"ma... | 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.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | /-
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.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | @@ -218,6 +218,24 @@
· exact hsum_lt
· decide
+private theorem montgomery_u_lt_two_fieldSize (x : UInt64)
+ (h : x.toNat < KoalaBear.fieldSize * UInt32.size) :
+ (let m : UInt32 := x.toUInt32 * montgomeryNegInv
+ (((x + m.toUInt64 * modulus64) >>> 32).toUInt32).toNat) <
+ 2 * KoalaBear.fieldSize ... | {
"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_3a129ab4328d_4 | 483832bc01abf921 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/KoalaBear/Fast.lean | Fast | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 1 | [
{
"theorem_name": "montgomeryReduceNat_cast",
"depth": 1,
"n_commands": 0,
"n_lines": 44,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let m := x % UInt32.size * montgomeryNegInv.toNat % UInt32.size\n let u := (x + m * KoalaBear.fieldSize) / UInt3... | [
{
"name": "montgomery_sum_dvd",
"text": "private theorem montgomery_sum_dvd (x : Nat) :\n UInt32.size ∣\n x + ((x % UInt32.size * montgomeryNegInv.toNat) % UInt32.size) * KoalaBear.fieldSize := by\n rw [← Nat.modEq_zero_iff_dvd]\n have hx : x ≡ x % UInt32.size [MOD UInt32.size] :=\n (Nat.mod_mo... | [
{
"name": "ofCanonicalNat_raw_cast",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 15,
"n_lines": 41,
"n_chars": 1997,
"n_subproofs": 5,
"n_tactics": 37,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 15,
"n_structural": 4,
"automation_only": false,
... | 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.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | /-
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.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | @@ -88,6 +88,40 @@
(UInt32.size : KoalaBear.Field) ≠ 0 := by
decide
+private theorem montgomery_sum_dvd (x : Nat) :
+ UInt32.size ∣
+ x + ((x % UInt32.size * montgomeryNegInv.toNat) % UInt32.size) * KoalaBear.fieldSize := by
+ rw [← Nat.modEq_zero_iff_dvd]
+ have hx : x ≡ x % UInt32.size [MOD UInt32... | {
"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_3a129ab4328d_5 | c93ee6f21de5a4a0 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/KoalaBear/Fast.lean | Fast | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 2 | [
{
"theorem_name": "montgomeryReduceBounded_cast",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n change ((montgomeryReduceBoundedRaw x).toNat : KoalaBear.Field) =\n (x.toNat : KoalaBear.Field) * (UInt3... | [
{
"name": "reduceUInt32Lt2Modulus_cast",
"text": "private theorem reduceUInt32Lt2Modulus_cast (x : UInt32)\n (h : x.toNat < 2 * KoalaBear.fieldSize) :\n ((reduceUInt32Lt2Modulus x h).val.toNat : KoalaBear.Field) =\n (x.toNat : KoalaBear.Field) := by\n change ((reduceUInt32Lt2ModulusRaw x).toNat ... | [
{
"name": "toNat_ofCanonicalNat",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 22,
"n_lines": 7,
"n_chars": 293,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_n... | 14 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | /-
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.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | @@ -263,6 +263,26 @@
Field :=
⟨reduceUInt32Lt2ModulusRaw x, reduceUInt32Lt2ModulusRaw_lt x h⟩
+private theorem reduceUInt32Lt2Modulus_cast (x : UInt32)
+ (h : x.toNat < 2 * KoalaBear.fieldSize) :
+ ((reduceUInt32Lt2Modulus x h).val.toNat : KoalaBear.Field) =
+ (x.toNat : KoalaBear.Field) := by
+ 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_3a129ab4328d_6 | 87e2813491eab52e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/KoalaBear/Fast.lean | Fast | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 4 | [
{
"theorem_name": "toField_eq_raw_mul_inv",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold toField toNat toCanonicalUInt32 raw\n have hred := montgomeryReduceBounded_cast x.val.toUInt64 (by\n rw ... | [
{
"name": "montgomeryReduceBounded_cast",
"text": "private theorem montgomeryReduceBounded_cast (x : UInt64)\n (h : x.toNat < KoalaBear.fieldSize * UInt32.size) :\n ((montgomeryReduceBounded x h).val.toNat : KoalaBear.Field) =\n (x.toNat : KoalaBear.Field) * (UInt32.size : KoalaBear.Field)⁻¹ := b... | [
{
"name": "pow_succ",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 26,
"n_lines": 9,
"n_chars": 213,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting": 4
... | 16 | /-
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.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | /-
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.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | @@ -334,6 +334,29 @@
(h : x.toNat < KoalaBear.fieldSize * UInt32.size) : Field :=
⟨montgomeryReduceBoundedRaw x, montgomeryReduceBoundedRaw_lt x h⟩
+private theorem montgomeryReduceBounded_cast (x : UInt64)
+ (h : x.toNat < KoalaBear.fieldSize * UInt32.size) :
+ ((montgomeryReduceBounded x h).val.toNat ... | {
"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_3a129ab4328d_7 | 5521f6bec9c6ec1c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/KoalaBear/Fast.lean | Fast | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 29 | 10 | [
{
"theorem_name": "raw_cast_eq_toField_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [toField_eq_raw_mul_inv]\n rw [mul_assoc]\n rw [inv_mul_cancel₀ uint32Size_ne_zero_in_field]\n rw [mul_one]",... | [
{
"name": "toField_eq_raw_mul_inv",
"text": "private theorem toField_eq_raw_mul_inv (x : Field) :\n toField x =\n (x.val.toNat : KoalaBear.Field) * (UInt32.size : KoalaBear.Field)⁻¹ := by\n unfold toField toNat toCanonicalUInt32 raw\n have hred := montgomeryReduceBounded_cast x.val.toUInt64 (by\n ... | [
{
"name": "toField_zpow",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 37,
"n_lines": 16,
"n_chars": 602,
"n_subproofs": 1,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 6,
"n_structural": 2,
"automation_only": false,
"max_nesting... | 25 | /-
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.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | /-
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.Fields.KoalaBear.Basic
import Mathlib.Algebra.Field.TransferInstance
import Mathlib.Data.Nat.ModEq
/-!
# Fast KoalaBear Field Operations
Thi... | @@ -442,9 +442,27 @@
rw [UInt32.toNat_toUInt64]
nlinarith [x.property, fieldSize_pos])
+private theorem toField_eq_raw_mul_inv (x : Field) :
+ toField x =
+ (x.val.toNat : KoalaBear.Field) * (UInt32.size : KoalaBear.Field)⁻¹ := by
+ unfold toField toNat toCanonicalUInt32 raw
+ have hred := montgom... | {
"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_0d00315d95db_0 | 6226c965e5b712e4 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 2 | [
{
"theorem_name": "ENNReal.coe_div_of_NNRat",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [ENNReal.coe_NNRat_coe_NNReal, ENNReal.coe_NNRat_coe_NNReal]\n rw [←ENNReal.coe_div (hr := by\n simp only [... | [
{
"name": "ENNReal.coe_NNRat_coe_NNReal",
"text": "lemma ENNReal.coe_NNRat_coe_NNReal (x : ℚ≥0) : (x : ENNReal) = ((x : ℝ≥0) : ENNReal) := by rfl\n-- We can use `NNRat.cast_div` or so after `ENNReal.coe_NNRat_coe_NNReal`\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 178,
"n_subproofs": 0,
... | [
{
"name": "ENNReal.coe_div_of_NNRat",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 359,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 0,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -49,8 +49,16 @@
-- lemma ENNReal.div_lt_div_right (hc₀ : c ≠ 0) (hc : c ≠ ∞) (hab : a < b) : a / c < b / c :=
-- (ENNReal.div_lt_div_iff_left hc₀ hc).2 hab
+lemma ENNReal.coe_NNRat_coe_NNReal (x : ℚ≥0) : (x : ENNReal) = ((x : ℝ≥0) : ENNReal) := by rfl
+-- We can use `NNRat.cast_div` or so after `ENNReal.coe_NN... | {
"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_0d00315d95db_1 | 1276a3a8b7b2700c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 2 | [
{
"theorem_name": "ENNReal.coe_div_of_NNRat",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [ENNReal.coe_NNRat_coe_NNReal, ENNReal.coe_NNRat_coe_NNReal]\n rw [←ENNReal.coe_div (hr := by\n simp only [... | [
{
"name": "ENNReal.coe_NNRat_coe_NNReal",
"text": "lemma ENNReal.coe_NNRat_coe_NNReal (x : ℚ≥0) : (x : ENNReal) = ((x : ℝ≥0) : ENNReal) := by rfl\n-- We can use `NNRat.cast_div` or so after `ENNReal.coe_NNRat_coe_NNReal`\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 178,
"n_subproofs": 0,
... | [
{
"name": "ENNReal.coe_NNRat_eq_coe_NNRat",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 435,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,
... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -49,10 +49,17 @@
-- lemma ENNReal.div_lt_div_right (hc₀ : c ≠ 0) (hc : c ≠ ∞) (hab : a < b) : a / c < b / c :=
-- (ENNReal.div_lt_div_iff_left hc₀ hc).2 hab
+lemma ENNReal.coe_NNRat_coe_NNReal (x : ℚ≥0) : (x : ENNReal) = ((x : ℝ≥0) : ENNReal) := by rfl
+-- We can use `NNRat.cast_div` or so after `ENNReal.coe_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_0d00315d95db_2 | f95f98d762e5fb29 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 4 | [
{
"theorem_name": "getBit_eq_testBit",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold getBit\n rw [Nat.testBit]\n simp only [and_one_is_mod, one_and_eq_mod_two, mod_two_bne_zero, beq_iff_eq]\n if ... | [
{
"name": "getBit_lt_2",
"text": "lemma getBit_lt_2 {k n : Nat} : getBit k n < 2 := by\n unfold getBit\n rw [Nat.and_one_is_mod]\n simp only [Nat.ofNat_pos, Nat.mod_lt]\n\n",
"fan_in": 4,
"n_lines": 6,
"n_chars": 136,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_autom... | [
{
"name": "getBit_eq_testBit",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 450,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -82,6 +82,11 @@
-- #eval Nat.popCount 13
+lemma getBit_lt_2 {k n : Nat} : getBit k n < 2 := by
+ unfold getBit
+ rw [Nat.and_one_is_mod]
+ simp only [Nat.ofNat_pos, Nat.mod_lt]
+
lemma getBit_eq_testBit (k n : Nat) : getBit k n = if n.testBit k then 1 else 0 := by
unfold getBit
rw [Nat.testBit]
@@ -90... | {
"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_0d00315d95db_3 | 848205c1032b3756 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 4 | [
{
"theorem_name": "getLowBits_lt_two_pow",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [getLowBits_eq_mod_two_pow]\n omega",
"n_chars": 44,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomati... | [
{
"name": "getLowBits_eq_mod_two_pow",
"text": "lemma getLowBits_eq_mod_two_pow {numLowBits : ℕ} (n : ℕ) :\n getLowBits numLowBits n = n % (2 ^ numLowBits) := by\n unfold getLowBits\n rw [Nat.shiftLeft_eq, one_mul]\n exact Nat.and_two_pow_sub_one_eq_mod n numLowBits\n\n",
"fan_in": 4,
"n_lines... | [
{
"name": "getLowBits_lt_two_pow",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 152,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -102,8 +102,16 @@
/-- Get the `numLowBits` least significant bits of `n`. -/
def getLowBits (numLowBits : ℕ) (n : ℕ) := n &&& ((1 <<< numLowBits) - 1)
+lemma getLowBits_eq_mod_two_pow {numLowBits : ℕ} (n : ℕ) :
+ getLowBits numLowBits n = n % (2 ^ numLowBits) := by
+ unfold getLowBits
+ rw [Nat.shiftLeft_eq... | {
"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_0d00315d95db_4 | 34febb9ce4f74b2f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 4 | [
{
"theorem_name": "getLowBits_lt_two_pow",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [getLowBits_eq_mod_two_pow]\n omega",
"n_chars": 44,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomati... | [
{
"name": "getLowBits_eq_mod_two_pow",
"text": "lemma getLowBits_eq_mod_two_pow {numLowBits : ℕ} (n : ℕ) :\n getLowBits numLowBits n = n % (2 ^ numLowBits) := by\n unfold getLowBits\n rw [Nat.shiftLeft_eq, one_mul]\n exact Nat.and_two_pow_sub_one_eq_mod n numLowBits\n\n",
"fan_in": 4,
"n_lines... | [
{
"name": "getLowBits_le_self",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -102,8 +102,16 @@
/-- Get the `numLowBits` least significant bits of `n`. -/
def getLowBits (numLowBits : ℕ) (n : ℕ) := n &&& ((1 <<< numLowBits) - 1)
-lemma getLowBits_le_self {n : ℕ} (numLowBits : ℕ) : getLowBits numLowBits n ≤ n := sorry
+lemma getLowBits_eq_mod_two_pow {numLowBits : ℕ} (n : ℕ) :
+ getLowB... | {
"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_0d00315d95db_5 | 340ddfdb957aff5d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 6 | [
{
"theorem_name": "and_eq_zero_iff_and_each_getBit_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h_and_zero k\n have h_k := shiftRight_and_one_distrib (n := n) (m := m) ... | [
{
"name": "eq_iff_eq_all_getBits",
"text": "lemma eq_iff_eq_all_getBits {n m : ℕ} : n = m ↔ ∀ k, getBit k n = getBit k m := by\n unfold getBit\n constructor\n · intro h_eq k -- h_eq : n = m\n rw [h_eq]\n · intro h_all_getBits -- h_all_getBits : ∀ k, (n >>> k) &&& 1 = (m >>> k) &&& 1\n apply Nat.eq... | [
{
"name": "and_eq_zero_iff_and_each_getBit_eq_zero",
"fan_in": 5,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 20,
"n_chars": 747,
"n_subproofs": 2,
"n_tactics": 16,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 6,
"n_structural": 7,
"automation_only... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -102,6 +102,18 @@
/-- Get the `numLowBits` least significant bits of `n`. -/
def getLowBits (numLowBits : ℕ) (n : ℕ) := n &&& ((1 <<< numLowBits) - 1)
+lemma eq_iff_eq_all_getBits {n m : ℕ} : n = m ↔ ∀ k, getBit k n = getBit k m := by
+ unfold getBit
+ constructor
+ · intro h_eq k -- h_eq : n = m
+ rw [h_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_0d00315d95db_6 | 2fe30b30fd11db26 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 3 | [
{
"theorem_name": "ge_two_pow_of_getBit_1",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Nat.getBit_eq_testBit] at h_getBit\n simp only [ite_eq_left_iff, Bool.not_eq_true, zero_ne_one, imp_false,\n ... | [
{
"name": "getBit_eq_testBit",
"text": "lemma getBit_eq_testBit (k n : Nat) : getBit k n = if n.testBit k then 1 else 0 := by\n unfold getBit\n rw [Nat.testBit]\n simp only [and_one_is_mod, one_and_eq_mod_two, mod_two_bne_zero, beq_iff_eq]\n if h: (n >>> k) % 2 = 1 then\n simp only [h, ↓reduceIte]\n ... | [
{
"name": "ge_two_pow_of_getBit_1",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 325,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"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: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -87,6 +87,18 @@
rw [Nat.and_one_is_mod]
simp only [Nat.ofNat_pos, Nat.mod_lt]
+lemma getBit_eq_testBit (k n : Nat) : getBit k n = if n.testBit k then 1 else 0 := by
+ unfold getBit
+ rw [Nat.testBit]
+ simp only [and_one_is_mod, one_and_eq_mod_two, mod_two_bne_zero, beq_iff_eq]
+ if h: (n >>> k) % 2 = 1 ... | {
"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_0d00315d95db_7 | f66575e979978df8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 2 | [
{
"theorem_name": "exists_ge_and_getBit_1_of_ge_two_pow",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let res := Nat.exists_ge_and_testBit_of_ge_two_pow (x := x) (n := n) (p := p)\n simp only [Nat.testBi... | [
{
"name": "testBit_true_eq_getBit_eq_1",
"text": "lemma testBit_true_eq_getBit_eq_1 (k n : Nat) : n.testBit k = ((Nat.getBit k n) = 1) := by\n unfold getBit\n rw [Nat.testBit]\n simp only [one_and_eq_mod_two, mod_two_bne_zero, beq_iff_eq, and_one_is_mod]\n\n",
"fan_in": 2,
"n_lines": 6,
"n_ch... | [
{
"name": "exists_ge_and_getBit_1_of_ge_two_pow",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 277,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": fa... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -78,6 +78,11 @@
-/
def getBit (k n : Nat) : Nat := (n >>> k) &&& 1
+lemma testBit_true_eq_getBit_eq_1 (k n : Nat) : n.testBit k = ((Nat.getBit k n) = 1) := by
+ unfold getBit
+ rw [Nat.testBit]
+ simp only [one_and_eq_mod_two, mod_two_bne_zero, beq_iff_eq, and_one_is_mod]
+
def popCount (n : Nat) := (Nat.dig... | {
"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_0d00315d95db_8 | f306ed22d1b1549e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 3 | [
{
"theorem_name": "ge_two_pow_of_getBit_1",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Nat.getBit_eq_testBit] at h_getBit\n simp only [ite_eq_left_iff, Bool.not_eq_true, zero_ne_one, imp_false,\n ... | [
{
"name": "getBit_eq_testBit",
"text": "lemma getBit_eq_testBit (k n : Nat) : getBit k n = if n.testBit k then 1 else 0 := by\n unfold getBit\n rw [Nat.testBit]\n simp only [and_one_is_mod, one_and_eq_mod_two, mod_two_bne_zero, beq_iff_eq]\n if h: (n >>> k) % 2 = 1 then\n simp only [h, ↓reduceIte]\n ... | [
{
"name": "getBit_1_of_ge_two_pow_and_lt_two_pow_succ",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 17,
"n_chars": 792,
"n_subproofs": 3,
"n_tactics": 18,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 6,
"automation_o... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -92,6 +92,18 @@
rw [Nat.and_one_is_mod]
simp only [Nat.ofNat_pos, Nat.mod_lt]
+lemma getBit_eq_testBit (k n : Nat) : getBit k n = if n.testBit k then 1 else 0 := by
+ unfold getBit
+ rw [Nat.testBit]
+ simp only [and_one_is_mod, one_and_eq_mod_two, mod_two_bne_zero, beq_iff_eq]
+ if h: (n >>> k) % 2 = 1 ... | {
"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_0d00315d95db_9 | 0076300e8e09448c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "and_two_pow_eq_zero_of_getBit_0",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply and_eq_zero_iff_and_each_getBit_eq_zero.mpr\n intro k\n have h_getBit_two_pow := getBit_two_pow (i... | [
{
"name": "and_eq_zero_iff_and_each_getBit_eq_zero",
"text": "lemma and_eq_zero_iff_and_each_getBit_eq_zero {n m : ℕ} :\n n &&& m = 0 ↔ ∀ k, Nat.getBit k n &&& Nat.getBit k m = 0 := by\n constructor\n · intro h_and_zero k\n have h_k := shiftRight_and_one_distrib (n := n) (m := m) (k := k)\n rw [←... | [
{
"name": "and_two_pow_eq_zero_of_getBit_0",
"fan_in": 3,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 17,
"n_chars": 591,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 5,
"n_structural": 2,
"automation_only": false... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -125,6 +125,25 @@
rw [Nat.and_assoc (y := m >>> k) (z := 1), Nat.and_comm (x := m>>>k) (y := 1), ←Nat.and_assoc]
rw [Nat.and_assoc]
+lemma and_eq_zero_iff_and_each_getBit_eq_zero {n m : ℕ} :
+ n &&& m = 0 ↔ ∀ k, Nat.getBit k n &&& Nat.getBit k m = 0 := by
+ constructor
+ · intro h_and_zero k
+ ha... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_0d00315d95db_10 | 8eede77f1edabbfa | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "and_two_pow_eq_zero_of_getBit_0",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply and_eq_zero_iff_and_each_getBit_eq_zero.mpr\n intro k\n have h_getBit_two_pow := getBit_two_pow (i... | [
{
"name": "getBit_two_pow",
"text": "lemma getBit_two_pow {i k : ℕ} : (getBit k (2^i) = if i == k then 1 else 0) := by\n have h_two_pow_i: 2^i = 1 <<< i := by\n simp only [Nat.shiftLeft_eq, one_mul]\n rw [getBit, h_two_pow_i]\n if h_i_eq_k: i = k then\n rw [h_i_eq_k.symm]\n simp only [Nat.and_on... | [
{
"name": "and_two_pow_eq_two_pow_of_getBit_eq_one",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 21,
"n_chars": 934,
"n_subproofs": 1,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 9,
"n_structural": 2,
"automation_only... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -144,8 +144,76 @@
rw [h_forall_k_eq k]
rw [Nat.zero_shiftRight, Nat.zero_and]
+lemma getBit_two_pow {i k : ℕ} : (getBit k (2^i) = if i == k then 1 else 0) := by
+ have h_two_pow_i: 2^i = 1 <<< i := by
+ simp only [Nat.shiftLeft_eq, one_mul]
+ rw [getBit, h_two_pow_i]
+ if h_i_eq_k: i = k then
+ ... | {
"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_0d00315d95db_11 | b41ef89577f1f4a8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 3 | [
{
"theorem_name": "and_by_split_lowBits",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by -- main tool : Nat.div_add_mod /2\n rw [h_n, h_m]\n -- ⊢ (n1 * 2 + bn) &&& (m1 * 2 + bm) = (n1 &&& m1) * 2 + (bn &&& b... | [
{
"name": "div_2_form",
"text": "lemma div_2_form {nD2 b : ℕ} (h_b : b < 2) :\n (nD2 * 2 + b) / 2 = nD2 := by\n omega\n\n",
"fan_in": 3,
"n_lines": 5,
"n_chars": 90,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural":... | [
{
"name": "and_by_split_lowBits",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 30,
"n_chars": 1738,
"n_subproofs": 6,
"n_tactics": 29,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 10,
"n_structural": 2,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -144,13 +144,17 @@
rw [h_forall_k_eq k]
rw [Nat.zero_shiftRight, Nat.zero_and]
+lemma div_2_form {nD2 b : ℕ} (h_b : b < 2) :
+ (nD2 * 2 + b) / 2 = nD2 := by
+ omega
+
lemma and_by_split_lowBits {n m n1 m1 bn bm : ℕ} (h_bn : bn < 2) (h_bm : bm < 2)
(h_n : n = n1 * 2 + bn) (h_m : m = m1 * 2 + bm)... | {
"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_0d00315d95db_12 | a172b285a71698b1 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 1 | [
{
"theorem_name": "sum_eq_xor_plus_twice_and",
"depth": 1,
"n_commands": 0,
"n_lines": 135,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n using Nat.binaryRec with\n | zero =>\n intro m\n rw [zero_add, Nat.zero_and, mul_zero, add_z... | [
{
"name": "and_by_split_lowBits",
"text": "lemma and_by_split_lowBits {n m n1 m1 bn bm : ℕ} (h_bn : bn < 2) (h_bm : bm < 2)\n (h_n : n = n1 * 2 + bn) (h_m : m = m1 * 2 + bm) :\n n &&& m = (n1 &&& m1) * 2 + (bn &&& bm) := by -- main tool : Nat.div_add_mod /2\n rw [h_n, h_m]\n -- ⊢ (n1 * 2 + bn) &&& (... | [
{
"name": "sum_eq_xor_plus_twice_and",
"fan_in": 5,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 137,
"n_chars": 5918,
"n_subproofs": 24,
"n_tactics": 155,
"cyclomatic": 2,
"n_automation": 24,
"n_rewrites": 34,
"n_structural": 25,
"automation_only": fals... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -148,6 +148,35 @@
(nD2 * 2 + b) / 2 = nD2 := by
omega
+lemma and_by_split_lowBits {n m n1 m1 bn bm : ℕ} (h_bn : bn < 2) (h_bm : bm < 2)
+ (h_n : n = n1 * 2 + bn) (h_m : m = m1 * 2 + bm) :
+ n &&& m = (n1 &&& m1) * 2 + (bn &&& bm) := by -- main tool : Nat.div_add_mod /2
+ rw [h_n, h_m]
+ -- ⊢ (n1 * ... | {
"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_0d00315d95db_13 | d46b1f4f33df655d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "add_shiftRight_distrib",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [sum_eq_xor_plus_twice_and, h_and_zero, mul_zero, add_zero]\n conv =>\n rhs\n rw [sum_eq_xor_plus_twice_an... | [
{
"name": "sum_eq_xor_plus_twice_and",
"text": "lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (n &&& m) := by\n induction n using Nat.binaryRec with\n | zero =>\n intro m\n rw [zero_add, Nat.zero_and, mul_zero, add_zero, Nat.zero_xor]\n | bit bn n2 ih =>\n intro m\... | [
{
"name": "add_shiftRight_distrib",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 11,
"n_chars": 378,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 6,
"n_structural": 0,
"automation_only": false,
"max... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -239,8 +239,151 @@
rw [h_result]
rw [←Nat.div_add_mod ((n1 * 2 + bn) ||| (m1 * 2 + bm)) 2, h_div_eq, h_mod_eq, Nat.div_add_mod]
+lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (n &&& m) := by
+ induction n using Nat.binaryRec with
+ | zero =>
+ intro m
+ rw [zero_add, ... | {
"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_0d00315d95db_14 | adcf9eae46d2cb38 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "add_shiftRight_distrib",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [sum_eq_xor_plus_twice_and, h_and_zero, mul_zero, add_zero]\n conv =>\n rhs\n rw [sum_eq_xor_plus_twice_an... | [
{
"name": "sum_eq_xor_plus_twice_and",
"text": "lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (n &&& m) := by\n induction n using Nat.binaryRec with\n | zero =>\n intro m\n rw [zero_add, Nat.zero_and, mul_zero, add_zero, Nat.zero_xor]\n | bit bn n2 ih =>\n intro m\... | [
{
"name": "sum_of_and_eq_zero_is_xor",
"fan_in": 4,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 5,
"n_chars": 147,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"m... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -239,8 +239,146 @@
rw [h_result]
rw [←Nat.div_add_mod ((n1 * 2 + bn) ||| (m1 * 2 + bm)) 2, h_div_eq, h_mod_eq, Nat.div_add_mod]
-lemma sum_of_and_eq_zero_is_xor {n m : ℕ} (h_n_AND_m : n &&& m = 0) : n + m = n ^^^ m := sorry
+lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (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_0d00315d95db_15 | 53e566671648ec88 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "and_two_pow_eq_zero_of_getBit_0",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply and_eq_zero_iff_and_each_getBit_eq_zero.mpr\n intro k\n have h_getBit_two_pow := getBit_two_pow (i... | [
{
"name": "and_eq_zero_iff_and_each_getBit_eq_zero",
"text": "lemma and_eq_zero_iff_and_each_getBit_eq_zero {n m : ℕ} :\n n &&& m = 0 ↔ ∀ k, Nat.getBit k n &&& Nat.getBit k m = 0 := by\n constructor\n · intro h_and_zero k\n have h_k := shiftRight_and_one_distrib (n := n) (m := m) (k := k)\n rw [←... | [
{
"name": "xor_of_and_eq_zero_is_or",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 27,
"n_chars": 1087,
"n_subproofs": 3,
"n_tactics": 24,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 4,
"n_structural": 6,
"automation_only": false,
... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -125,6 +125,25 @@
rw [Nat.and_assoc (y := m >>> k) (z := 1), Nat.and_comm (x := m>>>k) (y := 1), ←Nat.and_assoc]
rw [Nat.and_assoc]
+lemma and_eq_zero_iff_and_each_getBit_eq_zero {n m : ℕ} :
+ n &&& m = 0 ↔ ∀ k, Nat.getBit k n &&& Nat.getBit k m = 0 := by
+ constructor
+ · intro h_and_zero k
+ ha... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_0d00315d95db_16 | 529d4e2f2b60a18b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 1 | [
{
"theorem_name": "sum_eq_xor_plus_twice_and",
"depth": 1,
"n_commands": 0,
"n_lines": 135,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n using Nat.binaryRec with\n | zero =>\n intro m\n rw [zero_add, Nat.zero_and, mul_zero, add_z... | [
{
"name": "xor_by_split_lowBits",
"text": "lemma xor_by_split_lowBits {n m n1 m1 bn bm : ℕ} (h_bn : bn < 2) (h_bm : bm < 2)\n (h_n : n = n1 * 2 + bn) (h_m : m = m1 * 2 + bm) :\n n ^^^ m = (n1 ^^^ m1) * 2 + (bn ^^^ bm) := by\n rw [h_n, h_m]\n -- ⊢ (n1 * 2 + bn) ^^^ (m1 * 2 + bm) = (n1 ^^^ m1) * 2 + (... | [
{
"name": "sum_of_and_eq_zero_is_or",
"fan_in": 3,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 5,
"n_chars": 201,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"ma... | 9 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -177,6 +177,37 @@
rw [h_result]
rw [←Nat.div_add_mod ((n1 * 2 + bn) &&& (m1 * 2 + bm)) 2, h_div_eq, h_mod_eq, Nat.div_add_mod]
+lemma xor_by_split_lowBits {n m n1 m1 bn bm : ℕ} (h_bn : bn < 2) (h_bm : bm < 2)
+ (h_n : n = n1 * 2 + bn) (h_m : m = m1 * 2 + bm) :
+ n ^^^ m = (n1 ^^^ m1) * 2 + (bn ^^^ bm... | {
"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_0d00315d95db_17 | 25c5c5554367b62e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "add_shiftRight_distrib",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [sum_eq_xor_plus_twice_and, h_and_zero, mul_zero, add_zero]\n conv =>\n rhs\n rw [sum_eq_xor_plus_twice_an... | [
{
"name": "sum_eq_xor_plus_twice_and",
"text": "lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (n &&& m) := by\n induction n using Nat.binaryRec with\n | zero =>\n intro m\n rw [zero_add, Nat.zero_and, mul_zero, add_zero, Nat.zero_xor]\n | bit bn n2 ih =>\n intro m\... | [
{
"name": "xor_eq_sub_iff_submask",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 30,
"n_chars": 1424,
"n_subproofs": 2,
"n_tactics": 27,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 15,
"n_structural": 5,
"automation_only": false,
"... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -239,6 +239,142 @@
rw [h_result]
rw [←Nat.div_add_mod ((n1 * 2 + bn) ||| (m1 * 2 + bm)) 2, h_div_eq, h_mod_eq, Nat.div_add_mod]
+lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (n &&& m) := by
+ induction n using Nat.binaryRec with
+ | zero =>
+ intro m
+ rw [zero_add, ... | {
"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_0d00315d95db_18 | b020f0d1f75d8784 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 1 | [
{
"theorem_name": "sum_eq_xor_plus_twice_and",
"depth": 1,
"n_commands": 0,
"n_lines": 135,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n using Nat.binaryRec with\n | zero =>\n intro m\n rw [zero_add, Nat.zero_and, mul_zero, add_z... | [
{
"name": "or_by_split_lowBits",
"text": "lemma or_by_split_lowBits {n m n1 m1 bn bm : ℕ} (h_bn : bn < 2) (h_bm : bm < 2)\n (h_n : n = n1 * 2 + bn) (h_m : m = m1 * 2 + bm) :\n n ||| m = (n1 ||| m1) * 2 + (bn ||| bm) := by\n rw [h_n, h_m]\n -- ⊢ (n1 * 2 + bn) ||| (m1 * 2 + bm) = (n1 ||| m1) * 2 + (bn... | [
{
"name": "getBit_of_add_distrib",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 18,
"n_chars": 821,
"n_subproofs": 3,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": false,
"max... | 9 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -208,6 +208,37 @@
rw [h_result]
rw [←Nat.div_add_mod ((n1 * 2 + bn) ^^^ (m1 * 2 + bm)) 2, h_div_eq, h_mod_eq, Nat.div_add_mod]
+lemma or_by_split_lowBits {n m n1 m1 bn bm : ℕ} (h_bn : bn < 2) (h_bm : bm < 2)
+ (h_n : n = n1 * 2 + bn) (h_m : m = m1 * 2 + bm) :
+ n ||| m = (n1 ||| m1) * 2 + (bn ||| bm)... | {
"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_0d00315d95db_19 | f14e154a49a1e0ca | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 3 | [
{
"theorem_name": "and_by_split_lowBits",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by -- main tool : Nat.div_add_mod /2\n rw [h_n, h_m]\n -- ⊢ (n1 * 2 + bn) &&& (m1 * 2 + bm) = (n1 &&& m1) * 2 + (bn &&& b... | [
{
"name": "div_2_form",
"text": "lemma div_2_form {nD2 b : ℕ} (h_b : b < 2) :\n (nD2 * 2 + b) / 2 = nD2 := by\n omega\n\n",
"fan_in": 3,
"n_lines": 5,
"n_chars": 90,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural":... | [
{
"name": "add_two_pow_of_getBit_eq_zero_lt_two_pow",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 10,
"n_lines": 13,
"n_chars": 527,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 3,
"n_structural": 2,
"automation_onl... | 10 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -211,13 +211,17 @@
rw [getBit, getBit, h_getBit_two_pow]
rw [Nat.and_zero]
+lemma div_2_form {nD2 b : ℕ} (h_b : b < 2) :
+ (nD2 * 2 + b) / 2 = nD2 := by
+ omega
+
lemma and_by_split_lowBits {n m n1 m1 bn bm : ℕ} (h_bn : bn < 2) (h_bm : bm < 2)
(h_n : n = n1 * 2 + bn) (h_m : m = m1 * 2 + bm) :
... | {
"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_0d00315d95db_20 | c84a6d7c3599918d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "add_shiftRight_distrib",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [sum_eq_xor_plus_twice_and, h_and_zero, mul_zero, add_zero]\n conv =>\n rhs\n rw [sum_eq_xor_plus_twice_an... | [
{
"name": "sum_eq_xor_plus_twice_and",
"text": "lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (n &&& m) := by\n induction n using Nat.binaryRec with\n | zero =>\n intro m\n rw [zero_add, Nat.zero_and, mul_zero, add_zero, Nat.zero_xor]\n | bit bn n2 ih =>\n intro m\... | [
{
"name": "getBit_of_sub_two_pow_of_bit_1",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 10,
"n_lines": 23,
"n_chars": 813,
"n_subproofs": 2,
"n_tactics": 20,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 7,
"n_structural": 3,
"automation_only": false... | 10 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -304,6 +304,142 @@
rw [h_result]
rw [←Nat.div_add_mod ((n1 * 2 + bn) ||| (m1 * 2 + bm)) 2, h_div_eq, h_mod_eq, Nat.div_add_mod]
+lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (n &&& m) := by
+ induction n using Nat.binaryRec with
+ | zero =>
+ intro m
+ rw [zero_add, ... | {
"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_0d00315d95db_21 | 017aec6e3b2b2138 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 4 | [
{
"theorem_name": "getBit_eq_testBit",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold getBit\n rw [Nat.testBit]\n simp only [and_one_is_mod, one_and_eq_mod_two, mod_two_bne_zero, beq_iff_eq]\n if ... | [
{
"name": "getBit_lt_2",
"text": "lemma getBit_lt_2 {k n : Nat} : getBit k n < 2 := by\n unfold getBit\n rw [Nat.and_one_is_mod]\n simp only [Nat.ofNat_pos, Nat.mod_lt]\n\n",
"fan_in": 4,
"n_lines": 6,
"n_chars": 136,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_autom... | [
{
"name": "getBit_of_lowBits",
"fan_in": 4,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 28,
"n_chars": 1078,
"n_subproofs": 3,
"n_tactics": 25,
"cyclomatic": 1,
"n_automation": 10,
"n_rewrites": 6,
"n_structural": 3,
"automation_only": false,
"max_n... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -82,6 +82,11 @@
-- #eval Nat.popCount 13
+lemma getBit_lt_2 {k n : Nat} : getBit k n < 2 := by
+ unfold getBit
+ rw [Nat.and_one_is_mod]
+ simp only [Nat.ofNat_pos, Nat.mod_lt]
+
lemma getBit_eq_testBit (k n : Nat) : getBit k n = if n.testBit k then 1 else 0 := by
unfold getBit
rw [Nat.testBit]
@@ -90... | {
"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_0d00315d95db_22 | f01486ca3b1acbda | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 8 | [
{
"theorem_name": "getBit_eq_succ_getBit_of_mul_two",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_n_eq: n = (2*n) >>> 1 := by omega\n have res := (getBit_of_shiftRight (n := 2*n) (p := 1) k).symm\... | [
{
"name": "getBit_of_shiftRight",
"text": "lemma getBit_of_shiftRight {n p : ℕ} :\n ∀ k, getBit k (n >>> p) = getBit (k+p) n := by\n intro k\n unfold getBit\n rw [←Nat.shiftRight_add]\n rw [←add_comm]\n\n",
"fan_in": 8,
"n_lines": 8,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "getBit_eq_succ_getBit_of_mul_two",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 247,
"n_subproofs": 2,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -442,6 +442,13 @@
congr
rw [Nat.shiftLeft_eq, mul_comm]
+lemma getBit_of_shiftRight {n p : ℕ} :
+ ∀ k, getBit k (n >>> p) = getBit (k+p) n := by
+ intro k
+ unfold getBit
+ rw [←Nat.shiftRight_add]
+ rw [←add_comm]
+
lemma getBit_of_two_pow_sub_one {i k: ℕ} :
getBit k (2^i - 1) = if k < i then 1... | {
"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_0d00315d95db_23 | b8dd39a8b0c4d47d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 23 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 8 | [
{
"theorem_name": "getBit_eq_succ_getBit_of_mul_two",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_n_eq: n = (2*n) >>> 1 := by omega\n have res := (getBit_of_shiftRight (n := 2*n) (p := 1) k).symm\... | [
{
"name": "getBit_of_shiftRight",
"text": "lemma getBit_of_shiftRight {n p : ℕ} :\n ∀ k, getBit k (n >>> p) = getBit (k+p) n := by\n intro k\n unfold getBit\n rw [←Nat.shiftRight_add]\n rw [←add_comm]\n\n",
"fan_in": 8,
"n_lines": 8,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "getBit_eq_succ_getBit_of_mul_two_add_one",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 267,
"n_subproofs": 2,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only"... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -442,6 +442,13 @@
congr
rw [Nat.shiftLeft_eq, mul_comm]
+lemma getBit_of_shiftRight {n p : ℕ} :
+ ∀ k, getBit k (n >>> p) = getBit (k+p) n := by
+ intro k
+ unfold getBit
+ rw [←Nat.shiftRight_add]
+ rw [←add_comm]
+
lemma getBit_of_two_pow_sub_one {i k: ℕ} :
getBit k (2^i - 1) = if k < i then 1... | {
"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_0d00315d95db_24 | 2823c5e023a229d4 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 24 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 8 | [
{
"theorem_name": "getBit_eq_succ_getBit_of_mul_two",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_n_eq: n = (2*n) >>> 1 := by omega\n have res := (getBit_of_shiftRight (n := 2*n) (p := 1) k).symm\... | [
{
"name": "getBit_of_shiftRight",
"text": "lemma getBit_of_shiftRight {n p : ℕ} :\n ∀ k, getBit k (n >>> p) = getBit (k+p) n := by\n intro k\n unfold getBit\n rw [←Nat.shiftRight_add]\n rw [←add_comm]\n\n",
"fan_in": 8,
"n_lines": 8,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "getBit_eq_pred_getBit_of_div_two",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 287,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -442,6 +442,13 @@
congr
rw [Nat.shiftLeft_eq, mul_comm]
+lemma getBit_of_shiftRight {n p : ℕ} :
+ ∀ k, getBit k (n >>> p) = getBit (k+p) n := by
+ intro k
+ unfold getBit
+ rw [←Nat.shiftRight_add]
+ rw [←add_comm]
+
lemma getBit_of_two_pow_sub_one {i k: ℕ} :
getBit k (2^i - 1) = if k < i then 1... | {
"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_0d00315d95db_25 | e66969671940d24f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 25 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 8 | [
{
"theorem_name": "getBit_eq_succ_getBit_of_mul_two",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_n_eq: n = (2*n) >>> 1 := by omega\n have res := (getBit_of_shiftRight (n := 2*n) (p := 1) k).symm\... | [
{
"name": "getBit_of_shiftRight",
"text": "lemma getBit_of_shiftRight {n p : ℕ} :\n ∀ k, getBit k (n >>> p) = getBit (k+p) n := by\n intro k\n unfold getBit\n rw [←Nat.shiftRight_add]\n rw [←add_comm]\n\n",
"fan_in": 8,
"n_lines": 8,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "getBit_repr",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 126,
"n_chars": 5558,
"n_subproofs": 20,
"n_tactics": 131,
"cyclomatic": 2,
"n_automation": 19,
"n_rewrites": 33,
"n_structural": 33,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -442,6 +442,13 @@
congr
rw [Nat.shiftLeft_eq, mul_comm]
+lemma getBit_of_shiftRight {n p : ℕ} :
+ ∀ k, getBit k (n >>> p) = getBit (k+p) n := by
+ intro k
+ unfold getBit
+ rw [←Nat.shiftRight_add]
+ rw [←add_comm]
+
lemma getBit_of_two_pow_sub_one {i k: ℕ} :
getBit k (2^i - 1) = if k < i then 1... | {
"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_0d00315d95db_26 | d5ec85a25b9f357c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 26 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 8 | [
{
"theorem_name": "getBit_eq_succ_getBit_of_mul_two",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_n_eq: n = (2*n) >>> 1 := by omega\n have res := (getBit_of_shiftRight (n := 2*n) (p := 1) k).symm\... | [
{
"name": "getBit_of_shiftRight",
"text": "lemma getBit_of_shiftRight {n p : ℕ} :\n ∀ k, getBit k (n >>> p) = getBit (k+p) n := by\n intro k\n unfold getBit\n rw [←Nat.shiftRight_add]\n rw [←add_comm]\n\n",
"fan_in": 8,
"n_lines": 8,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "getBit_repr_unique",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 64,
"n_chars": 3408,
"n_subproofs": 9,
"n_tactics": 67,
"cyclomatic": 10,
"n_automation": 31,
"n_rewrites": 21,
"n_structural": 15,
"automation_only": false,
"m... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -442,6 +442,13 @@
congr
rw [Nat.shiftLeft_eq, mul_comm]
+lemma getBit_of_shiftRight {n p : ℕ} :
+ ∀ k, getBit k (n >>> p) = getBit (k+p) n := by
+ intro k
+ unfold getBit
+ rw [←Nat.shiftRight_add]
+ rw [←add_comm]
+
lemma getBit_of_two_pow_sub_one {i k: ℕ} :
getBit k (2^i - 1) = if k < i then 1... | {
"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_0d00315d95db_27 | f248fc31a7937ff0 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 27 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "add_shiftRight_distrib",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [sum_eq_xor_plus_twice_and, h_and_zero, mul_zero, add_zero]\n conv =>\n rhs\n rw [sum_eq_xor_plus_twice_an... | [
{
"name": "sum_eq_xor_plus_twice_and",
"text": "lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (n &&& m) := by\n induction n using Nat.binaryRec with\n | zero =>\n intro m\n rw [zero_add, Nat.zero_and, mul_zero, add_zero, Nat.zero_xor]\n | bit bn n2 ih =>\n intro m\... | [
{
"name": "getLowBits_succ",
"fan_in": 0,
"n_deps_direct": 8,
"n_deps_transitive": 17,
"n_lines": 68,
"n_chars": 3074,
"n_subproofs": 15,
"n_tactics": 63,
"cyclomatic": 1,
"n_automation": 21,
"n_rewrites": 13,
"n_structural": 4,
"automation_only": false,
"max_... | 16 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -306,8 +306,146 @@
rw [h_result]
rw [←Nat.div_add_mod ((n1 * 2 + bn) ||| (m1 * 2 + bm)) 2, h_div_eq, h_mod_eq, Nat.div_add_mod]
-lemma sum_of_and_eq_zero_is_xor {n m : ℕ} (h_n_AND_m : n &&& m = 0) : n + m = n ^^^ m := sorry
+lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (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_0d00315d95db_28 | 241fe44b7f667973 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 28 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "and_highBits_lowBits_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n change (n >>> numLowBits <<< numLowBits) &&& (getLowBits numLowBits n) = 0\n set highBits_no_shl := n >>> nu... | [
{
"name": "getBit_of_shiftLeft",
"text": "lemma getBit_of_shiftLeft {n p : ℕ} :\n ∀ k, getBit (k) (n <<< p) = if k < p then 0 else getBit (k - p) n := by\n intro k\n rw [getBit_of_multiple_of_power_of_two (n:=n) (p:=p) (k:=k).symm]\n congr\n rw [Nat.shiftLeft_eq, mul_comm]\n\n",
"fan_in": 5,
... | [
{
"name": "and_highBits_lowBits_eq_zero",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 9,
"n_lines": 25,
"n_chars": 1217,
"n_subproofs": 7,
"n_tactics": 22,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 5,
"n_structural": 2,
"automation_only": false,
... | 8 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -435,6 +435,13 @@
simp only [h_getBit_left_lt_eq, iff_true] at h_test
simp only [getBit, Nat.and_one_is_mod, h_test]
+lemma getBit_of_shiftLeft {n p : ℕ} :
+ ∀ k, getBit (k) (n <<< p) = if k < p then 0 else getBit (k - p) n := by
+ intro k
+ rw [getBit_of_multiple_of_power_of_two (n:=n) (p:=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_0d00315d95db_29 | 18b7699614cd2e0c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 29 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "and_highBits_lowBits_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n change (n >>> numLowBits <<< numLowBits) &&& (getLowBits numLowBits n) = 0\n set highBits_no_shl := n >>> nu... | [
{
"name": "getBit_of_shiftLeft",
"text": "lemma getBit_of_shiftLeft {n p : ℕ} :\n ∀ k, getBit (k) (n <<< p) = if k < p then 0 else getBit (k - p) n := by\n intro k\n rw [getBit_of_multiple_of_power_of_two (n:=n) (p:=p) (k:=k).symm]\n congr\n rw [Nat.shiftLeft_eq, mul_comm]\n\n",
"fan_in": 5,
... | [
{
"name": "num_eq_highBits_add_lowBits",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 18,
"n_lines": 28,
"n_chars": 1334,
"n_subproofs": 5,
"n_tactics": 22,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 8,
"n_structural": 2,
"automation_only": false,
... | 16 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -435,6 +435,13 @@
simp only [h_getBit_left_lt_eq, iff_true] at h_test
simp only [getBit, Nat.and_one_is_mod, h_test]
+lemma getBit_of_shiftLeft {n p : ℕ} :
+ ∀ k, getBit (k) (n <<< p) = if k < p then 0 else getBit (k - p) n := by
+ intro k
+ rw [getBit_of_multiple_of_power_of_two (n:=n) (p:=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_0d00315d95db_30 | 2f90cf8449f6e35b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 30 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "and_highBits_lowBits_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n change (n >>> numLowBits <<< numLowBits) &&& (getLowBits numLowBits n) = 0\n set highBits_no_shl := n >>> nu... | [
{
"name": "getBit_of_shiftLeft",
"text": "lemma getBit_of_shiftLeft {n p : ℕ} :\n ∀ k, getBit (k) (n <<< p) = if k < p then 0 else getBit (k - p) n := by\n intro k\n rw [getBit_of_multiple_of_power_of_two (n:=n) (p:=p) (k:=k).symm]\n congr\n rw [Nat.shiftLeft_eq, mul_comm]\n\n",
"fan_in": 5,
... | [
{
"name": "num_eq_highBits_xor_lowBits",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 20,
"n_lines": 7,
"n_chars": 318,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
... | 18 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -439,6 +439,13 @@
simp only [h_getBit_left_lt_eq, iff_true] at h_test
simp only [getBit, Nat.and_one_is_mod, h_test]
+lemma getBit_of_shiftLeft {n p : ℕ} :
+ ∀ k, getBit (k) (n <<< p) = if k < p then 0 else getBit (k - p) n := by
+ intro k
+ rw [getBit_of_multiple_of_power_of_two (n:=n) (p:=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_0d00315d95db_31 | 08cdc4d3d2491f3c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 31 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 8 | [
{
"theorem_name": "getBit_eq_succ_getBit_of_mul_two",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_n_eq: n = (2*n) >>> 1 := by omega\n have res := (getBit_of_shiftRight (n := 2*n) (p := 1) k).symm\... | [
{
"name": "getBit_of_shiftRight",
"text": "lemma getBit_of_shiftRight {n p : ℕ} :\n ∀ k, getBit k (n >>> p) = getBit (k+p) n := by\n intro k\n unfold getBit\n rw [←Nat.shiftRight_add]\n rw [←add_comm]\n\n",
"fan_in": 8,
"n_lines": 8,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "getBit_of_highBits",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 13,
"n_chars": 413,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
"max_ne... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -442,6 +442,13 @@
congr
rw [Nat.shiftLeft_eq, mul_comm]
+lemma getBit_of_shiftRight {n p : ℕ} :
+ ∀ k, getBit k (n >>> p) = getBit (k+p) n := by
+ intro k
+ unfold getBit
+ rw [←Nat.shiftRight_add]
+ rw [←add_comm]
+
lemma getBit_of_two_pow_sub_one {i k: ℕ} :
getBit k (2^i - 1) = if k < i then 1... | {
"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_0d00315d95db_32 | 2a89b876d2fa9f28 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 32 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 8 | [
{
"theorem_name": "getBit_eq_succ_getBit_of_mul_two",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_n_eq: n = (2*n) >>> 1 := by omega\n have res := (getBit_of_shiftRight (n := 2*n) (p := 1) k).symm\... | [
{
"name": "getBit_of_shiftRight",
"text": "lemma getBit_of_shiftRight {n p : ℕ} :\n ∀ k, getBit k (n >>> p) = getBit (k+p) n := by\n intro k\n unfold getBit\n rw [←Nat.shiftRight_add]\n rw [←add_comm]\n\n",
"fan_in": 8,
"n_lines": 8,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "getBit_of_highBits_no_shl",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 227,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"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: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -442,6 +442,13 @@
congr
rw [Nat.shiftLeft_eq, mul_comm]
+lemma getBit_of_shiftRight {n p : ℕ} :
+ ∀ k, getBit k (n >>> p) = getBit (k+p) n := by
+ intro k
+ unfold getBit
+ rw [←Nat.shiftRight_add]
+ rw [←add_comm]
+
lemma getBit_of_two_pow_sub_one {i k: ℕ} :
getBit k (2^i - 1) = if k < i then 1... | {
"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_0d00315d95db_33 | 306bb9fe29c6505b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 33 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 3 | [
{
"theorem_name": "ge_two_pow_of_getBit_1",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Nat.getBit_eq_testBit] at h_getBit\n simp only [ite_eq_left_iff, Bool.not_eq_true, zero_ne_one, imp_false,\n ... | [
{
"name": "getBit_eq_testBit",
"text": "lemma getBit_eq_testBit (k n : Nat) : getBit k n = if n.testBit k then 1 else 0 := by\n unfold getBit\n rw [Nat.testBit]\n simp only [and_one_is_mod, one_and_eq_mod_two, mod_two_bne_zero, beq_iff_eq]\n if h: (n >>> k) % 2 = 1 then\n simp only [h, ↓reduceIte]\n ... | [
{
"name": "getBit_of_lt_two_pow",
"fan_in": 4,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 15,
"n_chars": 540,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 1,
"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: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -87,6 +87,18 @@
rw [Nat.and_one_is_mod]
simp only [Nat.ofNat_pos, Nat.mod_lt]
+lemma getBit_eq_testBit (k n : Nat) : getBit k n = if n.testBit k then 1 else 0 := by
+ unfold getBit
+ rw [Nat.testBit]
+ simp only [and_one_is_mod, one_and_eq_mod_two, mod_two_bne_zero, beq_iff_eq]
+ if h: (n >>> k) % 2 = 1 ... | {
"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_0d00315d95db_34 | 1c48135883eaac4d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 34 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 6 | [
{
"theorem_name": "and_eq_zero_iff_and_each_getBit_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h_and_zero k\n have h_k := shiftRight_and_one_distrib (n := n) (m := m) ... | [
{
"name": "eq_iff_eq_all_getBits",
"text": "lemma eq_iff_eq_all_getBits {n m : ℕ} : n = m ↔ ∀ k, getBit k n = getBit k m := by\n unfold getBit\n constructor\n · intro h_eq k -- h_eq : n = m\n rw [h_eq]\n · intro h_all_getBits -- h_all_getBits : ∀ k, (n >>> k) &&& 1 = (m >>> k) &&& 1\n apply Nat.eq... | [
{
"name": "exist_bit_diff_if_diff",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 23,
"n_chars": 769,
"n_subproofs": 1,
"n_tactics": 20,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 3,
"n_structural": 5,
"automation_only": false,
"ma... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -102,6 +102,18 @@
/-- Get the `numLowBits` least significant bits of `n`. -/
def getLowBits (numLowBits : ℕ) (n : ℕ) := n &&& ((1 <<< numLowBits) - 1)
+lemma eq_iff_eq_all_getBits {n m : ℕ} : n = m ↔ ∀ k, getBit k n = getBit k m := by
+ unfold getBit
+ constructor
+ · intro h_eq k -- h_eq : n = m
+ rw [h_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_0d00315d95db_35 | 67e2019c5a60cb91 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 35 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 1 | [
{
"theorem_name": "sum_eq_xor_plus_twice_and",
"depth": 1,
"n_commands": 0,
"n_lines": 135,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n using Nat.binaryRec with\n | zero =>\n intro m\n rw [zero_add, Nat.zero_and, mul_zero, add_z... | [
{
"name": "and_by_split_lowBits",
"text": "lemma and_by_split_lowBits {n m n1 m1 bn bm : ℕ} (h_bn : bn < 2) (h_bm : bm < 2)\n (h_n : n = n1 * 2 + bn) (h_m : m = m1 * 2 + bm) :\n n &&& m = (n1 &&& m1) * 2 + (bn &&& bm) := by -- main tool : Nat.div_add_mod /2\n rw [h_n, h_m]\n -- ⊢ (n1 * 2 + bn) &&& (... | [
{
"name": "getBit_of_binaryFinMapToNat",
"fan_in": 0,
"n_deps_direct": 6,
"n_deps_transitive": 16,
"n_lines": 89,
"n_chars": 3934,
"n_subproofs": 10,
"n_tactics": 81,
"cyclomatic": 2,
"n_automation": 32,
"n_rewrites": 20,
"n_structural": 16,
"automation_only": fal... | 16 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -220,6 +220,35 @@
(nD2 * 2 + b) / 2 = nD2 := by
omega
+lemma and_by_split_lowBits {n m n1 m1 bn bm : ℕ} (h_bn : bn < 2) (h_bm : bm < 2)
+ (h_n : n = n1 * 2 + bn) (h_m : m = m1 * 2 + bm) :
+ n &&& m = (n1 &&& m1) * 2 + (bn &&& bm) := by -- main tool : Nat.div_add_mod /2
+ rw [h_n, h_m]
+ -- ⊢ (n1 * ... | {
"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_0d00315d95db_36 | 1ebc532b22538f57 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 36 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 8 | [
{
"theorem_name": "getBit_eq_succ_getBit_of_mul_two",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_n_eq: n = (2*n) >>> 1 := by omega\n have res := (getBit_of_shiftRight (n := 2*n) (p := 1) k).symm\... | [
{
"name": "getBit_of_shiftRight",
"text": "lemma getBit_of_shiftRight {n p : ℕ} :\n ∀ k, getBit k (n >>> p) = getBit (k+p) n := by\n intro k\n unfold getBit\n rw [←Nat.shiftRight_add]\n rw [←add_comm]\n\n",
"fan_in": 8,
"n_lines": 8,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "getBit_of_middleBits",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 8,
"n_chars": 293,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_ne... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -442,6 +442,13 @@
congr
rw [Nat.shiftLeft_eq, mul_comm]
+lemma getBit_of_shiftRight {n p : ℕ} :
+ ∀ k, getBit k (n >>> p) = getBit (k+p) n := by
+ intro k
+ unfold getBit
+ rw [←Nat.shiftRight_add]
+ rw [←add_comm]
+
lemma getBit_of_and {n m k: ℕ} : getBit k (n &&& m) = getBit k n &&& getBit k m := 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_0d00315d95db_37 | 06763378a6fcce0f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 37 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 4 | [
{
"theorem_name": "getLowBits_lt_two_pow",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [getLowBits_eq_mod_two_pow]\n omega",
"n_chars": 44,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomati... | [
{
"name": "getLowBits_eq_mod_two_pow",
"text": "lemma getLowBits_eq_mod_two_pow {numLowBits : ℕ} (n : ℕ) :\n getLowBits numLowBits n = n % (2 ^ numLowBits) := by\n unfold getLowBits\n rw [Nat.shiftLeft_eq, one_mul]\n exact Nat.and_two_pow_sub_one_eq_mod n numLowBits\n\n",
"fan_in": 4,
"n_lines... | [
{
"name": "getMiddleBits_lt_two_pow",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 230,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"ma... | 2 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -102,8 +102,16 @@
/-- Get the `numLowBits` least significant bits of `n`. -/
def getLowBits (numLowBits : ℕ) (n : ℕ) := n &&& ((1 <<< numLowBits) - 1)
+lemma getLowBits_eq_mod_two_pow {numLowBits : ℕ} (n : ℕ) :
+ getLowBits numLowBits n = n % (2 ^ numLowBits) := by
+ unfold getLowBits
+ rw [Nat.shiftLeft_eq... | {
"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_0d00315d95db_38 | 991dffbb3a9b82ba | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 38 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 4 | [
{
"theorem_name": "getLowBits_lt_two_pow",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [getLowBits_eq_mod_two_pow]\n omega",
"n_chars": 44,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomati... | [
{
"name": "getLowBits_eq_mod_two_pow",
"text": "lemma getLowBits_eq_mod_two_pow {numLowBits : ℕ} (n : ℕ) :\n getLowBits numLowBits n = n % (2 ^ numLowBits) := by\n unfold getLowBits\n rw [Nat.shiftLeft_eq, one_mul]\n exact Nat.and_two_pow_sub_one_eq_mod n numLowBits\n\n",
"fan_in": 4,
"n_lines... | [
{
"name": "getMiddleBits_eq_mod",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 252,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -102,6 +102,12 @@
/-- Get the `numLowBits` least significant bits of `n`. -/
def getLowBits (numLowBits : ℕ) (n : ℕ) := n &&& ((1 <<< numLowBits) - 1)
+lemma getLowBits_eq_mod_two_pow {numLowBits : ℕ} (n : ℕ) :
+ getLowBits numLowBits n = n % (2 ^ numLowBits) := by
+ unfold getLowBits
+ rw [Nat.shiftLeft_eq... | {
"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_0d00315d95db_39 | 03f93e8035da3864 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 39 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "and_highBits_lowBits_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n change (n >>> numLowBits <<< numLowBits) &&& (getLowBits numLowBits n) = 0\n set highBits_no_shl := n >>> nu... | [
{
"name": "getBit_of_shiftLeft",
"text": "lemma getBit_of_shiftLeft {n p : ℕ} :\n ∀ k, getBit (k) (n <<< p) = if k < p then 0 else getBit (k - p) n := by\n intro k\n rw [getBit_of_multiple_of_power_of_two (n:=n) (p:=p) (k:=k).symm]\n congr\n rw [Nat.shiftLeft_eq, mul_comm]\n\n",
"fan_in": 5,
... | [
{
"name": "getBit_joinBits",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 14,
"n_chars": 446,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 6 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -435,6 +435,13 @@
simp only [h_getBit_left_lt_eq, iff_true] at h_test
simp only [getBit, Nat.and_one_is_mod, h_test]
+lemma getBit_of_shiftLeft {n p : ℕ} :
+ ∀ k, getBit (k) (n <<< p) = if k < p then 0 else getBit (k - p) n := by
+ intro k
+ rw [getBit_of_multiple_of_power_of_two (n:=n) (p:=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_0d00315d95db_40 | 0c7a6f2075bea36d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 40 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "add_shiftRight_distrib",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [sum_eq_xor_plus_twice_and, h_and_zero, mul_zero, add_zero]\n conv =>\n rhs\n rw [sum_eq_xor_plus_twice_an... | [
{
"name": "sum_eq_xor_plus_twice_and",
"text": "lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (n &&& m) := by\n induction n using Nat.binaryRec with\n | zero =>\n intro m\n rw [zero_add, Nat.zero_and, mul_zero, add_zero, Nat.zero_xor]\n | bit bn n2 ih =>\n intro m\... | [
{
"name": "getLowBits_joinBits",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 17,
"n_lines": 13,
"n_chars": 539,
"n_subproofs": 1,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 5,
"n_structural": 1,
"automation_only": false,
"max_n... | 15 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -245,6 +245,142 @@
rw [h_result]
rw [←Nat.div_add_mod ((n1 * 2 + bn) ||| (m1 * 2 + bm)) 2, h_div_eq, h_mod_eq, Nat.div_add_mod]
+lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (n &&& m) := by
+ induction n using Nat.binaryRec with
+ | zero =>
+ intro m
+ rw [zero_add, ... | {
"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_0d00315d95db_41 | d53205556fd5be36 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Nat/Bitwise.lean | Bitwise | 41 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 5 | [
{
"theorem_name": "add_shiftRight_distrib",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [sum_eq_xor_plus_twice_and, h_and_zero, mul_zero, add_zero]\n conv =>\n rhs\n rw [sum_eq_xor_plus_twice_an... | [
{
"name": "sum_eq_xor_plus_twice_and",
"text": "lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (n &&& m) := by\n induction n using Nat.binaryRec with\n | zero =>\n intro m\n rw [zero_add, Nat.zero_and, mul_zero, add_zero, Nat.zero_xor]\n | bit bn n2 ih =>\n intro m\... | [
{
"name": "getHighBits_no_shl_joinBits",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 17,
"n_lines": 15,
"n_chars": 676,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 5,
"n_structural": 2,
"automation_only": false,
... | 15 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Fin.BigOperators
import Mathlib.Algebra.BigOperators.Ring.Finset
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.Data.Nat.Bitwise
i... | @@ -239,8 +239,151 @@
rw [h_result]
rw [←Nat.div_add_mod ((n1 * 2 + bn) ||| (m1 * 2 + bm)) 2, h_div_eq, h_mod_eq, Nat.div_add_mod]
+lemma sum_eq_xor_plus_twice_and (n : Nat) : ∀ m : ℕ, n + m = (n ^^^ m) + 2 * (n &&& m) := by
+ induction n using Nat.binaryRec with
+ | zero =>
+ intro m
+ rw [zero_add, ... | {
"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_a18f874f7d49_0 | 2459551f97e3a03c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/LinearAlgebra/Dense/KernelInPlaceCorrectness.lean | KernelInPlaceCorrectness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 3 | [
{
"theorem_name": "foldl_scale_self_eq_const",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro xs\n induction xs with\n | nil => intro _ d _; rfl\n | cons c xs ih =>\n intro hnodup d hagree\n ... | [
{
"name": "getD_setD_ne",
"text": "/-- `setD` at a different index leaves the queried entry unchanged. -/\nprivate theorem getD_setD_ne [Zero F] (d : Array F) {i j : Nat} (h : i ≠ j) (v : F) :\n (setD d i v).getD j 0 = d.getD j 0 := by\n unfold setD\n rw [Array.getD_eq_getD_getElem?, Array.getD_eq_getD... | [
{
"name": "foldl_scale_self_eq_const",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 24,
"n_chars": 1046,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 7,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.KernelInPlace
import CompPoly.LinearAlgebra.Dense.RowOpsCorrectness
import CompPoly.LinearAlgebra.Dense.RrefSemantics
/-!... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.LinearAlgebra.Dense.KernelInPlace
import CompPoly.LinearAlgebra.Dense.RowOpsCorrectness
import CompPoly.LinearAlgebra.Dense.RrefSemantics
/-!... | @@ -24,6 +24,13 @@
variable {F : Type*}
+/-- `setD` at a different index leaves the queried entry unchanged. -/
+private theorem getD_setD_ne [Zero F] (d : Array F) {i j : Nat} (h : i ≠ j) (v : F) :
+ (setD d i v).getD j 0 = d.getD j 0 := by
+ unfold setD
+ rw [Array.getD_eq_getD_getElem?, Array.getD_eq_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... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.