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_7f09cab7c7aa_2 | 08a55597685296ce | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/Subdomain.lean | Subdomain | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 3 | [
{
"theorem_name": "subdomain_toFinset_subset_subdomain_toFinset_of_le",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " fun x hx ↦ by\n aesop (add unsafe [mem_subdomain_of_mem_subdomain_of_le])",
"n_chars": 76... | [
{
"name": "mem_subdomain_of_mem_subdomain_of_le",
"text": "/-- If `x` is a member of `subdomain ω i` it is a member of\n any `subdomain ω j` with `j ≤ i`. -/\nlemma mem_subdomain_of_mem_subdomain_of_le {i j : ℕ} (h : x ∈ subdomain ω i) (hji : j ≤ i) :\n x ∈ subdomain ω j := by\n aesop\n (add simp [mem... | [
{
"name": "subdomain_toSubgroup_subset_subdomain_toSubgroup_of_le",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 398,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"au... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -66,11 +66,20 @@
x ∈ subdomain ω i ↔ x ∈ CosetFftDomainClass.subdomain ω i := by
simp [subdomain, mem_toFftDomain_iff_mul_mem, CosetFftDomain.map_0_eq_coset_generator]
+/-- If `x` is a member of `subdomain ω i` it is a member of
+ any `subdomain ω j` with `j ≤ i`. -/
+lemma mem_subdomain_of_mem_subdomain_of... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_7f09cab7c7aa_3 | 36e9139235d2c434 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/Subdomain.lean | Subdomain | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 3 | [
{
"theorem_name": "subdomain_toFinset_subset_subdomain_toFinset_of_le",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " fun x hx ↦ by\n aesop (add unsafe [mem_subdomain_of_mem_subdomain_of_le])",
"n_chars": 76... | [
{
"name": "mem_subdomain_of_mem_subdomain_of_le",
"text": "/-- If `x` is a member of `subdomain ω i` it is a member of\n any `subdomain ω j` with `j ≤ i`. -/\nlemma mem_subdomain_of_mem_subdomain_of_le {i j : ℕ} (h : x ∈ subdomain ω i) (hji : j ≤ i) :\n x ∈ subdomain ω j := by\n aesop\n (add simp [mem... | [
{
"name": "mem_subdomain_of_mem_subdomain_of_mem_fft_subdomain",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 14,
"n_chars": 558,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"auto... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -66,6 +66,14 @@
x ∈ subdomain ω i ↔ x ∈ CosetFftDomainClass.subdomain ω i := by
simp [subdomain, mem_toFftDomain_iff_mul_mem, CosetFftDomain.map_0_eq_coset_generator]
+/-- If `x` is a member of `subdomain ω i` it is a member of
+ any `subdomain ω j` with `j ≤ i`. -/
+lemma mem_subdomain_of_mem_subdomain_of_... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_7f09cab7c7aa_4 | 43d6b1aa7de91957 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/Subdomain.lean | Subdomain | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 3 | [
{
"theorem_name": "subdomain_toFinset_subset_subdomain_toFinset_of_le",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " fun x hx ↦ by\n aesop (add unsafe [mem_subdomain_of_mem_subdomain_of_le])",
"n_chars": 76... | [
{
"name": "mem_subdomain_of_mem_subdomain_of_le",
"text": "/-- If `x` is a member of `subdomain ω i` it is a member of\n any `subdomain ω j` with `j ≤ i`. -/\nlemma mem_subdomain_of_mem_subdomain_of_le {i j : ℕ} (h : x ∈ subdomain ω i) (hji : j ≤ i) :\n x ∈ subdomain ω j := by\n aesop\n (add simp [mem... | [
{
"name": "mem_subdomain_of_mem_fft_subdomain_of_mem_subdomain",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 12,
"n_chars": 459,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"auto... | 4 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -66,6 +66,14 @@
x ∈ subdomain ω i ↔ x ∈ CosetFftDomainClass.subdomain ω i := by
simp [subdomain, mem_toFftDomain_iff_mul_mem, CosetFftDomain.map_0_eq_coset_generator]
+/-- If `x` is a member of `subdomain ω i` it is a member of
+ any `subdomain ω j` with `j ≤ i`. -/
+lemma mem_subdomain_of_mem_subdomain_of_... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_e0d46e6511ed_0 | bd3364259e8f6974 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/CosetFftDomain/Ops.lean | Ops | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "neg_mem_domain_iff_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor <;> intro h\n · rw [show x = -(-x) by simp]\n exact neg_mem_domain_of_mem h\n · exact neg_mem_domai... | [
{
"name": "neg_mem_domain_of_mem",
"text": "/-- In a smooth coset FFT domain of nonzero logarithmic size,\n membership is closed under negation. -/\ntheorem neg_mem_domain_of_mem [nz : NeZero n] (h : x ∈ ω) :\n -x ∈ ω := by\n rw [show -x = (-1) * x by simp]\n exact mul_mem_of_mem_toFftDomain_of_mem (by ... | [
{
"name": "neg_mem_domain_iff_mem",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 326,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -60,13 +60,21 @@
variable {ω : D} {x : F}
/-- In a smooth coset FFT domain of nonzero logarithmic size,
+ membership is closed under negation. -/
+theorem neg_mem_domain_of_mem [nz : NeZero n] (h : x ∈ ω) :
+ -x ∈ ω := by
+ rw [show -x = (-1) * x by simp]
+ exact mul_mem_of_mem_toFftDomain_of_mem (by simp) h... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_fd1a3ae59133_0 | 47c72b299eaff7a9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/ToSubgroup.lean | ToSubgroup | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "mem_subgroup_iff_mem_domain",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by simp [mem_subgroup_iff_mem_finset]",
"n_chars": 38,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic"... | [
{
"name": "mem_subgroup_iff_mem_finset",
"text": "/-- A unit belongs to the subgroup associated to an FFT domain iff\n its value belongs to the finset of elements of the domain. -/\nlemma mem_subgroup_iff_mem_finset {x : Fˣ} :\n x ∈ toSubgroup ω ↔ x.val ∈ CosetFftDomainClass.toFinset ω := by\n aesop\n ... | [
{
"name": "mem_subgroup_iff_mem_domain",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 253,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -73,10 +73,18 @@
}
/-- A unit belongs to the subgroup associated to an FFT domain iff
+ its value belongs to the finset of elements of the domain. -/
+lemma mem_subgroup_iff_mem_finset {x : Fˣ} :
+ x ∈ toSubgroup ω ↔ x.val ∈ CosetFftDomainClass.toFinset ω := by
+ aesop
+ (add simp [toSubgroup, CosetFftDo... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b2e83819f96f_0 | 6b0260aae49b3613 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Finset/PickSubset.lean | PickSubset | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 3 | [
{
"theorem_name": "card_pick_subset",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n generalizing s with\n | zero => simp [Finset.pickSubset]\n | succ n ih =>\n simp_all only [pickSubset, s... | [
{
"name": "pick_subset_subset",
"text": "/-- `pickSubset s n` is indeed a subset of `s`. -/\nlemma pick_subset_subset {s : Finset α} {n : ℕ} :\n pickSubset s n ⊆ s := by\n induction n with\n | zero => simp\n | succ n ih =>\n by_cases h : (s \\ s.pickSubset n).Nonempty\n <;> try\n (simp on... | [
{
"name": "card_pick_subset",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 21,
"n_chars": 778,
"n_subproofs": 2,
"n_tactics": 16,
"cyclomatic": 2,
"n_automation": 9,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Data.Finset.Defs
import Mathlib.Data.Finset.Insert
import Mathlib.Data.Finset.Lattice.Basic
import Mathlib.Data.Finset.SDi... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Data.Finset.Defs
import Mathlib.Data.Finset.Insert
import Mathlib.Data.Finset.Lattice.Basic
import Mathlib.Data.Finset.SDi... | @@ -48,6 +48,19 @@
| zero => rfl
| succ n ih => simp [pickSubset, ih]
+/-- `pickSubset s n` is indeed a subset of `s`. -/
+lemma pick_subset_subset {s : Finset α} {n : ℕ} :
+ pickSubset s n ⊆ s := by
+ induction n with
+ | zero => simp
+ | succ n ih =>
+ by_cases h : (s \ s.pickSubset n).Nonempty
+ ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b2e83819f96f_1 | 824056bae961cb1c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Finset/PickSubset.lean | PickSubset | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 3 | [
{
"theorem_name": "card_pick_subset",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n generalizing s with\n | zero => simp [Finset.pickSubset]\n | succ n ih =>\n simp_all only [pickSubset, s... | [
{
"name": "pick_subset_subset",
"text": "/-- `pickSubset s n` is indeed a subset of `s`. -/\nlemma pick_subset_subset {s : Finset α} {n : ℕ} :\n pickSubset s n ⊆ s := by\n induction n with\n | zero => simp\n | succ n ih =>\n by_cases h : (s \\ s.pickSubset n).Nonempty\n <;> try\n (simp on... | [
{
"name": "pick_subset_eq_s_of_card_le_n",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 323,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Data.Finset.Defs
import Mathlib.Data.Finset.Insert
import Mathlib.Data.Finset.Lattice.Basic
import Mathlib.Data.Finset.SDi... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Data.Finset.Defs
import Mathlib.Data.Finset.Insert
import Mathlib.Data.Finset.Lattice.Basic
import Mathlib.Data.Finset.SDi... | @@ -48,6 +48,19 @@
| zero => rfl
| succ n ih => simp [pickSubset, ih]
+/-- `pickSubset s n` is indeed a subset of `s`. -/
+lemma pick_subset_subset {s : Finset α} {n : ℕ} :
+ pickSubset s n ⊆ s := by
+ induction n with
+ | zero => simp
+ | succ n ih =>
+ by_cases h : (s \ s.pickSubset n).Nonempty
+ ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b2e83819f96f_2 | ea423a37979c1f98 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Finset/PickSubset.lean | PickSubset | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 3 | [
{
"theorem_name": "card_pick_subset",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n generalizing s with\n | zero => simp [Finset.pickSubset]\n | succ n ih =>\n simp_all only [pickSubset, s... | [
{
"name": "pick_subset_subset",
"text": "/-- `pickSubset s n` is indeed a subset of `s`. -/\nlemma pick_subset_subset {s : Finset α} {n : ℕ} :\n pickSubset s n ⊆ s := by\n induction n with\n | zero => simp\n | succ n ih =>\n by_cases h : (s \\ s.pickSubset n).Nonempty\n <;> try\n (simp on... | [
{
"name": "pick_subset_eq_of_card_pick_subset_lt",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 353,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": f... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Data.Finset.Defs
import Mathlib.Data.Finset.Insert
import Mathlib.Data.Finset.Lattice.Basic
import Mathlib.Data.Finset.SDi... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Data.Finset.Defs
import Mathlib.Data.Finset.Insert
import Mathlib.Data.Finset.Lattice.Basic
import Mathlib.Data.Finset.SDi... | @@ -48,6 +48,19 @@
| zero => rfl
| succ n ih => simp [pickSubset, ih]
+/-- `pickSubset s n` is indeed a subset of `s`. -/
+lemma pick_subset_subset {s : Finset α} {n : ℕ} :
+ pickSubset s n ⊆ s := by
+ induction n with
+ | zero => simp
+ | succ n ih =>
+ by_cases h : (s \ s.pickSubset n).Nonempty
+ ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b2e83819f96f_3 | 1f23b5e98268a800 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Finset/PickSubset.lean | PickSubset | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 3 | [
{
"theorem_name": "card_pick_subset",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n generalizing s with\n | zero => simp [Finset.pickSubset]\n | succ n ih =>\n simp_all only [pickSubset, s... | [
{
"name": "pick_subset_subset",
"text": "/-- `pickSubset s n` is indeed a subset of `s`. -/\nlemma pick_subset_subset {s : Finset α} {n : ℕ} :\n pickSubset s n ⊆ s := by\n induction n with\n | zero => simp\n | succ n ih =>\n by_cases h : (s \\ s.pickSubset n).Nonempty\n <;> try\n (simp on... | [
{
"name": "pick_subset_card_eq_of_ne",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 309,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"m... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Data.Finset.Defs
import Mathlib.Data.Finset.Insert
import Mathlib.Data.Finset.Lattice.Basic
import Mathlib.Data.Finset.SDi... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.Data.Finset.Defs
import Mathlib.Data.Finset.Insert
import Mathlib.Data.Finset.Lattice.Basic
import Mathlib.Data.Finset.SDi... | @@ -48,6 +48,19 @@
| zero => rfl
| succ n ih => simp [pickSubset, ih]
+/-- `pickSubset s n` is indeed a subset of `s`. -/
+lemma pick_subset_subset {s : Finset α} {n : ℕ} :
+ pickSubset s n ⊆ s := by
+ induction n with
+ | zero => simp
+ | succ n ih =>
+ by_cases h : (s \ s.pickSubset n).Nonempty
+ ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_55bc81f4665a_3 | caf72c12b967d8d8 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/NormBounds/MicciancioYoung.lean | MicciancioYoung | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "sum_conv_sq_le",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n calc ∑ k ∈ Finset.range n, c k ^ 2\n ≤ ∑ k ∈ Finset.range n, (∑ i ∈ Finset.range n, da i * wb ((k + n - i) % n)) ^ 2 :... | [
{
"name": "weighted_cauchy_schwarz",
"text": "/-- **Weighted discrete Cauchy–Schwarz (integers).** For nonnegative weights `w`,\n`(∑ wᵢ xᵢ)² ≤ (∑ wᵢ)·(∑ wᵢ xᵢ²)`. The engine behind the `‖·‖₁ · ‖·‖₂` product bound. -/\nprivate lemma weighted_cauchy_schwarz {ι : Type*} (s : Finset ι) (w x : ι → ℤ)\n (hw : ... | [
{
"name": "sum_conv_sq_le",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 34,
"n_chars": 2150,
"n_subproofs": 0,
"n_tactics": 31,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 7,
"n_structural": 5,
"automation_only": false,
"max_nesti... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.NormBounds.Basic
/-!
# The Micciancio/Young Product Norm-Growth Bound
The Young/Micciancio inequality `‖(c·d)·... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.NormBounds.Basic
/-!
# The Micciancio/Young Product Norm-Growth Bound
The Young/Micciancio inequality `‖(c·d)·... | @@ -48,6 +48,16 @@
section Helpers
open Polynomial Finset
+/-- **Weighted discrete Cauchy–Schwarz (integers).** For nonnegative weights `w`,
+`(∑ wᵢ xᵢ)² ≤ (∑ wᵢ)·(∑ wᵢ xᵢ²)`. The engine behind the `‖·‖₁ · ‖·‖₂` product bound. -/
+private lemma weighted_cauchy_schwarz {ι : Type*} (s : Finset ι) (w x : ι → ℤ)
+ (... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_55bc81f4665a_4 | ad1e2f000cce290c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/NormBounds/MicciancioYoung.lean | MicciancioYoung | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 3 | [
{
"theorem_name": "hachi_natDegree",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CompPoly.CPolynomial.natDegree_toPoly, hachi_toPoly, ← Polynomial.C_1,\n Polynomial.natDegree_X_pow_add_C]\n\nomit... | [
{
"name": "hachi_toPoly",
"text": "/-- The underlying polynomial of the modulus `Φ = X^{2^α}+1`. -/\nprivate lemma hachi_toPoly :\n (Φ).φ.toPoly = (Polynomial.X : (ZMod q)[X]) ^ (2 ^ α) + 1 := by\n change (CompPoly.CPolynomial.X ^ (2 ^ α) + 1 : CompPoly.CPolynomial (ZMod q)).toPoly = _\n rw [CompPoly.C... | [
{
"name": "Rq.l2NormSq_mul_le",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 10,
"n_lines": 59,
"n_chars": 3280,
"n_subproofs": 12,
"n_tactics": 66,
"cyclomatic": 1,
"n_automation": 10,
"n_rewrites": 14,
"n_structural": 7,
"automation_only": false,
"m... | 10 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.NormBounds.Basic
/-!
# The Micciancio/Young Product Norm-Growth Bound
The Young/Micciancio inequality `‖(c·d)·... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.NormBounds.Basic
/-!
# The Micciancio/Young Product Norm-Growth Bound
The Young/Micciancio inequality `‖(c·d)·... | @@ -122,16 +122,55 @@
· intro a _; rfl
omit [NeZero q] in
+/-- The underlying polynomial of the modulus `Φ = X^{2^α}+1`. -/
+private lemma hachi_toPoly :
+ (Φ).φ.toPoly = (Polynomial.X : (ZMod q)[X]) ^ (2 ^ α) + 1 := by
+ change (CompPoly.CPolynomial.X ^ (2 ^ α) + 1 : CompPoly.CPolynomial (ZMod q)).toPoly = _... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_55bc81f4665a_5 | 0d7b30fa9068222a | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/NormBounds/MicciancioYoung.lean | MicciancioYoung | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 3 | [
{
"theorem_name": "hachi_natDegree",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CompPoly.CPolynomial.natDegree_toPoly, hachi_toPoly, ← Polynomial.C_1,\n Polynomial.natDegree_X_pow_add_C]\n\nomit... | [
{
"name": "hachi_toPoly",
"text": "/-- The underlying polynomial of the modulus `Φ = X^{2^α}+1`. -/\nprivate lemma hachi_toPoly :\n (Φ).φ.toPoly = (Polynomial.X : (ZMod q)[X]) ^ (2 ^ α) + 1 := by\n change (CompPoly.CPolynomial.X ^ (2 ^ α) + 1 : CompPoly.CPolynomial (ZMod q)).toPoly = _\n rw [CompPoly.C... | [
{
"name": "scalarVecMul_mul_l2NormSq_le",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 11,
"n_lines": 21,
"n_chars": 1439,
"n_subproofs": 1,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,... | 11 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.NormBounds.Basic
/-!
# The Micciancio/Young Product Norm-Growth Bound
The Young/Micciancio inequality `‖(c·d)·... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.NormBounds.Basic
/-!
# The Micciancio/Young Product Norm-Growth Bound
The Young/Micciancio inequality `‖(c·d)·... | @@ -122,16 +122,55 @@
· intro a _; rfl
omit [NeZero q] in
+/-- The underlying polynomial of the modulus `Φ = X^{2^α}+1`. -/
+private lemma hachi_toPoly :
+ (Φ).φ.toPoly = (Polynomial.X : (ZMod q)[X]) ^ (2 ^ α) + 1 := by
+ change (CompPoly.CPolynomial.X ^ (2 ^ α) + 1 : CompPoly.CPolynomial (ZMod q)).toPoly = _... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_7d3770b85404_0 | 300ad77de69f2064 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/JohnsonBound/Choose2.lean | Choose2 | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "choose_2_convex",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [choose_2_eq_half_f]\n refine ⟨convex_univ, fun x₁ _ x₂ _ α₁ α₂ hα₁ hα₂ h ↦ ?_⟩\n have := f_convex (x₁ := x₁) (x₂ := x... | [
{
"name": "choose_2_eq_half_f",
"text": "lemma choose_2_eq_half_f : choose_2 = (1 / 2) * f := by\n ext x; simp [choose_2, f]; ring\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 91,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_st... | [
{
"name": "choose_2_convex",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 481,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nesting... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import Mathlib.Analysis.Convex.Function
import Mathlib.Data.Set.Pairwise.Basic
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import Mathlib.Analysis.Convex.Function
import Mathlib.Data.Set.Pairwise.Basic
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ... | @@ -28,7 +28,16 @@
def choose_2 (x : ℚ) : ℚ := x * (x - 1) / 2
-theorem choose_2_convex : ConvexOn ℚ Set.univ choose_2 := sorry
+lemma choose_2_eq_half_f : choose_2 = (1 / 2) * f := by
+ ext x; simp [choose_2, f]; ring
+theorem choose_2_convex : ConvexOn ℚ Set.univ choose_2 := by
+ rw [choose_2_eq_half_f]
+ r... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_23056a8f40f0_0 | 1bd97489b137d77e | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/JohnsonBound/Basic.lean | Basic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "sqrt_le_J",
"depth": 1,
"n_commands": 0,
"n_lines": 27,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold J\n set frac := q / (q - 1) with hfrac\n have hfrac_ge : frac ≥ 1 := by\n rw [hfrac, ge_iff_le, one_le_div] <;> grin... | [
{
"name": "division_by_conjugate",
"text": "/-- Rationalization of `a - √b` via conjugate multiplication. -/\nlemma division_by_conjugate {a b : ℝ} (hpos : 0 ≤ b) (hnonzero : a + √b ≠ 0) :\n a - √b = (a ^ 2 - b) / (a + √b) := by\n rw [eq_div_iff hnonzero]\n ring_nf\n simp_all\n\n",
"fan_in": 2,
... | [
{
"name": "sqrt_le_J",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 32,
"n_chars": 1493,
"n_subproofs": 7,
"n_tactics": 28,
"cyclomatic": 2,
"n_automation": 16,
"n_rewrites": 11,
"n_structural": 2,
"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: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Lemmas
/-! # Johnson Bound Basics -/
namespace JohnsonBound
/-!
This module is based on the J... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Lemmas
/-! # Johnson Bound Basics -/
namespace JohnsonBound
/-!
This module is based on the J... | @@ -45,6 +45,13 @@
let frac := q / (q - 1)
(1 / frac) * (1 - √(1 - frac * δ))
+/-- Rationalization of `a - √b` via conjugate multiplication. -/
+lemma division_by_conjugate {a b : ℝ} (hpos : 0 ≤ b) (hnonzero : a + √b ≠ 0) :
+ a - √b = (a ^ 2 - b) / (a + √b) := by
+ rw [eq_div_iff hnonzero]
+ ring_nf
+ sim... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_23056a8f40f0_1 | 809c0d074f3b018a | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/JohnsonBound/Basic.lean | Basic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "sqrt_le_J",
"depth": 1,
"n_commands": 0,
"n_lines": 27,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold J\n set frac := q / (q - 1) with hfrac\n have hfrac_ge : frac ≥ 1 := by\n rw [hfrac, ge_iff_le, one_le_div] <;> grin... | [
{
"name": "division_by_conjugate",
"text": "/-- Rationalization of `a - √b` via conjugate multiplication. -/\nlemma division_by_conjugate {a b : ℝ} (hpos : 0 ≤ b) (hnonzero : a + √b ≠ 0) :\n a - √b = (a ^ 2 - b) / (a + √b) := by\n rw [eq_div_iff hnonzero]\n ring_nf\n simp_all\n\n",
"fan_in": 2,
... | [
{
"name": "johnson_condition_weak_implies_strong",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 134,
"n_chars": 7228,
"n_subproofs": 30,
"n_tactics": 130,
"cyclomatic": 1,
"n_automation": 29,
"n_rewrites": 19,
"n_structural": 18,
"automation... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Lemmas
/-! # Johnson Bound Basics -/
namespace JohnsonBound
/-!
This module is based on the J... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Lemmas
/-! # Johnson Bound Basics -/
namespace JohnsonBound
/-!
This module is based on the J... | @@ -45,6 +45,13 @@
let frac := q / (q - 1)
(1 / frac) * (1 - √(1 - frac * δ))
+/-- Rationalization of `a - √b` via conjugate multiplication. -/
+lemma division_by_conjugate {a b : ℝ} (hpos : 0 ≤ b) (hnonzero : a + √b ≠ 0) :
+ a - √b = (a ^ 2 - b) / (a + √b) := by
+ rw [eq_div_iff hnonzero]
+ ring_nf
+ sim... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_23056a8f40f0_2 | 201ee51f26240328 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/JohnsonBound/Basic.lean | Basic | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "johnson_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n suffices B.card * JohnsonDenominator B v ≤\n (card F : ℚ) / (card F - 1) * d B / n by\n rw [johnson_condition_s... | [
{
"name": "johnson_condition_strong_implies_2_le_B_card",
"text": "/-- The strong Johnson condition forces the code to have at least two codewords. -/\nlemma johnson_condition_strong_implies_2_le_B_card\n (h_johnson : JohnsonConditionStrong B v) :\n 2 ≤ B.card := by\n dsimp [JohnsonConditionStrong] a... | [
{
"name": "johnson_bound",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 5,
"n_lines": 18,
"n_chars": 749,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_nesting... | 5 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Lemmas
/-! # Johnson Bound Basics -/
namespace JohnsonBound
/-!
This module is based on the J... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Lemmas
/-! # Johnson Bound Basics -/
namespace JohnsonBound
/-!
This module is based on the J... | @@ -72,6 +72,24 @@
dsimp [JohnsonConditionStrong]
rcases card F with _ | _ | _ <;> aesop
+/-- The strong Johnson condition forces the code to have at least two codewords. -/
+lemma johnson_condition_strong_implies_2_le_B_card
+ (h_johnson : JohnsonConditionStrong B v) :
+ 2 ≤ B.card := by
+ dsimp [Johnso... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_23056a8f40f0_3 | 9eb2b3ef53d573d9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/JohnsonBound/Basic.lean | Basic | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "johnson_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n suffices B.card * JohnsonDenominator B v ≤\n (card F : ℚ) / (card F - 1) * d B / n by\n rw [johnson_condition_s... | [
{
"name": "johnson_condition_strong_implies_2_le_F_card",
"text": "/-- The strong Johnson condition forces the alphabet to have at least two elements. -/\nlemma johnson_condition_strong_implies_2_le_F_card\n (h_johnson : JohnsonConditionStrong B v) :\n 2 ≤ card F := by\n revert h_johnson\n dsimp [Jo... | [
{
"name": "johnson_bound_alphabet_free",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 9,
"n_lines": 202,
"n_chars": 12099,
"n_subproofs": 49,
"n_tactics": 187,
"cyclomatic": 3,
"n_automation": 69,
"n_rewrites": 11,
"n_structural": 23,
"automation_only": f... | 9 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Lemmas
/-! # Johnson Bound Basics -/
namespace JohnsonBound
/-!
This module is based on the J... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Lemmas
/-! # Johnson Bound Basics -/
namespace JohnsonBound
/-!
This module is based on the J... | @@ -235,6 +235,14 @@
0 < n := by
cases n <;> try simp [JohnsonConditionStrong] at *
+/-- The strong Johnson condition forces the alphabet to have at least two elements. -/
+lemma johnson_condition_strong_implies_2_le_F_card
+ (h_johnson : JohnsonConditionStrong B v) :
+ 2 ≤ card F := by
+ revert h_john... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_0 | 07adaf96d6f8536a | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 2 | [
{
"theorem_name": "folding_polynomial_def_base_case",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero_iff] at h\n rw [h]\n ... | [
{
"name": "folding_polynomial_eq_map_of_f_degree_lt_q_degree",
"text": "lemma folding_polynomial_eq_map_of_f_degree_lt_q_degree {q f : F[X]}\n (h : f.degree < q.degree) :\n foldingPolynomial q f = Polynomial.map C f := by\n unfold foldingPolynomial foldingPolynomialAux\n simp [h]\n\n",
"fan_in": 2... | [
{
"name": "folding_polynomial_def_base_case",
"fan_in": 4,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 384,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 4,
"n_automation": 1,
"n_rewrites": 3,
"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: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -89,6 +89,12 @@
noncomputable def foldingPolynomial (q f : F[X]) : F[X][Y] :=
foldingPolynomialAux q f f.natDegree
+lemma folding_polynomial_eq_map_of_f_degree_lt_q_degree {q f : F[X]}
+ (h : f.degree < q.degree) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ unfold foldingPolynomial foldingPolyno... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_1 | c8b68dd521a4afa8 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 1 | [
{
"theorem_name": "folding_polynomial_def_ind_case",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_fold :\n ∀ {deg : ℕ},\n deg ≥ f.natDegree →\n foldingPolynomial q f ... | [
{
"name": "folding_polynomial_aux_natDegree_fuel_is_enough",
"text": "private lemma folding_polynomial_aux_natDegree_fuel_is_enough {q f : F[X]} {fuel : ℕ}\n (h : f.natDegree ≤ fuel) :\n foldingPolynomialAux q f f.natDegree = foldingPolynomialAux q f fuel := by\n have h_foldingPolynomialAux :\n ∀ (deg... | [
{
"name": "folding_polynomial_def_ind_case",
"fan_in": 5,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 53,
"n_chars": 2406,
"n_subproofs": 6,
"n_tactics": 48,
"cyclomatic": 3,
"n_automation": 7,
"n_rewrites": 7,
"n_structural": 10,
"automation_only": fal... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -127,6 +127,64 @@
simp [map_C, folding_polynomial_C_q])
rw [folding_polynomial_eq_map_of_f_degree_lt_q_degree h]
+private lemma folding_polynomial_aux_natDegree_fuel_is_enough {q f : F[X]} {fuel : ℕ}
+ (h : f.natDegree ≤ fuel) :
+ foldingPolynomialAux q f f.natDegree = foldingPolynomialAux q f fuel := ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_2 | a1fabb3a9f6723ed | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 4 | [
{
"theorem_name": "eq_zero_of_folding_polynomial_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n : f.natDegree using Nat.strong_induction_on generalizing f with\n | h n' ih =>\n ... | [
{
"name": "folding_polynomial_def_base_case",
"text": "private lemma folding_polynomial_def_base_case {q f : F[X]}\n (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :\n foldingPolynomial q f = Polynomial.map C f := by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero... | [
{
"name": "eq_zero_of_folding_polynomial_eq_zero",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 52,
"n_chars": 2126,
"n_subproofs": 5,
"n_tactics": 50,
"cyclomatic": 5,
"n_automation": 17,
"n_rewrites": 6,
"n_structural": 8,
"automation_only... | 4 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -117,6 +117,16 @@
unfold foldingPolynomial foldingPolynomialAux
simp
+private lemma folding_polynomial_def_base_case {q f : F[X]}
+ (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ rcases h with h | h | h
+ <;> try (
+ rw [Polynomial.... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_3 | 9851eb2f713d998e | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 4 | [
{
"theorem_name": "eq_zero_of_folding_polynomial_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n : f.natDegree using Nat.strong_induction_on generalizing f with\n | h n' ih =>\n ... | [
{
"name": "folding_polynomial_def_base_case",
"text": "private lemma folding_polynomial_def_base_case {q f : F[X]}\n (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :\n foldingPolynomial q f = Polynomial.map C f := by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero... | [
{
"name": "folding_polynomial_ne_zero_of_ne_zero",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 5,
"n_chars": 183,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": t... | 5 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -117,6 +117,16 @@
unfold foldingPolynomial foldingPolynomialAux
simp
+private lemma folding_polynomial_def_base_case {q f : F[X]}
+ (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ rcases h with h | h | h
+ <;> try (
+ rw [Polynomial.... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_4 | 60600ef66c9fcc9b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 4 | [
{
"theorem_name": "eq_zero_of_folding_polynomial_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n : f.natDegree using Nat.strong_induction_on generalizing f with\n | h n' ih =>\n ... | [
{
"name": "folding_polynomial_def_base_case",
"text": "private lemma folding_polynomial_def_base_case {q f : F[X]}\n (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :\n foldingPolynomial q f = Polynomial.map C f := by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero... | [
{
"name": "substitution_property_of_folding_polynomial",
"fan_in": 3,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 82,
"n_chars": 3308,
"n_subproofs": 3,
"n_tactics": 80,
"cyclomatic": 4,
"n_automation": 18,
"n_rewrites": 6,
"n_structural": 7,
"automatio... | 4 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -117,6 +117,16 @@
unfold foldingPolynomial foldingPolynomialAux
simp
+private lemma folding_polynomial_def_base_case {q f : F[X]}
+ (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ rcases h with h | h | h
+ <;> try (
+ rw [Polynomial.... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_5 | 00da02f0aacd7294 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 4 | [
{
"theorem_name": "eq_zero_of_folding_polynomial_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n : f.natDegree using Nat.strong_induction_on generalizing f with\n | h n' ih =>\n ... | [
{
"name": "folding_polynomial_def_base_case",
"text": "private lemma folding_polynomial_def_base_case {q f : F[X]}\n (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :\n foldingPolynomial q f = Polynomial.map C f := by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero... | [
{
"name": "eval_property_of_folding_polynomial",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 16,
"n_chars": 664,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": f... | 5 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -117,6 +117,16 @@
unfold foldingPolynomial foldingPolynomialAux
simp
+private lemma folding_polynomial_def_base_case {q f : F[X]}
+ (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ rcases h with h | h | h
+ <;> try (
+ rw [Polynomial.... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_6 | 2c9e3eeaf69640df | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 4 | [
{
"theorem_name": "eq_zero_of_folding_polynomial_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n : f.natDegree using Nat.strong_induction_on generalizing f with\n | h n' ih =>\n ... | [
{
"name": "folding_polynomial_def_base_case",
"text": "private lemma folding_polynomial_def_base_case {q f : F[X]}\n (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :\n foldingPolynomial q f = Polynomial.map C f := by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero... | [
{
"name": "eval_property_of_folding_polynomial_x_k",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 9,
"n_chars": 368,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only":... | 6 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -117,6 +117,16 @@
unfold foldingPolynomial foldingPolynomialAux
simp
+private lemma folding_polynomial_def_base_case {q f : F[X]}
+ (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ rcases h with h | h | h
+ <;> try (
+ rw [Polynomial.... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_7 | 4b5dd06c40c5fce7 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 2 | [
{
"theorem_name": "folding_polynomial_def_base_case",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero_iff] at h\n rw [h]\n ... | [
{
"name": "folding_polynomial_eq_map_of_f_degree_lt_q_degree",
"text": "lemma folding_polynomial_eq_map_of_f_degree_lt_q_degree {q f : F[X]}\n (h : f.degree < q.degree) :\n foldingPolynomial q f = Polynomial.map C f := by\n unfold foldingPolynomial foldingPolynomialAux\n simp [h]\n\n",
"fan_in": 2... | [
{
"name": "folding_polynomial_deg_y_bound",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 53,
"n_chars": 2355,
"n_subproofs": 3,
"n_tactics": 50,
"cyclomatic": 5,
"n_automation": 14,
"n_rewrites": 6,
"n_structural": 10,
"automation_only": fal... | 3 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -89,6 +89,12 @@
noncomputable def foldingPolynomial (q f : F[X]) : F[X][Y] :=
foldingPolynomialAux q f f.natDegree
+lemma folding_polynomial_eq_map_of_f_degree_lt_q_degree {q f : F[X]}
+ (h : f.degree < q.degree) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ unfold foldingPolynomial foldingPolyno... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_8 | 201e2eea8412dbfa | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 2 | [
{
"theorem_name": "folding_polynomial_def_base_case",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero_iff] at h\n rw [h]\n ... | [
{
"name": "folding_polynomial_eq_map_of_f_degree_lt_q_degree",
"text": "lemma folding_polynomial_eq_map_of_f_degree_lt_q_degree {q f : F[X]}\n (h : f.degree < q.degree) :\n foldingPolynomial q f = Polynomial.map C f := by\n unfold foldingPolynomial foldingPolynomialAux\n simp [h]\n\n",
"fan_in": 2... | [
{
"name": "folding_polynomial_deg_y_bound_x_k",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 13,
"n_chars": 475,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": tru... | 4 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -89,6 +89,12 @@
noncomputable def foldingPolynomial (q f : F[X]) : F[X][Y] :=
foldingPolynomialAux q f f.natDegree
+lemma folding_polynomial_eq_map_of_f_degree_lt_q_degree {q f : F[X]}
+ (h : f.degree < q.degree) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ unfold foldingPolynomial foldingPolyno... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_9 | 7815e449abe4b3be | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 4 | [
{
"theorem_name": "eq_zero_of_folding_polynomial_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n : f.natDegree using Nat.strong_induction_on generalizing f with\n | h n' ih =>\n ... | [
{
"name": "folding_polynomial_def_base_case",
"text": "private lemma folding_polynomial_def_base_case {q f : F[X]}\n (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :\n foldingPolynomial q f = Polynomial.map C f := by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero... | [
{
"name": "folding_polynomial_deg_x_bound",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 10,
"n_lines": 11,
"n_chars": 409,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,... | 9 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -117,6 +117,16 @@
unfold foldingPolynomial foldingPolynomialAux
simp
+private lemma folding_polynomial_def_base_case {q f : F[X]}
+ (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ rcases h with h | h | h
+ <;> try (
+ rw [Polynomial.... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_10 | ff3edfffe685bc81 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 4 | [
{
"theorem_name": "eq_zero_of_folding_polynomial_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n : f.natDegree using Nat.strong_induction_on generalizing f with\n | h n' ih =>\n ... | [
{
"name": "folding_polynomial_def_base_case",
"text": "private lemma folding_polynomial_def_base_case {q f : F[X]}\n (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :\n foldingPolynomial q f = Polynomial.map C f := by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero... | [
{
"name": "folding_polynomial_is_the_reminder",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 7,
"n_lines": 10,
"n_chars": 427,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": fal... | 6 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -117,6 +117,16 @@
unfold foldingPolynomial foldingPolynomialAux
simp
+private lemma folding_polynomial_def_base_case {q f : F[X]}
+ (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ rcases h with h | h | h
+ <;> try (
+ rw [Polynomial.... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_11 | a47a52934f17c00b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 4 | [
{
"theorem_name": "eq_zero_of_folding_polynomial_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n : f.natDegree using Nat.strong_induction_on generalizing f with\n | h n' ih =>\n ... | [
{
"name": "folding_polynomial_def_base_case",
"text": "private lemma folding_polynomial_def_base_case {q f : F[X]}\n (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :\n foldingPolynomial q f = Polynomial.map C f := by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero... | [
{
"name": "folding_polynomial_is_unique",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 9,
"n_lines": 52,
"n_chars": 2406,
"n_subproofs": 7,
"n_tactics": 48,
"cyclomatic": 4,
"n_automation": 13,
"n_rewrites": 8,
"n_structural": 7,
"automation_only": false,... | 7 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -117,6 +117,16 @@
unfold foldingPolynomial foldingPolynomialAux
simp
+private lemma folding_polynomial_def_base_case {q f : F[X]}
+ (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ rcases h with h | h | h
+ <;> try (
+ rw [Polynomial.... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_12 | 2a3626dd04eaa671 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 4 | [
{
"theorem_name": "eq_zero_of_folding_polynomial_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n : f.natDegree using Nat.strong_induction_on generalizing f with\n | h n' ih =>\n ... | [
{
"name": "folding_polynomial_def_base_case",
"text": "private lemma folding_polynomial_def_base_case {q f : F[X]}\n (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :\n foldingPolynomial q f = Polynomial.map C f := by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero... | [
{
"name": "folded_poly_degree_bound",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 15,
"n_lines": 103,
"n_chars": 4957,
"n_subproofs": 4,
"n_tactics": 100,
"cyclomatic": 8,
"n_automation": 28,
"n_rewrites": 11,
"n_structural": 14,
"automation_only": false... | 13 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -117,6 +117,16 @@
unfold foldingPolynomial foldingPolynomialAux
simp
+private lemma folding_polynomial_def_base_case {q f : F[X]}
+ (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ rcases h with h | h | h
+ <;> try (
+ rw [Polynomial.... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_13 | 9fa2d4e77df463f6 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 4 | [
{
"theorem_name": "eq_zero_of_folding_polynomial_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n : f.natDegree using Nat.strong_induction_on generalizing f with\n | h n' ih =>\n ... | [
{
"name": "folding_polynomial_def_base_case",
"text": "private lemma folding_polynomial_def_base_case {q f : F[X]}\n (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :\n foldingPolynomial q f = Polynomial.map C f := by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero... | [
{
"name": "folding_polynomial_is_unique'",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 16,
"n_lines": 39,
"n_chars": 1737,
"n_subproofs": 3,
"n_tactics": 28,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 3,
"n_structural": 3,
"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: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -117,6 +117,16 @@
unfold foldingPolynomial foldingPolynomialAux
simp
+private lemma folding_polynomial_def_base_case {q f : F[X]}
+ (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ rcases h with h | h | h
+ <;> try (
+ rw [Polynomial.... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_14 | c131dd5ab88f8664 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 4 | [
{
"theorem_name": "eq_zero_of_folding_polynomial_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n : f.natDegree using Nat.strong_induction_on generalizing f with\n | h n' ih =>\n ... | [
{
"name": "folding_polynomial_def_base_case",
"text": "private lemma folding_polynomial_def_base_case {q f : F[X]}\n (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :\n foldingPolynomial q f = Polynomial.map C f := by\n rcases h with h | h | h\n <;> try (\n rw [Polynomial.degree_le_zero... | [
{
"name": "polyFold_natDegree_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 10,
"n_lines": 21,
"n_chars": 821,
"n_subproofs": 1,
"n_tactics": 19,
"cyclomatic": 4,
"n_automation": 7,
"n_rewrites": 3,
"n_structural": 6,
"automation_only": false,
"ma... | 9 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -117,6 +117,16 @@
unfold foldingPolynomial foldingPolynomialAux
simp
+private lemma folding_polynomial_def_base_case {q f : F[X]}
+ (h : f.degree < q.degree ∨ f.degree ≤ 0 ∨ q.degree ≤ 0) :
+ foldingPolynomial q f = Polynomial.map C f := by
+ rcases h with h | h | h
+ <;> try (
+ rw [Polynomial.... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_15 | 9434cf04d98c3cde | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 1 | [
{
"theorem_name": "X_pow_div_mod_decomp",
"depth": 1,
"n_commands": 0,
"n_lines": 20,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Polynomial.ext\n intro n\n rw [Polynomial.coeff_add, Polynomial.finsetSum_coeff, Polynomial.coeff_X_pow_mul',... | [
{
"name": "coeff_iterate_divX",
"text": "/-- Iterating `Polynomial.divX` shifts coefficients down by the iteration count. -/\nprivate lemma coeff_iterate_divX (f : F[X]) (k n : ℕ) :\n (Polynomial.divX^[k] f).coeff n = f.coeff (n + k) := by\n induction k generalizing f n with\n | zero => simp\n | succ ... | [
{
"name": "X_pow_div_mod_decomp",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 26,
"n_chars": 977,
"n_subproofs": 3,
"n_tactics": 23,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 5,
"n_structural": 6,
"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, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -422,6 +422,15 @@
variable {F : Type*} [Field F]
+/-- Iterating `Polynomial.divX` shifts coefficients down by the iteration count. -/
+private lemma coeff_iterate_divX (f : F[X]) (k n : ℕ) :
+ (Polynomial.divX^[k] f).coeff n = f.coeff (n + k) := by
+ induction k generalizing f n with
+ | zero => simp
+ | ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_16 | f151f0f25704085a | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 5 | [
{
"theorem_name": "eq_zero_of_folding_polynomial_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n : f.natDegree using Nat.strong_induction_on generalizing f with\n | h n' ih =>\n ... | [
{
"name": "folding_polynomial_def_ind_case",
"text": "private lemma folding_polynomial_def_ind_case {q f : F[X]}\n (h₁ : f.degree ≥ q.degree)\n (h₂ : q.degree > 0) :\n foldingPolynomial q f = (Polynomial.map Polynomial.C (f % q)) +\n Polynomial.C Polynomial.X * foldingPolynomial q (f / q) := by\n ... | [
{
"name": "polyFold_step",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 21,
"n_chars": 1007,
"n_subproofs": 3,
"n_tactics": 19,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 9,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 3 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -185,6 +185,58 @@
· exact ih (by omega) _ (by omega) (by omega)
exact h_foldingPolynomialAux _ _ le_rfl h
+private lemma folding_polynomial_def_ind_case {q f : F[X]}
+ (h₁ : f.degree ≥ q.degree)
+ (h₂ : q.degree > 0) :
+ foldingPolynomial q f = (Polynomial.map Polynomial.C (f % q)) +
+ Polynomi... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_8f1bf34c6619_17 | 61e05704baaa94c9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Polynomial/FoldingPolynomial.lean | FoldingPolynomial | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 25 | 1 | [
{
"theorem_name": "folding_polynomial_def_ind_case",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_fold :\n ∀ {deg : ℕ},\n deg ≥ f.natDegree →\n foldingPolynomial q f ... | [
{
"name": "folding_polynomial_aux_natDegree_fuel_is_enough",
"text": "private lemma folding_polynomial_aux_natDegree_fuel_is_enough {q f : F[X]} {fuel : ℕ}\n (h : f.natDegree ≤ fuel) :\n foldingPolynomialAux q f f.natDegree = foldingPolynomialAux q f fuel := by\n have h_foldingPolynomialAux :\n ∀ (deg... | [
{
"name": "cpolyFold_natDegree_le",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 20,
"n_lines": 8,
"n_chars": 391,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max... | 19 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov, Aristotle (Harmonic)
-/
import ArkLib.Data.Polynomial.Bivariate
import Mathlib.Algebra.Polynomial.Basic
import Mathlib.Tactic.Cases
import M... | @@ -127,6 +127,64 @@
simp [map_C, folding_polynomial_C_q])
rw [folding_polynomial_eq_map_of_f_degree_lt_q_degree h]
+private lemma folding_polynomial_aux_natDegree_fuel_is_enough {q f : F[X]} {fuel : ℕ}
+ (h : f.natDegree ≤ fuel) :
+ foldingPolynomialAux q f f.natDegree = foldingPolynomialAux q f fuel := ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1dd1dfc36987_0 | 932589b78fa1049b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/Multilinear.lean | Multilinear | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "eqPolynomial_zeroOne",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold eqPolynomial; congr; funext i; simp [singleEqPolynomial_zeroOne]",
"n_chars": 77,
"n_subproofs": 0,
... | [
{
"name": "singleEqPolynomial_zeroOne",
"text": "theorem singleEqPolynomial_zeroOne (r : Fin 2) (x : MvPolynomial σ R) :\n singleEqPolynomial (r : R) x = if r = 0 then 1 - x else x := by\n fin_cases r <;> simp\n\n-- @[simp]\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 176,
"n_subproofs": 0,... | [
{
"name": "eqPolynomial_zeroOne",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 219,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import CompPoly.Data.MvPolynomial.Notation
import ArkLib.Data.MvPolynomial.Interpolation
/-!
# Multilinear Polynomials
This is the special case of polynomial i... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import CompPoly.Data.MvPolynomial.Notation
import ArkLib.Data.MvPolynomial.Interpolation
/-!
# Multilinear Polynomials
This is the special case of polynomial i... | @@ -48,6 +48,11 @@
unfold singleEqPolynomial; simp
-- @[simp]
+theorem singleEqPolynomial_zeroOne (r : Fin 2) (x : MvPolynomial σ R) :
+ singleEqPolynomial (r : R) x = if r = 0 then 1 - x else x := by
+ fin_cases r <;> simp
+
+-- @[simp]
variable [Fintype σ]
abbrev eqPolynomial' : R[X (σ ⊕ σ)] :=
@@ -64,7... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1dd1dfc36987_3 | 0f29378d745e2971 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/Multilinear.lean | Multilinear | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "eqPolynomial_degreeOf",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (mem_restrictDegree_iff_degreeOf_le _ _).mp\n exact eqPolynomial_mem_restrictDegree r",
"n_chars": 97,
... | [
{
"name": "eqPolynomial_mem_restrictDegree",
"text": "theorem eqPolynomial_mem_restrictDegree (r : σ → R) : (eqPolynomial r) ∈ R⦃≤ 1⦄[X σ] := by\n classical\n rw [mem_restrictDegree_iff_degreeOf_le]\n intro i\n calc\n _ ≤ ∑ j : σ, degreeOf i (singleEqPolynomial (r j) (X j)) := by\n exact degreeO... | [
{
"name": "MLE_mem_restrictDegree",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 18,
"n_chars": 667,
"n_subproofs": 0,
"n_tactics": 17,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
"ma... | 4 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import CompPoly.Data.MvPolynomial.Notation
import ArkLib.Data.MvPolynomial.Interpolation
/-!
# Multilinear Polynomials
This is the special case of polynomial i... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import CompPoly.Data.MvPolynomial.Notation
import ArkLib.Data.MvPolynomial.Interpolation
/-!
# Multilinear Polynomials
This is the special case of polynomial i... | @@ -129,8 +129,23 @@
_ = if i = j then 1 else 0 := by norm_num
omit [DecidableEq σ] in
-theorem eqPolynomial_degreeOf (r : σ → R) (i : σ) : degreeOf i (eqPolynomial r) ≤ 1 := sorry
+theorem eqPolynomial_mem_restrictDegree (r : σ → R) : (eqPolynomial r) ∈ R⦃≤ 1⦄[X σ] := by
+ classical
+ rw [mem_restrictDegree_... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1dd1dfc36987_4 | b2f49e5dd4ef0a37 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/Multilinear.lean | Multilinear | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "eqPolynomial_degreeOf",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply (mem_restrictDegree_iff_degreeOf_le _ _).mp\n exact eqPolynomial_mem_restrictDegree r",
"n_chars": 97,
... | [
{
"name": "eqPolynomial_mem_restrictDegree",
"text": "theorem eqPolynomial_mem_restrictDegree (r : σ → R) : (eqPolynomial r) ∈ R⦃≤ 1⦄[X σ] := by\n classical\n rw [mem_restrictDegree_iff_degreeOf_le]\n intro i\n calc\n _ ≤ ∑ j : σ, degreeOf i (singleEqPolynomial (r j) (X j)) := by\n exact degreeO... | [
{
"name": "MLE_degreeOf",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 5,
"n_chars": 188,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": ... | 4 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import CompPoly.Data.MvPolynomial.Notation
import ArkLib.Data.MvPolynomial.Interpolation
/-!
# Multilinear Polynomials
This is the special case of polynomial i... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import CompPoly.Data.MvPolynomial.Notation
import ArkLib.Data.MvPolynomial.Interpolation
/-!
# Multilinear Polynomials
This is the special case of polynomial i... | @@ -129,8 +129,23 @@
_ = if i = j then 1 else 0 := by norm_num
omit [DecidableEq σ] in
-theorem eqPolynomial_degreeOf (r : σ → R) (i : σ) : degreeOf i (eqPolynomial r) ≤ 1 := sorry
+theorem eqPolynomial_mem_restrictDegree (r : σ → R) : (eqPolynomial r) ∈ R⦃≤ 1⦄[X σ] := by
+ classical
+ rw [mem_restrictDegree_... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_0 | 8485c37e8f167bad | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "dot_comm",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 186,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,8 +99,13 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `dot` is symmetric. -/
-theorem dot_comm {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_1 | f4ad3db0150c08f0 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "dot_add_left",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 243,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,8 +99,13 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `dot` distributes over addition in the first argument. -/
-theorem dot_add_... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_2 | ee970665e9daa703 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "dot_add_right",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 245,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": ... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,8 +99,13 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `dot` distributes over addition in the second argument. -/
-theorem dot_add... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_3 | 114444ec5a794dfe | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "dot_scalarVecMul",
"fan_in": 4,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 303,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,9 +99,15 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `dot` pulls out a left scalar from the second argument. -/
theorem dot_sca... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_4 | 1d5c554eca9652e1 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "matVecMul_add",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 6,
"n_chars": 287,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,8 +99,13 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `dot` distributes over addition in the second argument. -/
-theorem dot_add... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_5 | b43f70dd4a275f7a | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "matVecMul_matrix_add",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 348,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,9 +99,16 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- Matrix–vector multiplication distributes over addition of matrices. -/
the... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_6 | a0e9079f4c15ccf8 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "matVecMul_matrix_smul",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 8,
"n_chars": 374,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,9 +99,16 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- Matrix–vector multiplication pulls out a scalar from the matrix. -/
theore... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_7 | aa0e7c76428a04d3 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "matVecMul_scalarVecMul",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 6,
"n_chars": 320,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,9 +99,15 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `dot` pulls out a left scalar from the second argument. -/
theorem dot_sca... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_8 | 4d7a2b58a362ec29 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "matMul_apply",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 269,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,9 +99,14 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `matMul` entrywise: `(matMul M N) i k = ∑ⱼ Mᵢⱼ Nⱼₖ`. -/
theorem matMul_app... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_9 | c4397be70c9fbd13 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "matVecMul_matMul",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 12,
"n_chars": 559,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesti... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,15 +99,23 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `matMul` entrywise: `(matMul M N) i k = ∑ⱼ Mᵢⱼ Nⱼₖ`. -/
theorem matMul_ap... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_10 | 1649a37fd31e9b22 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "splitForm_add_right",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 6,
"n_chars": 292,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nest... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,8 +99,13 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `dot` distributes over addition in the second argument. -/
-theorem dot_add... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_11 | c3df77fda2d80419 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "splitForm_smul_right",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 6,
"n_chars": 315,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nes... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,9 +99,15 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `dot` pulls out a left scalar from the second argument. -/
theorem dot_sca... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_12 | 1dfca7c0b583fea2 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "splitForm_add_left",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 6,
"n_chars": 277,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesti... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,8 +99,13 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `dot` distributes over addition in the first argument. -/
-theorem dot_add_... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_13 | 5194dc6b32c73925 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "splitForm_smul_left",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 7,
"n_chars": 334,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nes... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,12 +99,19 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `dot` is symmetric. -/
-theorem dot_comm {k : ℕ} (u v : PolyVec P k) : u ⬝... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_14 | 8006f4a660f27889 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "splitForm_matrix_add",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 6,
"n_chars": 280,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nes... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,12 +99,20 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `dot` distributes over addition in the second argument. -/
-theorem dot_ad... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_15 | d11d86f9f7eeea43 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "splitForm_matrix_smul",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 6,
"n_chars": 286,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_ne... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,13 +99,22 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `dot` pulls out a left scalar from the second argument. -/
theorem dot_sc... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_16 | 3eb71494612b6902 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "splitForm_transpose",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 10,
"n_chars": 585,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,6 +99,10 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- The **split bilinear form** `⟨u, M *ᵥ v⟩` (`uᵀ M v`) underlying the Greyhou... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_17 | 2a347637376d08ca | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "splitForm_comp",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 8,
"n_chars": 522,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,15 +99,23 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `matMul` entrywise: `(matMul M N) i k = ∑ⱼ Mᵢⱼ Nⱼₖ`. -/
theorem matMul_ap... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_18 | 9a2200cd73d23cde | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "dot_sub",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 242,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2
}
... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,6 +99,10 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- The **split bilinear form** `⟨u, M *ᵥ v⟩` (`uᵀ M v`) underlying the Greyhou... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_19 | d4c26dc1abf9cb27 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "matVecMul_sub",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 6,
"n_chars": 266,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,6 +99,10 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- The **split bilinear form** `⟨u, M *ᵥ v⟩` (`uᵀ M v`) underlying the Greyhou... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_20 | 765d56373e1619c9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "scalarVecMul_mul_ne_of_ne",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro h; apply hvw\n rw [mul_comm d c] at h\n exact scalarVecMul_injective_of_isUnit (hc.mul hd) h",
"n_cha... | [
{
"name": "scalarVecMul_injective_of_isUnit",
"text": "/-- Left scalar multiplication by a unit is injective. -/\ntheorem scalarVecMul_injective_of_isUnit {cols : ℕ} {c : P} (hc : IsUnit c) :\n Function.Injective (scalarVecMul (cols := cols) c) := by\n intro v w h\n funext i\n have : scalarVecMul c v ... | [
{
"name": "scalarVecMul_mul_ne_of_ne",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 354,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -113,10 +113,22 @@
variable {P : Type u} [CommRing P]
+/-- Left scalar multiplication by a unit is injective. -/
+theorem scalarVecMul_injective_of_isUnit {cols : ℕ} {c : P} (hc : IsUnit c) :
+ Function.Injective (scalarVecMul (cols := cols) c) := by
+ intro v w h
+ funext i
+ have : scalarVecMul c v i = ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_6301ad6b217f_21 | b1b7847771463179 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/Vectors.lean | Vectors | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 10 | [
{
"theorem_name": "dot_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [dot_eq_sum]; exact Finset.sum_congr rfl (fun i _ => mul_comm _ _)",
"n_chars": 82,
"n_subproofs": 0,
"n_tac... | [
{
"name": "dot_eq_sum",
"text": "/-- `dot` as a `Finset.sum` of coordinatewise products. -/\ntheorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by\n rw [dot, List.sum_ofFn]\n\n",
"fan_in": 10,
"n_lines": 5,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "matVecMul_scalarVecMul_mul_eq_of_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"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": fal... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import Mathlib.LinearAlgebra.Matrix.Defs
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Tactic.Ring
/-!
# Vectors And Matrices For The Lattice Lay... | @@ -99,9 +99,15 @@
variable {P : Type u} [CommSemiring P]
+/-- `dot` as a `Finset.sum` of coordinatewise products. -/
+theorem dot_eq_sum {k : ℕ} (u v : PolyVec P k) : u ⬝ᵥ v = ∑ i : Fin k, u i * v i := by
+ rw [dot, List.sum_ofFn]
+
/-- `dot` pulls out a left scalar from the second argument. -/
theorem dot_sca... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_58db9f8b8efa_0 | 0cc4c771ecdb8a63 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/PolynomialEvalSplit.lean | PolynomialEvalSplit | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 2 | [
{
"theorem_name": "monomialBasis_split",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [monomialBasis_get, monomialBasis_get, monomialBasis_get]\n exact basisProd_split (fun b v => if b then v else 1) x... | [
{
"name": "basisProd_split",
"text": "/-- Tensor split of a factorized basis vector along `splitEquiv`. -/\nprivate theorem basisProd_split [CommSemiring R] (g : Bool → R → R)\n (xl : Vector R nl) (xh : Vector R nh) (x : Fin (2 ^ nh)) (y : Fin (2 ^ nl)) :\n (∏ j : Fin (nl + nh),\n g ((BitVec.of... | [
{
"name": "monomialBasis_split",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 462,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nes... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | @@ -74,6 +74,47 @@
factor `g`. The following lemma is the combinatorial heart of the split: along `splitEquiv`, this
product factors as the product over the low variables times the product over the high variables. -/
+/-- Tensor split of a factorized basis vector along `splitEquiv`. -/
+private theorem basisProd_sp... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_58db9f8b8efa_1 | 57867adc8745768f | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/PolynomialEvalSplit.lean | PolynomialEvalSplit | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "evalSplit_eq_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [evalSplit, splitForm]\n rw [eval_eq_sum,\n ← Equiv.sum_comp (splitEquiv nl nh) (fun i => p.get i * (monom... | [
{
"name": "eval_eq_sum",
"text": "/-- Evaluation as a `Finset.sum` against the monomial basis. -/\ntheorem eval_eq_sum (p : CMlPolynomial R (nl + nh)) (v : Vector R (nl + nh)) :\n eval p v = ∑ i : Fin (2 ^ (nl + nh)), p.get i * (monomialBasis v).get i := by\n rw [eval, Vector.dotProduct_eq_root_dotProdu... | [
{
"name": "evalSplit_eq_eval",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 20,
"n_chars": 899,
"n_subproofs": 0,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 4,
"n_structural": 4,
"automation_only": false,
"max_nes... | 4 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | @@ -121,6 +121,11 @@
open CMlPolynomial
+/-- Evaluation as a `Finset.sum` against the monomial basis. -/
+theorem eval_eq_sum (p : CMlPolynomial R (nl + nh)) (v : Vector R (nl + nh)) :
+ eval p v = ∑ i : Fin (2 ^ (nl + nh)), p.get i * (monomialBasis v).get i := by
+ rw [eval, Vector.dotProduct_eq_root_dotProdu... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_58db9f8b8efa_2 | 4acdb6fc5d059b5b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/PolynomialEvalSplit.lean | PolynomialEvalSplit | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "toMatrix_add",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i j; simp only [toMatrix, Matrix.add_apply]; exact coeff_add p q _",
"n_chars": 79,
"n_subproofs": 0,
"n_ta... | [
{
"name": "coeff_add",
"text": "/-- Coefficientwise additivity of `CMlPolynomial` (the `+` is `Vector.zipWith (·+·)`). -/\nprivate theorem coeff_add (p q : CMlPolynomial R (nl + nh)) (k : Fin (2 ^ (nl + nh))) :\n (p + q).get k = p.get k + q.get k := by\n change (Vector.zipWith (· + ·) p q).get k = p.get... | [
{
"name": "toMatrix_add",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 256,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | @@ -95,9 +95,16 @@
def evalSplit (p : CMlPolynomial R (nl + nh)) (xl : Vector R nl) (xh : Vector R nh) : R :=
splitForm (toMatrix p) (monomialBasis xl).get (monomialBasis xh).get
+/-- Coefficientwise additivity of `CMlPolynomial` (the `+` is `Vector.zipWith (·+·)`). -/
+private theorem coeff_add (p q : CMlPolynom... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_58db9f8b8efa_3 | cef9e7a979e0c1b5 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/PolynomialEvalSplit.lean | PolynomialEvalSplit | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "toMatrix_smul",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i j; simp only [toMatrix, Matrix.smul_apply, smul_eq_mul]; exact coeff_smul r p _",
"n_chars": 94,
"n_subproof... | [
{
"name": "coeff_smul",
"text": "/-- Coefficientwise scalar multiplication of `CMlPolynomial` (the `•` is `Vector.map (r * ·)`). -/\nprivate theorem coeff_smul (r : R) (p : CMlPolynomial R (nl + nh)) (k : Fin (2 ^ (nl + nh))) :\n (r • p).get k = r * p.get k := by\n change (Vector.map (fun a => r * a) p)... | [
{
"name": "toMatrix_smul",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 282,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | @@ -95,9 +95,16 @@
def evalSplit (p : CMlPolynomial R (nl + nh)) (xl : Vector R nl) (xh : Vector R nh) : R :=
splitForm (toMatrix p) (monomialBasis xl).get (monomialBasis xh).get
+/-- Coefficientwise scalar multiplication of `CMlPolynomial` (the `•` is `Vector.map (r * ·)`). -/
+private theorem coeff_smul (r : R)... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_58db9f8b8efa_4 | 2bba715b37584bff | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/PolynomialEvalSplit.lean | PolynomialEvalSplit | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "toMatrix_add",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i j; simp only [toMatrix, Matrix.add_apply]; exact coeff_add p q _",
"n_chars": 79,
"n_subproofs": 0,
"n_ta... | [
{
"name": "coeff_add",
"text": "/-- Coefficientwise additivity of `CMlPolynomial` (the `+` is `Vector.zipWith (·+·)`). -/\nprivate theorem coeff_add (p q : CMlPolynomial R (nl + nh)) (k : Fin (2 ^ (nl + nh))) :\n (p + q).get k = p.get k + q.get k := by\n change (Vector.zipWith (· + ·) p q).get k = p.get... | [
{
"name": "evalSplit_add",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 395,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": ... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | @@ -95,9 +95,16 @@
def evalSplit (p : CMlPolynomial R (nl + nh)) (xl : Vector R nl) (xh : Vector R nh) : R :=
splitForm (toMatrix p) (monomialBasis xl).get (monomialBasis xh).get
+/-- Coefficientwise additivity of `CMlPolynomial` (the `+` is `Vector.zipWith (·+·)`). -/
+private theorem coeff_add (p q : CMlPolynom... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_58db9f8b8efa_5 | 52aa34ad4fbd5b9b | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/PolynomialEvalSplit.lean | PolynomialEvalSplit | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "toMatrix_smul",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i j; simp only [toMatrix, Matrix.smul_apply, smul_eq_mul]; exact coeff_smul r p _",
"n_chars": 94,
"n_subproof... | [
{
"name": "coeff_smul",
"text": "/-- Coefficientwise scalar multiplication of `CMlPolynomial` (the `•` is `Vector.map (r * ·)`). -/\nprivate theorem coeff_smul (r : R) (p : CMlPolynomial R (nl + nh)) (k : Fin (2 ^ (nl + nh))) :\n (r • p).get k = r * p.get k := by\n change (Vector.map (fun a => r * a) p)... | [
{
"name": "evalSplit_smul",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 333,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | @@ -95,9 +95,16 @@
def evalSplit (p : CMlPolynomial R (nl + nh)) (xl : Vector R nl) (xh : Vector R nh) : R :=
splitForm (toMatrix p) (monomialBasis xl).get (monomialBasis xh).get
+/-- Coefficientwise scalar multiplication of `CMlPolynomial` (the `•` is `Vector.map (r * ·)`). -/
+private theorem coeff_smul (r : R)... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_58db9f8b8efa_6 | 5a9691e648d124a7 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/PolynomialEvalSplit.lean | PolynomialEvalSplit | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 2 | [
{
"theorem_name": "monomialBasis_split",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [monomialBasis_get, monomialBasis_get, monomialBasis_get]\n exact basisProd_split (fun b v => if b then v else 1) x... | [
{
"name": "basisProd_split",
"text": "/-- Tensor split of a factorized basis vector along `splitEquiv`. -/\nprivate theorem basisProd_split [CommSemiring R] (g : Bool → R → R)\n (xl : Vector R nl) (xh : Vector R nh) (x : Fin (2 ^ nh)) (y : Fin (2 ^ nl)) :\n (∏ j : Fin (nl + nh),\n g ((BitVec.of... | [
{
"name": "lagrangeBasis_split",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 466,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nes... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | @@ -74,6 +74,47 @@
factor `g`. The following lemma is the combinatorial heart of the split: along `splitEquiv`, this
product factors as the product over the low variables times the product over the high variables. -/
+/-- Tensor split of a factorized basis vector along `splitEquiv`. -/
+private theorem basisProd_sp... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_58db9f8b8efa_7 | 5fcbd1401aae9847 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/PolynomialEvalSplit.lean | PolynomialEvalSplit | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "evalSplitEval_eq_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [evalSplitEval, splitForm]\n rw [evalEval_eq_sum,\n ← Equiv.sum_comp (splitEquiv nl nh) (fun i => p.ge... | [
{
"name": "evalEval_eq_sum",
"text": "/-- Evaluation as a `Finset.sum` against the Lagrange basis. -/\ntheorem evalEval_eq_sum (p : CMlPolynomialEval R (nl + nh)) (v : Vector R (nl + nh)) :\n eval p v = ∑ i : Fin (2 ^ (nl + nh)), p.get i * (lagrangeBasis v).get i := by\n rw [eval, Vector.dotProduct_eq_r... | [
{
"name": "evalSplitEval_eq_eval",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 21,
"n_chars": 960,
"n_subproofs": 0,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 4,
"n_structural": 4,
"automation_only": false,
"max... | 4 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.Vectors
import CompPoly.Multilinear.Basic
import Mathlib.Algebra.BigOperators.Fin
import Mathlib.Logic.Equiv.Fin.Basic
/-!
# M... | @@ -146,6 +146,11 @@
open CMlPolynomialEval
+/-- Evaluation as a `Finset.sum` against the Lagrange basis. -/
+theorem evalEval_eq_sum (p : CMlPolynomialEval R (nl + nh)) (v : Vector R (nl + nh)) :
+ eval p v = ∑ i : Fin (2 ^ (nl + nh)), p.get i * (lagrangeBasis v).get i := by
+ rw [eval, Vector.dotProduct_eq_r... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1c9e40ccb2c8_0 | f6db91841f16ef08 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/Ops.lean | Ops | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 6 | [
{
"theorem_name": "mul_mem_of_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CosetFftDomainClass.mem_def] at *\n obtain ⟨⟨i₁, hi₁⟩, ⟨i₂, hi₂⟩⟩ := hx₁, hx₂\n exists (i₁ + i₂)\n aesop (add simp [a... | [
{
"name": "apply_add_eq_mul",
"text": "/-- Evaluation of an FFT domain turns addition in the index type\n into multiplication in the field. -/\nlemma apply_add_eq_mul :\n ω (i + j) = ω i * ω j := by\n simp [CosetFftDomainClass.map_add]\n\n",
"fan_in": 6,
"n_lines": 7,
"n_chars": 200,
"n_s... | [
{
"name": "mul_mem_of_mem",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 358,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nesting... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -55,16 +55,28 @@
lemma apply_zero_eq_one :
ω 0 = 1 := generator_eq_one _
+/-- Evaluation of an FFT domain turns addition in the index type
+ into multiplication in the field. -/
+lemma apply_add_eq_mul :
+ ω (i + j) = ω i * ω j := by
+ simp [CosetFftDomainClass.map_add]
+
/-- The product of two elements of... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1c9e40ccb2c8_1 | a94ce2b79cc13dcf | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/Ops.lean | Ops | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 6 | [
{
"theorem_name": "mul_mem_of_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CosetFftDomainClass.mem_def] at *\n obtain ⟨⟨i₁, hi₁⟩, ⟨i₂, hi₂⟩⟩ := hx₁, hx₂\n exists (i₁ + i₂)\n aesop (add simp [a... | [
{
"name": "apply_add_eq_mul",
"text": "/-- Evaluation of an FFT domain turns addition in the index type\n into multiplication in the field. -/\nlemma apply_add_eq_mul :\n ω (i + j) = ω i * ω j := by\n simp [CosetFftDomainClass.map_add]\n\n",
"fan_in": 6,
"n_lines": 7,
"n_chars": 200,
"n_s... | [
{
"name": "apply_neg_eq_inv",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 255,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -55,11 +55,19 @@
lemma apply_zero_eq_one :
ω 0 = 1 := generator_eq_one _
+/-- Evaluation of an FFT domain turns addition in the index type
+ into multiplication in the field. -/
+lemma apply_add_eq_mul :
+ ω (i + j) = ω i * ω j := by
+ simp [CosetFftDomainClass.map_add]
+
/-- Evaluation at the negated inde... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1c9e40ccb2c8_2 | dabba55f616538b9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/Ops.lean | Ops | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 6 | [
{
"theorem_name": "mul_mem_of_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CosetFftDomainClass.mem_def] at *\n obtain ⟨⟨i₁, hi₁⟩, ⟨i₂, hi₂⟩⟩ := hx₁, hx₂\n exists (i₁ + i₂)\n aesop (add simp [a... | [
{
"name": "apply_add_eq_mul",
"text": "/-- Evaluation of an FFT domain turns addition in the index type\n into multiplication in the field. -/\nlemma apply_add_eq_mul :\n ω (i + j) = ω i * ω j := by\n simp [CosetFftDomainClass.map_add]\n\n",
"fan_in": 6,
"n_lines": 7,
"n_chars": 200,
"n_s... | [
{
"name": "domain_sub_eq_div_domain",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 10,
"n_chars": 261,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"m... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -55,16 +55,29 @@
lemma apply_zero_eq_one :
ω 0 = 1 := generator_eq_one _
+/-- Evaluation of an FFT domain turns addition in the index type
+ into multiplication in the field. -/
+lemma apply_add_eq_mul :
+ ω (i + j) = ω i * ω j := by
+ simp [CosetFftDomainClass.map_add]
+
/-- Evaluation at the negated inde... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1c9e40ccb2c8_3 | cfe66f28da3a005d | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/Ops.lean | Ops | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 6 | [
{
"theorem_name": "mul_mem_of_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CosetFftDomainClass.mem_def] at *\n obtain ⟨⟨i₁, hi₁⟩, ⟨i₂, hi₂⟩⟩ := hx₁, hx₂\n exists (i₁ + i₂)\n aesop (add simp [a... | [
{
"name": "apply_add_eq_mul",
"text": "/-- Evaluation of an FFT domain turns addition in the index type\n into multiplication in the field. -/\nlemma apply_add_eq_mul :\n ω (i + j) = ω i * ω j := by\n simp [CosetFftDomainClass.map_add]\n\n",
"fan_in": 6,
"n_lines": 7,
"n_chars": 200,
"n_s... | [
{
"name": "apply_nsmul",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 278,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2... | 1 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -55,11 +55,19 @@
lemma apply_zero_eq_one :
ω 0 = 1 := generator_eq_one _
+/-- Evaluation of an FFT domain turns addition in the index type
+ into multiplication in the field. -/
+lemma apply_add_eq_mul :
+ ω (i + j) = ω i * ω j := by
+ simp [CosetFftDomainClass.map_add]
+
/-- Evaluation at the negated inde... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1c9e40ccb2c8_4 | 85fb63629444039f | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/Ops.lean | Ops | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 6 | [
{
"theorem_name": "mul_mem_of_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CosetFftDomainClass.mem_def] at *\n obtain ⟨⟨i₁, hi₁⟩, ⟨i₂, hi₂⟩⟩ := hx₁, hx₂\n exists (i₁ + i₂)\n aesop (add simp [a... | [
{
"name": "apply_add_eq_mul",
"text": "/-- Evaluation of an FFT domain turns addition in the index type\n into multiplication in the field. -/\nlemma apply_add_eq_mul :\n ω (i + j) = ω i * ω j := by\n simp [CosetFftDomainClass.map_add]\n\n",
"fan_in": 6,
"n_lines": 7,
"n_chars": 200,
"n_s... | [
{
"name": "apply_eq_pow_of_generator",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 232,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"m... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -55,11 +55,19 @@
lemma apply_zero_eq_one :
ω 0 = 1 := generator_eq_one _
+/-- Evaluation of an FFT domain turns addition in the index type
+ into multiplication in the field. -/
+lemma apply_add_eq_mul :
+ ω (i + j) = ω i * ω j := by
+ simp [CosetFftDomainClass.map_add]
+
/-- Evaluation at the negated inde... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_1c9e40ccb2c8_5 | a9c2be4c7affaffd | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Domain/FftDomain/Ops.lean | Ops | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 6 | [
{
"theorem_name": "mul_mem_of_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CosetFftDomainClass.mem_def] at *\n obtain ⟨⟨i₁, hi₁⟩, ⟨i₂, hi₂⟩⟩ := hx₁, hx₂\n exists (i₁ + i₂)\n aesop (add simp [a... | [
{
"name": "apply_add_eq_mul",
"text": "/-- Evaluation of an FFT domain turns addition in the index type\n into multiplication in the field. -/\nlemma apply_add_eq_mul :\n ω (i + j) = ω i * ω j := by\n simp [CosetFftDomainClass.map_add]\n\n",
"fan_in": 6,
"n_lines": 7,
"n_chars": 200,
"n_s... | [
{
"name": "eq_iff_generators_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 8,
"n_chars": 276,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 4,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 3,
"automation_only": false,
"max_ne... | 4 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Julian Sutherland, Ilia Vlasov, Aristotle (Harmonic)
-/
import Mathlib.GroupTheory.SpecificGroups.Cyclic
import Mathlib.Algebra.Group.Fin.Basic
import Mathlib.Algebra.Group.... | @@ -55,11 +55,19 @@
lemma apply_zero_eq_one :
ω 0 = 1 := generator_eq_one _
+/-- Evaluation of an FFT domain turns addition in the index type
+ into multiplication in the field. -/
+lemma apply_add_eq_mul :
+ ω (i + j) = ω i * ω j := by
+ simp [CosetFftDomainClass.map_add]
+
/-- Evaluation at the negated inde... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_c28c98c32636_0 | 26be2c21b13f9f04 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/JohnsonBound/Lemmas.lean | Lemmas | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "sum_K_eq_card",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw (occs := [2]) [Fis_cover_B (B := B) (i := i)]\n rw [card_biUnion (by simp [Fis_pairwise_disjoint])]",
"n_chars": 108,... | [
{
"name": "Fis_pairwise_disjoint",
"text": "/-- The sets `Fi B i α` are pairwise disjoint. -/\n@[simp]\nlemma Fis_pairwise_disjoint : Set.PairwiseDisjoint Set.univ (Fi B i) := by\n unfold Fi\n rintro x - y - h₁ _ h₂ h₃ _ contra\n specialize h₂ contra; specialize h₃ contra; aesop\n\n",
"fan_in": 1,
... | [
{
"name": "sum_K_eq_card",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 222,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting":... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | @@ -32,9 +32,18 @@
@[simp]
lemma Fis_cover_B : B = univ.biUnion (Fi B i) := by aesop (add simp [Fi])
+/-- The sets `Fi B i α` are pairwise disjoint. -/
+@[simp]
+lemma Fis_pairwise_disjoint : Set.PairwiseDisjoint Set.univ (Fi B i) := by
+ unfold Fi
+ rintro x - y - h₁ _ h₂ h₃ _ contra
+ specialize h₂ contra; spe... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_c28c98c32636_1 | 57ed129d4cb995d0 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/JohnsonBound/Lemmas.lean | Lemmas | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "sum_choose_K'",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← sum_K_eq_card (i := i), Nat.cast_sum]\n set x1 : ℚ := card F - 1\n have hx1 : x1 ≠ 0 := by simp [x1, sub_eq_zero]; o... | [
{
"name": "sum_K_eq_card",
"text": "/-- The cardinalities `K B i α` sum to `|B|`. -/\n@[simp]\nlemma sum_K_eq_card : ∑ α : F, K B i α = B.card := by\n rw (occs := [2]) [Fis_cover_B (B := B) (i := i)]\n rw [card_biUnion (by simp [Fis_pairwise_disjoint])]\n\n",
"fan_in": 1,
"n_lines": 7,
"n_char... | [
{
"name": "le_sum_choose_K",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 14,
"n_chars": 628,
"n_subproofs": 1,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nestin... | 4 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | @@ -39,6 +39,12 @@
rintro x - y - h₁ _ h₂ h₃ _ contra
specialize h₂ contra; specialize h₃ contra; aesop
+/-- The cardinalities `K B i α` sum to `|B|`. -/
+@[simp]
+lemma sum_K_eq_card : ∑ α : F, K B i α = B.card := by
+ rw (occs := [2]) [Fis_cover_B (B := B) (i := i)]
+ rw [card_biUnion (by simp [Fis_pairwise... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_c28c98c32636_3 | 873d4325fbedd3df | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/JohnsonBound/Lemmas.lean | Lemmas | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "k_and_e",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [e, k, sum_hamming_weight_sum]; field_simp; grind only",
"n_chars": 65,
"n_subproofs": 0,
"n_tactics": 4,
"cyc... | [
{
"name": "sum_hamming_weight_sum",
"text": "/-- Sum of Hamming weights equals `n · |B|` minus total zero-coordinate counts. -/\n@[simp]\nlemma sum_hamming_weight_sum [Zero F] :\n ∑ x ∈ B, (‖x‖₀ : ℚ) = n * B.card - ∑ i, K B i 0 := by\n simp only [hamming_weight_eq_sum, Nat.cast_sum, Nat.cast_ite, CharP.... | [
{
"name": "k_and_e'",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 6,
"n_chars": 185,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting": 1
... | 4 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | @@ -113,10 +113,27 @@
lemma hamming_weight_eq_sum [Zero F] {x : Fin n → F} :
‖x‖₀ = ∑ i, if x i = 0 then 0 else 1 := by simp [hammingNorm, sum_ite]
+/-- Sum of Hamming weights equals `n · |B|` minus total zero-coordinate counts. -/
+@[simp]
+lemma sum_hamming_weight_sum [Zero F] :
+ ∑ x ∈ B, (‖x‖₀ : ℚ) = n *... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_c28c98c32636_4 | 6bc16b37facc8006 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/JohnsonBound/Lemmas.lean | Lemmas | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "le_sum_choose_K",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [sum_choose_K_i]\n have : ∑ α, choose_2 ↑(K B i α) =\n choose_2 ↑(K B i 0) + ∑ α with α ≠ 0, choose_2 ↑(K B... | [
{
"name": "sum_choose_K'",
"text": "/-- Jensen's inequality applied to `choose_2` for nonzero coordinates. -/\nlemma sum_choose_K' [Zero F] (h_card : 2 ≤ card F) :\n (card F - 1) * choose_2 ((B.card - K B i 0) / (card F - 1)) ≤\n ∑ α with α ≠ 0, choose_2 (K B i α) := by\n rw [← sum_K_eq_card (i := i)... | [
{
"name": "le_sum_sum_choose_K",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 38,
"n_chars": 1965,
"n_subproofs": 6,
"n_tactics": 35,
"cyclomatic": 1,
"n_automation": 13,
"n_rewrites": 6,
"n_structural": 4,
"automation_only": false,
"max... | 6 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | @@ -60,6 +60,32 @@
exact card_le_card fun _ ha ↦ by
simp only [mem_filter, mem_univ, true_and] at ha; exact ha.1
+/-- Jensen's inequality applied to `choose_2` for nonzero coordinates. -/
+lemma sum_choose_K' [Zero F] (h_card : 2 ≤ card F) :
+ (card F - 1) * choose_2 ((B.card - K B i 0) / (card F - 1)) ≤
+... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_c28c98c32636_5 | a940022c017fd0a9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/JohnsonBound/Lemmas.lean | Lemmas | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 2 | [
{
"theorem_name": "Bi_card",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Bi_biUnion_F2i, card_biUnion (by simp [F2i_disjoint])]\n simp_rw [F2i_card]",
"n_chars": 85,
"n_subproofs": 0,
"n_... | [
{
"name": "F2i_card",
"text": "/-- `|F2i B i α| = K(α) · (K(α) - 1)`. -/\nlemma F2i_card {α : F} : (F2i B i α).card = K B i α * (K B i α - 1) := by\n simp only [F2i, K, Fi, Finset.card_filter, Finset.mem_product]\n simp only [ne_eq, Finset.sum_boole, Nat.cast_id]\n rw [show (Finset.univ.filter (fun x : (... | [
{
"name": "Bi_card",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 6,
"n_chars": 209,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
}... | 3 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | @@ -178,6 +178,16 @@
simp only [disjoint_left, Prod.forall]
unfold F2i; aesop
+/-- `|F2i B i α| = K(α) · (K(α) - 1)`. -/
+lemma F2i_card {α : F} : (F2i B i α).card = K B i α * (K B i α - 1) := by
+ simp only [F2i, K, Fi, Finset.card_filter, Finset.mem_product]
+ simp only [ne_eq, Finset.sum_boole, Nat.cast_id... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_c28c98c32636_6 | 12d86fe10c1065b0 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/JohnsonBound/Lemmas.lean | Lemmas | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 2 | [
{
"theorem_name": "Bi_card",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Bi_biUnion_F2i, card_biUnion (by simp [F2i_disjoint])]\n simp_rw [F2i_card]",
"n_chars": 85,
"n_subproofs": 0,
"n_... | [
{
"name": "F2i_card",
"text": "/-- `|F2i B i α| = K(α) · (K(α) - 1)`. -/\nlemma F2i_card {α : F} : (F2i B i α).card = K B i α * (K B i α - 1) := by\n simp only [F2i, K, Fi, Finset.card_filter, Finset.mem_product]\n simp only [ne_eq, Finset.sum_boole, Nat.cast_id]\n rw [show (Finset.univ.filter (fun x : (... | [
{
"name": "sum_of_not_equals",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 26,
"n_chars": 1307,
"n_subproofs": 1,
"n_tactics": 31,
"cyclomatic": 3,
"n_automation": 13,
"n_rewrites": 12,
"n_structural": 4,
"automation_only": false,
"max_... | 3 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | @@ -178,6 +178,16 @@
simp only [disjoint_left, Prod.forall]
unfold F2i; aesop
+/-- `|F2i B i α| = K(α) · (K(α) - 1)`. -/
+lemma F2i_card {α : F} : (F2i B i α).card = K B i α * (K B i α - 1) := by
+ simp only [F2i, K, Fi, Finset.card_filter, Finset.mem_product]
+ simp only [ne_eq, Finset.sum_boole, Nat.cast_id... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_c28c98c32636_11 | 9a4178e5d4b5d0cf | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/JohnsonBound/Lemmas.lean | Lemmas | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 28 | 1 | [
{
"theorem_name": "k_and_e",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [e, k, sum_hamming_weight_sum]; field_simp; grind only",
"n_chars": 65,
"n_subproofs": 0,
"n_tactics": 4,
"cyc... | [
{
"name": "sum_hamming_weight_sum",
"text": "/-- Sum of Hamming weights equals `n · |B|` minus total zero-coordinate counts. -/\n@[simp]\nlemma sum_hamming_weight_sum [Zero F] :\n ∑ x ∈ B, (‖x‖₀ : ℚ) = n * B.card - ∑ i, K B i 0 := by\n simp only [hamming_weight_eq_sum, Nat.cast_sum, Nat.cast_ite, CharP.... | [
{
"name": "almost_johnson_lhs_div_B_card",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 18,
"n_chars": 875,
"n_subproofs": 3,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 4,
"n_structural": 0,
"automation_only": false,
... | 5 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, František Silváši
-/
import ArkLib.Data.CodingTheory.JohnsonBound.Expectations
/-! # Johnson Bound Lemmas -/
namespace JohnsonBound
open Real Finset Fintype
/... | @@ -113,10 +113,27 @@
lemma hamming_weight_eq_sum [Zero F] {x : Fin n → F} :
‖x‖₀ = ∑ i, if x i = 0 then 0 else 1 := by simp [hammingNorm, sum_ite]
+/-- Sum of Hamming weights equals `n · |B|` minus total zero-coordinate counts. -/
+@[simp]
+lemma sum_hamming_weight_sum [Zero F] :
+ ∑ x ∈ B, (‖x‖₀ : ℚ) = n *... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_c393829053a4_0 | 0efc75d044f6fba9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/SchwartzZippelCounting.lean | SchwartzZippelCounting | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "prob_eval_zero_le_div",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n by\n classical\n convert ENNReal.div_le_div_of_mul_le hm_pos _ _ using 1\n · convert uniform_prob_eq_card_div _\n ... | [
{
"name": "ENNReal.div_le_div_of_mul_le",
"text": "lemma ENNReal.div_le_div_of_mul_le {k n d m : ℕ}\n (hm_pos : 0 < m) (hn_pos : 0 < n) (h : k * m ≤ d * n) :\n (k : ℝ≥0∞) / n ≤ d / m := by\n rw [ENNReal.div_le_iff_le_mul] <;> norm_cast\n · rw [← ENNReal.toReal_le_toReal] <;> norm_num\n · rw [div_... | [
{
"name": "prob_eval_zero_le_div",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 22,
"n_chars": 1118,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"ma... | 4 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, Aristotle
-/
import ArkLib.Data.Probability.Notation
import Mathlib.Algebra.MvPolynomial.SchwartzZippel
import Mathlib.Data.Rat.Star
import Mathlib.Probab... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, Aristotle
-/
import ArkLib.Data.Probability.Notation
import Mathlib.Algebra.MvPolynomial.SchwartzZippel
import Mathlib.Data.Rat.Star
import Mathlib.Probab... | @@ -102,6 +102,17 @@
exact fun b hb hb' => ⟨fun i => ⟨b i, hb i⟩, hb', rfl⟩
/- If `k * m ≤ d * n` with `m > 0` and `n > 0`, then `k / n ≤ d / m` in `ℝ≥0∞`. -/
+lemma ENNReal.div_le_div_of_mul_le {k n d m : ℕ}
+ (hm_pos : 0 < m) (hn_pos : 0 < n) (h : k * m ≤ d * n) :
+ (k : ℝ≥0∞) / n ≤ d / m := by
+ rw [E... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_d7777aeacdce_0 | 30d5af42131dba23 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Lattices/CyclotomicRing/Galois/FixedSubring.lean | FixedSubring | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "fixedSubring_le_conjFixedSubring",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro x hx\n rw [mem_conjFixedSubring_iff]\n exact ((mem_fixedSubring_iff α k x).mp hx).1",
"n_chars... | [
{
"name": "mem_conjFixedSubring_iff",
"text": "/-- Membership in `R_q^{σ_{-1}}`: fixed by `σ_{-1}`. -/\ntheorem mem_conjFixedSubring_iff (α : ℕ) (x : Rq (powTwoCyclotomic (R := R) α)) :\n x ∈ conjFixedSubring α ↔ conjAut α x = x := by\n simp only [conjFixedSubring, RingHom.mem_eqLocus, RingHom.id_apply]... | [
{
"name": "fixedSubring_le_conjFixedSubring",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 348,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,... | 2 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Galois.Trace
/-!
# The Fixed Subring `R_q^H`
Hachi [NOZ26, §3, Lemma 5] shows that the subring `R_q^H` of elem... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Data.Lattices.CyclotomicRing.Galois.Trace
/-!
# The Fixed Subring `R_q^H`
Hachi [NOZ26, §3, Lemma 5] shows that the subring `R_q^H` of elem... | @@ -54,10 +54,18 @@
noncomputable def conjFixedSubring (α : ℕ) : Subring (Rq (powTwoCyclotomic (R := R) α)) :=
RingHom.eqLocus (conjAut α) (RingHom.id _)
+/-- Membership in `R_q^{σ_{-1}}`: fixed by `σ_{-1}`. -/
+theorem mem_conjFixedSubring_iff (α : ℕ) (x : Rq (powTwoCyclotomic (R := R) α)) :
+ x ∈ conjFixedSu... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_bf3b9e99a306_0 | 97eaba6cfaf7a108 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/InnerOuter/Security.lean | Security | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "inner_relation_of_verified",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hB₁ := hv₁.block i\n have hB₂ := hv₂.block i\n have hne : scaledMessage 𝓜(q, α) opening₁ opening₂ i -\n... | [
{
"name": "inner_commit_eq_of_flatten_eq",
"text": "/-- Equal flattened inner decompositions make verified inner messages collide. -/\ntheorem inner_commit_eq_of_flatten_eq {base : ZMod q} {βSq γ κ : Nat}\n {pp : PublicParams Φ innerRows messageRows messageDigits outerRows blocks innerDigits}\n {u : C... | [
{
"name": "inner_relation_of_verified",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 39,
"n_chars": 2317,
"n_subproofs": 7,
"n_tactics": 23,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
... | 3 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Correctness
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Arithmetic
/-!
# Weak-Binding Secu... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Correctness
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Arithmetic
/-!
# Weak-Binding Secu... | @@ -140,6 +140,28 @@
/-! ## Security: pinned to the power-of-two modulus `𝓜(q, α)` -/
omit [NeZero q] in
+/-- Equal flattened inner decompositions make verified inner messages collide. -/
+theorem inner_commit_eq_of_flatten_eq {base : ZMod q} {βSq γ κ : Nat}
+ {pp : PublicParams Φ innerRows messageRows messageD... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_bf3b9e99a306_1 | f2f54c5b3e5cde00 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/InnerOuter/Security.lean | Security | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "outputToModuleSIS_valid_of_verified",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold outputToModuleSIS\n by_cases hflat : PolyVec.flattenBlocks opening₁.innerDecomp =\n PolyV... | [
{
"name": "firstDiff?_some_of_differs",
"text": "theorem firstDiff?_some_of_differs {T : Type*} [DecidableEq T] {n : Nat}\n {x y : Fin n → T} (h : (firstDiff? x y).isSome = true) :\n ∃ i : Fin n, firstDiff? x y = some i :=\n Option.isSome_iff_exists.mp h\n\n",
"fan_in": 1,
"n_lines": 6,
"... | [
{
"name": "outputToModuleSIS_valid_of_verified",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 7,
"n_lines": 34,
"n_chars": 1923,
"n_subproofs": 2,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": ... | 7 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Correctness
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Arithmetic
/-!
# Weak-Binding Secu... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Correctness
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Arithmetic
/-!
# Weak-Binding Secu... | @@ -57,6 +57,11 @@
def firstDiff? {T : Type*} [DecidableEq T] {n : Nat} (x y : Fin n → T) : Option (Fin n) :=
(List.finRange n).find? (fun i => decide (x i ≠ y i))
+theorem firstDiff?_some_of_differs {T : Type*} [DecidableEq T] {n : Nat}
+ {x y : Fin n → T} (h : (firstDiff? x y).isSome = true) :
+ ∃ i : Fin... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_bf3b9e99a306_2 | 0f1a476c3a1444e5 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/InnerOuter/Security.lean | Security | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "outputToModuleSIS_valid_of_verified",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold outputToModuleSIS\n by_cases hflat : PolyVec.flattenBlocks opening₁.innerDecomp =\n PolyV... | [
{
"name": "firstDiff?_some_of_differs",
"text": "theorem firstDiff?_some_of_differs {T : Type*} [DecidableEq T] {n : Nat}\n {x y : Fin n → T} (h : (firstDiff? x y).isSome = true) :\n ∃ i : Fin n, firstDiff? x y = some i :=\n Option.isSome_iff_exists.mp h\n\n",
"fan_in": 1,
"n_lines": 6,
"... | [
{
"name": "outputToModuleSIS_valid",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 28,
"n_chars": 1488,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"m... | 9 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Correctness
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Arithmetic
/-!
# Weak-Binding Secu... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Correctness
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Arithmetic
/-!
# Weak-Binding Secu... | @@ -57,6 +57,11 @@
def firstDiff? {T : Type*} [DecidableEq T] {n : Nat} (x y : Fin n → T) : Option (Fin n) :=
(List.finRange n).find? (fun i => decide (x i ≠ y i))
+theorem firstDiff?_some_of_differs {T : Type*} [DecidableEq T] {n : Nat}
+ {x y : Fin n → T} (h : (firstDiff? x y).isSome = true) :
+ ∃ i : Fin... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_bf3b9e99a306_3 | 938e3609a3bcd20f | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/InnerOuter/Security.lean | Security | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "sample_advantage_le_moduleSIS",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let pp : PublicParams 𝓜(q, α)\n innerRows messageRows messageDigits outerRows blocks innerDigits :=\n ... | [
{
"name": "probOutput_pure_bool_le_or",
"text": "/-- Boolean monotonicity of `pure` outcome probability into a disjunction. -/\ntheorem probOutput_pure_bool_le_or (win inner outer : Bool)\n (h : win = true → inner = true ∨ outer = true) :\n Pr[= true | ((pure win) : ProbComp Bool)] ≤\n Pr[= true ... | [
{
"name": "sample_advantage_le_moduleSIS",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 11,
"n_lines": 35,
"n_chars": 2043,
"n_subproofs": 1,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false... | 11 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Correctness
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Arithmetic
/-!
# Weak-Binding Secu... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Correctness
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Arithmetic
/-!
# Weak-Binding Secu... | @@ -53,6 +53,14 @@
/-! ## Generic helpers -/
+/-- Boolean monotonicity of `pure` outcome probability into a disjunction. -/
+theorem probOutput_pure_bool_le_or (win inner outer : Bool)
+ (h : win = true → inner = true ∨ outer = true) :
+ Pr[= true | ((pure win) : ProbComp Bool)] ≤
+ Pr[= true | ((pure i... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_bf3b9e99a306_4 | 8080b39ffa896eea | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Commitments/Functional/Hachi/InnerOuter/Security.lean | Security | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "outputToModuleSIS_valid_of_verified",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold outputToModuleSIS\n by_cases hflat : PolyVec.flattenBlocks opening₁.innerDecomp =\n PolyV... | [
{
"name": "firstDiff?_some_of_differs",
"text": "theorem firstDiff?_some_of_differs {T : Type*} [DecidableEq T] {n : Nat}\n {x y : Fin n → T} (h : (firstDiff? x y).isSome = true) :\n ∃ i : Fin n, firstDiff? x y = some i :=\n Option.isSome_iff_exists.mp h\n\n",
"fan_in": 1,
"n_lines": 6,
"... | [
{
"name": "advantage_le_moduleSIS",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 12,
"n_lines": 36,
"n_chars": 2106,
"n_subproofs": 2,
"n_tactics": 24,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 4,
"n_structural": 5,
"automation_only": false,
"... | 12 | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Correctness
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Arithmetic
/-!
# Weak-Binding Secu... | /-
Copyright (c) 2024-2026 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Tobias Rothmann
-/
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Correctness
import ArkLib.Commitments.Functional.Hachi.InnerOuter.Arithmetic
/-!
# Weak-Binding Secu... | @@ -65,6 +65,11 @@
def firstDiff? {T : Type*} [DecidableEq T] {n : Nat} (x y : Fin n → T) : Option (Fin n) :=
(List.finRange n).find? (fun i => decide (x i ≠ y i))
+theorem firstDiff?_some_of_differs {T : Type*} [DecidableEq T] {n : Nat}
+ {x y : Fin n → T} (h : (firstDiff? x y).isSome = true) :
+ ∃ i : Fin... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_33a5ae4a73f6_0 | 43b8fbb67a47e1a4 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/LinearMvExtension.lean | LinearMvExtension | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "bitExpo_le_one",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by aesop (add simp [bitExpo_apply])",
"n_chars": 36,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_aut... | [
{
"name": "bitExpo_apply",
"text": "lemma bitExpo_apply (i : ℕ) (j : Fin m) :\n (bitExpo i : Fin m →₀ ℕ) j = if Nat.testBit i j.1 then 1 else 0 := by\n simp [bitExpo, Finsupp.onFinset_apply]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 164,
"n_subproofs": 0,
"n_tactics": 2,
"cycloma... | [
{
"name": "bitExpo_le_one",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 126,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 1 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Mirco Richter (Least Authority), Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import A... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Mirco Richter (Least Authority), Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import A... | @@ -57,8 +57,12 @@
Polynomial.sum,
Finset.smul_sum])
+lemma bitExpo_apply (i : ℕ) (j : Fin m) :
+ (bitExpo i : Fin m →₀ ℕ) j = if Nat.testBit i j.1 then 1 else 0 := by
+ simp [bitExpo, Finsupp.onFinset_apply]
+
lemma bitExpo_le_one (i : ℕ) (j : Fin m) :
- (bitExpo i : Fin m →₀ ℕ) j ≤ 1 := sorry
... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_33a5ae4a73f6_1 | e88fa0bd3300681c | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/LinearMvExtension.lean | LinearMvExtension | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "linearMvExtension_degreeOf_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_monomial_degrees {x} (hx : x ∈ p.val.support) :\n (degreeOf i (monomial (bitExpo x) (p.val.coeff... | [
{
"name": "bitExpo_le_one",
"text": "lemma bitExpo_le_one (i : ℕ) (j : Fin m) :\n (bitExpo i : Fin m →₀ ℕ) j ≤ 1 := by aesop (add simp [bitExpo_apply])\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 126,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 2,
"n_r... | [
{
"name": "linearMvExtension_degreeOf_lt",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 643,
"n_subproofs": 2,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 2 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Mirco Richter (Least Authority), Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import A... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Mirco Richter (Least Authority), Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import A... | @@ -61,10 +61,14 @@
(bitExpo i : Fin m →₀ ℕ) j = if Nat.testBit i j.1 then 1 else 0 := by
simp [bitExpo, Finsupp.onFinset_apply]
+lemma bitExpo_le_one (i : ℕ) (j : Fin m) :
+ (bitExpo i : Fin m →₀ ℕ) j ≤ 1 := by aesop (add simp [bitExpo_apply])
+
lemma linearMvExtension_degreeOf_lt {p : Polynomial.degreeLT F ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_33a5ae4a73f6_2 | 5ee7f114e5eae9fc | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/LinearMvExtension.lean | LinearMvExtension | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "powAlgHom_degree",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [←Polynomial.natDegree_le_iff_degree_le]\n exact powAlgHom_natDegree",
"n_chars": 79,
"n_subproofs": 0,
"n... | [
{
"name": "powAlgHom_natDegree",
"text": "lemma powAlgHom_natDegree {p : MvPolynomial (Fin m) F} :\n (powAlgHom p).natDegree ≤ p.totalDegree * (2 ^ m - 1) := by\n have h_deg {d} (hd : d ∈ p.support) :\n (powAlgHom (MvPolynomial.monomial d (p.coeff d))).natDegree ≤\n d.sum (fun i k => 2^i.val * k... | [
{
"name": "powAlgHom_degree",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 269,
"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) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Mirco Richter (Least Authority), Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import A... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Mirco Richter (Least Authority), Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import A... | @@ -90,8 +90,48 @@
MvPolynomial (Fin m) F →ₐ[F] Polynomial F :=
aeval fun j => Polynomial.X ^ (2 ^ (j : ℕ))
+lemma powAlgHom_natDegree {p : MvPolynomial (Fin m) F} :
+ (powAlgHom p).natDegree ≤ p.totalDegree * (2 ^ m - 1) := by
+ have h_deg {d} (hd : d ∈ p.support) :
+ (powAlgHom (MvPolynomial.monomial ... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_33a5ae4a73f6_3 | 692a5310b4f52a45 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/LinearMvExtension.lean | LinearMvExtension | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "powContraction_is_right_inverse_to_linearMvExtension",
"depth": 1,
"n_commands": 0,
"n_lines": 39,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_comp : powContraction (linearMvExtensionLMap p) =\n ∑ i ∈ Finset.range (2... | [
{
"name": "binary_repr_sum",
"text": "private lemma binary_repr_sum (m i : ℕ) (hi : i < 2 ^ m) :\n ∑ j ∈ Finset.range m, (if Nat.testBit i j then 2 ^ j else 0) = i := by\n induction m generalizing i with\n | zero => simp_all\n | succ m ih =>\n rw [Finset.sum_range_succ']\n simp only [Nat.testBit... | [
{
"name": "powContraction_is_right_inverse_to_linearMvExtension",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 43,
"n_chars": 2055,
"n_subproofs": 5,
"n_tactics": 42,
"cyclomatic": 3,
"n_automation": 12,
"n_rewrites": 9,
"n_structural": 7,
"... | 1 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Mirco Richter (Least Authority), Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import A... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Mirco Richter (Least Authority), Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import A... | @@ -94,6 +94,28 @@
MvPolynomial (Fin m) F →ₗ[F] Polynomial F :=
powAlgHom.toLinearMap
+private lemma binary_repr_sum (m i : ℕ) (hi : i < 2 ^ m) :
+ ∑ j ∈ Finset.range m, (if Nat.testBit i j then 2 ^ j else 0) = i := by
+ induction m generalizing i with
+ | zero => simp_all
+ | succ m ih =>
+ rw [Fins... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_33a5ae4a73f6_4 | 3bbbdc412183b170 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/MvPolynomial/LinearMvExtension.lean | LinearMvExtension | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "powAlgHom_is_right_inverse_to_linearMvExtension",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [←powContraction_is_right_inverse_to_linearMvExtension]\n rfl",
"n_chars": 72,
... | [
{
"name": "powContraction_is_right_inverse_to_linearMvExtension",
"text": "lemma powContraction_is_right_inverse_to_linearMvExtension\n (p : Polynomial.degreeLT F (2 ^ m)) :\n powContraction.comp linearMvExtensionLMap p = p := by\n have h_comp : powContraction (linearMvExtensionLMap p) =\n ∑ i ∈... | [
{
"name": "powAlgHom_is_right_inverse_to_linearMvExtension",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 208,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automatio... | 2 | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Mirco Richter (Least Authority), Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import A... | /-
Copyright (c) 2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Ilia Vlasov, Mirco Richter (Least Authority), Aristotle (Harmonic)
-/
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkLib.Data.CodingTheory.Basic.Distance
import A... | @@ -116,9 +116,53 @@
/- Evaluating m-variate polynomials on (X^(2⁰), ... , X^(2ᵐ⁻¹) ) is
right inverse to linear multivariate extensions on F^(< 2ᵐ)[X] -/
+lemma powContraction_is_right_inverse_to_linearMvExtension
+ (p : Polynomial.degreeLT F (2 ^ m)) :
+ powContraction.comp linearMvExtensionLMap p = p :... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_9c248762c0f7_0 | 4b3b7cba5d1377a3 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/ProximityGap/ProximityGenerators.lean | ProximityGenerators | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "poly_gen_is_zero_evading",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n unfold IsZeroEvadingGenerator\n simp only [ne_eq, bind_pure_comp, sSup_le_iff, Set.mem_setOf_eq, fo... | [
{
"name": "minSeedCard_le",
"text": "/-- The minimum of the cardinality of a family of nonempty sets is smaller than the cardinality of\neach set in the family. -/\nlemma minSeedCard_le {F : Type} {s : ℕ} (S : Fin s → Set F)\n [∀ i, Fintype ↥(S i)] (hs : 0 < s) (i : Fin s) :\n minSeedCard S ≤ (S i).to... | [
{
"name": "poly_gen_is_zero_evading",
"fan_in": 0,
"n_deps_direct": 8,
"n_deps_transitive": 3,
"n_lines": 36,
"n_chars": 1921,
"n_subproofs": 0,
"n_tactics": 21,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 4,
"n_structural": 8,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova
-/
import ArkLib.Data.CodingTheory.Basic.LinearCode
import ArkLib.Data.MvPolynomial.Degrees
import ArkLib.Data.MvPolynomial.SchwartzZippelCounting
/-!
# P... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova
-/
import ArkLib.Data.CodingTheory.Basic.LinearCode
import ArkLib.Data.MvPolynomial.Degrees
import ArkLib.Data.MvPolynomial.SchwartzZippelCounting
/-!
# P... | @@ -158,6 +158,15 @@
exact Fintype.card_pos_iff.mpr (Set.nonempty_coe_sort.2 (hne i))
· norm_num
+/-- The minimum of the cardinality of a family of nonempty sets is smaller than the cardinality of
+each set in the family. -/
+lemma minSeedCard_le {F : Type} {s : ℕ} (S : Fin s → Set F)
+ [∀ i, Fintype ↥(S i... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_fbd97bae9659_0 | a50624cf7d9446c9 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Matrix/Vandermonde.lean | Vandermonde | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "rank_nonsquare_eq_deg_of_deg_le",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n suffices ((Vandermonde.nonsquare (ι' := n) α).subUpFull (Fin.castLE h)).rank = n by\n exact Matrix.rank_... | [
{
"name": "subUpFull_of_vandermonde_is_vandermonde",
"text": "/-- The maximal upper square submatrix of a Vandermonde matrix is a Vandermonde matrix. -/\nlemma subUpFull_of_vandermonde_is_vandermonde (h : n ≤ m) :\n Matrix.vandermonde (α ∘ Fin.castLE h) =\n Matrix.subUpFull (nonsquare n α) (Fin.castLE h... | [
{
"name": "rank_nonsquare_eq_deg_of_deg_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 624,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.MvPolynomial.LinearMvExtension
import ArkLib.Data.Polynomial.Interface
import CompPoly.Data.Polynomi... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.MvPolynomial.LinearMvExtension
import ArkLib.Data.Polynomial.Interface
import CompPoly.Data.Polynomi... | @@ -32,6 +32,13 @@
variable [CommRing F] {m n : ℕ} {α : Fin m → F}
+/-- The maximal upper square submatrix of a Vandermonde matrix is a Vandermonde matrix. -/
+lemma subUpFull_of_vandermonde_is_vandermonde (h : n ≤ m) :
+ Matrix.vandermonde (α ∘ Fin.castLE h) =
+ Matrix.subUpFull (nonsquare n α) (Fin.castLE h)... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_fbd97bae9659_1 | 9c06499e92e9ba55 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Matrix/Vandermonde.lean | Vandermonde | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "rank_nonsquare_eq_deg_of_ι_le",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n suffices ((Vandermonde.nonsquare (ι' := n) α).subLeftFull (Fin.castLE h)).rank = m by\n exact Matrix.full_... | [
{
"name": "subLeftFull_of_vandermonde_is_vandermonde",
"text": "/-- The maximal left square submatrix of a Vandermonde matrix is a Vandermonde matrix. -/\nlemma subLeftFull_of_vandermonde_is_vandermonde (h : m ≤ n) :\n Matrix.vandermonde α = Matrix.subLeftFull (nonsquare n α) (Fin.castLE h) := by\n ext ... | [
{
"name": "rank_nonsquare_eq_deg_of_ι_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 536,
"n_subproofs": 1,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.MvPolynomial.LinearMvExtension
import ArkLib.Data.Polynomial.Interface
import CompPoly.Data.Polynomi... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.MvPolynomial.LinearMvExtension
import ArkLib.Data.Polynomial.Interface
import CompPoly.Data.Polynomi... | @@ -39,6 +39,12 @@
ext r c
simp [Matrix.vandermonde, Matrix.subUpFull, nonsquare]
+/-- The maximal left square submatrix of a Vandermonde matrix is a Vandermonde matrix. -/
+lemma subLeftFull_of_vandermonde_is_vandermonde (h : m ≤ n) :
+ Matrix.vandermonde α = Matrix.subLeftFull (nonsquare n α) (Fin.castLE h... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_fbd97bae9659_2 | 697ea8b1aaf646f5 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Matrix/Vandermonde.lean | Vandermonde | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "rank_nonsquare_rows_eq_min",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases h : m ≤ n\n · rw [rank_nonsquare_eq_deg_of_ι_le inj h]; simp [h]\n · rw [rank_nonsquare_eq_deg_of_deg... | [
{
"name": "rank_nonsquare_eq_deg_of_deg_le",
"text": "/-- The rank of a non-square Vandermonde matrix with more rows than columns is the number of\n columns. -/\nlemma rank_nonsquare_eq_deg_of_deg_le (inj : Function.Injective α) (h : n ≤ m) :\n (Vandermonde.nonsquare (ι' := n) α).rank = n := by\n suffi... | [
{
"name": "rank_nonsquare_rows_eq_min",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 8,
"n_chars": 273,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"... | 4 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.MvPolynomial.LinearMvExtension
import ArkLib.Data.Polynomial.Interface
import CompPoly.Data.Polynomi... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.MvPolynomial.LinearMvExtension
import ArkLib.Data.Polynomial.Interface
import CompPoly.Data.Polynomi... | @@ -49,6 +49,19 @@
variable [IsDomain F]
+/-- The rank of a non-square Vandermonde matrix with more rows than columns is the number of
+ columns. -/
+lemma rank_nonsquare_eq_deg_of_deg_le (inj : Function.Injective α) (h : n ≤ m) :
+ (Vandermonde.nonsquare (ι' := n) α).rank = n := by
+ suffices ((Vandermonde.n... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_fbd97bae9659_3 | c8f7852f85b1c244 | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/Matrix/Vandermonde.lean | Vandermonde | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "mulVecLin_coeff_vandermondens_eq_eval_matrixOfPolynomials",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext i\n have hLHS :\n (Vandermonde.nonsquare (ι' := n) v).mulVecLin (Fin.l... | [
{
"name": "nonsquare_mulVecLin",
"text": "lemma nonsquare_mulVecLin [CommSemiring F] {ι' : ℕ} {α₁ : ι ↪ F} {α₂ : Fin ι' → F} {i : ι} :\n (nonsquare ι' α₁).mulVecLin α₂ i = ∑ x, α₂ x * α₁ i ^ x.1 := by\n simp [nonsquare, mulVec_eq_sum]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 227,
"n_s... | [
{
"name": "mulVecLin_coeff_vandermondens_eq_eval_matrixOfPolynomials",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 21,
"n_chars": 1026,
"n_subproofs": 2,
"n_tactics": 16,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 3,
... | 1 | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.MvPolynomial.LinearMvExtension
import ArkLib.Data.Polynomial.Interface
import CompPoly.Data.Polynomi... | /-
Copyright (c) 2024 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Katerina Hristova, František Silváši, Julian Sutherland
-/
import ArkLib.Data.MvPolynomial.LinearMvExtension
import ArkLib.Data.Polynomial.Interface
import CompPoly.Data.Polynomi... | @@ -24,6 +24,10 @@
def nonsquare [Semiring F] (ι' : ℕ) (α : ι → F) : Matrix ι (Fin ι') F :=
Matrix.of fun i j => (α i) ^ j.1
+lemma nonsquare_mulVecLin [CommSemiring F] {ι' : ℕ} {α₁ : ι ↪ F} {α₂ : Fin ι' → F} {i : ι} :
+ (nonsquare ι' α₁).mulVecLin α₂ i = ∑ x, α₂ x * α₁ i ^ x.1 := by
+ simp [nonsquare, mulVec... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_5ebf7a92aca2_0 | 3eaf7490820eb45f | lean | lean | github.com/Verified-zkEVM/ArkLib | 5a83bfb4383503d70d7b5a05355d396855b3151b | ArkLib/Data/CodingTheory/BerlekampWelch/BerlekampWelch.lean | BerlekampWelch | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "not_exists_of_decoder_eq_none",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rintro ⟨p, hp, hpk⟩\n have := decoder_eq_some he hn h_inj hpk hp\n aesop",
"n_chars": 82,
"n_subpro... | [
{
"name": "decoder_eq_some",
"text": "/--\n**Correctness theorem for Berlekamp-Welch decoder**:\nIf a codeword is close to a polynomial `p` of degree `< k`\nthen the decoder succeeds and returns `some p`.\n\n### Parameters:\n- `e k : ℕ` - Error capacity and degree bound\n- `[NeZero n]` - Non-zero codeword l... | [
{
"name": "not_exists_of_decoder_eq_none",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 25,
"n_chars": 871,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"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: František Silváši, Ilia Vlasov
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkL... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: František Silváši, Ilia Vlasov
-/
import Mathlib.Algebra.Field.Basic
import Mathlib.Algebra.Polynomial.Basic
import ArkLib.Data.CodingTheory.Basic.DecodingRadius
import ArkL... | @@ -69,6 +69,44 @@
none
/--
+**Correctness theorem for Berlekamp-Welch decoder**:
+If a codeword is close to a polynomial `p` of degree `< k`
+then the decoder succeeds and returns `some p`.
+
+### Parameters:
+- `e k : ℕ` - Error capacity and degree bound
+- `[NeZero n]` - Non-zero codeword length
+- `ωs :... | {
"repo": "ArkLib",
"git_repo": "github.com/Verified-zkEVM/ArkLib",
"revision": "5a83bfb4383503d70d7b5a05355d396855b3151b",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_b5c3a849beed_0 | cd536966a5546f58 | lean | lean | github.com/NethermindEth/Clear | 6ef2e7eda01080e5d5fd7474354c1a71adab5071 | Clear/JumpLemmas.lean | JumpLemmas | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "isJump_multifill'",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold multifill\n rcases s <;> simp only\n induction List.zip vars vals with\n | nil => simp only [isJump, State.inse... | [
{
"name": "isJump_insert'",
"text": "/--\n Varstore inserts preserve jumps.\n-/\n@[simp]\nlemma isJump_insert' : isJump c (s⟦var↦x⟧) = isJump c s := by unfold isJump State.insert; aesop\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 153,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": ... | [
{
"name": "isJump_multifill'",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 350,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 4,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
"max_nes... | 1 | import Clear.OutOfFuelLemmas
-- TODO(chore): Tag with appropriate aesops, not the general ones.
namespace Clear.JumpLemmas
open Clear Ast Expr Stmt State EVMState PrimOps Interpreter SizeLemmas ExecLemmas OutOfFuelLemmas
section
variable {s s₁ s₂ : State}
{expr rhs cond : Expr}
{args : List Expr}... | import Clear.OutOfFuelLemmas
-- TODO(chore): Tag with appropriate aesops, not the general ones.
namespace Clear.JumpLemmas
open Clear Ast Expr Stmt State EVMState PrimOps Interpreter SizeLemmas ExecLemmas OutOfFuelLemmas
section
variable {s s₁ s₂ : State}
{expr rhs cond : Expr}
{args : List Expr}... | @@ -27,6 +27,12 @@
{c : Jump}
/--
+ Varstore inserts preserve jumps.
+-/
+@[simp]
+lemma isJump_insert' : isJump c (s⟦var↦x⟧) = isJump c s := by unfold isJump State.insert; aesop
+
+/--
Setting the EVM state preserves jumps.
-/
@[simp]
@@ -47,7 +53,10 @@
rcases s <;> simp only
induction List.zi... | {
"repo": "Clear",
"git_repo": "github.com/NethermindEth/Clear",
"revision": "6ef2e7eda01080e5d5fd7474354c1a71adab5071",
"lean_toolchain": "leanprover/lean4:v4.9.1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemma... |
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