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_72213d59b68c_4 | 329cd3e63b0b49cd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Forward.lean | Forward | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 37 | 4 | [
{
"theorem_name": "forwardMathPairsSpec_get_upper_current",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [forwardMathPairsSpec, forwardMathValueAt,\n butterfly_upper_div_block stage block j hj,\n ... | [
{
"name": "butterfly_upper_mod_half",
"text": "private theorem butterfly_upper_mod_half (stage block j : Nat) (hj : j < 2 ^ stage) :\n (block * 2 ^ (stage + 1) + j + 2 ^ stage) % 2 ^ stage = j := by\n rw [show block * 2 ^ (stage + 1) + j + 2 ^ stage =\n (block * 2 + 1) * 2 ^ stage + j by\n rw [p... | [
{
"name": "forwardMathPairsSpec_get_upper_next",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 570,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": tr... | 2 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | @@ -160,12 +160,24 @@
omega
rw [Nat.div_eq_of_lt hlt, add_zero]
+private theorem butterfly_upper_mod_half (stage block j : Nat) (hj : j < 2 ^ stage) :
+ (block * 2 ^ (stage + 1) + j + 2 ^ stage) % 2 ^ stage = j := by
+ rw [show block * 2 ^ (stage + 1) + j + 2 ^ stage =
+ (block * 2 + 1) * 2 ^ stage +... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_72213d59b68c_5 | d568b3109e2656a9 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Forward.lean | Forward | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 37 | 4 | [
{
"theorem_name": "forwardMathPairsSpec_get_upper_current",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [forwardMathPairsSpec, forwardMathValueAt,\n butterfly_upper_div_block stage block j hj,\n ... | [
{
"name": "butterfly_upper_mod_half",
"text": "private theorem butterfly_upper_mod_half (stage block j : Nat) (hj : j < 2 ^ stage) :\n (block * 2 ^ (stage + 1) + j + 2 ^ stage) % 2 ^ stage = j := by\n rw [show block * 2 ^ (stage + 1) + j + 2 ^ stage =\n (block * 2 + 1) * 2 ^ stage + j by\n rw [p... | [
{
"name": "forwardMathValueAt_succ_lower",
"fan_in": 1,
"n_deps_direct": 7,
"n_deps_transitive": 7,
"n_lines": 55,
"n_chars": 2200,
"n_subproofs": 1,
"n_tactics": 47,
"cyclomatic": 1,
"n_automation": 11,
"n_rewrites": 22,
"n_structural": 4,
"automation_only": fals... | 7 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | @@ -165,6 +165,15 @@
rw [Nat.mul_add_mod_self_right]
exact Nat.mod_eq_of_lt hj
+private theorem butterfly_upper_mod_half (stage block j : Nat) (hj : j < 2 ^ stage) :
+ (block * 2 ^ (stage + 1) + j + 2 ^ stage) % 2 ^ stage = j := by
+ rw [show block * 2 ^ (stage + 1) + j + 2 ^ stage =
+ (block * 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_72213d59b68c_6 | bdf708f3481472d4 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Forward.lean | Forward | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 37 | 2 | [
{
"theorem_name": "forwardMathValueAt_succ_lower",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [forwardMathValueAt,\n butterfly_lower_div_block stage block j hj,\n butterfly_lower_mod_half sta... | [
{
"name": "butterfly_upper_div_half",
"text": "private theorem butterfly_upper_div_half (stage block j : Nat) (hj : j < 2 ^ stage) :\n (block * 2 ^ (stage + 1) + j + 2 ^ stage) / 2 ^ stage = block * 2 + 1 := by\n rw [show block * 2 ^ (stage + 1) + j + 2 ^ stage =\n (block * 2 + 1) * 2 ^ stage + j b... | [
{
"name": "forwardMathValueAt_succ_upper",
"fan_in": 1,
"n_deps_direct": 10,
"n_deps_transitive": 11,
"n_lines": 71,
"n_chars": 2751,
"n_subproofs": 2,
"n_tactics": 63,
"cyclomatic": 1,
"n_automation": 13,
"n_rewrites": 31,
"n_structural": 4,
"automation_only": fa... | 11 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | @@ -186,6 +186,16 @@
rw [Nat.mul_add_div (Nat.two_pow_pos stage)]
rw [Nat.div_eq_of_lt hj, add_zero]
+private theorem butterfly_upper_div_half (stage block j : Nat) (hj : j < 2 ^ stage) :
+ (block * 2 ^ (stage + 1) + j + 2 ^ stage) / 2 ^ stage = block * 2 + 1 := by
+ rw [show block * 2 ^ (stage + 1) + j + 2... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_72213d59b68c_7 | ab30f71141f7a292 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Forward.lean | Forward | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 37 | 1 | [
{
"theorem_name": "forwardMathPairsSpec_get_unchanged",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [forwardMathPairsSpec, Array.getElem_ofFn]\n by_cases hltBlock : i / 2 ^ (stage + 1) < block... | [
{
"name": "eq_lower_or_upper_of_block_pair",
"text": "private theorem eq_lower_or_upper_of_block_pair\n (stage block j i : Nat)\n (hblock : i / 2 ^ (stage + 1) = block) (hpair : i % 2 ^ stage = j) :\n i = block * 2 ^ (stage + 1) + j ∨\n i = block * 2 ^ (stage + 1) + j + 2 ^ stage := by\n let ... | [
{
"name": "forwardMathPairsSpec_get_unchanged",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 28,
"n_chars": 1357,
"n_subproofs": 2,
"n_tactics": 18,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 7,
"n_structural": 3,
"automation_only": f... | 1 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | @@ -149,6 +149,49 @@
rw [size_butterflyStageSpec]
exact ih
+private theorem eq_lower_or_upper_of_block_pair
+ (stage block j i : Nat)
+ (hblock : i / 2 ^ (stage + 1) = block) (hpair : i % 2 ^ stage = j) :
+ i = block * 2 ^ (stage + 1) + j ∨
+ i = block * 2 ^ (stage + 1) + j + 2 ^ stage := ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_72213d59b68c_8 | 5ac05d9bf89eced2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Forward.lean | Forward | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 37 | 2 | [
{
"theorem_name": "forwardMathValueAt_succ_lower",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [forwardMathValueAt,\n butterfly_lower_div_block stage block j hj,\n butterfly_lower_mod_half sta... | [
{
"name": "stageTwiddle_eq_stride",
"text": "private theorem stageTwiddle_eq_stride\n (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :\n stageTwiddle D stage = D.omega ^ (2 ^ (D.logN - (stage + 1))) := by\n unfold stageTwiddle\n congr 1\n rw [Domain.n]\n exact Nat.pow_div (Nat.succ_le_of_l... | [
{
"name": "butterflyInnerStep_forwardMathPairsSpec_succ",
"fan_in": 1,
"n_deps_direct": 8,
"n_deps_transitive": 22,
"n_lines": 67,
"n_chars": 3154,
"n_subproofs": 4,
"n_tactics": 48,
"cyclomatic": 2,
"n_automation": 9,
"n_rewrites": 17,
"n_structural": 7,
"automat... | 22 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | @@ -219,6 +219,14 @@
rw [pow_succ]
omega)
+private theorem stageTwiddle_eq_stride
+ (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :
+ stageTwiddle D stage = D.omega ^ (2 ^ (D.logN - (stage + 1))) := by
+ unfold stageTwiddle
+ congr 1
+ rw [Domain.n]
+ exact Nat.pow_div (Nat.succ_le_of_lt ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_72213d59b68c_9 | 583374b43f7cb8ba | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Forward.lean | Forward | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 37 | 2 | [
{
"theorem_name": "forwardMathValueAt_succ_lower",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [forwardMathValueAt,\n butterfly_lower_div_block stage block j hj,\n butterfly_lower_mod_half sta... | [
{
"name": "stageTwiddle_eq_stride",
"text": "private theorem stageTwiddle_eq_stride\n (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :\n stageTwiddle D stage = D.omega ^ (2 ^ (D.logN - (stage + 1))) := by\n unfold stageTwiddle\n congr 1\n rw [Domain.n]\n exact Nat.pow_div (Nat.succ_le_of_l... | [
{
"name": "butterflyBlockStep_aux_forwardMathPairsSpec",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 24,
"n_lines": 28,
"n_chars": 1031,
"n_subproofs": 2,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 4,
"automatio... | 24 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | @@ -227,6 +227,14 @@
rw [pow_succ]
omega)
+private theorem stageTwiddle_eq_stride
+ (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :
+ stageTwiddle D stage = D.omega ^ (2 ^ (D.logN - (stage + 1))) := by
+ unfold stageTwiddle
+ congr 1
+ rw [Domain.n]
+ exact Nat.pow_div (Nat.succ_le_of_lt ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_72213d59b68c_10 | be04696604d64435 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Forward.lean | Forward | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 37 | 2 | [
{
"theorem_name": "forwardMathValueAt_succ_lower",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [forwardMathValueAt,\n butterfly_lower_div_block stage block j hj,\n butterfly_lower_mod_half sta... | [
{
"name": "stageTwiddle_eq_stride",
"text": "private theorem stageTwiddle_eq_stride\n (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :\n stageTwiddle D stage = D.omega ^ (2 ^ (D.logN - (stage + 1))) := by\n unfold stageTwiddle\n congr 1\n rw [Domain.n]\n exact Nat.pow_div (Nat.succ_le_of_l... | [
{
"name": "butterflyBlockStep_forwardMathBlocksSpec_succ",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 26,
"n_lines": 15,
"n_chars": 564,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automatio... | 26 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | @@ -262,6 +262,14 @@
rw [pow_succ]
omega)
+private theorem stageTwiddle_eq_stride
+ (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :
+ stageTwiddle D stage = D.omega ^ (2 ^ (D.logN - (stage + 1))) := by
+ unfold stageTwiddle
+ congr 1
+ rw [Domain.n]
+ exact Nat.pow_div (Nat.succ_le_of_lt ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_72213d59b68c_11 | eff7aec9506346cd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Forward.lean | Forward | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 37 | 2 | [
{
"theorem_name": "forwardMathValueAt_succ_lower",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [forwardMathValueAt,\n butterfly_lower_div_block stage block j hj,\n butterfly_lower_mod_half sta... | [
{
"name": "stageTwiddle_eq_stride",
"text": "private theorem stageTwiddle_eq_stride\n (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :\n stageTwiddle D stage = D.omega ^ (2 ^ (D.logN - (stage + 1))) := by\n unfold stageTwiddle\n congr 1\n rw [Domain.n]\n exact Nat.pow_div (Nat.succ_le_of_l... | [
{
"name": "butterflyStageSpec_aux_forwardMathBlocksSpec",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 28,
"n_lines": 21,
"n_chars": 708,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation... | 28 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | @@ -270,6 +270,14 @@
rw [pow_succ]
omega)
+private theorem stageTwiddle_eq_stride
+ (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :
+ stageTwiddle D stage = D.omega ^ (2 ^ (D.logN - (stage + 1))) := by
+ unfold stageTwiddle
+ congr 1
+ rw [Domain.n]
+ exact Nat.pow_div (Nat.succ_le_of_lt ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_72213d59b68c_12 | 6691d09186eb70ff | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Forward.lean | Forward | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 37 | 2 | [
{
"theorem_name": "forwardMathValueAt_succ_lower",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [forwardMathValueAt,\n butterfly_lower_div_block stage block j hj,\n butterfly_lower_mod_half sta... | [
{
"name": "stageTwiddle_eq_stride",
"text": "private theorem stageTwiddle_eq_stride\n (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :\n stageTwiddle D stage = D.omega ^ (2 ^ (D.logN - (stage + 1))) := by\n unfold stageTwiddle\n congr 1\n rw [Domain.n]\n exact Nat.pow_div (Nat.succ_le_of_l... | [
{
"name": "butterflyStageSpec_forwardMathStageSpec_succ",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 30,
"n_lines": 13,
"n_chars": 652,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation... | 30 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | @@ -308,6 +308,14 @@
rw [pow_succ]
omega)
+private theorem stageTwiddle_eq_stride
+ (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :
+ stageTwiddle D stage = D.omega ^ (2 ^ (D.logN - (stage + 1))) := by
+ unfold stageTwiddle
+ congr 1
+ rw [Domain.n]
+ exact Nat.pow_div (Nat.succ_le_of_lt ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_72213d59b68c_13 | ec682926a914d717 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Forward.lean | Forward | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 37 | 1 | [
{
"theorem_name": "forwardMathValueAt_succ_upper",
"depth": 1,
"n_commands": 0,
"n_lines": 63,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [forwardMathValueAt,\n butterfly_upper_div_block stage block j hj,\n butterfly_upper_mod_blockSiz... | [
{
"name": "stage_stride_half_eq_domain_half",
"text": "private theorem stage_stride_half_eq_domain_half\n (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :\n 2 ^ stage * 2 ^ (D.logN - (stage + 1)) = D.n / 2 := by\n rw [Domain.n, Nat.pow_div (show 1 ≤ D.logN by omega) (by decide : 0 < 2)]\n rw... | [
{
"name": "forwardStagePureSpec_eq_forwardMathStageSpec",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 34,
"n_lines": 20,
"n_chars": 751,
"n_subproofs": 2,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 5,
"automatio... | 32 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | @@ -327,6 +327,14 @@
rw [Domain.n]
exact Nat.pow_div (Nat.succ_le_of_lt hstage) (by decide : 0 < 2)
+private theorem stage_stride_half_eq_domain_half
+ (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :
+ 2 ^ stage * 2 ^ (D.logN - (stage + 1)) = D.n / 2 := by
+ rw [Domain.n, Nat.pow_div (show 1 ≤ D... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_72213d59b68c_14 | 9806471714d83a1d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Forward.lean | Forward | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 37 | 1 | [
{
"theorem_name": "forwardMathValueAt_succ_upper",
"depth": 1,
"n_commands": 0,
"n_lines": 63,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [forwardMathValueAt,\n butterfly_upper_div_block stage block j hj,\n butterfly_upper_mod_blockSiz... | [
{
"name": "stage_stride_half_eq_domain_half",
"text": "private theorem stage_stride_half_eq_domain_half\n (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :\n 2 ^ stage * 2 ^ (D.logN - (stage + 1)) = D.n / 2 := by\n rw [Domain.n, Nat.pow_div (show 1 ≤ D.logN by omega) (by decide : 0 < 2)]\n rw... | [
{
"name": "forwardStageSpec_final_eq_forwardSpec",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 38,
"n_lines": 15,
"n_chars": 591,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 4,
"automation_only":... | 35 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | @@ -343,6 +343,14 @@
rw [Domain.n]
exact Nat.pow_div (Nat.succ_le_of_lt hstage) (by decide : 0 < 2)
+private theorem stage_stride_half_eq_domain_half
+ (D : Domain R) (stage : Nat) (hstage : stage < D.logN) :
+ 2 ^ stage * 2 ^ (D.logN - (stage + 1)) = D.n / 2 := by
+ rw [Domain.n, Nat.pow_div (show 1 ≤ D... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_72213d59b68c_15 | 5e2ea300d21dab47 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTT/Forward.lean | Forward | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 37 | 1 | [
{
"theorem_name": "forwardMathValueAt_succ_upper",
"depth": 1,
"n_commands": 0,
"n_lines": 63,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [forwardMathValueAt,\n butterfly_upper_div_block stage block j hj,\n butterfly_upper_mod_blockSiz... | [
{
"name": "omega_pow_add_domain_mul",
"text": "private theorem omega_pow_add_domain_mul (D : Domain R) (e k : Nat) :\n D.omega ^ (e + D.n * k) = D.omega ^ e := by\n rw [pow_add, omega_pow_domain_mul D k, mul_one]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 169,
"n_subproofs": 0,
"n_t... | [
{
"name": "forwardImpl_correct",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 40,
"n_lines": 7,
"n_chars": 229,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 0,
"automation_only": false,
"max_ne... | 37 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Salih Erdem Koçak, Doran Pamukçu
-/
import CompPoly.Univariate.NTT.Transform
/-!
# Forward NTT
This file provides spec-level forward NTT definitions together with an
iterative radix-2 impl... | @@ -357,6 +357,10 @@
simpa [Domain.n] using D.primitive.pow_eq_one
rw [pow_mul, h, one_pow]
+private theorem omega_pow_add_domain_mul (D : Domain R) (e k : Nat) :
+ D.omega ^ (e + D.n * k) = D.omega ^ e := by
+ rw [pow_add, omega_pow_domain_mul D k, mul_one]
+
private theorem omega_pow_domain_half_eq_neg... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c091ba091cb1_0 | 8586249f4b7b32bf | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "coeffs_of_comp_minus_x",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hpos : 0 < f.degree\n · rw [coeffs_of_comp_minus_x_pos_degree hpos]\n · have : f.natDegree = 0 := b... | [
{
"name": "coeffs_of_comp_minus_x_pos_degree",
"text": "private lemma coeffs_of_comp_minus_x_pos_degree {f : Polynomial F} {n : ℕ} (h : 0 < f.degree) :\n (f.comp (-X)).coeff n = if Even n then f.coeff n else -f.coeff n := by\n revert n\n apply degree_pos_induction_on (h0 := h) (P := fun f => _)\n · ae... | [
{
"name": "coeffs_of_comp_minus_x",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 362,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 3,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Julian Sutherland, Ilia Vlasov
-/
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.LinearCombination
... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Julian Sutherland, Ilia Vlasov
-/
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.LinearCombination
... | @@ -40,10 +40,18 @@
open Polynomial
+private lemma coeffs_of_comp_minus_x_pos_degree {f : Polynomial F} {n : ℕ} (h : 0 < f.degree) :
+ (f.comp (-X)).coeff n = if Even n then f.coeff n else -f.coeff n := by
+ revert n
+ apply degree_pos_induction_on (h0 := h) (P := fun f => _)
+ · aesop (add simp coeff_X)
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c091ba091cb1_1 | caae56a0143cd692 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Basic.lean | Basic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "comp_x_square_coeff",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hpos : 0 < f.degree\n · rw [comp_x_square_coeff_pos_deg hpos]\n · obtain ⟨_, hx⟩ :=\n show ∃ x, C x = f... | [
{
"name": "comp_x_square_coeff_pos_deg",
"text": "private lemma comp_x_square_coeff_pos_deg {f : Polynomial F} {n : ℕ} (h : 0 < f.degree) :\n (f.comp (X * X)).coeff n = if Even n then f.coeff (n / 2) else 0 := by\n revert n\n apply degree_pos_induction_on (h0 := h) (P := fun f => _)\n · rintro _ _ (_ ... | [
{
"name": "comp_x_square_coeff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 459,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 3,
"n_automation": 5,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Julian Sutherland, Ilia Vlasov
-/
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.LinearCombination
... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Julian Sutherland, Ilia Vlasov
-/
import Mathlib.Algebra.Polynomial.FieldDivision
import Mathlib.Tactic.FieldSimp
import Mathlib.Tactic.LinearCombination
... | @@ -40,10 +40,23 @@
open Polynomial
+private lemma comp_x_square_coeff_pos_deg {f : Polynomial F} {n : ℕ} (h : 0 < f.degree) :
+ (f.comp (X * X)).coeff n = if Even n then f.coeff (n / 2) else 0 := by
+ revert n
+ apply degree_pos_induction_on (h0 := h) (P := fun f => _)
+ · rintro _ _ (_ | n) <;>
+ aesop ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_866431bdaa38_0 | 9db650c7292a2f81 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multivariate/Rename.lean | Rename | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "foldl_add_comm'",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [Std.ExtTreeMap.foldl_eq_foldl_toList]\n exact list_foldl_add_comm g t.toList 0",
"n_chars": 95,
"n_subp... | [
{
"name": "list_foldl_add_comm",
"text": "/-- In a commutative additive monoid, the order of addition in a list fold\ndoes not matter. -/\nlemma list_foldl_add_comm {β K V : Type*} [AddCommMonoid β]\n (g : K → V → β) (l : List (K × V)) (init : β) :\n List.foldl (fun acc pair => acc + g pair.1 pair.2) ... | [
{
"name": "foldl_add_comm'",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 473,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Multivariate.Operations
import Mathlib.Algebra.MvPolynomial.Rename
/-!
# Properties of variable renaming for `CMvPolynomial`
This file proves properties... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Multivariate.Operations
import Mathlib.Algebra.MvPolynomial.Rename
/-!
# Properties of variable renaming for `CMvPolynomial`
This file proves properties... | @@ -31,12 +31,27 @@
/-! ### Helper lemmas for `fromCMvPolynomial_rename` -/
+/-- In a commutative additive monoid, the order of addition in a list fold
+does not matter. -/
+lemma list_foldl_add_comm {β K V : Type*} [AddCommMonoid β]
+ (g : K → V → β) (l : List (K × V)) (init : β) :
+ List.foldl (fun acc pai... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_866431bdaa38_1 | faf7baae3be521bd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multivariate/Rename.lean | Rename | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 3 | [
{
"theorem_name": "fromCMvPolynomial_rename",
"depth": 1,
"n_commands": 0,
"n_lines": 30,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Express rename as a `Finsupp.sum` via `foldl_eq_sum`\n have step1 : CMvPolynomial.rename f p =\n Finsupp... | [
{
"name": "fromCMvPolynomial_monomial",
"text": "/-- `fromCMvPolynomial` maps `CMvPolynomial.monomial` to\n`MvPolynomial.monomial`. -/\nlemma fromCMvPolynomial_monomial {k : ℕ} (mono : CMvMonomial k) (c : R) :\n fromCMvPolynomial (CMvPolynomial.monomial mono c) =\n MvPolynomial.monomial (CMvMonomial.t... | [
{
"name": "fromCMvPolynomial_rename",
"fan_in": 6,
"n_deps_direct": 4,
"n_deps_transitive": 5,
"n_lines": 39,
"n_chars": 1494,
"n_subproofs": 1,
"n_tactics": 29,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 8,
"n_structural": 1,
"automation_only": false,
... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Multivariate.Operations
import Mathlib.Algebra.MvPolynomial.Rename
/-!
# Properties of variable renaming for `CMvPolynomial`
This file proves properties... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Multivariate.Operations
import Mathlib.Algebra.MvPolynomial.Rename
/-!
# Properties of variable renaming for `CMvPolynomial`
This file proves properties... | @@ -72,6 +72,34 @@
rw [Finsupp.notMem_support_iff] at hxs
simp [hxs]
+/-- `fromCMvPolynomial` maps `CMvPolynomial.monomial` to
+`MvPolynomial.monomial`. -/
+lemma fromCMvPolynomial_monomial {k : ℕ} (mono : CMvMonomial k) (c : R) :
+ fromCMvPolynomial (CMvPolynomial.monomial mono c) =
+ MvPolynomial.monomi... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_866431bdaa38_2 | 554ddd1de4edba8a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multivariate/Rename.lean | Rename | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "fromCMvPolynomial_C",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [C_eq_monomial, fromCMvPolynomial_monomial, toFinsupp_zero,\n ← MvPolynomial.C_apply]",
"n_chars": 100,
... | [
{
"name": "C_eq_monomial",
"text": "/-- `CMvPolynomial.C c` equals `CMvPolynomial.monomial 0 c`. -/\nlemma C_eq_monomial {k : ℕ} (c : R) :\n CMvPolynomial.C (n := k) c = CMvPolynomial.monomial 0 c := by\n by_cases hc : c = 0\n · subst hc; ext m\n unfold CMvPolynomial.coeff CMvPolynomial.C CMvPolynom... | [
{
"name": "fromCMvPolynomial_C",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 10,
"n_chars": 338,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_ne... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Multivariate.Operations
import Mathlib.Algebra.MvPolynomial.Rename
/-!
# Properties of variable renaming for `CMvPolynomial`
This file proves properties... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Multivariate.Operations
import Mathlib.Algebra.MvPolynomial.Rename
/-!
# Properties of variable renaming for `CMvPolynomial`
This file proves properties... | @@ -150,6 +150,27 @@
/-! ### Bridging lemmas for `C` and `X` -/
+/-- `CMvPolynomial.C c` equals `CMvPolynomial.monomial 0 c`. -/
+lemma C_eq_monomial {k : ℕ} (c : R) :
+ CMvPolynomial.C (n := k) c = CMvPolynomial.monomial 0 c := by
+ by_cases hc : c = 0
+ · subst hc; ext m
+ unfold CMvPolynomial.coeff CMvP... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_866431bdaa38_3 | fa52014394c4d68b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multivariate/Rename.lean | Rename | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 6 | [
{
"theorem_name": "rename_C",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply fromCMvPolynomial_injective\n rw [fromCMvPolynomial_rename, fromCMvPolynomial_C,\n fromCMvPolynomial_C]\n exact MvPolyn... | [
{
"name": "fromCMvPolynomial_rename",
"text": "/-- `CMvPolynomial.rename` agrees with `MvPolynomial.rename` under the\n`fromCMvPolynomial` equivalence. -/\nlemma fromCMvPolynomial_rename (f : Fin n → Fin m)\n (p : CMvPolynomial n R) :\n fromCMvPolynomial (CMvPolynomial.rename f p) =\n MvPolynomial.... | [
{
"name": "rename_C",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 11,
"n_chars": 337,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nesting": 4
... | 9 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Multivariate.Operations
import Mathlib.Algebra.MvPolynomial.Rename
/-!
# Properties of variable renaming for `CMvPolynomial`
This file proves properties... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Multivariate.Operations
import Mathlib.Algebra.MvPolynomial.Rename
/-!
# Properties of variable renaming for `CMvPolynomial`
This file proves properties... | @@ -112,6 +112,44 @@
/-! ### Main correspondence lemma -/
+/-- `CMvPolynomial.rename` agrees with `MvPolynomial.rename` under the
+`fromCMvPolynomial` equivalence. -/
+lemma fromCMvPolynomial_rename (f : Fin n → Fin m)
+ (p : CMvPolynomial n R) :
+ fromCMvPolynomial (CMvPolynomial.rename f p) =
+ MvPolyno... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_866431bdaa38_4 | 3c4453c3aea7dd7a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multivariate/Rename.lean | Rename | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "fromCMvPolynomial_X",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [X_eq_monomial, fromCMvPolynomial_monomial,\n toFinsupp_unitMono]\n rfl",
"n_chars": 82,
"n_subproofs": ... | [
{
"name": "X_eq_monomial",
"text": "/-- `CMvPolynomial.X i` equals `CMvPolynomial.monomial eᵢ 1`\nwhere `eᵢ` is the `i`-th standard basis vector. -/\nlemma X_eq_monomial {k : ℕ} (i : Fin k) :\n CMvPolynomial.X (R := R) i = CMvPolynomial.monomial\n (Vector.ofFn (fun j => if j = i then 1 else 0))\n ... | [
{
"name": "fromCMvPolynomial_X",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 10,
"n_chars": 285,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_ne... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Multivariate.Operations
import Mathlib.Algebra.MvPolynomial.Rename
/-!
# Properties of variable renaming for `CMvPolynomial`
This file proves properties... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Multivariate.Operations
import Mathlib.Algebra.MvPolynomial.Rename
/-!
# Properties of variable renaming for `CMvPolynomial`
This file proves properties... | @@ -197,6 +197,19 @@
fromCMvPolynomial_C]
exact MvPolynomial.rename_C f c
+/-- `CMvPolynomial.X i` equals `CMvPolynomial.monomial eᵢ 1`
+where `eᵢ` is the `i`-th standard basis vector. -/
+lemma X_eq_monomial {k : ℕ} (i : Fin k) :
+ CMvPolynomial.X (R := R) i = CMvPolynomial.monomial
+ (Vector.ofFn (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_ffc47f671d4c_0 | 2790d9f912bbaf09 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 2 | [
{
"theorem_name": "lastNonzero_some_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · apply lastNonzero_spec\n intro h_prop\n have ⟨ k', h_some'⟩ := lastNonzero_some k.is_lt h_prop.left... | [
{
"name": "lastNonzero_spec",
"text": "/-- `lastNonzero` returns the largest index with a non-zero coefficient. -/\ntheorem lastNonzero_spec [Zero R] [BEq R] [LawfulBEq R] {p : CPolynomial.Raw R} {k} :\n p.lastNonzero = some k\n → p[k] ≠ 0 ∧ (∀ j, (hj : j < p.size) → j > k → p[j] = 0) := by\n intro (h ... | [
{
"name": "lastNonzero_some_iff",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 11,
"n_chars": 473,
"n_subproofs": 2,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_n... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -121,6 +121,19 @@
(h : p[i] ≠ 0) : ∃ k, p.lastNonzero = some k :=
Array.findIdxRev?_eq_some ⟨i, hi, bne_iff_ne.mpr h⟩
+/-- `lastNonzero` returns the largest index with a non-zero coefficient. -/
+theorem lastNonzero_spec [Zero R] [BEq R] [LawfulBEq R] {p : CPolynomial.Raw R} {k} :
+ p.lastNonzero = some... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_1 | c072696327e7ee5e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 2 | [
{
"theorem_name": "lastNonzero_some_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · apply lastNonzero_spec\n intro h_prop\n have ⟨ k', h_some'⟩ := lastNonzero_some k.is_lt h_prop.left... | [
{
"name": "lastNonzero_some",
"text": "/-- If there is a non-zero coefficient, `lastNonzero` is `some`. -/\ntheorem lastNonzero_some [Zero R] [BEq R] [LawfulBEq R]\n {p : CPolynomial.Raw R} {i} (hi : i < p.size)\n (h : p[i] ≠ 0) : ∃ k, p.lastNonzero = some k :=\n Array.findIdxRev?_eq_some ⟨i, hi, bne... | [
{
"name": "lastNonzero_induct",
"fan_in": 4,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 20,
"n_chars": 940,
"n_subproofs": 2,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_nes... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -115,6 +115,12 @@
rw [bne_iff_ne, ne_eq, not_not]
apply_assumption
+/-- If there is a non-zero coefficient, `lastNonzero` is `some`. -/
+theorem lastNonzero_some [Zero R] [BEq R] [LawfulBEq R]
+ {p : CPolynomial.Raw R} {i} (hi : i < p.size)
+ (h : p[i] ≠ 0) : ∃ k, p.lastNonzero = some k :=
+ Array.fin... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_2 | c51ddbbb555420f5 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 4 | [
{
"theorem_name": "induct",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero =>\n have h_empty : p.trim = #[] := by unfold trim; rw [h_n... | [
{
"name": "lastNonzero_induct",
"text": "/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:\n ```\n induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero => ...\n | case2 p k h_some h_nonzero h_max => ...\n ```\n-/\ntheorem lastNonzero_induct [Zero R] [... | [
{
"name": "induct",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 20,
"n_chars": 944,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 4,
"n_structural": 3,
"automation_only": false,
"max_nesting": 4
}... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -138,6 +138,25 @@
def lastNonzeroProp [Zero R] {p : CPolynomial.Raw R} (k : Fin p.size) : Prop :=
p[k] ≠ 0 ∧ (∀ j, (hj : j < p.size) → j > k → p[j] = 0)
+/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:
+ ```
+ induction p using lastNonzero_induct with
+ | case1 p h_none h_... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_3 | 403a9e788a5200e6 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 4 | [
{
"theorem_name": "induct",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero =>\n have h_empty : p.trim = #[] := by unfold trim; rw [h_n... | [
{
"name": "lastNonzero_induct",
"text": "/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:\n ```\n induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero => ...\n | case2 p k h_some h_nonzero h_max => ...\n ```\n-/\ntheorem lastNonzero_induct [Zero R] [... | [
{
"name": "elim",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 15,
"n_chars": 673,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting": 2
}
] | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -138,6 +138,25 @@
def lastNonzeroProp [Zero R] {p : CPolynomial.Raw R} (k : Fin p.size) : Prop :=
p[k] ≠ 0 ∧ (∀ j, (hj : j < p.size) → j > k → p[j] = 0)
+/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:
+ ```
+ induction p using lastNonzero_induct with
+ | case1 p h_none h_... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_4 | 17bf6780122c7dee | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 4 | [
{
"theorem_name": "induct",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero =>\n have h_empty : p.trim = #[] := by unfold trim; rw [h_n... | [
{
"name": "lastNonzero_induct",
"text": "/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:\n ```\n induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero => ...\n | case2 p k h_some h_nonzero h_max => ...\n ```\n-/\ntheorem lastNonzero_induct [Zero R] [... | [
{
"name": "coeff_eq_getElem_of_lt",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 20,
"n_chars": 812,
"n_subproofs": 3,
"n_tactics": 16,
"cyclomatic": 3,
"n_automation": 6,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,
"ma... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -138,6 +138,25 @@
def lastNonzeroProp [Zero R] {p : CPolynomial.Raw R} (k : Fin p.size) : Prop :=
p[k] ≠ 0 ∧ (∀ j, (hj : j < p.size) → j > k → p[j] = 0)
+/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:
+ ```
+ induction p using lastNonzero_induct with
+ | case1 p h_none h_... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_5 | a883db3a72067b30 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 4 | [
{
"theorem_name": "induct",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero =>\n have h_empty : p.trim = #[] := by unfold trim; rw [h_n... | [
{
"name": "lastNonzero_induct",
"text": "/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:\n ```\n induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero => ...\n | case2 p k h_some h_nonzero h_max => ...\n ```\n-/\ntheorem lastNonzero_induct [Zero R] [... | [
{
"name": "coeff_eq_coeff",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 7,
"n_lines": 10,
"n_chars": 313,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting... | 7 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -138,6 +138,25 @@
def lastNonzeroProp [Zero R] {p : CPolynomial.Raw R} (k : Fin p.size) : Prop :=
p[k] ≠ 0 ∧ (∀ j, (hj : j < p.size) → j > k → p[j] = 0)
+/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:
+ ```
+ induction p using lastNonzero_induct with
+ | case1 p h_none h_... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_6 | f9938c64117fe148 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 4 | [
{
"theorem_name": "induct",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero =>\n have h_empty : p.trim = #[] := by unfold trim; rw [h_n... | [
{
"name": "lastNonzero_induct",
"text": "/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:\n ```\n induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero => ...\n | case2 p k h_some h_nonzero h_max => ...\n ```\n-/\ntheorem lastNonzero_induct [Zero R] [... | [
{
"name": "eq_degree_of_equiv",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 7,
"n_lines": 32,
"n_chars": 1275,
"n_subproofs": 10,
"n_tactics": 30,
"cyclomatic": 3,
"n_automation": 5,
"n_rewrites": 5,
"n_structural": 5,
"automation_only": false,
"max_... | 7 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -159,6 +159,25 @@
have k_is_k' := lastNonzero_unique (lastNonzero_spec h_some') h_prop
rwa [← k_is_k']
+/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:
+ ```
+ induction p using lastNonzero_induct with
+ | case1 p h_none h_all_zero => ...
+ | case2 p k h_some h_nonzero ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_7 | fa65790c04466cce | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 2 | [
{
"theorem_name": "elim",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by induction p using induct with\n | case1 p h_empty h_all_zero => left; exact ⟨h_empty, h_all_zero⟩\n | case2 p k h_extract h_nonzero h_m... | [
{
"name": "induct",
"text": "/-- eliminator for `p.trim`; use with the induction tactic as follows:\n ```\n induction p using induct with\n | case1 p h_empty h_all_zero => ...\n | case2 p k h_extract h_nonzero h_max => ...\n ```\n-/\ntheorem induct [Zero R] [BEq R] [LawfulBEq R] {motive : CPolynomial.R... | [
{
"name": "eq_of_equiv",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 13,
"n_lines": 24,
"n_chars": 791,
"n_subproofs": 1,
"n_tactics": 23,
"cyclomatic": 4,
"n_automation": 5,
"n_rewrites": 7,
"n_structural": 5,
"automation_only": false,
"max_nesting"... | 13 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -178,6 +178,25 @@
have ⟨ h_nonzero, h_max ⟩ := lastNonzero_spec h_some
exact case2 p k h_some h_nonzero h_max
+/-- eliminator for `p.trim`; use with the induction tactic as follows:
+ ```
+ induction p using induct with
+ | case1 p h_empty h_all_zero => ...
+ | case2 p k h_extract h_nonzero h_max => ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_8 | 249e2e27f50d31c7 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 2 | [
{
"theorem_name": "elim",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by induction p using induct with\n | case1 p h_empty h_all_zero => left; exact ⟨h_empty, h_all_zero⟩\n | case2 p k h_extract h_nonzero h_m... | [
{
"name": "induct",
"text": "/-- eliminator for `p.trim`; use with the induction tactic as follows:\n ```\n induction p using induct with\n | case1 p h_empty h_all_zero => ...\n | case2 p k h_extract h_nonzero h_max => ...\n ```\n-/\ntheorem induct [Zero R] [BEq R] [LawfulBEq R] {motive : CPolynomial.R... | [
{
"name": "trim_equiv",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 8,
"n_lines": 5,
"n_chars": 125,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 8 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -157,6 +157,25 @@
have ⟨ h_nonzero, h_max ⟩ := lastNonzero_spec h_some
exact case2 p k h_some h_nonzero h_max
+/-- eliminator for `p.trim`; use with the induction tactic as follows:
+ ```
+ induction p using induct with
+ | case1 p h_empty h_all_zero => ...
+ | case2 p k h_extract h_nonzero h_max => ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_9 | 9953c8d71c2d8b71 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "coeff_eq_coeff",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases (Nat.lt_or_ge i p.size) with hi | hi\n · rw [coeff_eq_getElem_of_lt hi]\n simp [hi]\n · have hi' : i ≥ p.trim.si... | [
{
"name": "coeff_eq_getElem_of_lt",
"text": "theorem coeff_eq_getElem_of_lt [Zero R] [BEq R] [LawfulBEq R]\n {p : CPolynomial.Raw R} {i} (hi : i < p.size) :\n p.trim.coeff i = p[i] := by\n induction p using induct with\n | case1 p h_empty h_all_zero =>\n specialize h_all_zero i hi\n simp [h_em... | [
{
"name": "trim_twice",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 15,
"n_lines": 6,
"n_chars": 147,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": 2... | 15 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -205,11 +205,31 @@
attribute [simp] Array.getElem?_eq_none
+theorem coeff_eq_getElem_of_lt [Zero R] [BEq R] [LawfulBEq R]
+ {p : CPolynomial.Raw R} {i} (hi : i < p.size) :
+ p.trim.coeff i = p[i] := by
+ induction p using induct with
+ | case1 p h_empty h_all_zero =>
+ specialize h_all_zero i hi
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_10 | 9fcae00c1809d321 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "canonical_of_size_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro h\n suffices h_empty : p = #[] by rw [h_empty]; exact canonical_empty\n exact Array.eq_empty_of_size_eq_zero... | [
{
"name": "canonical_empty",
"text": "theorem canonical_empty [Zero R] [BEq R] : (mk (R := R) #[]).trim = #[] := by\n have : (mk (R:=R) #[]).lastNonzero = none := by\n simp [lastNonzero]\n apply Array.findIdxRev?_empty_none\n rfl\n rw [trim, this]\n\n",
"fan_in": 1,
"n_lines": 8,
"n_c... | [
{
"name": "canonical_of_size_zero",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 230,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -163,8 +163,18 @@
def equiv [Zero R] (p q : CPolynomial.Raw R) : Prop :=
∀ i, p.coeff i = q.coeff i
+theorem canonical_empty [Zero R] [BEq R] : (mk (R := R) #[]).trim = #[] := by
+ have : (mk (R:=R) #[]).lastNonzero = none := by
+ simp [lastNonzero]
+ apply Array.findIdxRev?_empty_none
+ rfl
+ rw [t... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_11 | 67ca376889dc83cd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 4 | [
{
"theorem_name": "induct",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero =>\n have h_empty : p.trim = #[] := by unfold trim; rw [h_n... | [
{
"name": "lastNonzero_induct",
"text": "/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:\n ```\n induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero => ...\n | case2 p k h_some h_nonzero h_max => ...\n ```\n-/\ntheorem lastNonzero_induct [Zero R] [... | [
{
"name": "canonical_nonempty_iff",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 27,
"n_chars": 813,
"n_subproofs": 4,
"n_tactics": 24,
"cyclomatic": 3,
"n_automation": 4,
"n_rewrites": 4,
"n_structural": 7,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -138,6 +138,25 @@
def lastNonzeroProp [Zero R] {p : CPolynomial.Raw R} (k : Fin p.size) : Prop :=
p[k] ≠ 0 ∧ (∀ j, (hj : j < p.size) → j > k → p[j] = 0)
+/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:
+ ```
+ induction p using lastNonzero_induct with
+ | case1 p h_none h_... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_12 | 9dd7a13a300fa46c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "canonical_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h hp\n rwa [← lastNonzero_last_iff hp, ← canonical_nonempty_iff hp]\n · rintro h\n rcases Nat.e... | [
{
"name": "canonical_nonempty_iff",
"text": "theorem canonical_nonempty_iff [Zero R] [BEq R] [LawfulBEq R]\n {p : CPolynomial.Raw R} (hp : p.size > 0) :\n p.trim = p ↔ p.lastNonzero = some ⟨ p.size - 1, Nat.pred_lt_self hp ⟩ := by\n unfold trim\n induction p using lastNonzero_induct with\n | case1 ... | [
{
"name": "isCanonical_iff_trim_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 9,
"n_lines": 7,
"n_chars": 217,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -176,6 +176,32 @@
suffices h_empty : p = #[] by rw [h_empty]; exact canonical_empty
exact Array.eq_empty_of_size_eq_zero h
+theorem canonical_nonempty_iff [Zero R] [BEq R] [LawfulBEq R]
+ {p : CPolynomial.Raw R} (hp : p.size > 0) :
+ p.trim = p ↔ p.lastNonzero = some ⟨ p.size - 1, Nat.pred_lt_self hp ⟩... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_13 | bb35f83036d7363a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 4 | [
{
"theorem_name": "induct",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero =>\n have h_empty : p.trim = #[] := by unfold trim; rw [h_n... | [
{
"name": "lastNonzero_induct",
"text": "/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:\n ```\n induction p using lastNonzero_induct with\n | case1 p h_none h_all_zero => ...\n | case2 p k h_some h_nonzero h_max => ...\n ```\n-/\ntheorem lastNonzero_induct [Zero R] [... | [
{
"name": "isCanonical_iff_size_eq_zero_or_getLastD_ne_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 15,
"n_chars": 544,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 4,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 8,
"automa... | 6 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -138,6 +138,25 @@
def lastNonzeroProp [Zero R] {p : CPolynomial.Raw R} (k : Fin p.size) : Prop :=
p[k] ≠ 0 ∧ (∀ j, (hj : j < p.size) → j > k → p[j] = 0)
+/-- eliminator for `p.lastNonzero`, e.g. use with the induction tactic as follows:
+ ```
+ induction p using lastNonzero_induct with
+ | case1 p h_none h_... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_14 | e1f51ea5083588a1 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "canonical_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h hp\n rwa [← lastNonzero_last_iff hp, ← canonical_nonempty_iff hp]\n · rintro h\n rcases Nat.e... | [
{
"name": "canonical_nonempty_iff",
"text": "theorem canonical_nonempty_iff [Zero R] [BEq R] [LawfulBEq R]\n {p : CPolynomial.Raw R} (hp : p.size > 0) :\n p.trim = p ↔ p.lastNonzero = some ⟨ p.size - 1, Nat.pred_lt_self hp ⟩ := by\n unfold trim\n induction p using lastNonzero_induct with\n | case1 ... | [
{
"name": "trim_eq_iff_size_eq_zero_or_getLastD_ne_zero",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 12,
"n_lines": 7,
"n_chars": 312,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_... | 12 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -209,6 +209,32 @@
suffices h_empty : p = #[] by rw [h_empty]; exact canonical_empty
exact Array.eq_empty_of_size_eq_zero h
+theorem canonical_nonempty_iff [Zero R] [BEq R] [LawfulBEq R]
+ {p : CPolynomial.Raw R} (hp : p.size > 0) :
+ p.trim = p ↔ p.lastNonzero = some ⟨ p.size - 1, Nat.pred_lt_self hp ⟩... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_15 | 965b92f64c9efada | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "canonical_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h hp\n rwa [← lastNonzero_last_iff hp, ← canonical_nonempty_iff hp]\n · rintro h\n rcases Nat.e... | [
{
"name": "canonical_nonempty_iff",
"text": "theorem canonical_nonempty_iff [Zero R] [BEq R] [LawfulBEq R]\n {p : CPolynomial.Raw R} (hp : p.size > 0) :\n p.trim = p ↔ p.lastNonzero = some ⟨ p.size - 1, Nat.pred_lt_self hp ⟩ := by\n unfold trim\n induction p using lastNonzero_induct with\n | case1 ... | [
{
"name": "trim_eq_of_isCanonical",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 9,
"n_lines": 6,
"n_chars": 155,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -176,6 +176,32 @@
suffices h_empty : p = #[] by rw [h_empty]; exact canonical_empty
exact Array.eq_empty_of_size_eq_zero h
+theorem canonical_nonempty_iff [Zero R] [BEq R] [LawfulBEq R]
+ {p : CPolynomial.Raw R} (hp : p.size > 0) :
+ p.trim = p ↔ p.lastNonzero = some ⟨ p.size - 1, Nat.pred_lt_self hp ⟩... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_16 | fcd5316157d65861 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "canonical_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h hp\n rwa [← lastNonzero_last_iff hp, ← canonical_nonempty_iff hp]\n · rintro h\n rcases Nat.e... | [
{
"name": "canonical_nonempty_iff",
"text": "theorem canonical_nonempty_iff [Zero R] [BEq R] [LawfulBEq R]\n {p : CPolynomial.Raw R} (hp : p.size > 0) :\n p.trim = p ↔ p.lastNonzero = some ⟨ p.size - 1, Nat.pred_lt_self hp ⟩ := by\n unfold trim\n induction p using lastNonzero_induct with\n | case1 ... | [
{
"name": "isCanonical_of_trim_eq",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 9,
"n_lines": 6,
"n_chars": 154,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"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: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -176,6 +176,32 @@
suffices h_empty : p = #[] by rw [h_empty]; exact canonical_empty
exact Array.eq_empty_of_size_eq_zero h
+theorem canonical_nonempty_iff [Zero R] [BEq R] [LawfulBEq R]
+ {p : CPolynomial.Raw R} (hp : p.size > 0) :
+ p.trim = p ↔ p.lastNonzero = some ⟨ p.size - 1, Nat.pred_lt_self hp ⟩... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_17 | e610c38b2f9825d8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "trim_twice",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply eq_of_equiv\n apply trim_equiv",
"n_chars": 42,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n... | [
{
"name": "trim_equiv",
"text": "theorem trim_equiv [Zero R] [BEq R] [LawfulBEq R] (p : CPolynomial.Raw R) :\n equiv p.trim p := by\n apply coeff_eq_coeff\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 125,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
... | [
{
"name": "isCanonical_trim",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 22,
"n_lines": 5,
"n_chars": 149,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 22 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -301,8 +301,14 @@
· rw [← coeff_eq_getElem, ← coeff_eq_getElem]
rw [coeff_eq_coeff, coeff_eq_coeff, h _]
+theorem trim_equiv [Zero R] [BEq R] [LawfulBEq R] (p : CPolynomial.Raw R) :
+ equiv p.trim p := by
+ apply coeff_eq_coeff
+
theorem trim_twice [Zero R] [BEq R] [LawfulBEq R] (p : CPolynomial.Raw R... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_18 | 3bb67cc300f973c1 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "canonical_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h hp\n rwa [← lastNonzero_last_iff hp, ← canonical_nonempty_iff hp]\n · rintro h\n rcases Nat.e... | [
{
"name": "canonical_nonempty_iff",
"text": "theorem canonical_nonempty_iff [Zero R] [BEq R] [LawfulBEq R]\n {p : CPolynomial.Raw R} (hp : p.size > 0) :\n p.trim = p ↔ p.lastNonzero = some ⟨ p.size - 1, Nat.pred_lt_self hp ⟩ := by\n unfold trim\n induction p using lastNonzero_induct with\n | case1 ... | [
{
"name": "push_trim",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 9,
"n_lines": 9,
"n_chars": 215,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nesting": 2
... | 9 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -176,6 +176,32 @@
suffices h_empty : p = #[] by rw [h_empty]; exact canonical_empty
exact Array.eq_empty_of_size_eq_zero h
+theorem canonical_nonempty_iff [Zero R] [BEq R] [LawfulBEq R]
+ {p : CPolynomial.Raw R} (hp : p.size > 0) :
+ p.trim = p ↔ p.lastNonzero = some ⟨ p.size - 1, Nat.pred_lt_self hp ⟩... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_19 | b77af4536217af8a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "canonical_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h hp\n rwa [← lastNonzero_last_iff hp, ← canonical_nonempty_iff hp]\n · rintro h\n rcases Nat.e... | [
{
"name": "canonical_nonempty_iff",
"text": "theorem canonical_nonempty_iff [Zero R] [BEq R] [LawfulBEq R]\n {p : CPolynomial.Raw R} (hp : p.size > 0) :\n p.trim = p ↔ p.lastNonzero = some ⟨ p.size - 1, Nat.pred_lt_self hp ⟩ := by\n unfold trim\n induction p using lastNonzero_induct with\n | case1 ... | [
{
"name": "non_zero_map",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 19,
"n_chars": 615,
"n_subproofs": 4,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 5,
"automation_only": false,
"max_nesting"... | 9 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -176,6 +176,32 @@
suffices h_empty : p = #[] by rw [h_empty]; exact canonical_empty
exact Array.eq_empty_of_size_eq_zero h
+theorem canonical_nonempty_iff [Zero R] [BEq R] [LawfulBEq R]
+ {p : CPolynomial.Raw R} (hp : p.size > 0) :
+ p.trim = p ↔ p.lastNonzero = some ⟨ p.size - 1, Nat.pred_lt_self hp ⟩... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_20 | a2f847f3bb119699 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "coeff_eq_coeff",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases (Nat.lt_or_ge i p.size) with hi | hi\n · rw [coeff_eq_getElem_of_lt hi]\n simp [hi]\n · have hi' : i ≥ p.trim.si... | [
{
"name": "size_le_size",
"text": "theorem size_le_size [Zero R] [BEq R] (p : CPolynomial.Raw R) : p.trim.size ≤ p.size := by\n unfold trim\n match h : p.lastNonzero with\n | none => simp\n | some i => simp [Array.size_extract]\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 196,
"n_subproof... | [
{
"name": "canonical_ext",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 14,
"n_lines": 11,
"n_chars": 365,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nesting... | 14 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -197,6 +197,12 @@
have h_extract : p.trim = p.extract 0 (k + 1) := by unfold trim; rw [h_some]
exact case2 p k h_extract h_nonzero h_max
+theorem size_le_size [Zero R] [BEq R] (p : CPolynomial.Raw R) : p.trim.size ≤ p.size := by
+ unfold trim
+ match h : p.lastNonzero with
+ | none => simp
+ | some i... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ffc47f671d4c_21 | e2bbdec9d4ca8b90 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Raw/Core.lean | Core | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "canonical_of_size_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro h\n suffices h_empty : p = #[] by rw [h_empty]; exact canonical_empty\n exact Array.eq_empty_of_size_eq_zero... | [
{
"name": "canonical_empty",
"text": "theorem canonical_empty [Zero R] [BEq R] : (mk (R := R) #[]).trim = #[] := by\n have : (mk (R:=R) #[]).lastNonzero = none := by\n simp [lastNonzero]\n apply Array.findIdxRev?_empty_none\n rfl\n rw [trim, this]\n\n",
"fan_in": 1,
"n_lines": 8,
"n_c... | [
{
"name": "isCanonical_ext",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 21,
"n_lines": 6,
"n_chars": 238,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 21 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Gregor Mitscha-Baude, Derek Sorensen, Desmond Coles
-/
import Mathlib.Algebra.Tropical.Basic
import Mathlib.RingTheory.Polynomial.Basic
import CompPoly.Data.Array.Lemmas
/-!
# Ra... | @@ -301,8 +301,18 @@
· rw [← coeff_eq_getElem, ← coeff_eq_getElem]
rw [coeff_eq_coeff, coeff_eq_coeff, h _]
+theorem canonical_empty [Zero R] [BEq R] : (mk (R := R) #[]).trim = #[] := by
+ have : (mk (R:=R) #[]).lastNonzero = none := by
+ simp [lastNonzero]
+ apply Array.findIdxRev?_empty_none
+ rfl... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c1ca8894a79d_0 | f0d37ad35daa9d1f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/List/Lemmas.lean | Lemmas | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "foldl_split_outer",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv_lhs => rw [← append_getLast_dropLast l h]\n rw [foldl_append]\n rfl",
"n_chars": 80,
"n_subproofs": 0,
... | [
{
"name": "append_getLast_dropLast",
"text": "theorem append_getLast_dropLast {α : Type u} (l : List α) (h : l ≠ []) :\n l.dropLast ++ [l.getLast h] = l := by\n induction l with\n | nil =>\n contradiction\n | cons hd tl ih =>\n cases tl with\n | nil =>\n simp [dropLast, getLast]\n | c... | [
{
"name": "foldl_split_outer",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 309,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen, Gregor Mitscha-Baude
-/
import Mathlib.Algebra.GroupWithZero.Nat
import Mathlib.Data.List.GetD
import Mathlib.Order.Lattice.Nat
import Mathlib.T... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen, Gregor Mitscha-Baude
-/
import Mathlib.Algebra.GroupWithZero.Nat
import Mathlib.Data.List.GetD
import Mathlib.Order.Lattice.Nat
import Mathlib.T... | @@ -15,9 +15,26 @@
namespace List
+theorem append_getLast_dropLast {α : Type u} (l : List α) (h : l ≠ []) :
+ l.dropLast ++ [l.getLast h] = l := by
+ induction l with
+ | nil =>
+ contradiction
+ | cons hd tl ih =>
+ cases tl with
+ | nil =>
+ simp [dropLast, getLast]
+ | cons hd' tl' =>
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c1ca8894a79d_1 | ddae1c82f9eff0b7 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/List/Lemmas.lean | Lemmas | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "foldl_split_outer",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv_lhs => rw [← append_getLast_dropLast l h]\n rw [foldl_append]\n rfl",
"n_chars": 80,
"n_subproofs": 0,
... | [
{
"name": "append_getLast_dropLast",
"text": "theorem append_getLast_dropLast {α : Type u} (l : List α) (h : l ≠ []) :\n l.dropLast ++ [l.getLast h] = l := by\n induction l with\n | nil =>\n contradiction\n | cons hd tl ih =>\n cases tl with\n | nil =>\n simp [dropLast, getLast]\n | c... | [
{
"name": "foldr_split_inner",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 309,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen, Gregor Mitscha-Baude
-/
import Mathlib.Algebra.GroupWithZero.Nat
import Mathlib.Data.List.GetD
import Mathlib.Order.Lattice.Nat
import Mathlib.T... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen, Gregor Mitscha-Baude
-/
import Mathlib.Algebra.GroupWithZero.Nat
import Mathlib.Data.List.GetD
import Mathlib.Order.Lattice.Nat
import Mathlib.T... | @@ -15,9 +15,26 @@
namespace List
+theorem append_getLast_dropLast {α : Type u} (l : List α) (h : l ≠ []) :
+ l.dropLast ++ [l.getLast h] = l := by
+ induction l with
+ | nil =>
+ contradiction
+ | cons hd tl ih =>
+ cases tl with
+ | nil =>
+ simp [dropLast, getLast]
+ | cons hd' tl' =>
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c1ca8894a79d_2 | 02eedddabed264af | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/List/Lemmas.lean | Lemmas | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "rightpad_eq_if_rightpad_eq_of_ge",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro hEq\n rw [rightpad_eq_rightpad_append_replicate_of_ge l _ n h]\n rw [rightpad_eq_rightpad_append_... | [
{
"name": "rightpad_eq_rightpad_append_replicate_of_ge",
"text": "theorem rightpad_eq_rightpad_append_replicate_of_ge\n (l : List α) (m n : Nat) (h : n ≤ m) :\n rightpad m unit l = rightpad n unit l ++ replicate (m - max n l.length) unit := by\n simp [rightpad]; omega\n\n",
"fan_in": 1,
"n_line... | [
{
"name": "rightpad_eq_if_rightpad_eq_of_ge",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 18,
"n_chars": 916,
"n_subproofs": 2,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": fals... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen, Gregor Mitscha-Baude
-/
import Mathlib.Algebra.GroupWithZero.Nat
import Mathlib.Data.List.GetD
import Mathlib.Order.Lattice.Nat
import Mathlib.T... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Chung Thai Nguyen, Gregor Mitscha-Baude
-/
import Mathlib.Algebra.GroupWithZero.Nat
import Mathlib.Data.List.GetD
import Mathlib.Order.Lattice.Nat
import Mathlib.T... | @@ -45,9 +45,27 @@
@[simp] theorem rightpad_eq_self (l : List α) (n : Nat) (h : n ≤ l.length) :
rightpad n unit l = l := by simp [rightpad, Nat.sub_eq_zero_of_le h]
+theorem rightpad_eq_rightpad_append_replicate_of_ge
+ (l : List α) (m n : Nat) (h : n ≤ m) :
+ rightpad m unit l = rightpad n unit l ++ replic... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_305623742156_0 | 0bf28a15a33ee627 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Kronecker.lean | Kronecker | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 2 | [
{
"theorem_name": "shiftPow_eq_mul_X_pow",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff_coeff]\n intro n\n rw [coeff_shiftPow, coeff_mul_X_pow]",
"n_chars": 72,
"n_subproofs": 0,
"... | [
{
"name": "coeff_mul_X_pow",
"text": "/-- Coefficient of `c * X ^ m`. -/\ntheorem coeff_mul_X_pow [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (c : CPolynomial R) (m n : ℕ) :\n coeff (c * X ^ m) n = if m ≤ n then coeff c (n - m) else 0 := by\n induction m generalizing n with\n | zero => simp ... | [
{
"name": "shiftPow_eq_mul_X_pow",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 252,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_n... | 2 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | @@ -46,6 +46,22 @@
variable {R : Type*}
+/-- Coefficient of `c * X ^ m`. -/
+theorem coeff_mul_X_pow [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (c : CPolynomial R) (m n : ℕ) :
+ coeff (c * X ^ m) n = if m ≤ n then coeff c (n - m) else 0 := by
+ induction m generalizing n with
+ | zero => simp [pow... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_305623742156_1 | d53dc0f3b24c87d5 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Kronecker.lean | Kronecker | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 2 | [
{
"theorem_name": "shiftPow_eq_mul_X_pow",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff_coeff]\n intro n\n rw [coeff_shiftPow, coeff_mul_X_pow]",
"n_chars": 72,
"n_subproofs": 0,
"... | [
{
"name": "coeff_mul_X_pow",
"text": "/-- Coefficient of `c * X ^ m`. -/\ntheorem coeff_mul_X_pow [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (c : CPolynomial R) (m n : ℕ) :\n coeff (c * X ^ m) n = if m ≤ n then coeff c (n - m) else 0 := by\n induction m generalizing n with\n | zero => simp ... | [
{
"name": "coeff_kroneckerPack",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 26,
"n_chars": 1330,
"n_subproofs": 6,
"n_tactics": 26,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 7,
"n_structural": 7,
"automation_only": false,
"max_... | 3 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | @@ -52,6 +52,22 @@
by_contra hc
exact absurd (le_natDegree_of_ne_zero hc) (Nat.not_le.2 h)
+/-- Coefficient of `c * X ^ m`. -/
+theorem coeff_mul_X_pow [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (c : CPolynomial R) (m n : ℕ) :
+ coeff (c * X ^ m) n = if m ≤ n then coeff c (n - m) else 0 := 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_305623742156_2 | b270e77f2c73f725 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Kronecker.lean | Kronecker | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "shiftPow_eq_mul_X_pow",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff_coeff]\n intro n\n rw [coeff_shiftPow, coeff_mul_X_pow]",
"n_chars": 72,
"n_subproofs": 0,
"... | [
{
"name": "coeff_shiftPow",
"text": "/-- Coefficient of `shiftPow m p`. -/\ntheorem coeff_shiftPow [Zero R] [BEq R] [LawfulBEq R] (m : ℕ) (p : CPolynomial R) (n : ℕ) :\n coeff (shiftPow m p) n = if m ≤ n then coeff p (n - m) else 0 := by\n show ((p.val.mulPowX m).trim).coeff n = _\n rw [CPolynomial.Raw... | [
{
"name": "kroneckerPackFast_eq",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 9,
"n_chars": 343,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_ne... | 4 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | @@ -66,9 +66,25 @@
def shiftPow [Zero R] [BEq R] [LawfulBEq R] (m : ℕ) (p : CPolynomial R) : CPolynomial R :=
⟨(p.val.mulPowX m).trim, CPolynomial.Raw.Trim.isCanonical_trim _⟩
+/-- Coefficient of `shiftPow m p`. -/
+theorem coeff_shiftPow [Zero R] [BEq R] [LawfulBEq R] (m : ℕ) (p : CPolynomial R) (n : ℕ) :
+ c... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_305623742156_3 | 44470d999d6bf979 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Kronecker.lean | Kronecker | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 2 | [
{
"theorem_name": "coeff_kroneckerUnpack",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hkey : i = (D * j + i) % D ∧ j = (D * j + i) / D :=\n ⟨(gap_mod hi).symm, (gap_div hD hi).symm⟩\n unfold kr... | [
{
"name": "gap_mod",
"text": "/-- The remainder of the packed position `D * j + i` is `i`. -/\nprivate theorem gap_mod (hi : i < D) : (D * j + i) % D = i := by\n rw [Nat.add_comm, Nat.add_mul_mod_self_left, Nat.mod_eq_of_lt hi]\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 198,
"n_subproofs":... | [
{
"name": "coeff_kroneckerUnpack",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 22,
"n_chars": 833,
"n_subproofs": 2,
"n_tactics": 18,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 7,
"n_structural": 5,
"automation_only": false,
"max... | 2 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | @@ -58,6 +58,10 @@
variable {D i j : ℕ}
+/-- The remainder of the packed position `D * j + i` is `i`. -/
+private theorem gap_mod (hi : i < D) : (D * j + i) % D = i := by
+ rw [Nat.add_comm, Nat.add_mul_mod_self_left, Nat.mod_eq_of_lt hi]
+
/-- The quotient of the packed position `D * j + i` is `j`. -/
private ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_305623742156_4 | 20743cf140a0b192 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Kronecker.lean | Kronecker | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 2 | [
{
"theorem_name": "coeff_kroneckerUnpack",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hkey : i = (D * j + i) % D ∧ j = (D * j + i) / D :=\n ⟨(gap_mod hi).symm, (gap_div hD hi).symm⟩\n unfold kr... | [
{
"name": "gap_div",
"text": "/-- The quotient of the packed position `D * j + i` is `j`. -/\nprivate theorem gap_div (hD : 0 < D) (hi : i < D) : (D * j + i) / D = j := by\n rw [Nat.add_comm, Nat.add_mul_div_left i j hD, Nat.div_eq_of_lt hi, Nat.zero_add]\n\n",
"fan_in": 2,
"n_lines": 5,
"n_cha... | [
{
"name": "kroneckerUnpackFast_eq",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 24,
"n_chars": 1067,
"n_subproofs": 1,
"n_tactics": 21,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 9,
"n_structural": 3,
"automation_only": false,
"m... | 6 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | @@ -68,6 +68,10 @@
private theorem gap_mod (hi : i < D) : (D * j + i) % D = i := by
rw [Nat.add_comm, Nat.add_mul_mod_self_left, Nat.mod_eq_of_lt hi]
+/-- The quotient of the packed position `D * j + i` is `j`. -/
+private theorem gap_div (hD : 0 < D) (hi : i < D) : (D * j + i) / D = j := by
+ rw [Nat.add_comm, ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_305623742156_5 | 2a23a79b7f291ec8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Kronecker.lean | Kronecker | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 2 | [
{
"theorem_name": "coeff_kroneckerUnpack",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hkey : i = (D * j + i) % D ∧ j = (D * j + i) / D :=\n ⟨(gap_mod hi).symm, (gap_div hD hi).symm⟩\n unfold kr... | [
{
"name": "gap_div",
"text": "/-- The quotient of the packed position `D * j + i` is `j`. -/\nprivate theorem gap_div (hD : 0 < D) (hi : i < D) : (D * j + i) / D = j := by\n rw [Nat.add_comm, Nat.add_mul_div_left i j hD, Nat.div_eq_of_lt hi, Nat.zero_add]\n\n",
"fan_in": 2,
"n_lines": 5,
"n_cha... | [
{
"name": "kroneckerUnpack_kroneckerPack",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 8,
"n_lines": 20,
"n_chars": 1017,
"n_subproofs": 2,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 5,
"n_structural": 4,
"automation_only": false,... | 8 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | @@ -84,6 +84,10 @@
private theorem gap_mod (hi : i < D) : (D * j + i) % D = i := by
rw [Nat.add_comm, Nat.add_mul_mod_self_left, Nat.mod_eq_of_lt hi]
+/-- The quotient of the packed position `D * j + i` is `j`. -/
+private theorem gap_div (hD : 0 < D) (hi : i < D) : (D * j + i) / D = j := by
+ rw [Nat.add_comm, ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_305623742156_6 | dfe17937927e17f9 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Kronecker.lean | Kronecker | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 2 | [
{
"theorem_name": "coeff_kroneckerUnpack",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hkey : i = (D * j + i) % D ∧ j = (D * j + i) / D :=\n ⟨(gap_mod hi).symm, (gap_div hD hi).symm⟩\n unfold kr... | [
{
"name": "gap_div",
"text": "/-- The quotient of the packed position `D * j + i` is `j`. -/\nprivate theorem gap_div (hD : 0 < D) (hi : i < D) : (D * j + i) / D = j := by\n rw [Nat.add_comm, Nat.add_mul_div_left i j hD, Nat.div_eq_of_lt hi, Nat.zero_add]\n\n",
"fan_in": 2,
"n_lines": 5,
"n_cha... | [
{
"name": "kroneckerUnpack_mul",
"fan_in": 3,
"n_deps_direct": 2,
"n_deps_transitive": 10,
"n_lines": 10,
"n_chars": 443,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_n... | 10 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | @@ -84,6 +84,10 @@
private theorem gap_mod (hi : i < D) : (D * j + i) % D = i := by
rw [Nat.add_comm, Nat.add_mul_mod_self_left, Nat.mod_eq_of_lt hi]
+/-- The quotient of the packed position `D * j + i` is `j`. -/
+private theorem gap_div (hD : 0 < D) (hi : i < D) : (D * j + i) / D = j := by
+ rw [Nat.add_comm, ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_305623742156_7 | 148a4b15a532d48c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Kronecker.lean | Kronecker | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "kroneckerUnpack_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← kroneckerPack_mul]\n exact kroneckerUnpack_kroneckerPack hD (p * q) hpq",
"n_chars": 85,
"n_subproofs": ... | [
{
"name": "kroneckerPack_mul",
"text": "/-- Packing is multiplicative. -/\ntheorem kroneckerPack_mul [CommSemiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (D : ℕ) (p q : CBivariate R) :\n kroneckerPack D (p * q) = kroneckerPack D p * kroneckerPack D q := by\n unfold kroneckerPack\n simp only [CPol... | [
{
"name": "kroneckerUnpackFast_mul",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 16,
"n_lines": 9,
"n_chars": 484,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"ma... | 16 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | @@ -125,6 +125,15 @@
(CPolynomial.support P).sum
(fun k => monomialXY (k % D) (k / D) (CPolynomial.coeff P k))
+/-- Packing is multiplicative. -/
+theorem kroneckerPack_mul [CommSemiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (D : ℕ) (p q : CBivariate R) :
+ kroneckerPack D (p * q) = kroneckerPack D ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_305623742156_8 | 417e2a2f2c4bd4eb | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Kronecker.lean | Kronecker | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "kroneckerUnpack_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← kroneckerPack_mul]\n exact kroneckerUnpack_kroneckerPack hD (p * q) hpq",
"n_chars": 85,
"n_subproofs": ... | [
{
"name": "kroneckerPack_mul",
"text": "/-- Packing is multiplicative. -/\ntheorem kroneckerPack_mul [CommSemiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (D : ℕ) (p q : CBivariate R) :\n kroneckerPack D (p * q) = kroneckerPack D p * kroneckerPack D q := by\n unfold kroneckerPack\n simp only [CPol... | [
{
"name": "kroneckerUnpack_withFallback",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 11,
"n_lines": 13,
"n_chars": 619,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
... | 11 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | @@ -105,6 +105,15 @@
(CPolynomial.support P).sum
(fun k => monomialXY (k % D) (k / D) (CPolynomial.coeff P k))
+/-- Packing is multiplicative. -/
+theorem kroneckerPack_mul [CommSemiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (D : ℕ) (p q : CBivariate R) :
+ kroneckerPack D (p * q) = kroneckerPack D ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_305623742156_9 | b2af3d8410a37a1c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Kronecker.lean | Kronecker | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "kroneckerUnpack_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← kroneckerPack_mul]\n exact kroneckerUnpack_kroneckerPack hD (p * q) hpq",
"n_chars": 85,
"n_subproofs": ... | [
{
"name": "kroneckerPack_mul",
"text": "/-- Packing is multiplicative. -/\ntheorem kroneckerPack_mul [CommSemiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (D : ℕ) (p q : CBivariate R) :\n kroneckerPack D (p * q) = kroneckerPack D p * kroneckerPack D q := by\n unfold kroneckerPack\n simp only [CPol... | [
{
"name": "kroneckerUnpack_withFallbackFast",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 11,
"n_lines": 14,
"n_chars": 633,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": fals... | 11 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Univariate.ToPoly
import CompPoly.Univariate.NTT.FastMul
import CompPoly.Univariate.NTTFast.Correctness
/-!
# Kronecker ... | @@ -105,6 +105,15 @@
(CPolynomial.support P).sum
(fun k => monomialXY (k % D) (k / D) (CPolynomial.coeff P k))
+/-- Packing is multiplicative. -/
+theorem kroneckerPack_mul [CommSemiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (D : ℕ) (p q : CBivariate R) :
+ kroneckerPack D (p * q) = kroneckerPack D ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_bb6d995d75e5_0 | 4c4a527ecc0dd7b6 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Radix4DIF.lean | Radix4DIF | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "difButterfly_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n change\n (let u := (difButterfly v j0 j1 acc).getD i0 0\n let vv := (difButterfly v j0 j1 acc).getD i1 0\n ((... | [
{
"name": "getD_difButterfly_of_ne",
"text": "private theorem getD_difButterfly_of_ne\n (w : R) (i0 i1 k : Nat) (acc : Array R) (hk0 : k ≠ i0) (hk1 : k ≠ i1) :\n (difButterfly w i0 i1 acc).getD k 0 = acc.getD k 0 := by\n have h0 : i0 ≠ k := fun h ↦ hk0 h.symm\n have h1 : i1 ≠ k := fun h ↦ hk1 h.symm... | [
{
"name": "difButterfly_comm",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 24,
"n_chars": 1117,
"n_subproofs": 0,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 10,
"n_structural": 0,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.DIF
/-!
# Radix-4 DIF NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-frequency sta... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.DIF
/-!
# Radix-4 DIF NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-frequency sta... | @@ -26,11 +26,40 @@
let v := acc.getD i1 0
(acc.set! i0 (u + v)).set! i1 (w * (u - v))
+private theorem getD_difButterfly_of_ne
+ (w : R) (i0 i1 k : Nat) (acc : Array R) (hk0 : k ≠ i0) (hk1 : k ≠ i1) :
+ (difButterfly w i0 i1 acc).getD k 0 = acc.getD k 0 := by
+ have h0 : i0 ≠ k := fun h ↦ hk0 h.symm
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_bb6d995d75e5_1 | c47000b8d35dc677 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Radix4DIF.lean | Radix4DIF | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "runStagesDIFRadix4WithTwiddles_eq_difMathStageSpec",
"depth": 1,
"n_commands": 0,
"n_lines": 116,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let radixStep : Nat → Array R → Array R :=\n fun pass acc ↦\n let highStage :=... | [
{
"name": "butterflyRadix4StageDIFWithTwiddles_eq_two_stages",
"text": "private theorem butterflyRadix4StageDIFWithTwiddles_eq_two_stages\n (D : NTT.Domain R) (lowStage : Nat) (twiddlesHigh twiddlesLow a : Array R)\n (ha : a.size = D.n) (hstage : lowStage + 1 < D.logN) :\n butterflyRadix4StageDIFWi... | [
{
"name": "runStagesDIFRadix4WithTwiddles_eq_difMathStageSpec",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 121,
"n_chars": 5437,
"n_subproofs": 16,
"n_tactics": 116,
"cyclomatic": 2,
"n_automation": 18,
"n_rewrites": 20,
"n_structural": 13,
... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.DIF
/-!
# Radix-4 DIF NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-frequency sta... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.DIF
/-!
# Radix-4 DIF NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-frequency sta... | @@ -559,6 +559,42 @@
(2 * blocks) 0 (butterflyDIFBlocks twiddlesHigh (4 * q) (2 * q) blocks 0 acc)
(by simp))
+private theorem butterflyRadix4StageDIFWithTwiddles_eq_two_stages
+ (D : NTT.Domain R) (lowStage : Nat) (twiddlesHigh twiddlesLow a : Array R)
+ (ha : a.size = D.n) (hstag... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_bb6d995d75e5_2 | ac95b78c8ed2dc95 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/NTTFast/Correctness/Radix4DIF.lean | Radix4DIF | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "runStagesDIFRadix4WithTwiddles_eq_difMathStageSpec",
"depth": 1,
"n_commands": 0,
"n_lines": 116,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let radixStep : Nat → Array R → Array R :=\n fun pass acc ↦\n let highStage :=... | [
{
"name": "butterflyRadix4StageDIFWithTwiddles_eq_two_stages",
"text": "private theorem butterflyRadix4StageDIFWithTwiddles_eq_two_stages\n (D : NTT.Domain R) (lowStage : Nat) (twiddlesHigh twiddlesLow a : Array R)\n (ha : a.size = D.n) (hstage : lowStage + 1 < D.logN) :\n butterflyRadix4StageDIFWi... | [
{
"name": "runStagesDIFRadix4WithTwiddles_correct",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 406,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": ... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.DIF
/-!
# Radix-4 DIF NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-frequency sta... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.NTTFast.Correctness.DIF
/-!
# Radix-4 DIF NTTFast correctness
Correctness proofs for the mixed radix-4 decimation-in-frequency sta... | @@ -559,6 +559,42 @@
(2 * blocks) 0 (butterflyDIFBlocks twiddlesHigh (4 * q) (2 * q) blocks 0 acc)
(by simp))
+private theorem butterflyRadix4StageDIFWithTwiddles_eq_two_stages
+ (D : NTT.Domain R) (lowStage : Nat) (twiddlesHigh twiddlesLow a : Array R)
+ (ha : a.size = D.n) (hstag... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_a61c196698e8_0 | d31a84e03540d217 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/CMvEquiv.lean | CMvEquiv | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "bivariateEquiv_CC",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold bivariateEquiv\n simp [ringEquiv, Polynomial.map_C, CC_toPoly,\n CMvPolynomial.isEmptyRingEquiv_symm_apply... | [
{
"name": "isEmptyRingEquiv_symm_apply",
"text": "/-- `isEmptyRingEquiv.symm` maps scalars to constants. -/\n@[simp]\nlemma isEmptyRingEquiv_symm_apply\n {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R] (r : R) :\n CMvPolynomial.isEmptyRingEquiv.symm r = CMvPolynomial.C r := by\n unfold CMvPolynomi... | [
{
"name": "bivariateEquiv_CC",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 340,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 2 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Multivariate.CMvPolynomial
import CompPoly.Multivariate.MvPolyEquiv.Instances
import Com... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Multivariate.CMvPolynomial
import CompPoly.Multivariate.MvPolyEquiv.Instances
import Com... | @@ -50,6 +50,15 @@
open CPoly
+/-- `isEmptyRingEquiv.symm` maps scalars to constants. -/
+@[simp]
+lemma isEmptyRingEquiv_symm_apply
+ {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R] (r : R) :
+ CMvPolynomial.isEmptyRingEquiv.symm r = CMvPolynomial.C r := by
+ unfold CMvPolynomial.isEmptyRingEquiv
+ rw ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_a61c196698e8_1 | 676ca5646f93ffbd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/CMvEquiv.lean | CMvEquiv | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "bivariateEquiv_CC",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold bivariateEquiv\n simp [ringEquiv, Polynomial.map_C, CC_toPoly,\n CMvPolynomial.isEmptyRingEquiv_symm_apply... | [
{
"name": "isEmptyRingEquiv_symm_apply",
"text": "/-- `isEmptyRingEquiv.symm` maps scalars to constants. -/\n@[simp]\nlemma isEmptyRingEquiv_symm_apply\n {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R] (r : R) :\n CMvPolynomial.isEmptyRingEquiv.symm r = CMvPolynomial.C r := by\n unfold CMvPolynomi... | [
{
"name": "bivariateEquiv_symm_C",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 8,
"n_chars": 254,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_n... | 3 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Multivariate.CMvPolynomial
import CompPoly.Multivariate.MvPolyEquiv.Instances
import Com... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Multivariate.CMvPolynomial
import CompPoly.Multivariate.MvPolyEquiv.Instances
import Com... | @@ -50,6 +50,15 @@
open CPoly
+/-- `isEmptyRingEquiv.symm` maps scalars to constants. -/
+@[simp]
+lemma isEmptyRingEquiv_symm_apply
+ {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R] (r : R) :
+ CMvPolynomial.isEmptyRingEquiv.symm r = CMvPolynomial.C r := by
+ unfold CMvPolynomial.isEmptyRingEquiv
+ rw ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_a61c196698e8_2 | d77c319a91076997 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/CMvEquiv.lean | CMvEquiv | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "bivariateEquiv_symm_X0",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply bivariateEquiv.injective\n simp [bivariateEquiv_Y]",
"n_chars": 62,
"n_subproofs": 0,
"n_tactics"... | [
{
"name": "bivariateEquiv_Y",
"text": "/-- `bivariateEquiv` maps `CBivariate.Y` to the first variable. -/\nlemma bivariateEquiv_Y :\n bivariateEquiv (CBivariate.Y : CBivariate R) =\n CMvPolynomial.X 0 := by\n -- `finSuccEquiv_symm_X` is applied here by `simp`\n simp [bivariateEquiv, ringEquiv, Y_t... | [
{
"name": "bivariateEquiv_symm_X0",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 254,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"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: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Multivariate.CMvPolynomial
import CompPoly.Multivariate.MvPolyEquiv.Instances
import Com... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Multivariate.CMvPolynomial
import CompPoly.Multivariate.MvPolyEquiv.Instances
import Com... | @@ -134,10 +134,19 @@
toPolyEquiv.trans <|
embedCoeffs.trans <| foldInner.trans foldOuter
+/-- `bivariateEquiv` maps `CBivariate.Y` to the first variable. -/
+lemma bivariateEquiv_Y :
+ bivariateEquiv (CBivariate.Y : CBivariate R) =
+ CMvPolynomial.X 0 := by
+ -- `finSuccEquiv_symm_X` is applied here... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_a61c196698e8_3 | 67b65acc79313bc2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/CMvEquiv.lean | CMvEquiv | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "bivariateEquiv_symm_X1",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply bivariateEquiv.injective\n simp [bivariateEquiv_X]",
"n_chars": 62,
"n_subproofs": 0,
"n_tactics"... | [
{
"name": "bivariateEquiv_X",
"text": "/-- `bivariateEquiv` maps `CBivariate.X` to the second variable. -/\nlemma bivariateEquiv_X :\n bivariateEquiv (CBivariate.X : CBivariate R) =\n CMvPolynomial.X 1 := by\n -- `finSuccEquiv_symm_X` is applied here by `simp`\n simp [bivariateEquiv, ringEquiv, X_... | [
{
"name": "bivariateEquiv_symm_X1",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 255,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"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: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Multivariate.CMvPolynomial
import CompPoly.Multivariate.MvPolyEquiv.Instances
import Com... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import CompPoly.Multivariate.CMvPolynomial
import CompPoly.Multivariate.MvPolyEquiv.Instances
import Com... | @@ -134,10 +134,19 @@
toPolyEquiv.trans <|
embedCoeffs.trans <| foldInner.trans foldOuter
+/-- `bivariateEquiv` maps `CBivariate.X` to the second variable. -/
+lemma bivariateEquiv_X :
+ bivariateEquiv (CBivariate.X : CBivariate R) =
+ CMvPolynomial.X 1 := by
+ -- `finSuccEquiv_symm_X` is applied her... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_f7e8bc1c0902_2 | 7e80856cba535cd1 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/BabyBear.lean | BabyBear | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "sqChain_twoAdicGenerators_shift",
"depth": 1,
"n_commands": 0,
"n_lines": 27,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n generalizing k with\n | zero =>\n simp [sqChain]\n | succ n ih =>\n calc\n ... | [
{
"name": "twoAdicGenerators_succ_square_eq",
"text": "/-- Consecutive BabyBear two-adic generators square to the previous generator. -/\n@[simp] lemma twoAdicGenerators_succ_square_eq (idx : Nat) (h : idx < twoAdicity) :\n haveI : idx + 1 < twoAdicGenerators.length := by simp [twoAdicGenerators_length, ... | [
{
"name": "twoAdicGenerators_pow_twoPow_eq_one",
"fan_in": 3,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 16,
"n_chars": 702,
"n_subproofs": 2,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": f... | 5 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Valerii Huhnin
-/
import CompPoly.Fields.Basic
import CompPoly.Fields.PrattCertificate
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.RingTheory.RootsOfUnity.Pr... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Valerii Huhnin
-/
import CompPoly.Fields.Basic
import CompPoly.Fields.PrattCertificate
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.RingTheory.RootsOfUnity.Pr... | @@ -109,6 +109,12 @@
fin_cases idx
<;> simp [twoAdicGenerators] <;> decide
+/-- Consecutive BabyBear two-adic generators square to the previous generator. -/
+@[simp] lemma twoAdicGenerators_succ_square_eq (idx : Nat) (h : idx < twoAdicity) :
+ haveI : idx + 1 < twoAdicGenerators.length := by simp [twoAdicGe... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_f7e8bc1c0902_3 | b593819ffa83c1bf | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/BabyBear.lean | BabyBear | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "twoAdicGenerators_pow_twoPow_eq_one",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← sqChain_eq_pow_two_pow]\n rcases bits with ⟨n, hn⟩\n have hshift :\n sqChain twoAdicGener... | [
{
"name": "sqChain_eq_pow_two_pow",
"text": "/-- Repeated squaring agrees with exponentiation by a power of two. -/\nprivate theorem sqChain_eq_pow_two_pow (g : Field) (n : Nat) :\n sqChain g n = g ^ (2 ^ n) := by\n induction n with\n | zero => simp [sqChain]\n | succ n ih => simp [sqChain, ih, pow_su... | [
{
"name": "twoAdicGenerators_pow_ne_one_aux",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 21,
"n_chars": 951,
"n_subproofs": 3,
"n_tactics": 16,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": fals... | 6 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Valerii Huhnin
-/
import CompPoly.Fields.Basic
import CompPoly.Fields.PrattCertificate
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.RingTheory.RootsOfUnity.Pr... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Valerii Huhnin
-/
import CompPoly.Fields.Basic
import CompPoly.Fields.PrattCertificate
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.RingTheory.RootsOfUnity.Pr... | @@ -121,6 +121,13 @@
| 0 => g
| n + 1 => let h := sqChain g n; h * h
+/-- Repeated squaring agrees with exponentiation by a power of two. -/
+private theorem sqChain_eq_pow_two_pow (g : Field) (n : Nat) :
+ sqChain g n = g ^ (2 ^ n) := by
+ induction n with
+ | zero => simp [sqChain]
+ | succ n ih => 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_f7e8bc1c0902_4 | 1adb66a9c96cfe90 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/BabyBear.lean | BabyBear | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "twoAdicGenerators_pow_twoPow_eq_one",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← sqChain_eq_pow_two_pow]\n rcases bits with ⟨n, hn⟩\n have hshift :\n sqChain twoAdicGener... | [
{
"name": "sqChain_eq_pow_two_pow",
"text": "/-- Repeated squaring agrees with exponentiation by a power of two. -/\nprivate theorem sqChain_eq_pow_two_pow (g : Field) (n : Nat) :\n sqChain g n = g ^ (2 ^ n) := by\n induction n with\n | zero => simp [sqChain]\n | succ n ih => simp [sqChain, ih, pow_su... | [
{
"name": "twoAdicGenerators_pow_twoPow_ne_one_of_lt",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 8,
"n_chars": 356,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only... | 7 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Valerii Huhnin
-/
import CompPoly.Fields.Basic
import CompPoly.Fields.PrattCertificate
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.RingTheory.RootsOfUnity.Pr... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Valerii Huhnin
-/
import CompPoly.Fields.Basic
import CompPoly.Fields.PrattCertificate
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.RingTheory.RootsOfUnity.Pr... | @@ -121,6 +121,13 @@
| 0 => g
| n + 1 => let h := sqChain g n; h * h
+/-- Repeated squaring agrees with exponentiation by a power of two. -/
+private theorem sqChain_eq_pow_two_pow (g : Field) (n : Nat) :
+ sqChain g n = g ^ (2 ^ n) := by
+ induction n with
+ | zero => simp [sqChain]
+ | succ n ih => 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_f7e8bc1c0902_5 | 423d387d3a956483 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/BabyBear.lean | BabyBear | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "twoAdicGenerators_pow_twoPow_eq_one",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← sqChain_eq_pow_two_pow]\n rcases bits with ⟨n, hn⟩\n have hshift :\n sqChain twoAdicGener... | [
{
"name": "sqChain_twoAdicGenerators_shift",
"text": "/-- Repeated squaring walks backward through the precomputed two-adic generator table. -/\nprivate theorem sqChain_twoAdicGenerators_shift (k n : Nat) (hkn : k + n ≤ twoAdicity) :\n sqChain twoAdicGenerators[(⟨k + n, by omega⟩ : Fin (twoAdicity + 1))]... | [
{
"name": "isPrimitiveRoot_twoAdicGenerator",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 19,
"n_chars": 734,
"n_subproofs": 2,
"n_tactics": 15,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 5,
"automation_only": fals... | 9 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Valerii Huhnin
-/
import CompPoly.Fields.Basic
import CompPoly.Fields.PrattCertificate
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.RingTheory.RootsOfUnity.Pr... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Valerii Huhnin
-/
import CompPoly.Fields.Basic
import CompPoly.Fields.PrattCertificate
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.RingTheory.RootsOfUnity.Pr... | @@ -128,6 +128,37 @@
| zero => simp [sqChain]
| succ n ih => simp [sqChain, ih, pow_succ, pow_mul]
+/-- Repeated squaring walks backward through the precomputed two-adic generator table. -/
+private theorem sqChain_twoAdicGenerators_shift (k n : Nat) (hkn : k + n ≤ twoAdicity) :
+ sqChain twoAdicGenerators[(... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_f7e8bc1c0902_6 | ae012c43d1a187f8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/BabyBear.lean | BabyBear | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "twoAdicGenerators_pow_twoPow_eq_one",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← sqChain_eq_pow_two_pow]\n rcases bits with ⟨n, hn⟩\n have hshift :\n sqChain twoAdicGener... | [
{
"name": "sqChain_eq_pow_two_pow",
"text": "/-- Repeated squaring agrees with exponentiation by a power of two. -/\nprivate theorem sqChain_eq_pow_two_pow (g : Field) (n : Nat) :\n sqChain g n = g ^ (2 ^ n) := by\n induction n with\n | zero => simp [sqChain]\n | succ n ih => simp [sqChain, ih, pow_su... | [
{
"name": "twoAdicGenerator_unit_mem_rootsOfUnity",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 10,
"n_chars": 453,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only":... | 6 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Valerii Huhnin
-/
import CompPoly.Fields.Basic
import CompPoly.Fields.PrattCertificate
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.RingTheory.RootsOfUnity.Pr... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Valerii Huhnin
-/
import CompPoly.Fields.Basic
import CompPoly.Fields.PrattCertificate
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.RingTheory.RootsOfUnity.Pr... | @@ -121,6 +121,13 @@
| 0 => g
| n + 1 => let h := sqChain g n; h * h
+/-- Repeated squaring agrees with exponentiation by a power of two. -/
+private theorem sqChain_eq_pow_two_pow (g : Field) (n : Nat) :
+ sqChain g n = g ^ (2 ^ n) := by
+ induction n with
+ | zero => simp [sqChain]
+ | succ n ih => 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_f7e8bc1c0902_7 | 644e3d4f187d3637 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/BabyBear.lean | BabyBear | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "twoAdicGenerators_pow_twoPow_eq_one",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← sqChain_eq_pow_two_pow]\n rcases bits with ⟨n, hn⟩\n have hshift :\n sqChain twoAdicGener... | [
{
"name": "sqChain_twoAdicGenerators_shift",
"text": "/-- Repeated squaring walks backward through the precomputed two-adic generator table. -/\nprivate theorem sqChain_twoAdicGenerators_shift (k n : Nat) (hkn : k + n ≤ twoAdicity) :\n sqChain twoAdicGenerators[(⟨k + n, by omega⟩ : Fin (twoAdicity + 1))]... | [
{
"name": "twoAdicGenerators_order",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 11,
"n_chars": 462,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"ma... | 9 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Valerii Huhnin
-/
import CompPoly.Fields.Basic
import CompPoly.Fields.PrattCertificate
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.RingTheory.RootsOfUnity.Pr... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao, Valerii Huhnin
-/
import CompPoly.Fields.Basic
import CompPoly.Fields.PrattCertificate
import Mathlib.Algebra.Order.Ring.Star
import Mathlib.RingTheory.RootsOfUnity.Pr... | @@ -128,6 +128,37 @@
| zero => simp [sqChain]
| succ n ih => simp [sqChain, ih, pow_succ, pow_mul]
+/-- Repeated squaring walks backward through the precomputed two-adic generator table. -/
+private theorem sqChain_twoAdicGenerators_shift (k n : Nat) (hkn : k + n ≤ twoAdicity) :
+ sqChain twoAdicGenerators[(... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_ef268d1ecce0_0 | de668215b340c105 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Data/Polynomial/MonomialBasis.lean | MonomialBasis | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "finiteDimensional_degreeLT",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h : 0 < Module.finrank L (L⦃< n⦄[X]) := by\n rw [finrank_degreeLT_n n]\n omega\n exact FiniteDimensi... | [
{
"name": "finrank_degreeLT_n",
"text": "theorem finrank_degreeLT_n (n : ℕ) : Module.finrank L (L⦃< n⦄[X]) = n := by\n have monomial_basis : Basis (Fin n) (R := L) (M := L⦃< n⦄[X]) := monomialBasisOfDegreeLT (n := n)\n rw [Module.finrank_eq_card_basis monomial_basis]\n rw [Fintype.card_fin]\n\n",
"fa... | [
{
"name": "finiteDimensional_degreeLT",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 247,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.MvPolynomial.Notation
import Mathlib.Algebra.Lie.OfAssociative
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Li... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.MvPolynomial.Notation
import Mathlib.Algebra.Lie.OfAssociative
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Li... | @@ -122,9 +122,16 @@
· exact h_li_submodule
· exact le_of_eq (hab := h_span_submodule.symm)
+theorem finrank_degreeLT_n (n : ℕ) : Module.finrank L (L⦃< n⦄[X]) = n := by
+ have monomial_basis : Basis (Fin n) (R := L) (M := L⦃< n⦄[X]) := monomialBasisOfDegreeLT (n := n)
+ rw [Module.finrank_eq_card_basis monomi... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_93c0e93d7c7f_0 | 0beb1d6d85691e4a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/ManyEval/Correctness.lean | Correctness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "vector_array_foldl_push_toList",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n convert array_foldl_push_toList p.toArray acc using 1\n simp",
"n_chars": 66,
"n_subproofs": 0,
... | [
{
"name": "array_foldl_push_toList",
"text": "private lemma array_foldl_push_toList {α : Type*} (xs acc : Array α) :\n (Array.foldl (fun acc x ↦ acc.push x) acc xs 0 xs.size).toList =\n acc.toList ++ xs.toList := by\n cases xs with\n | mk xs =>\n induction xs generalizing acc with\n | ni... | [
{
"name": "vector_array_foldl_push_toList",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 276,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
... | 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.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | @@ -16,9 +16,20 @@
variable {R : Type*} {n : Nat}
+private lemma array_foldl_push_toList {α : Type*} (xs acc : Array α) :
+ (Array.foldl (fun acc x ↦ acc.push x) acc xs 0 xs.size).toList =
+ acc.toList ++ xs.toList := by
+ cases xs with
+ | mk xs =>
+ induction xs generalizing acc 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_93c0e93d7c7f_1 | 396b8cfdbf1c4232 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/ManyEval/Correctness.lean | Correctness | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "valuesByPolynomialListLoop_toList",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction polys generalizing acc with\n | nil => simp\n | cons p polys ih =>\n simp only [List.fol... | [
{
"name": "vector_array_foldl_push_toList",
"text": "private lemma vector_array_foldl_push_toList (p : CMlPolynomialEval R n) (acc : Array R) :\n (Array.foldl (fun acc x ↦ acc.push x) acc p.toArray 0 (2 ^ n)).toList =\n acc.toList ++ p.toArray.toList := by\n convert array_foldl_push_toList p.toArra... | [
{
"name": "valuesByPolynomialListLoop_toList",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 16,
"n_chars": 554,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": fals... | 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.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | @@ -25,6 +25,12 @@
| nil => simp
| cons _ _ _ => simp
+private lemma vector_array_foldl_push_toList (p : CMlPolynomialEval R n) (acc : Array R) :
+ (Array.foldl (fun acc x ↦ acc.push x) acc p.toArray 0 (2 ^ n)).toList =
+ acc.toList ++ p.toArray.toList := by
+ convert array_foldl_push_toList 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_93c0e93d7c7f_2 | 37c37a7566482ac3 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/ManyEval/Correctness.lean | Correctness | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "valuesByPolynomialListLoop_toList",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction polys generalizing acc with\n | nil => simp\n | cons p polys ih =>\n simp only [List.fol... | [
{
"name": "vector_array_foldl_push_toList",
"text": "private lemma vector_array_foldl_push_toList (p : CMlPolynomialEval R n) (acc : Array R) :\n (Array.foldl (fun acc x ↦ acc.push x) acc p.toArray 0 (2 ^ n)).toList =\n acc.toList ++ p.toArray.toList := by\n convert array_foldl_push_toList p.toArra... | [
{
"name": "valuesByPolynomial_toList",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 331,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"m... | 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.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | @@ -25,6 +25,12 @@
| nil => simp
| cons _ _ _ => simp
+private lemma vector_array_foldl_push_toList (p : CMlPolynomialEval R n) (acc : Array R) :
+ (Array.foldl (fun acc x ↦ acc.push x) acc p.toArray 0 (2 ^ n)).toList =
+ acc.toList ++ p.toArray.toList := by
+ convert array_foldl_push_toList 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_93c0e93d7c7f_3 | efdcb50b7a7ee32d | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/ManyEval/Correctness.lean | Correctness | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "valuesByPolynomial_getD",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [array_getD_toList]\n rw [valuesByPolynomial_toList]\n have hwidth : ∀ p ∈ polys.toList, (p.toArray.toList).l... | [
{
"name": "valuesByPolynomial_toList",
"text": "private lemma valuesByPolynomial_toList (polys : Array (CMlPolynomialEval R n)) :\n (valuesByPolynomial polys).toList =\n polys.toList.flatMap (fun p ↦ p.toArray.toList) := by\n cases polys with\n | mk polys =>\n simpa [valuesByPolynomial] using... | [
{
"name": "valuesByPolynomial_getD",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 21,
"n_chars": 779,
"n_subproofs": 3,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
"m... | 6 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | @@ -46,6 +46,14 @@
rw [vector_array_foldl_push_toList]
simp [List.append_assoc]
+private lemma valuesByPolynomial_toList (polys : Array (CMlPolynomialEval R n)) :
+ (valuesByPolynomial polys).toList =
+ polys.toList.flatMap (fun p ↦ p.toArray.toList) := by
+ cases polys with
+ | mk polys =>
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_93c0e93d7c7f_4 | e98324b247e35f03 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/ManyEval/Correctness.lean | Correctness | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "valuesByPolynomial_getD",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [array_getD_toList]\n rw [valuesByPolynomial_toList]\n have hwidth : ∀ p ∈ polys.toList, (p.toArray.toList).l... | [
{
"name": "valuesByPolynomial_toList",
"text": "private lemma valuesByPolynomial_toList (polys : Array (CMlPolynomialEval R n)) :\n (valuesByPolynomial polys).toList =\n polys.toList.flatMap (fun p ↦ p.toArray.toList) := by\n cases polys with\n | mk polys =>\n simpa [valuesByPolynomial] using... | [
{
"name": "foldLayeredPolyLoop_valuesByPolynomial_toList",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 53,
"n_chars": 2495,
"n_subproofs": 9,
"n_tactics": 46,
"cyclomatic": 1,
"n_automation": 11,
"n_rewrites": 9,
"n_structural": 0,
"automat... | 7 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | @@ -46,6 +46,14 @@
rw [vector_array_foldl_push_toList]
simp [List.append_assoc]
+private lemma valuesByPolynomial_toList (polys : Array (CMlPolynomialEval R n)) :
+ (valuesByPolynomial polys).toList =
+ polys.toList.flatMap (fun p ↦ p.toArray.toList) := by
+ cases polys with
+ | mk polys =>
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_93c0e93d7c7f_5 | 2f0b895fa9c50e17 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/ManyEval/Correctness.lean | Correctness | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "valuesByPolynomial_getD",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [array_getD_toList]\n rw [valuesByPolynomial_toList]\n have hwidth : ∀ p ∈ polys.toList, (p.toArray.toList).l... | [
{
"name": "valuesByPolynomial_toList",
"text": "private lemma valuesByPolynomial_toList (polys : Array (CMlPolynomialEval R n)) :\n (valuesByPolynomial polys).toList =\n polys.toList.flatMap (fun p ↦ p.toArray.toList) := by\n cases polys with\n | mk polys =>\n simpa [valuesByPolynomial] using... | [
{
"name": "foldLayeredLayerLoop_valuesByPolynomial_toList",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 8,
"n_lines": 40,
"n_chars": 1819,
"n_subproofs": 3,
"n_tactics": 32,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 5,
"n_structural": 1,
"automat... | 8 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | @@ -46,6 +46,14 @@
rw [vector_array_foldl_push_toList]
simp [List.append_assoc]
+private lemma valuesByPolynomial_toList (polys : Array (CMlPolynomialEval R n)) :
+ (valuesByPolynomial polys).toList =
+ polys.toList.flatMap (fun p ↦ p.toArray.toList) := by
+ cases polys with
+ | mk polys =>
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_93c0e93d7c7f_6 | 66be110c32f6d8e4 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/ManyEval/Correctness.lean | Correctness | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "evalManyMle_eq_map_evalMle",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Array.toList_inj.mp\n simp [evalManyMle, evalManyMleLoop_toList]",
"n_chars": 76,
"n_subproofs": ... | [
{
"name": "evalManyMleLoop_toList",
"text": "private lemma evalManyMleLoop_toList [CommRing R]\n (polys : Array (CMlPolynomialEval R n)) (x : Vector R n) (i : Nat) (acc : Array R) :\n (evalManyMleLoop polys x i acc).toList =\n acc.toList ++ (polys.toList.drop i).map (fun p ↦ evalMle p x) := by\n ... | [
{
"name": "evalManyMle_eq_map_evalMle",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 331,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | @@ -16,10 +16,35 @@
variable {R : Type*} {n : Nat}
+private lemma evalManyMleLoop_toList [CommRing R]
+ (polys : Array (CMlPolynomialEval R n)) (x : Vector R n) (i : Nat) (acc : Array R) :
+ (evalManyMleLoop polys x i acc).toList =
+ acc.toList ++ (polys.toList.drop i).map (fun p ↦ evalMle p x) := 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_93c0e93d7c7f_7 | 6b7b85692b9370db | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/ManyEval/Correctness.lean | Correctness | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "valuesByPolynomial_getD",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [array_getD_toList]\n rw [valuesByPolynomial_toList]\n have hwidth : ∀ p ∈ polys.toList, (p.toArray.toList).l... | [
{
"name": "List.getD_flatMap_fixed_length",
"text": "private lemma List.getD_flatMap_fixed_length {α β : Type*} (xs : List α) (f : α → List β)\n (width : Nat) (d : β)\n (hwidth : ∀ a ∈ xs, (f a).length = width)\n {polyIdx j : Nat} (hpoly : polyIdx < xs.length) (hj : j < width) :\n (xs.flatMap f)... | [
{
"name": "evalManyMleByLayers_eq_map_evalMle",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 12,
"n_lines": 28,
"n_chars": 1283,
"n_subproofs": 2,
"n_tactics": 23,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 5,
"n_structural": 4,
"automation_only": ... | 12 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | @@ -59,11 +59,56 @@
cases a
simp
+private lemma List.getD_flatMap_fixed_length {α β : Type*} (xs : List α) (f : α → List β)
+ (width : Nat) (d : β)
+ (hwidth : ∀ a ∈ xs, (f a).length = width)
+ {polyIdx j : Nat} (hpoly : polyIdx < xs.length) (hj : j < width) :
+ (xs.flatMap f).getD (polyIdx * width ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_93c0e93d7c7f_8 | 8cd61a80a60a5361 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multilinear/ManyEval/Correctness.lean | Correctness | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "evalManyMleByLayers_eq_map_evalMle",
"depth": 1,
"n_commands": 0,
"n_lines": 23,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n with\n | zero =>\n apply Array.toList_inj.mp\n simp [evalManyMleByLayers, evalMa... | [
{
"name": "List.flatMap_singleton",
"text": "private lemma List.flatMap_singleton {α β : Type*} (xs : List α) (f : α → β) :\n xs.flatMap (fun x ↦ [f x]) = xs.map f := by\n induction xs with\n | nil => simp\n | cons _ _ ih => simp [ih]\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 202,
"n... | [
{
"name": "evalManyMleByLayers_eq_evalManyMle",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 15,
"n_lines": 7,
"n_chars": 334,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": fal... | 15 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Multilinear.ManyEval.Basic
/-!
# Multilinear Many-Polynomial Evaluation Correctness
Correctness theorem statements for many-polynomial multilinear evaluat... | @@ -110,6 +110,12 @@
rfl
rw [hget]
+private lemma List.flatMap_singleton {α β : Type*} (xs : List α) (f : α → β) :
+ xs.flatMap (fun x ↦ [f x]) = xs.map f := by
+ induction xs with
+ | nil => simp
+ | cons _ _ ih => simp [ih]
+
private lemma List.flatMap_map {α β γ : Type*} (xs : List α) (f : α → β)
... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c8e36198eed3_0 | 2167421ee29534b9 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Impl.lean | Impl | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 11 | [
{
"theorem_name": "mul_assoc",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply toQuot_injective\n rw [toQuot_mul, toQuot_mul, toQuot_mul, toQuot_mul]\n apply _root_.mul_assoc",
"n_chars": 107,
... | [
{
"name": "toQuot_mul",
"text": "/-- Multiplication homomorphism: `clMul + reduce_clMul` implements polynomial multiplication\nmod P. -/\nlemma toQuot_mul (a b : ConcreteBF128Ghash) : toQuot (a * b) = toQuot a * toQuot b := by\n unfold toQuot\n have h_clMul : toPoly (clMul a b) = toPoly a * toPoly b := t... | [
{
"name": "toPoly_split_256",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 15,
"n_lines": 96,
"n_chars": 4598,
"n_subproofs": 23,
"n_tactics": 97,
"cyclomatic": 1,
"n_automation": 15,
"n_rewrites": 41,
"n_structural": 12,
"automation_only": false,
"ma... | 8 | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | @@ -500,20 +500,55 @@
let h_a_eq_0 := eq_of_toQuot_eq (h := h)
exact h_a_ne_zero h_a_eq_0
-lemma mul_assoc (a b c : ConcreteBF128Ghash) : a * b * c = a * (b * c) := sorry
+/-- Multiplication homomorphism: `clMul + reduce_clMul` implements polynomial multiplication
+mod P. -/
+lemma toQuot_mul (a b : ConcreteBF1... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c8e36198eed3_1 | 702d99f750ecd6b8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Impl.lean | Impl | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "zsmul_neg",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_neg : Int.negSucc n = - (n + 1 : ℤ) := rfl\n rw [h_neg]\n rw [int_neg_mod_two (n + 1)]\n simp\n rfl",
"n_chars": 1... | [
{
"name": "int_neg_mod_two",
"text": "lemma int_neg_mod_two (n : ℤ) : (-n) % 2 = n % 2 := by\n simp only [Int.neg_emod_two]\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 89,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structura... | [
{
"name": "zsmul_neg",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 312,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | @@ -395,9 +395,17 @@
norm_cast
exact nsmul_succ n x
+lemma int_neg_mod_two (n : ℤ) : (-n) % 2 = n % 2 := by
+ simp only [Int.neg_emod_two]
+
lemma zsmul_neg (n : ℕ) (x : ConcreteBF128Ghash) :
(if (Int.negSucc n) % 2 = 0 then (0 : ConcreteBF128Ghash) else x)
- = -(if (n + 1 : ℤ) % 2 = 0 then (0 : Concr... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c8e36198eed3_2 | c55e963083513a51 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Impl.lean | Impl | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 10 | [
{
"theorem_name": "eq_of_toQuot_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n toQuot_injective h",
"n_chars": 21,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
... | [
{
"name": "toQuot_injective",
"text": "/-- Injectivity of `toQuot`.\n If two elements map to the same quotient value, they must be equal.\n Proof uses deg(toPoly a) < 128 and P has degree 128. -/\nlemma toQuot_injective : Function.Injective toQuot := by\n intro a b h\n unfold toQuot at h\n have h_sub :... | [
{
"name": "eq_of_toQuot_eq",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 108,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | @@ -444,6 +444,40 @@
rw [←BF128Ghash_card]
rw [FiniteField.pow_card (toQuot a)]
+/-- Injectivity of `toQuot`.
+ If two elements map to the same quotient value, they must be equal.
+ Proof uses deg(toPoly a) < 128 and P has degree 128. -/
+lemma toQuot_injective : Function.Injective toQuot := by
+ intro a b h... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c8e36198eed3_3 | f20535b851be9bf5 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Impl.lean | Impl | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "toQuot_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_contra h\n rw [← toQuot_zero] at h\n let h_a_eq_0 := eq_of_toQuot_eq (h := h)\n exact h_a_ne_zero h_a_eq_0",
"n_ch... | [
{
"name": "eq_of_toQuot_eq",
"text": "lemma eq_of_toQuot_eq {a b : ConcreteBF128Ghash} (h : toQuot a = toQuot b) : a = b :=\n toQuot_injective h\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 108,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites... | [
{
"name": "toQuot_ne_zero",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 208,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting"... | 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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | @@ -491,8 +491,15 @@
have h_pos : 128 > 0 := by norm_num
simp [toQuot, toPoly_one_eq_one h_pos, map_one]
-lemma toQuot_ne_zero (a : ConcreteBF128Ghash) (h_a_ne_zero : a ≠ 0) : toQuot a ≠ 0 := sorry
+lemma eq_of_toQuot_eq {a b : ConcreteBF128Ghash} (h : toQuot a = toQuot b) : a = b :=
+ toQuot_injective h
+le... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c8e36198eed3_4 | 15c6117b33721346 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Impl.lean | Impl | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 2 | [
{
"theorem_name": "left_distrib",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply toQuot_injective\n rw [toQuot_add, toQuot_mul, toQuot_add, toQuot_mul, toQuot_mul]\n rw [←mul_add (a := toQuot a) (b :... | [
{
"name": "toQuot_add",
"text": "lemma toQuot_add (a b : ConcreteBF128Ghash) : toQuot (a + b) = toQuot a + toQuot b := by\n unfold toQuot\n have h_add_eq_xor : a + b = a ^^^ b := rfl\n rw [h_add_eq_xor, toPoly_xor]\n exact map_add (AdjoinRoot.mk ghashPoly) (toPoly a) (toPoly b)\n\n",
"fan_in": 2,
... | [
{
"name": "toQuot_mul",
"fan_in": 11,
"n_deps_direct": 1,
"n_deps_transitive": 15,
"n_lines": 16,
"n_chars": 825,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 3,
"automation_only": false,
"max_nesting"... | 8 | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | @@ -478,6 +478,12 @@
exact h_diff_ne_zero h_zero
exact eq_of_sub_eq_zero h_diff_eq_zero
+lemma toQuot_add (a b : ConcreteBF128Ghash) : toQuot (a + b) = toQuot a + toQuot b := by
+ unfold toQuot
+ have h_add_eq_xor : a + b = a ^^^ b := rfl
+ rw [h_add_eq_xor, toPoly_xor]
+ exact map_add (AdjoinRoot.mk ghas... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c8e36198eed3_5 | 3575835301429748 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Impl.lean | Impl | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 2 | [
{
"theorem_name": "poly_reduce_step",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_add_eq : X^128 = ghashPoly + ghashTail := by\n rw [ghashPoly_eq_X_pow_add_tail, add_assoc]\n rw [ZMod2Poly.a... | [
{
"name": "add_self_cancel",
"text": "lemma add_self_cancel (a : ConcreteBF128Ghash) : a + a = 0 := by\n apply BitVec.xor_self\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 90,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_struct... | [
{
"name": "natCast_succ",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 420,
"n_subproofs": 2,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | @@ -149,7 +149,9 @@
/-- The Algebraic Identity: A * X^128 ≡ A * R (mod P) -/
lemma poly_reduce_step (A : Polynomial (ZMod 2)) :
(A * X^128) % ghashPoly = (A * ghashTail) % ghashPoly := by
- have h_add_eq : X^128 = ghashPoly + ghashTail := sorry
+ have h_add_eq : X^128 = ghashPoly + ghashTail := by
+ rw [gha... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c8e36198eed3_6 | 8d6708f0f3a606b1 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Impl.lean | Impl | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 2 | [
{
"theorem_name": "toQuot_pow_2k",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction k generalizing a with\n | zero =>\n simp only [pow_2k, pow_zero, pow_one]\n | succ n ih =>\n simp only [pow... | [
{
"name": "toQuot_square",
"text": "lemma toQuot_square (a : ConcreteBF128Ghash) : toQuot (square a) = (toQuot a)^2 := by\n unfold square\n rw [toQuot_mul]; exact Eq.symm (pow_two (toQuot a))\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 157,
"n_subproofs": 0,
"n_tactics": 4,
"cyclom... | [
{
"name": "toQuot_pow_2k",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 16,
"n_lines": 11,
"n_chars": 303,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nesting... | 10 | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | @@ -660,12 +660,19 @@
simp [Inv.inv]
unfold inv_itoh_tsujii
simp
+lemma toQuot_square (a : ConcreteBF128Ghash) : toQuot (square a) = (toQuot a)^2 := by
+ unfold square
+ rw [toQuot_mul]; exact Eq.symm (pow_two (toQuot a))
+
lemma toQuot_pow_2k (a : ConcreteBF128Ghash) (k : Nat) :
toQuot (pow_2k a k) = ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c8e36198eed3_7 | 36edceb07fbfa0ae | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Impl.lean | Impl | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "toQuot_inv_itoh_tsujii",
"depth": 1,
"n_commands": 0,
"n_lines": 64,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold inv_itoh_tsujii\n let q := toQuot a\n have h_u1 : toQuot a = target_val q 1 := by\n simp only [target_v... | [
{
"name": "toQuot_pow_2k",
"text": "lemma toQuot_pow_2k (a : ConcreteBF128Ghash) (k : Nat) :\n toQuot (pow_2k a k) = (toQuot a)^(2^k) := by\n induction k generalizing a with\n | zero =>\n simp only [pow_2k, pow_zero, pow_one]\n | succ n ih =>\n simp only [pow_2k]\n rw [ih, toQuot_square]\n ... | [
{
"name": "toQuot_inv_itoh_tsujii",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 22,
"n_lines": 67,
"n_chars": 3143,
"n_subproofs": 15,
"n_tactics": 65,
"cyclomatic": 1,
"n_automation": 40,
"n_rewrites": 5,
"n_structural": 14,
"automation_only": false,
... | 14 | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | @@ -664,6 +664,16 @@
unfold square
rw [toQuot_mul]; exact Eq.symm (pow_two (toQuot a))
+lemma toQuot_pow_2k (a : ConcreteBF128Ghash) (k : Nat) :
+ toQuot (pow_2k a k) = (toQuot a)^(2^k) := by
+ induction k generalizing a with
+ | zero =>
+ simp only [pow_2k, pow_zero, pow_one]
+ | succ n ih =>
+ sim... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_c8e36198eed3_8 | 2a53f11f1933c062 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Impl.lean | Impl | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 19 | 1 | [
{
"theorem_name": "toQuot_inv_itoh_tsujii",
"depth": 1,
"n_commands": 0,
"n_lines": 64,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold inv_itoh_tsujii\n let q := toQuot a\n have h_u1 : toQuot a = target_val q 1 := by\n simp only [target_v... | [
{
"name": "itoh_tsujii_step",
"text": "/-- Fundamental Itoh-Tsujii Step Lemma:\n If `x = a^(2^n - 1)` and `y = a^(2^m - 1)`, then `(x^(2^m)) * y = a^(2^(n+m) - 1)`.\n This corresponds to the code `(pow_2k u_n m) * u_m`. -/\nlemma itoh_tsujii_step {a x y : PolyQuot} {n m : ℕ}\n (hn : n > 0) (hm : m > 0)... | [
{
"name": "mul_inv_cancel",
"fan_in": 0,
"n_deps_direct": 7,
"n_deps_transitive": 26,
"n_lines": 19,
"n_chars": 746,
"n_subproofs": 4,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 8,
"n_structural": 3,
"automation_only": false,
"max_nesti... | 18 | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | /-
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, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.BF128Ghash.Basic
/-! # BF128Ghash Computable Specification (GF(2^128))
We define the field ... | @@ -677,35 +677,106 @@
/-- The target value for step k: a^(2^k - 1) -/
noncomputable def target_val (a : PolyQuot) (k : ℕ) : PolyQuot := a ^ (2^k - 1)
+/-- Fundamental Itoh-Tsujii Step Lemma:
+ If `x = a^(2^n - 1)` and `y = a^(2^m - 1)`, then `(x^(2^m)) * y = a^(2^(n+m) - 1)`.
+ This corresponds to the code `(pow... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_59948f5d8be5_0 | 875cfc5d2bf443ff | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Roots/SmoothSubgroup/Correctness.lean | Correctness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "smoothLeafLinearFactors_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold smoothLeafLinearFactors at h\n exact linearFactorsFromLeafValues_sound _ _ h",
"n_chars": 89,
... | [
{
"name": "linearFactorsFromLeafValues_sound",
"text": "/-- Leaf extraction emits only represented nonconstant linear factors. -/\nprivate theorem linearFactorsFromLeafValues_sound {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (points values : Array F) {factor : CPolynomial F}\n (h : factor ∈ (li... | [
{
"name": "smoothLeafLinearFactors_sound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 482,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | @@ -24,13 +24,56 @@
namespace FiniteField
+/-- Leaf extraction emits only represented nonconstant linear factors. -/
+private theorem linearFactorsFromLeafValues_sound {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (points values : Array F) {factor : CPolynomial F}
+ (h : factor ∈ (linearFactorsFromLeafV... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_59948f5d8be5_1 | 263184566f231c0f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Roots/SmoothSubgroup/Correctness.lean | Correctness | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "smoothLeafLinearFactors_complete",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hcoset with ⟨k, hk, ha⟩\n refine ⟨CPolynomial.linearFactor a, ?_, linearFactor_isRootFactorCandid... | [
{
"name": "mem_linearFactorsFromLeafValues_of_get_eq_zero",
"text": "/-- A point whose batch value is zero contributes its explicit linear factor. -/\nprivate theorem mem_linearFactorsFromLeafValues_of_get_eq_zero {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (points values : Array F) {idx : Nat} (h... | [
{
"name": "smoothLeafLinearFactors_complete",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 29,
"n_chars": 1229,
"n_subproofs": 4,
"n_tactics": 19,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 5,
"n_structural": 4,
"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.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | @@ -24,6 +24,59 @@
namespace FiniteField
+/-- A point whose batch value is zero contributes its explicit linear factor. -/
+private theorem mem_linearFactorsFromLeafValues_of_get_eq_zero {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (points values : Array F) {idx : Nat} (hidx : idx < points.size)
+ (hva... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_59948f5d8be5_2 | ad34ed66d2a51f82 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Roots/SmoothSubgroup/Correctness.lean | Correctness | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "smoothCosetLinearFactorsWithSchedule_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 87,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro schedule\n induction schedule with\n | nil =>\n intro order alpha gamma p factor h... | [
{
"name": "smoothLeafLinearFactors_sound",
"text": "/-- Smooth leaf extraction emits only represented nonconstant linear factors. -/\nprivate theorem smoothLeafLinearFactors_sound {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (E : BatchEvalContext F) (alpha gamma : F) (order : Nat) (p : CPolynomial ... | [
{
"name": "smoothCosetLinearFactorsWithSchedule_sound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 97,
"n_chars": 4774,
"n_subproofs": 1,
"n_tactics": 87,
"cyclomatic": 6,
"n_automation": 11,
"n_rewrites": 16,
"n_structural": 23,
"automati... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | @@ -65,6 +65,16 @@
exact hacc fac hfac
exact haux points.toList.zipIdx #[] (by simp) h
+/-- Smooth leaf extraction emits only represented nonconstant linear factors. -/
+private theorem smoothLeafLinearFactors_sound {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (E : BatchEvalContext F) (alpha ga... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_59948f5d8be5_3 | e0bfc7438c6bbe30 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Roots/SmoothSubgroup/Correctness.lean | Correctness | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "smoothCosetLinearFactorsWithSchedule_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 87,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro schedule\n induction schedule with\n | nil =>\n intro order alpha gamma p factor h... | [
{
"name": "smoothLeafLinearFactors_sound",
"text": "/-- Smooth leaf extraction emits only represented nonconstant linear factors. -/\nprivate theorem smoothLeafLinearFactors_sound {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n (E : BatchEvalContext F) (alpha gamma : F) (order : Nat) (p : CPolynomial ... | [
{
"name": "smoothLinearFactorsAlgorithmWith_sound",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 31,
"n_chars": 1502,
"n_subproofs": 0,
"n_tactics": 22,
"cyclomatic": 3,
"n_automation": 6,
"n_rewrites": 7,
"n_structural": 5,
"automation_only... | 3 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | @@ -65,6 +65,16 @@
exact hacc fac hfac
exact haux points.toList.zipIdx #[] (by simp) h
+/-- Smooth leaf extraction emits only represented nonconstant linear factors. -/
+private theorem smoothLeafLinearFactors_sound {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ (E : BatchEvalContext F) (alpha ga... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_59948f5d8be5_4 | a21e064ab5c68aa2 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Roots/SmoothSubgroup/Correctness.lean | Correctness | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "smooth_coset_split_root_partition",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hx with ⟨k, _hklt, rfl⟩\n refine ⟨k % ell, Nat.mod_lt k hell_pos, ?_⟩\n apply smooth_coset_split... | [
{
"name": "smooth_coset_split_root_partition_mod",
"text": "/-- A smooth coset split maps the residue class `k % ell` to the child-coset equation. -/\ntheorem smooth_coset_split_root_partition_mod {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n {alpha gamma : F} {order ell k : Nat}\n (hgamma_pow : ... | [
{
"name": "smooth_coset_split_root_partition",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 702,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 5,
"automation_only": fals... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | @@ -24,6 +24,43 @@
namespace FiniteField
+/-- A smooth coset split maps the residue class `k % ell` to the child-coset equation. -/
+theorem smooth_coset_split_root_partition_mod {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ {alpha gamma : F} {order ell k : Nat}
+ (hgamma_pow : gamma ^ order = 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_59948f5d8be5_5 | 7d47ff6c6fc9c853 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Roots/SmoothSubgroup/Correctness.lean | Correctness | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "smooth_coset_split_root_partition",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hx with ⟨k, _hklt, rfl⟩\n refine ⟨k % ell, Nat.mod_lt k hell_pos, ?_⟩\n apply smooth_coset_split... | [
{
"name": "smooth_coset_split_root_partition_mod",
"text": "/-- A smooth coset split maps the residue class `k % ell` to the child-coset equation. -/\ntheorem smooth_coset_split_root_partition_mod {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n {alpha gamma : F} {order ell k : Nat}\n (hgamma_pow : ... | [
{
"name": "smoothCosetLinearFactorsWithSchedule_complete",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 200,
"n_chars": 10131,
"n_subproofs": 27,
"n_tactics": 183,
"cyclomatic": 13,
"n_automation": 19,
"n_rewrites": 32,
"n_structural": 44,
"... | 3 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | @@ -105,6 +105,43 @@
hsize hval
simpa [hpoint] using hmem
+/-- A smooth coset split maps the residue class `k % ell` to the child-coset equation. -/
+theorem smooth_coset_split_root_partition_mod {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ {alpha gamma : F} {order ell k : Nat}
+ (hgamma_pow : gam... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_59948f5d8be5_6 | fd2205d1d1910e0e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Univariate/Roots/SmoothSubgroup/Correctness.lean | Correctness | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "smooth_coset_split_root_partition",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases hx with ⟨k, _hklt, rfl⟩\n refine ⟨k % ell, Nat.mod_lt k hell_pos, ?_⟩\n apply smooth_coset_split... | [
{
"name": "smooth_coset_split_root_partition_mod",
"text": "/-- A smooth coset split maps the residue class `k % ell` to the child-coset equation. -/\ntheorem smooth_coset_split_root_partition_mod {F : Type*}\n [Field F] [BEq F] [LawfulBEq F]\n {alpha gamma : F} {order ell k : Nat}\n (hgamma_pow : ... | [
{
"name": "smoothLinearFactorsAlgorithmWith_complete",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 71,
"n_chars": 3483,
"n_subproofs": 12,
"n_tactics": 57,
"cyclomatic": 5,
"n_automation": 9,
"n_rewrites": 12,
"n_structural": 11,
"automatio... | 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.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Univariate.Roots.Correctness
import CompPoly.Univariate.Roots.RootProduct
import CompPoly.Univariate.Roots.SmoothSubgroup.Basic
import Mathlib... | @@ -105,6 +105,43 @@
hsize hval
simpa [hpoint] using hmem
+/-- A smooth coset split maps the residue class `k % ell` to the child-coset equation. -/
+theorem smooth_coset_split_root_partition_mod {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F]
+ {alpha gamma : F} {order ell k : Nat}
+ (hgamma_pow : gam... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_241420177c61_0 | ba0489e17b997e99 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Concrete/Core.lean | Core | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 1 | [
{
"theorem_name": "BitVec.dcast_one",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [←BitVec.bitvec_cast_eq_dcast]\n exact BitVec.cast_one (h:=h)",
"n_chars": 72,
"n_subproofs": 0,
"n_tactic... | [
{
"name": "BitVec.bitvec_cast_eq_dcast",
"text": "theorem BitVec.bitvec_cast_eq_dcast {n m : Nat} (h : n = m) (bv : BitVec n) :\n BitVec.cast h bv = DCast.dcast h bv := by\n simp only [BitVec.cast, BitVec.instDCast]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 169,
"n_subproofs": 0,
"... | [
{
"name": "BitVec.dcast_one",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 161,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | @@ -27,6 +27,10 @@
funext bv -- bv : BitVec n
rw [BitVec.cast_eq, id_eq]
+theorem BitVec.bitvec_cast_eq_dcast {n m : Nat} (h : n = m) (bv : BitVec n) :
+ BitVec.cast h bv = DCast.dcast h bv := by
+ simp only [BitVec.cast, BitVec.instDCast]
+
theorem BitVec.dcast_id {n : Nat} (bv : BitVec n) :
DCas... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_241420177c61_2 | 763ba6adad4c0183 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Concrete/Core.lean | Core | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 1 | [
{
"theorem_name": "Nat.reconstruct_from_hi_and_lo_parts",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Nat.shiftRight_lo_mod_2_pow_hi_shiftLeft_lo (n:=n) (hi_len:=hi_len)\n (lo_len:=lo_len) (h_n:=h_... | [
{
"name": "Nat.shiftRight_lo_mod_2_pow_hi_shiftLeft_lo",
"text": "theorem Nat.shiftRight_lo_mod_2_pow_hi_shiftLeft_lo (n hi_len lo_len : ℕ)\n (h_n : n < 2 ^ (hi_len + lo_len)) :\n (((n >>> lo_len) % (2 ^ hi_len)) <<< lo_len) = (n - n % 2 ^ lo_len) := by\n rw [Nat.shiftLeft_eq]\n have n_shr_lo_mod_2_po... | [
{
"name": "Nat.reconstruct_from_hi_and_lo_parts",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 462,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": f... | 1 | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | @@ -101,9 +101,42 @@
have h_le : lo_size - 1 + 1 ≤ lo_size := by rw [Nat.sub_add_cancel (by omega)]
simp only [h_le, ↓reduceDIte]
+theorem Nat.shiftRight_lo_mod_2_pow_hi_shiftLeft_lo (n hi_len lo_len : ℕ)
+ (h_n : n < 2 ^ (hi_len + lo_len)) :
+ (((n >>> lo_len) % (2 ^ hi_len)) <<< lo_len) = (n - n % 2 ^ lo_... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_241420177c61_3 | d95e530c42fbf89a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Concrete/Core.lean | Core | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 1 | [
{
"theorem_name": "Nat.reconstruct_from_hi_and_lo_parts_or_ver",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw (occs := .pos [1]) [Nat.reconstruct_from_hi_and_lo_parts (n:=n) (hi_len:=hi_len)\n (lo_le... | [
{
"name": "Nat.reconstruct_from_hi_and_lo_parts",
"text": "theorem Nat.reconstruct_from_hi_and_lo_parts (n hi_len lo_len : ℕ)\n (h_n : n < 2 ^ (hi_len + lo_len)) :\n n = (((n >>> lo_len) % (2 ^ hi_len)) <<< lo_len) + (n % (2 ^ lo_len)) := by\n rw [Nat.shiftRight_lo_mod_2_pow_hi_shiftLeft_lo (n:=n) (h... | [
{
"name": "Nat.reconstruct_from_hi_and_lo_parts_or_ver",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 11,
"n_chars": 584,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_o... | 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 CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | @@ -128,9 +128,25 @@
exact Nat.dvd_sub_mod n
rw [Nat.div_mul_cancel h_div1]
+theorem Nat.reconstruct_from_hi_and_lo_parts (n hi_len lo_len : ℕ)
+ (h_n : n < 2 ^ (hi_len + lo_len)) :
+ n = (((n >>> lo_len) % (2 ^ hi_len)) <<< lo_len) + (n % (2 ^ lo_len)) := by
+ rw [Nat.shiftRight_lo_mod_2_pow_hi_shiftL... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_241420177c61_4 | 7e7a980bd4fa29a5 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Concrete/Core.lean | Core | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 1 | [
{
"theorem_name": "sub_middle_of_pow2_with_one_canceled",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n calc 2 ^ k - 1 - 2 ^ (k - 1) + 1 = 2 ^ k - 2 ^ (k - 1) - 1 + 1 := by omega\n _ = 2 ^ k - 2 ^ (k - ... | [
{
"name": "one_le_sub_middle_of_pow2",
"text": "lemma one_le_sub_middle_of_pow2 {k : ℕ} (h_k : 1 ≤ k) : 1 ≤ 2 ^ k - 2 ^ (k - 1) := by\n have l1 : 2 ^ (k - 1 + 1) = 2 ^ k := by congr 1; omega\n have res := one_le_sub_consecutive_two_pow (n:=k - 1)\n rw [l1] at res\n exact res\n\n",
"fan_in": 1,
"... | [
{
"name": "sub_middle_of_pow2_with_one_canceled",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 629,
"n_subproofs": 0,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 6,
"n_structural": 2,
"automation_only": ... | 1 | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | @@ -232,8 +232,26 @@
section NumericLemmas
+lemma one_le_sub_middle_of_pow2 {k : ℕ} (h_k : 1 ≤ k) : 1 ≤ 2 ^ k - 2 ^ (k - 1) := by
+ have l1 : 2 ^ (k - 1 + 1) = 2 ^ k := by congr 1; omega
+ have res := one_le_sub_consecutive_two_pow (n:=k - 1)
+ rw [l1] at res
+ exact res
+
lemma sub_middle_of_pow2_with_one_ca... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_241420177c61_5 | d67555ad166ebe54 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Concrete/Core.lean | Core | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 1 | [
{
"theorem_name": "zsmul_neg'",
"depth": 1,
"n_commands": 0,
"n_lines": 46,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have negSucc_eq_minus_of_n_plus_1 : Int.negSucc n = - (n + 1) := by rfl\n rw [negSucc_eq_minus_of_n_plus_1]\n have n_succ_eq_... | [
{
"name": "neg_mod_2_eq_0_iff_mod_2_eq_0",
"text": "lemma neg_mod_2_eq_0_iff_mod_2_eq_0 {n : ℤ} : ( - n) % 2 = 0 ↔ n % 2 = 0 := by\n constructor\n · intro h\n apply Int.dvd_iff_emod_eq_zero.mp\n apply Int.dvd_neg.mp\n exact Int.dvd_iff_emod_eq_zero.mpr h\n · intro h\n apply Int.dvd_iff_emod_e... | [
{
"name": "zsmul_neg'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 51,
"n_chars": 2284,
"n_subproofs": 11,
"n_tactics": 42,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 14,
"n_structural": 3,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | @@ -387,6 +387,18 @@
norm_cast
exact nsmul_succ n x
+lemma neg_mod_2_eq_0_iff_mod_2_eq_0 {n : ℤ} : ( - n) % 2 = 0 ↔ n % 2 = 0 := by
+ constructor
+ · intro h
+ apply Int.dvd_iff_emod_eq_zero.mp
+ apply Int.dvd_neg.mp
+ exact Int.dvd_iff_emod_eq_zero.mpr h
+ · intro h
+ apply Int.dvd_iff_emod_eq_z... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_241420177c61_6 | cbe78b05de19d57f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Concrete/Core.lean | Core | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 1 | [
{
"theorem_name": "BitVec.extractLsb_eq_and_pow_2_minus_1_ofNat",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold BitVec.extractLsb BitVec.extractLsb'\n simp only [Nat.sub_zero, Nat.shiftRight_zero]\... | [
{
"name": "setWidth_eq_ofNat_mod",
"text": "theorem setWidth_eq_ofNat_mod {n num_bits : Nat} (x : BitVec n) :\n BitVec.setWidth num_bits x = BitVec.ofNat num_bits (x.toNat % 2 ^ num_bits) := by\n simp only [BitVec.ofNat_toNat, ← BitVec.toNat_setWidth, BitVec.setWidth_eq]\n\n",
"fan_in": 1,
"n_li... | [
{
"name": "BitVec.extractLsb_eq_and_pow_2_minus_1_ofNat",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 805,
"n_subproofs": 3,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 1,
"automation... | 1 | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | @@ -513,6 +513,10 @@
unfold BitVec.extractLsb BitVec.extractLsb'
rfl
+theorem setWidth_eq_ofNat_mod {n num_bits : Nat} (x : BitVec n) :
+ BitVec.setWidth num_bits x = BitVec.ofNat num_bits (x.toNat % 2 ^ num_bits) := by
+ simp only [BitVec.ofNat_toNat, ← BitVec.toNat_setWidth, BitVec.setWidth_eq]
+
theorem... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_241420177c61_8 | 72d10fcf9e34fcbb | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/Tower/Concrete/Core.lean | Core | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 36 | 1 | [
{
"theorem_name": "eq_join_iff_dcast_eq_append",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n constructor\n · intro hx\n have hx' := hx\n rw [join_eq_dcast_append (k:=k) (h_pos:=h_pos)... | [
{
"name": "join_eq_dcast_append",
"text": "theorem join_eq_dcast_append {k : ℕ} (h_pos : k > 0) (hi lo : ConcreteBTField (k - 1)) :\n join (k:=k) h_pos hi lo =\n dcast (h_sum_two_same_pow2 (k:=k) (h_pos:=h_pos))\n (BitVec.append (msbs:=hi) (lsbs:=lo)) := by\n unfold join\n simp [dcast_eq_ro... | [
{
"name": "eq_join_iff_dcast_eq_append",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 2,
"n_lines": 29,
"n_chars": 1040,
"n_subproofs": 3,
"n_tactics": 21,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 5,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | /-
Copyright (c) 2024 - 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao
-/
import CompPoly.Data.Classes.DCast
import CompPoly.Fields.Binary.Tower.Abstract.Basis
/-!
# Concrete Binary Tower Core
Core definitions f... | @@ -593,6 +593,13 @@
simpa using (BitVec.dcast_bitvec_toNat_eq (x:=x) (h_width_eq:=h)).symm
rw [h_toNat]
+theorem join_eq_dcast_append {k : ℕ} (h_pos : k > 0) (hi lo : ConcreteBTField (k - 1)) :
+ join (k:=k) h_pos hi lo =
+ dcast (h_sum_two_same_pow2 (k:=k) (h_pos:=h_pos))
+ (BitVec.append (ms... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"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.