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_40782fc021a1_0 | 9a082ed061d12285 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/Keccak/Chi.lean | Chi | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "soundness",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n circuit_proof_start [ Xor64.circuit, And.And64.circuit, And.And8.circuit, Not.circuit,\n Xor64.Assumptions, Xor64.Spec, And.A... | [
{
"name": "chi_loop",
"text": "lemma chi_loop (state : Vector ℕ 25) :\n Specs.Keccak256.chi state = .mapFinRange 25 fun i => state[i] ^^^ ((not64 state[i + 5]) &&& state[i + 10]) := by\n rw [Specs.Keccak256.chi, Vector.mapFinRange, Vector.finRange, Vector.map_mk, Vector.eq_mk, List.map_toArray]\n rfl\n... | [
{
"name": "soundness",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 518,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 4
... | 1 | import Clean.Types.U64
import Clean.Circuit.Loops
import Clean.Gadgets.Xor.Xor64
import Clean.Gadgets.And.And64
import Clean.Gadgets.Not.Not64
import Clean.Gadgets.Keccak.KeccakState
import Clean.Specs.Keccak256
namespace Gadgets.Keccak256.Chi
variable {p : ℕ} [Fact p.Prime] [Fact (p > 512)]
open Not (not64_bytewise n... | import Clean.Types.U64
import Clean.Circuit.Loops
import Clean.Gadgets.Xor.Xor64
import Clean.Gadgets.And.And64
import Clean.Gadgets.Not.Not64
import Clean.Gadgets.Keccak.KeccakState
import Clean.Specs.Keccak256
namespace Gadgets.Keccak256.Chi
variable {p : ℕ} [Fact p.Prime] [Fact (p > 512)]
open Not (not64_bytewise n... | @@ -26,8 +26,25 @@
elaborate_circuit
-- rewrite the chi spec as a loop
-theorem soundness : Soundness (F p) main Assumptions Spec := sorry
+lemma chi_loop (state : Vector ℕ 25) :
+ Specs.Keccak256.chi state = .mapFinRange 25 fun i => state[i] ^^^ ((not64 state[i + 5]) &&& state[i + 10]) := by
+ rw [Specs.Kecc... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c647d82ea04d_0 | d38e429cd6b62463 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/Ch32.lean | Ch32 | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "testBit_binary_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n with\n | zero => exact k.elim0\n | succ m ih =>\n rw [Fin.sum_univ_castSucc]; simp only [Fin.val_castS... | [
{
"name": "sum_bool_lt_two_pow",
"text": "private lemma sum_bool_lt_two_pow (n : ℕ) (f : Fin n → ℕ) (hf : ∀ i, f i ≤ 1) :\n ∑ i : Fin n, f i * 2^i.val < 2^n := by\n induction n with\n | zero => simp\n | succ m ih =>\n rw [Fin.sum_univ_castSucc]; simp only [Fin.val_castSucc, Fin.val_last]\n have ... | [
{
"name": "testBit_binary_sum",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 1118,
"n_subproofs": 4,
"n_tactics": 25,
"cyclomatic": 6,
"n_automation": 7,
"n_rewrites": 6,
"n_structural": 4,
"automation_only": false,
"max_n... | 1 | import Clean.Gadgets.SHA256.BitwiseOps
import Clean.Specs.SHA256
section
variable {p : ℕ} [Fact p.Prime]
namespace Gadgets.SHA256
/-!
# Choice function Ch(e, f, g) for SHA-256
Ch(e, f, g) = (e AND f) XOR (NOT e AND g) = g + e·(f − g).
Per bit: ch = g + e·(f − g), which equals f when e = 1 and g when e = 0.
One R1CS... | import Clean.Gadgets.SHA256.BitwiseOps
import Clean.Specs.SHA256
section
variable {p : ℕ} [Fact p.Prime]
namespace Gadgets.SHA256
/-!
# Choice function Ch(e, f, g) for SHA-256
Ch(e, f, g) = (e AND f) XOR (NOT e AND g) = g + e·(f − g).
Per bit: ch = g + e·(f − g), which equals f when e = 1 and g when e = 0.
One R1CS... | @@ -46,6 +46,19 @@
## Helper lemmas
-/
+private lemma sum_bool_lt_two_pow (n : ℕ) (f : Fin n → ℕ) (hf : ∀ i, f i ≤ 1) :
+ ∑ i : Fin n, f i * 2^i.val < 2^n := by
+ induction n with
+ | zero => simp
+ | succ m ih =>
+ rw [Fin.sum_univ_castSucc]; simp only [Fin.val_castSucc, Fin.val_last]
+ have ihm : ∑ i ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_5cc65a48ebe0_0 | 51708ab814a5d769 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/Xor32.lean | Xor32 | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "testBit_binary_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n with\n | zero => exact k.elim0\n | succ m ih =>\n rw [Fin.sum_univ_castSucc]; simp only [Fin.val_castS... | [
{
"name": "sum_bool_lt_two_pow",
"text": "private lemma sum_bool_lt_two_pow (n : ℕ) (f : Fin n → ℕ) (hf : ∀ i, f i ≤ 1) :\n ∑ i : Fin n, f i * 2^i.val < 2^n := by\n induction n with\n | zero => simp\n | succ m ih =>\n rw [Fin.sum_univ_castSucc]; simp only [Fin.val_castSucc, Fin.val_last]\n have ... | [
{
"name": "testBit_binary_sum",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 1118,
"n_subproofs": 4,
"n_tactics": 25,
"cyclomatic": 6,
"n_automation": 7,
"n_rewrites": 6,
"n_structural": 4,
"automation_only": false,
"max_n... | 1 | import Clean.Gadgets.SHA256.BitwiseOps
section
variable {p : ℕ} [Fact p.Prime]
namespace Gadgets.SHA256
/-!
# 32-bit Bitwise XOR for SHA-256
Per bit: z = a + b − 2·a·b (correct when a, b ∈ {0, 1}).
Witnesses 32 output bits.
-/
/-- Bitwise XOR of two 32-bit words.
Per bit: z = a + b − 2·a·b (correct when a, b... | import Clean.Gadgets.SHA256.BitwiseOps
section
variable {p : ℕ} [Fact p.Prime]
namespace Gadgets.SHA256
/-!
# 32-bit Bitwise XOR for SHA-256
Per bit: z = a + b − 2·a·b (correct when a, b ∈ {0, 1}).
Witnesses 32 output bits.
-/
/-- Bitwise XOR of two 32-bit words.
Per bit: z = a + b − 2·a·b (correct when a, b... | @@ -41,6 +41,19 @@
## Helper lemmas for valueBits and bitwise XOR
-/
+private lemma sum_bool_lt_two_pow (n : ℕ) (f : Fin n → ℕ) (hf : ∀ i, f i ≤ 1) :
+ ∑ i : Fin n, f i * 2^i.val < 2^n := by
+ induction n with
+ | zero => simp
+ | succ m ih =>
+ rw [Fin.sum_univ_castSucc]; simp only [Fin.val_castSucc, Fin.... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_0 | 35bb8a2c0f5526bc | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 3 | [
{
"theorem_name": "rotRight64_testBit_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [rotRight64_def _ _ h, Nat.testBit_or, Nat.testBit_shiftRight, Nat.testBit_mod_two_pow,\n Nat.testBit_shiftL... | [
{
"name": "rotRight64_def",
"text": "/--\n Alternative definition of rotRight64 using bitwise operations.\n-/\nlemma rotRight64_def (x : ℕ) (off : ℕ) (hx : x < 2^64) :\n rotRight64 x off = x >>> (off % 64) ||| x <<< (64 - off % 64) % 2^64 := by\n rw [rotRight64_eq_bv_rotate _ hx]\n simp only [Nat.toUI... | [
{
"name": "rotRight64_testBit_of_lt",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 545,
"n_subproofs": 2,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"m... | 1 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -97,11 +97,26 @@
rw [h_eq3]
/--
+ Alternative definition of rotRight64 using bitwise operations.
+-/
+lemma rotRight64_def (x : ℕ) (off : ℕ) (hx : x < 2^64) :
+ rotRight64 x off = x >>> (off % 64) ||| x <<< (64 - off % 64) % 2^64 := by
+ rw [rotRight64_eq_bv_rotate _ hx]
+ simp only [Nat.toUInt64_eq, B... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_1 | 3d42d2791fed16fa | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 3 | [
{
"theorem_name": "rotRight64_testBit_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [rotRight64_def _ _ h, Nat.testBit_or, Nat.testBit_shiftRight, Nat.testBit_mod_two_pow,\n Nat.testBit_shiftL... | [
{
"name": "rotRight64_def",
"text": "/--\n Alternative definition of rotRight64 using bitwise operations.\n-/\nlemma rotRight64_def (x : ℕ) (off : ℕ) (hx : x < 2^64) :\n rotRight64 x off = x >>> (off % 64) ||| x <<< (64 - off % 64) % 2^64 := by\n rw [rotRight64_eq_bv_rotate _ hx]\n simp only [Nat.toUI... | [
{
"name": "rotRight64_testBit_of_ge",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 709,
"n_subproofs": 2,
"n_tactics": 14,
"cyclomatic": 2,
"n_automation": 7,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"... | 1 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -97,12 +97,33 @@
rw [h_eq3]
/--
+ Alternative definition of rotRight64 using bitwise operations.
+-/
+lemma rotRight64_def (x : ℕ) (off : ℕ) (hx : x < 2^64) :
+ rotRight64 x off = x >>> (off % 64) ||| x <<< (64 - off % 64) % 2^64 := by
+ rw [rotRight64_eq_bv_rotate _ hx]
+ simp only [Nat.toUInt64_eq, B... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_2 | 76f1b7a729811b62 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 1 | [
{
"theorem_name": "rotRight64_testBit",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n\n split\n · rw [rotRight64_testBit_of_lt]\n repeat omega\n · rw [rotRight64_testBit_of_ge]\n repeat omega",
... | [
{
"name": "rotRight64_testBit_of_ge",
"text": "/--\n Testing a bit of the result of a rotation in the range [64 - r % 64, 64) is equivalent to\n testing the bit of the original number in the range [i - (64 - r % 64), i).\n-/\nlemma rotRight64_testBit_of_ge (x r i : ℕ) (h : x < 2^64) (hi : i ≥ 64 - r % 64)... | [
{
"name": "rotRight64_testBit",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 13,
"n_chars": 326,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 4,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nes... | 3 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -118,6 +118,25 @@
simp [h_i']
omega
+/--
+ Testing a bit of the result of a rotation in the range [64 - r % 64, 64) is equivalent to
+ testing the bit of the original number in the range [i - (64 - r % 64), i).
+-/
+lemma rotRight64_testBit_of_ge (x r i : ℕ) (h : x < 2^64) (hi : i ≥ 64 - r % 64) :
+ (ro... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_3 | 007c7c444d41b968 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 1 | [
{
"theorem_name": "rotRight64_toBits",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [toBits, Vector.rotate]\n ext i hi\n · simp\n simp only [Vector.size_toArray, Vector.getElem_toArray,\n Vecto... | [
{
"name": "rotRight64_testBit",
"text": "lemma rotRight64_testBit (x r i : ℕ) (h : x < 2^64) :\n (rotRight64 x r).testBit i =\n if i < 64 - r % 64 then\n x.testBit (r % 64 + i)\n else (decide (i < 64) && x.testBit (i - (64 - r % 64))) := by\n\n split\n · rw [rotRight64_testBit_of_lt]\n re... | [
{
"name": "rotRight64_toBits",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 17,
"n_chars": 598,
"n_subproofs": 0,
"n_tactics": 13,
"cyclomatic": 3,
"n_automation": 6,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nes... | 4 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -137,11 +137,33 @@
omega
linarith
+lemma rotRight64_testBit (x r i : ℕ) (h : x < 2^64) :
+ (rotRight64 x r).testBit i =
+ if i < 64 - r % 64 then
+ x.testBit (r % 64 + i)
+ else (decide (i < 64) && x.testBit (i - (64 - r % 64))) := by
+
+ split
+ · rw [rotRight64_testBit_of_lt]
+ repeat ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_4 | 08c1fb3f7ac00a3b | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 3 | [
{
"theorem_name": "rotRight64_testBit_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [rotRight64_def _ _ h, Nat.testBit_or, Nat.testBit_shiftRight, Nat.testBit_mod_two_pow,\n Nat.testBit_shiftL... | [
{
"name": "rotRight64_def",
"text": "/--\n Alternative definition of rotRight64 using bitwise operations.\n-/\nlemma rotRight64_def (x : ℕ) (off : ℕ) (hx : x < 2^64) :\n rotRight64 x off = x >>> (off % 64) ||| x <<< (64 - off % 64) % 2^64 := by\n rw [rotRight64_eq_bv_rotate _ hx]\n simp only [Nat.toUI... | [
{
"name": "rotRight64_lt",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 187,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 1 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -96,8 +96,20 @@
rw [h_eq3]
+/--
+ Alternative definition of rotRight64 using bitwise operations.
+-/
+lemma rotRight64_def (x : ℕ) (off : ℕ) (hx : x < 2^64) :
+ rotRight64 x off = x >>> (off % 64) ||| x <<< (64 - off % 64) % 2^64 := by
+ rw [rotRight64_eq_bv_rotate _ hx]
+ simp only [Nat.toUInt64_eq, ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_5 | 3285d9d7a702138d | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 1 | [
{
"theorem_name": "rotRight64_composition",
"depth": 1,
"n_commands": 0,
"n_lines": 20,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h1 : (rotRight64 (rotRight64 x n) m) < 2^64 := by\n repeat apply rotRight64_lt\n assumption\n\n have h2... | [
{
"name": "rotRight64_lt",
"text": "theorem rotRight64_lt (x r : ℕ) (h : x < 2^64) :\n rotRight64 x r < 2^64 := by\n rw [rotRight64_def _ _ h]\n have := Nat.shiftRight_le x (r % 64)\n apply Nat.or_lt_two_pow <;> omega\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 187,
"n_subproofs": 1,
... | [
{
"name": "rotRight64_composition",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 29,
"n_chars": 892,
"n_subproofs": 3,
"n_tactics": 14,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,
"ma... | 6 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -165,13 +165,38 @@
split <;> (congr; omega)
linarith
+theorem rotRight64_lt (x r : ℕ) (h : x < 2^64) :
+ rotRight64 x r < 2^64 := by
+ rw [rotRight64_def _ _ h]
+ have := Nat.shiftRight_le x (r % 64)
+ apply Nat.or_lt_two_pow <;> omega
+
/--
Rotating a 64-bit value by `n` bits and then by `m` bits ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_6 | a45e847555261221 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 3 | [
{
"theorem_name": "rotRight32_testBit_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [rotRight32_def _ _ h, Nat.testBit_or, Nat.testBit_shiftRight, Nat.testBit_mod_two_pow,\n Nat.testBit_shiftL... | [
{
"name": "rotRight32_def",
"text": "/--\n Alternative definition of rotRight32 using bitwise operations.\n-/\nlemma rotRight32_def (x : ℕ) (off : ℕ) (hx : x < 2^32) :\n rotRight32 x off = x >>> (off % 32) ||| x <<< (32 - off % 32) % 2^32 := by\n rw [rotRight32_eq_bv_rotate _ hx]\n simp only [Nat.toUI... | [
{
"name": "rotRight32_testBit_of_lt",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 545,
"n_subproofs": 2,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"m... | 1 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -162,11 +162,26 @@
rw [h_eq3]
/--
+ Alternative definition of rotRight32 using bitwise operations.
+-/
+lemma rotRight32_def (x : ℕ) (off : ℕ) (hx : x < 2^32) :
+ rotRight32 x off = x >>> (off % 32) ||| x <<< (32 - off % 32) % 2^32 := by
+ rw [rotRight32_eq_bv_rotate _ hx]
+ simp only [Nat.toUInt32_eq,... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_7 | 75186e162b51eb97 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 3 | [
{
"theorem_name": "rotRight32_testBit_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [rotRight32_def _ _ h, Nat.testBit_or, Nat.testBit_shiftRight, Nat.testBit_mod_two_pow,\n Nat.testBit_shiftL... | [
{
"name": "rotRight32_def",
"text": "/--\n Alternative definition of rotRight32 using bitwise operations.\n-/\nlemma rotRight32_def (x : ℕ) (off : ℕ) (hx : x < 2^32) :\n rotRight32 x off = x >>> (off % 32) ||| x <<< (32 - off % 32) % 2^32 := by\n rw [rotRight32_eq_bv_rotate _ hx]\n simp only [Nat.toUI... | [
{
"name": "rotRight32_testBit_of_ge",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 709,
"n_subproofs": 2,
"n_tactics": 14,
"cyclomatic": 2,
"n_automation": 7,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"... | 1 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -162,11 +162,32 @@
rw [h_eq3]
/--
+ Alternative definition of rotRight32 using bitwise operations.
+-/
+lemma rotRight32_def (x : ℕ) (off : ℕ) (hx : x < 2^32) :
+ rotRight32 x off = x >>> (off % 32) ||| x <<< (32 - off % 32) % 2^32 := by
+ rw [rotRight32_eq_bv_rotate _ hx]
+ simp only [Nat.toUInt32_eq,... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_8 | 8af2decfccaeae32 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 1 | [
{
"theorem_name": "rotRight32_testBit",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n\n split\n · rw [rotRight32_testBit_of_lt]\n repeat omega\n · rw [rotRight32_testBit_of_ge]\n repeat omega",
... | [
{
"name": "rotRight32_testBit_of_ge",
"text": "/--\n Testing a bit of the result of a rotation in the range [32 - r % 32, 32) is equivalent to\n testing the bit of the original number in the range [i - (32 - r % 32), i).\n-/\nlemma rotRight32_testBit_of_ge (x r i : ℕ) (h : x < 2^32) (hi : i ≥ 32 - r % 32)... | [
{
"name": "rotRight32_testBit",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 13,
"n_chars": 326,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 4,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nes... | 3 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -183,6 +183,25 @@
simp [h_i']
omega
+/--
+ Testing a bit of the result of a rotation in the range [32 - r % 32, 32) is equivalent to
+ testing the bit of the original number in the range [i - (32 - r % 32), i).
+-/
+lemma rotRight32_testBit_of_ge (x r i : ℕ) (h : x < 2^32) (hi : i ≥ 32 - r % 32) :
+ (ro... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_9 | 9302e4b2b7d6272d | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 1 | [
{
"theorem_name": "rotRight32_toBits",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [toBits, Vector.rotate]\n ext i hi\n · simp\n simp only [Vector.size_toArray, Vector.getElem_toArray,\n Vecto... | [
{
"name": "rotRight32_testBit",
"text": "lemma rotRight32_testBit (x r i : ℕ) (h : x < 2^32) :\n (rotRight32 x r).testBit i =\n if i < 32 - r % 32 then\n x.testBit (r % 32 + i)\n else (decide (i < 32) && x.testBit (i - (32 - r % 32))) := by\n\n split\n · rw [rotRight32_testBit_of_lt]\n re... | [
{
"name": "rotRight32_toBits",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 17,
"n_chars": 598,
"n_subproofs": 0,
"n_tactics": 13,
"cyclomatic": 3,
"n_automation": 6,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nes... | 4 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -202,11 +202,33 @@
omega
linarith
+lemma rotRight32_testBit (x r i : ℕ) (h : x < 2^32) :
+ (rotRight32 x r).testBit i =
+ if i < 32 - r % 32 then
+ x.testBit (r % 32 + i)
+ else (decide (i < 32) && x.testBit (i - (32 - r % 32))) := by
+
+ split
+ · rw [rotRight32_testBit_of_lt]
+ repeat ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_10 | ca176d23a7cc18e3 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 3 | [
{
"theorem_name": "rotRight32_testBit_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [rotRight32_def _ _ h, Nat.testBit_or, Nat.testBit_shiftRight, Nat.testBit_mod_two_pow,\n Nat.testBit_shiftL... | [
{
"name": "rotRight32_def",
"text": "/--\n Alternative definition of rotRight32 using bitwise operations.\n-/\nlemma rotRight32_def (x : ℕ) (off : ℕ) (hx : x < 2^32) :\n rotRight32 x off = x >>> (off % 32) ||| x <<< (32 - off % 32) % 2^32 := by\n rw [rotRight32_eq_bv_rotate _ hx]\n simp only [Nat.toUI... | [
{
"name": "rotRight32_lt",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 187,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 1 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -161,8 +161,20 @@
rw [h_eq3]
+/--
+ Alternative definition of rotRight32 using bitwise operations.
+-/
+lemma rotRight32_def (x : ℕ) (off : ℕ) (hx : x < 2^32) :
+ rotRight32 x off = x >>> (off % 32) ||| x <<< (32 - off % 32) % 2^32 := by
+ rw [rotRight32_eq_bv_rotate _ hx]
+ simp only [Nat.toUInt32_eq... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_11 | 70b230c6b67a62ad | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 1 | [
{
"theorem_name": "rotRight32_composition",
"depth": 1,
"n_commands": 0,
"n_lines": 20,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h1 : (rotRight32 (rotRight32 x n) m) < 2^32 := by\n repeat apply rotRight32_lt\n assumption\n\n have h2... | [
{
"name": "rotRight32_lt",
"text": "theorem rotRight32_lt (x r : ℕ) (h : x < 2^32) :\n rotRight32 x r < 2^32 := by\n rw [rotRight32_def _ _ h]\n have := Nat.shiftRight_le x (r % 32)\n apply Nat.or_lt_two_pow <;> omega\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 187,
"n_subproofs": 1,
... | [
{
"name": "rotRight32_composition",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 29,
"n_chars": 924,
"n_subproofs": 3,
"n_tactics": 14,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,
"ma... | 6 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -230,13 +230,38 @@
split <;> (congr; omega)
linarith
+theorem rotRight32_lt (x r : ℕ) (h : x < 2^32) :
+ rotRight32 x r < 2^32 := by
+ rw [rotRight32_def _ _ h]
+ have := Nat.shiftRight_le x (r % 32)
+ apply Nat.or_lt_two_pow <;> omega
+
/--
Rotating a 32-bit value by `n` bits and then by `m` bits ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_12 | f978fdd3db7bdbe5 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 1 | [
{
"theorem_name": "mul_div_256_off",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Nat.mul_div_assoc, div_256_two_power ho h]\n rw [show 256=2^8 by rfl, ←Nat.pow_mul]\n ac_rfl\n rw [show 256=2^8 by r... | [
{
"name": "div_256_two_power",
"text": "lemma div_256_two_power {offset : ℕ} (ho : offset < 8) {i : ℕ} (h : i > 0):\n 256^i / 2^offset = 256^(i-1) * 2^(8-offset) := by\n rw [show 256 = 2^8 by rfl, ←Nat.pow_mul, Nat.pow_div]\n rw [←Nat.pow_mul, ←Nat.pow_add]\n rw [Nat.mul_sub_left_distrib, Nat.mul_one]... | [
{
"name": "mul_div_256_off",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 332,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 5,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 1 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -161,8 +161,22 @@
rw [h_eq3]
+lemma div_256_two_power {offset : ℕ} (ho : offset < 8) {i : ℕ} (h : i > 0):
+ 256^i / 2^offset = 256^(i-1) * 2^(8-offset) := by
+ rw [show 256 = 2^8 by rfl, ←Nat.pow_mul, Nat.pow_div]
+ rw [←Nat.pow_mul, ←Nat.pow_add]
+ rw [Nat.mul_sub_left_distrib, Nat.mul_one]
+ rw [Na... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_13 | 56d905b85b3f71a4 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 1 | [
{
"theorem_name": "shifted_decomposition_eq'",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Nat.pow_minus_one_mul hi, ←Nat.mul_assoc, shifted_decomposition_eq ho]",
"n_chars": 82,
"n_subproofs"... | [
{
"name": "shifted_decomposition_eq",
"text": "lemma shifted_decomposition_eq {offset : ℕ} (ho : offset < 8) {x1 x2 : ℕ} :\n (x1 / 2 ^ offset + x2 % 2 ^ offset * 2 ^ (8-offset)) * 256 =\n (2^offset * (x1 / 2^offset) + (x2 % 2^offset) * 256) * 2^(8-offset) := by\n ring_nf\n simp only [Nat.add_left_in... | [
{
"name": "shifted_decomposition_eq'",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 6,
"n_chars": 333,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"m... | 2 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -165,9 +165,18 @@
nth_rw 2 [←Nat.pow_one x]
rw [←Nat.pow_add, Nat.add_sub_of_le (by linarith [hy])]
+lemma shifted_decomposition_eq {offset : ℕ} (ho : offset < 8) {x1 x2 : ℕ} :
+ (x1 / 2 ^ offset + x2 % 2 ^ offset * 2 ^ (8-offset)) * 256 =
+ (2^offset * (x1 / 2^offset) + (x2 % 2^offset) * 256) * 2^(8-o... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_14 | 184e645f612daf55 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 1 | [
{
"theorem_name": "shifted_decomposition_eq''",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [shifted_decomposition_eq' ho hi]\n ring_nf\n rw [Nat.mul_assoc _ _ 256, Nat.mul_comm _ 256, Nat.pow_minus_... | [
{
"name": "shifted_decomposition_eq'",
"text": "lemma shifted_decomposition_eq' {offset : ℕ} (ho : offset < 8) {x1 x2 i : ℕ} (hi : i > 0) :\n (x1 / 2 ^ offset + x2 % 2 ^ offset * 2 ^ (8-offset)) * 256^i =\n (2^offset * (x1 / 2^offset) + (x2 % 2^offset) * 256) * 2^(8-offset) * 256^(i-1) := by\n rw [Na... | [
{
"name": "shifted_decomposition_eq''",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 400,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"... | 3 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -173,10 +173,18 @@
rw [Nat.mul_assoc, ←Nat.pow_add, Nat.add_sub_of_le (by linarith)]
rfl
+lemma shifted_decomposition_eq' {offset : ℕ} (ho : offset < 8) {x1 x2 i : ℕ} (hi : i > 0) :
+ (x1 / 2 ^ offset + x2 % 2 ^ offset * 2 ^ (8-offset)) * 256^i =
+ (2^offset * (x1 / 2^offset) + (x2 % 2^offset) * 256) *... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_095a415acc30_15 | 1dffee418453a32d | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Rotation.lean | Rotation | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 17 | 1 | [
{
"theorem_name": "soundness_simp'",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [←Nat.mul_one (x % 2 ^ offset * 2 ^ (8 - offset))]\n rw [←Nat.mul_one (2 ^ offset * (x / 2 ^ offset) * 2 ^ (8 - offset)... | [
{
"name": "soundness_simp",
"text": "lemma soundness_simp {offset : ℕ} {x y : ℕ} :\n x % 2 ^ offset * 2 ^ (8-offset) * y + 2 ^ offset * (x / 2 ^ offset) * 2 ^ (8-offset) * y =\n x * y * 2^ (8-offset) := by\n rw [Nat.mul_assoc, Nat.mul_assoc, ←Nat.add_mul, add_comm, Nat.div_add_mod]\n ac_rfl\n\n",
... | [
{
"name": "soundness_simp'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 331,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 0,
"automation_only": false,
"max_nesting... | 1 | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | import Clean.Utils.Bitwise
import Clean.Utils.Vector
import Mathlib.Data.Nat.Bitwise
import Clean.Utils.Bits
namespace Utils.Rotation
open Bits (toBits toBits_injective)
/--
When shifting left by `N - o` in an N-bit context, the low `o` bits of `x`
do not affect the result -- they get shifted past the N-bit bound... | @@ -161,9 +161,18 @@
rw [h_eq3]
+lemma soundness_simp {offset : ℕ} {x y : ℕ} :
+ x % 2 ^ offset * 2 ^ (8-offset) * y + 2 ^ offset * (x / 2 ^ offset) * 2 ^ (8-offset) * y =
+ x * y * 2^ (8-offset) := by
+ rw [Nat.mul_assoc, Nat.mul_assoc, ←Nat.add_mul, add_comm, Nat.div_add_mod]
+ ac_rfl
+
lemma soundn... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_6e57f256c64a_0 | 083615cc4d6e33cd | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/FiniteField.lean | FiniteField | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "FiniteField.val_inj_F",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← FiniteField.val_F, ← FiniteField.val_F]\n exact FiniteField.val_inj",
"n_chars": 83,
"n_subproofs": 0,... | [
{
"name": "val_inj",
"text": "/-- `val` is injective, as a simp lemma: value equality reduces to field equality.\nTagged `circuit_norm` so that witness-IR `feq` conditions normalize to propositional\nfield equality in circuit proofs. -/\n@[circuit_norm]\ntheorem val_inj {x y : F} : val x = val y ↔ x = y := ... | [
{
"name": "FiniteField.val_inj_F",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 9,
"n_chars": 515,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_n... | 2 | /-
This file defines a typeclass `FiniteField` that abstracts the properties of finite fields
needed by circuit gadgets. The goal is to provide a common interface that both prime fields
(`ZMod p`) and binary fields (`GF(2^n)`) can satisfy, enabling gadgets to be written
generically over any finite field.
The key abstr... | /-
This file defines a typeclass `FiniteField` that abstracts the properties of finite fields
needed by circuit gadgets. The goal is to provide a common interface that both prime fields
(`ZMod p`) and binary fields (`GF(2^n)`) can satisfy, enabling gadgets to be written
generically over any finite field.
The key abstr... | @@ -56,6 +56,12 @@
theorem ext_iff {x y : F} : x = y ↔ val x = val y :=
⟨fun h => h ▸ rfl, ext⟩
+/-- `val` is injective, as a simp lemma: value equality reduces to field equality.
+Tagged `circuit_norm` so that witness-IR `feq` conditions normalize to propositional
+field equality in circuit proofs. -/
+@[circuit... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_b0e4cb7e657c_0 | e64b33298a76f7ae | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Vector.lean | Vector | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "inductPush_listCons_push",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv => lhs; simp only [listCons, inductPush]\n apply (cast_eq_iff_heq).mpr\n have h_push_len : (xs.push a).toL... | [
{
"name": "cast_heq",
"text": "theorem cast_heq {v : Vector α n} (h : n = m) : HEq (v.cast h) v := by\n subst h\n rw [heq_eq_eq, cast_rfl]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 110,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,... | [
{
"name": "inductPush_listCons_push",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 21,
"n_chars": 947,
"n_subproofs": 4,
"n_tactics": 16,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
"... | 1 | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | @@ -41,6 +41,10 @@
let tl ← mapMonad ⟨ .mk as, rfl ⟩
pure ⟨ .mk <| hd :: tl.toList, by simpa using h⟩
+theorem cast_heq {v : Vector α n} (h : n = m) : HEq (v.cast h) v := by
+ subst h
+ rw [heq_eq_eq, cast_rfl]
+
universe u
def induct {motive : {n : ℕ} → Vector α n → Sort u}
@@ -86,7 +90,11 @@
appl... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_b0e4cb7e657c_1 | 6cc77a4354357fd3 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Vector.lean | Vector | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "inductPush_listCons_push",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv => lhs; simp only [listCons, inductPush]\n apply (cast_eq_iff_heq).mpr\n have h_push_len : (xs.push a).toL... | [
{
"name": "cast_heq",
"text": "theorem cast_heq {v : Vector α n} (h : n = m) : HEq (v.cast h) v := by\n subst h\n rw [heq_eq_eq, cast_rfl]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 110,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,... | [
{
"name": "inductPush_push",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 16,
"n_chars": 630,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": false,
"max_nesti... | 3 | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | @@ -41,6 +41,10 @@
let tl ← mapMonad ⟨ .mk as, rfl ⟩
pure ⟨ .mk <| hd :: tl.toList, by simpa using h⟩
+theorem cast_heq {v : Vector α n} (h : n = m) : HEq (v.cast h) v := by
+ subst h
+ rw [heq_eq_eq, cast_rfl]
+
universe u
def induct {motive : {n : ℕ} → Vector α n → Sort u}
@@ -91,7 +95,11 @@
appl... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_b0e4cb7e657c_2 | c2ea78fd758b64a3 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Vector.lean | Vector | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "mapFinRange_eq_map",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext i\n simp only [Vector.getElem_mapFinRange, Vector.getElem_map]\n simp",
"n_chars": 79,
"n_subproofs": 0,
... | [
{
"name": "getElem_mapFinRange",
"text": "theorem getElem_mapFinRange {n} {create : Fin n → α} :\n ∀ (i : ℕ) (hi : i < n), (mapFinRange n create)[i] = create ⟨ i, hi ⟩ := by\n simp [mapFinRange, finRange]\n\n",
"fan_in": 5,
"n_lines": 5,
"n_chars": 177,
"n_subproofs": 0,
"n_tactics":... | [
{
"name": "mapFinRange_eq_map",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 207,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nest... | 1 | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | @@ -78,8 +78,15 @@
def mapFinRange (n : ℕ) (create : Fin n → α) : Vector α n := finRange n |>.map create
+theorem getElem_mapFinRange {n} {create : Fin n → α} :
+ ∀ (i : ℕ) (hi : i < n), (mapFinRange n create)[i] = create ⟨ i, hi ⟩ := by
+ simp [mapFinRange, finRange]
+
lemma mapFinRange_eq_map {n : ℕ} (v : V... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_b0e4cb7e657c_3 | 282396f234b82669 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Vector.lean | Vector | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "mapFinRange_eq_map",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext i\n simp only [Vector.getElem_mapFinRange, Vector.getElem_map]\n simp",
"n_chars": 79,
"n_subproofs": 0,
... | [
{
"name": "getElem_mapFinRange",
"text": "theorem getElem_mapFinRange {n} {create : Fin n → α} :\n ∀ (i : ℕ) (hi : i < n), (mapFinRange n create)[i] = create ⟨ i, hi ⟩ := by\n simp [mapFinRange, finRange]\n\n",
"fan_in": 5,
"n_lines": 5,
"n_chars": 177,
"n_subproofs": 0,
"n_tactics":... | [
{
"name": "mapFinRange_eq_self",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 173,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nes... | 1 | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | @@ -78,8 +78,14 @@
def mapFinRange (n : ℕ) (create : Fin n → α) : Vector α n := finRange n |>.map create
+theorem getElem_mapFinRange {n} {create : Fin n → α} :
+ ∀ (i : ℕ) (hi : i < n), (mapFinRange n create)[i] = create ⟨ i, hi ⟩ := by
+ simp [mapFinRange, finRange]
+
lemma mapFinRange_eq_self {α : Type} {n... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_b0e4cb7e657c_4 | ee65fd2fb456a35d | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Vector.lean | Vector | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "mapFinRange_eq_map",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext i\n simp only [Vector.getElem_mapFinRange, Vector.getElem_map]\n simp",
"n_chars": 79,
"n_subproofs": 0,
... | [
{
"name": "getElem_mapFinRange",
"text": "theorem getElem_mapFinRange {n} {create : Fin n → α} :\n ∀ (i : ℕ) (hi : i < n), (mapFinRange n create)[i] = create ⟨ i, hi ⟩ := by\n simp [mapFinRange, finRange]\n\n",
"fan_in": 5,
"n_lines": 5,
"n_chars": 177,
"n_subproofs": 0,
"n_tactics":... | [
{
"name": "map_mapFinRange",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 241,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting... | 1 | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | @@ -78,9 +78,15 @@
def mapFinRange (n : ℕ) (create : Fin n → α) : Vector α n := finRange n |>.map create
+theorem getElem_mapFinRange {n} {create : Fin n → α} :
+ ∀ (i : ℕ) (hi : i < n), (mapFinRange n create)[i] = create ⟨ i, hi ⟩ := by
+ simp [mapFinRange, finRange]
+
lemma map_mapFinRange {n : ℕ} {create :... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_b0e4cb7e657c_5 | d5538405709ef75c | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Vector.lean | Vector | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "getElem_mapRange",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros i hi\n induction n\n case zero => simp at hi\n case succ n ih =>\n rw [mapRange_succ]\n by_cases hi' : i ... | [
{
"name": "mapRange_succ",
"text": "theorem mapRange_succ {n} {create : ℕ → α} :\n mapRange (n + 1) create = (mapRange n create).push (create n) := rfl\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 124,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n... | [
{
"name": "getElem_mapRange",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 372,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
"max_nest... | 1 | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | @@ -83,8 +83,21 @@
| 0 => #v[]
| k + 1 => mapRange k create |>.push (create k)
+theorem mapRange_succ {n} {create : ℕ → α} :
+ mapRange (n + 1) create = (mapRange n create).push (create n) := rfl
+
theorem getElem_mapRange {n} {create : ℕ → α} :
- ∀ (i : ℕ) (hi : i < n), (mapRange n create)[i] = create i... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_b0e4cb7e657c_6 | 65e5e9ad140f7529 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Vector.lean | Vector | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "getElem_mapRange",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros i hi\n induction n\n case zero => simp at hi\n case succ n ih =>\n rw [mapRange_succ]\n by_cases hi' : i ... | [
{
"name": "mapRange_succ",
"text": "theorem mapRange_succ {n} {create : ℕ → α} :\n mapRange (n + 1) create = (mapRange n create).push (create n) := rfl\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 124,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n... | [
{
"name": "map_mapRange",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 223,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting": ... | 2 | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | @@ -83,8 +83,21 @@
| 0 => #v[]
| k + 1 => mapRange k create |>.push (create k)
+theorem mapRange_succ {n} {create : ℕ → α} :
+ mapRange (n + 1) create = (mapRange n create).push (create n) := rfl
+
theorem getElem_mapRange {n} {create : ℕ → α} :
- ∀ (i : ℕ) (hi : i < n), (mapRange n create)[i] = create i... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_b0e4cb7e657c_7 | 04fc9405dba5c7a8 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Vector.lean | Vector | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "mapFinRange_eq_map",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext i\n simp only [Vector.getElem_mapFinRange, Vector.getElem_map]\n simp",
"n_chars": 79,
"n_subproofs": 0,
... | [
{
"name": "getElem_mapFinRange",
"text": "theorem getElem_mapFinRange {n} {create : Fin n → α} :\n ∀ (i : ℕ) (hi : i < n), (mapFinRange n create)[i] = create ⟨ i, hi ⟩ := by\n simp [mapFinRange, finRange]\n\n",
"fan_in": 5,
"n_lines": 5,
"n_chars": 177,
"n_subproofs": 0,
"n_tactics":... | [
{
"name": "mapRange_eq_mapFinRange",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 6,
"n_chars": 212,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max... | 3 | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | @@ -78,6 +78,10 @@
def mapFinRange (n : ℕ) (create : Fin n → α) : Vector α n := finRange n |>.map create
+theorem getElem_mapFinRange {n} {create : Fin n → α} :
+ ∀ (i : ℕ) (hi : i < n), (mapFinRange n create)[i] = create ⟨ i, hi ⟩ := by
+ simp [mapFinRange, finRange]
+
def mapRange (n : ℕ) (create : ℕ → α) :... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_b0e4cb7e657c_8 | 0451f5c45863145f | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Vector.lean | Vector | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 5 | [
{
"theorem_name": "mapFinRange_eq_map",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext i\n simp only [Vector.getElem_mapFinRange, Vector.getElem_map]\n simp",
"n_chars": 79,
"n_subproofs": 0,
... | [
{
"name": "getElem_mapFinRange",
"text": "theorem getElem_mapFinRange {n} {create : Fin n → α} :\n ∀ (i : ℕ) (hi : i < n), (mapFinRange n create)[i] = create ⟨ i, hi ⟩ := by\n simp [mapFinRange, finRange]\n\n",
"fan_in": 5,
"n_lines": 5,
"n_chars": 177,
"n_subproofs": 0,
"n_tactics":... | [
{
"name": "zip_mapRange",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 300,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 3 | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | @@ -78,6 +78,10 @@
def mapFinRange (n : ℕ) (create : Fin n → α) : Vector α n := finRange n |>.map create
+theorem getElem_mapFinRange {n} {create : Fin n → α} :
+ ∀ (i : ℕ) (hi : i < n), (mapFinRange n create)[i] = create ⟨ i, hi ⟩ := by
+ simp [mapFinRange, finRange]
+
def mapRange (n : ℕ) (create : ℕ → α) :... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_b0e4cb7e657c_9 | f4d376a0f219cd52 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Vector.lean | Vector | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "toChunks_push",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [toChunks]\n nth_rw 1 [← cast_take_append_of_eq_length (v := vs) (w := v)]\n nth_rw 2 [← cast_drop_append_of_eq_l... | [
{
"name": "cast_take_append_of_eq_length",
"text": "theorem cast_take_append_of_eq_length {v : Vector α n} {w : Vector α m} :\n (v ++ w |>.take n |>.cast Nat.min_add_right_self) = v := by\n have hv_length : v.toArray.toList.length = n := by simp\n rw [cast_mk, ←toArray_inj, take_eq_extract, toArray_ext... | [
{
"name": "toChunks_push",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 332,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": ... | 2 | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | @@ -88,6 +88,15 @@
| 0 => #v[]
| k + 1 => (fill k a).push a
+theorem cast_take_append_of_eq_length {v : Vector α n} {w : Vector α m} :
+ (v ++ w |>.take n |>.cast Nat.min_add_right_self) = v := by
+ have hv_length : v.toArray.toList.length = n := by simp
+ rw [cast_mk, ←toArray_inj, take_eq_extract, toArra... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_b0e4cb7e657c_10 | f1ad59847b2a5da5 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Vector.lean | Vector | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "toChunks_push",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [toChunks]\n nth_rw 1 [← cast_take_append_of_eq_length (v := vs) (w := v)]\n nth_rw 2 [← cast_drop_append_of_eq_l... | [
{
"name": "cast_take_append_of_eq_length",
"text": "theorem cast_take_append_of_eq_length {v : Vector α n} {w : Vector α m} :\n (v ++ w |>.take n |>.cast Nat.min_add_right_self) = v := by\n have hv_length : v.toArray.toList.length = n := by simp\n rw [cast_mk, ←toArray_inj, take_eq_extract, toArray_ext... | [
{
"name": "flatten_toChunks",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 9,
"n_chars": 270,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 3 | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | @@ -88,6 +88,15 @@
| 0 => #v[]
| k + 1 => (fill k a).push a
+theorem cast_take_append_of_eq_length {v : Vector α n} {w : Vector α m} :
+ (v ++ w |>.take n |>.cast Nat.min_add_right_self) = v := by
+ have hv_length : v.toArray.toList.length = n := by simp
+ rw [cast_mk, ←toArray_inj, take_eq_extract, toArra... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_b0e4cb7e657c_11 | 10232deff8a4cc2f | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Vector.lean | Vector | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "mapM_push",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [←append_singleton, mapM_append, mapM_singleton]\n simp only [bind_pure_comp, Functor.map_map, append_singleton]",
"n_cha... | [
{
"name": "mapM_singleton",
"text": "theorem mapM_singleton (a : α) {m : Type → Type} [Monad m] [LawfulMonad m] (f : α → m β) :\n #v[a].mapM f = (do pure #v[←f a]) := by\n apply map_toArray_inj.mp\n simp\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 179,
"n_subproofs": 0,
"n_tactics":... | [
{
"name": "mapM_push",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 339,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 1 | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | import Mathlib.Analysis.Normed.Ring.Lemmas
import Mathlib.Combinatorics.Enumerative.Composition
import Init.Data.List.Find
variable {α β : Type} {n m : ℕ}
open Vector (finRange)
namespace Vector
def fromList (l : List α) : Vector α l.length := ⟨ .mk l, rfl ⟩
def len (_ : Vector α n) : ℕ := n
-- Helper lemma: A vec... | @@ -99,11 +99,18 @@
let tail : Vector α (n*m) := (v.take (n*m)).cast h_tail
(tail.toChunks m).push head
+theorem mapM_singleton (a : α) {m : Type → Type} [Monad m] [LawfulMonad m] (f : α → m β) :
+ #v[a].mapM f = (do pure #v[←f a]) := by
+ apply map_toArray_inj.mp
+ simp
+
theorem mapM_push (as : Vect... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c620536a3e71_0 | 5df1e7975586f86a | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/And32.lean | And32 | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "testBit_binary_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n with\n | zero => exact k.elim0\n | succ m ih =>\n rw [Fin.sum_univ_castSucc]; simp only [Fin.val_castS... | [
{
"name": "sum_bool_lt_two_pow",
"text": "private lemma sum_bool_lt_two_pow (n : ℕ) (f : Fin n → ℕ) (hf : ∀ i, f i ≤ 1) :\n ∑ i : Fin n, f i * 2^i.val < 2^n := by\n induction n with\n | zero => simp\n | succ m ih =>\n rw [Fin.sum_univ_castSucc]; simp only [Fin.val_castSucc, Fin.val_last]\n have ... | [
{
"name": "testBit_binary_sum",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 1118,
"n_subproofs": 4,
"n_tactics": 25,
"cyclomatic": 6,
"n_automation": 7,
"n_rewrites": 6,
"n_structural": 4,
"automation_only": false,
"max_n... | 1 | import Clean.Gadgets.SHA256.BitwiseOps
namespace Gadgets.SHA256.And32
variable {p : ℕ} [Fact p.Prime]
/-!
# 32-bit Bitwise AND for SHA-256
Per bit: z = a · b (correct when a, b ∈ {0, 1}).
Witnesses 32 output bits.
-/
structure Inputs (F : Type) where
a : fields 32 F
b : fields 32 F
deriving ProvableStruct
/--... | import Clean.Gadgets.SHA256.BitwiseOps
namespace Gadgets.SHA256.And32
variable {p : ℕ} [Fact p.Prime]
/-!
# 32-bit Bitwise AND for SHA-256
Per bit: z = a · b (correct when a, b ∈ {0, 1}).
Witnesses 32 output bits.
-/
structure Inputs (F : Type) where
a : fields 32 F
b : fields 32 F
deriving ProvableStruct
/--... | @@ -32,6 +32,19 @@
## Helper lemmas for valueBits and bitwise AND
-/
+private lemma sum_bool_lt_two_pow (n : ℕ) (f : Fin n → ℕ) (hf : ∀ i, f i ≤ 1) :
+ ∑ i : Fin n, f i * 2^i.val < 2^n := by
+ induction n with
+ | zero => simp
+ | succ m ih =>
+ rw [Fin.sum_univ_castSucc]; simp only [Fin.val_castSucc, Fin.... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c620536a3e71_1 | 23bdefd0156f1822 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/And32.lean | And32 | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "bool_finsum_and",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Nat.eq_of_testBit_eq; intro j\n by_cases hj : j < n\n · have hfg : ∀ i : Fin n, (f i &&& g i) = 0 ∨ (f i &&& g i) ... | [
{
"name": "testBit_binary_sum",
"text": "private lemma testBit_binary_sum (n : ℕ) (f : Fin n → ℕ) (hf : ∀ i, f i = 0 ∨ f i = 1) (k : Fin n) :\n Nat.testBit (∑ i : Fin n, f i * 2^i.val) k.val = decide (f k = 1) := by\n induction n with\n | zero => exact k.elim0\n | succ m ih =>\n rw [Fin.sum_univ_ca... | [
{
"name": "bool_finsum_and",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 20,
"n_chars": 1240,
"n_subproofs": 4,
"n_tactics": 24,
"cyclomatic": 15,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 10,
"automation_only": false,
"max_ne... | 2 | import Clean.Gadgets.SHA256.BitwiseOps
namespace Gadgets.SHA256.And32
variable {p : ℕ} [Fact p.Prime]
/-!
# 32-bit Bitwise AND for SHA-256
Per bit: z = a · b (correct when a, b ∈ {0, 1}).
Witnesses 32 output bits.
-/
structure Inputs (F : Type) where
a : fields 32 F
b : fields 32 F
deriving ProvableStruct
/--... | import Clean.Gadgets.SHA256.BitwiseOps
namespace Gadgets.SHA256.And32
variable {p : ℕ} [Fact p.Prime]
/-!
# 32-bit Bitwise AND for SHA-256
Per bit: z = a · b (correct when a, b ∈ {0, 1}).
Witnesses 32 output bits.
-/
structure Inputs (F : Type) where
a : fields 32 F
b : fields 32 F
deriving ProvableStruct
/--... | @@ -45,13 +45,38 @@
have h2 : 2^m + 2^m = 2^(m+1) := by ring
omega
+private lemma testBit_binary_sum (n : ℕ) (f : Fin n → ℕ) (hf : ∀ i, f i = 0 ∨ f i = 1) (k : Fin n) :
+ Nat.testBit (∑ i : Fin n, f i * 2^i.val) k.val = decide (f k = 1) := by
+ induction n with
+ | zero => exact k.elim0
+ | succ m ih ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c620536a3e71_2 | ed311a0430323f31 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/And32.lean | And32 | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "soundness",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n circuit_proof_start\n rw [h_holds]; clear h_holds\n obtain ⟨ha, hb⟩ := h_assumptions\n obtain ⟨h_input_a, h_input_b⟩ := h_inp... | [
{
"name": "bool_finsum_and",
"text": "private lemma bool_finsum_and (n : ℕ) (f g : Fin n → ℕ) (hf : ∀ i, f i = 0 ∨ f i = 1)\n (hg : ∀ i, g i = 0 ∨ g i = 1) :\n (∑ i : Fin n, f i * 2^i.val) &&& (∑ i : Fin n, g i * 2^i.val)\n = ∑ i : Fin n, (f i &&& g i) * 2^i.val := by\n apply Nat.eq_of_testBit_eq;... | [
{
"name": "soundness",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 21,
"n_chars": 980,
"n_subproofs": 3,
"n_tactics": 24,
"cyclomatic": 6,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 9,
"automation_only": false,
"max_nesting": 6... | 3 | import Clean.Gadgets.SHA256.BitwiseOps
namespace Gadgets.SHA256.And32
variable {p : ℕ} [Fact p.Prime]
/-!
# 32-bit Bitwise AND for SHA-256
Per bit: z = a · b (correct when a, b ∈ {0, 1}).
Witnesses 32 output bits.
-/
structure Inputs (F : Type) where
a : fields 32 F
b : fields 32 F
deriving ProvableStruct
/--... | import Clean.Gadgets.SHA256.BitwiseOps
namespace Gadgets.SHA256.And32
variable {p : ℕ} [Fact p.Prime]
/-!
# 32-bit Bitwise AND for SHA-256
Per bit: z = a · b (correct when a, b ∈ {0, 1}).
Witnesses 32 output bits.
-/
structure Inputs (F : Type) where
a : fields 32 F
b : fields 32 F
deriving ProvableStruct
/--... | @@ -66,10 +66,47 @@
have hklast : k = Fin.last m := Fin.ext hkeq; subst hklast
rcases hf (Fin.last m) with h | h <;> simp [h, fm]
+private lemma bool_finsum_and (n : ℕ) (f g : Fin n → ℕ) (hf : ∀ i, f i = 0 ∨ f i = 1)
+ (hg : ∀ i, g i = 0 ∨ g i = 1) :
+ (∑ i : Fin n, f i * 2^i.val) &&& (∑ i : Fin n... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c9854e24f23c_3 | 4cb27563c92563cb | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Circomlib/CompConstantLemmas.lean | CompConstantLemmas | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 60 | 1 | [
{
"theorem_name": "fromBits_shiftRight_mod4",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [shiftRight_mod4_eq_bits, fromBits_testBit_eq bits k h_bits (Nat.lt_of_succ_lt hk),\n fromBits_testBit_eq ... | [
{
"name": "fromBits_testBit_eq",
"text": "/-- Extract bit value from toBits_fromBits: bits[k] equals the k-th bit of fromBits bits -/\nlemma fromBits_testBit_eq {n : ℕ} (bits : Vector ℕ n) (k : ℕ)\n (h_bits : ∀ (i : ℕ) (hi : i < n), bits[i] = 0 ∨ bits[i] = 1)\n (hk : k < n) :\n bits[k] = (fromBits ... | [
{
"name": "fromBits_shiftRight_mod4",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 447,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"ma... | 2 | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Circomlib.Bitify
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime] [Fact (p < 2^254)] [Fact (p > 2^253)]
namespace CompConstant
/-! ## Helper Definitions -/
/-- The b coefficient for iteration i: b_i = 2^128 - 2^i -/
@[reducible] def bCoeff... | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Circomlib.Bitify
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime] [Fact (p < 2^254)] [Fact (p > 2^253)]
namespace CompConstant
/-! ## Helper Definitions -/
/-- The b coefficient for iteration i: b_i = 2^128 - 2^i -/
@[reducible] def bCoeff... | @@ -50,11 +50,25 @@
rw [Nat.pow_succ, Nat.div_div_eq_div_mul, mul_comm]
omega
+/-- Extract bit value from toBits_fromBits: bits[k] equals the k-th bit of fromBits bits -/
+lemma fromBits_testBit_eq {n : ℕ} (bits : Vector ℕ n) (k : ℕ)
+ (h_bits : ∀ (i : ℕ) (hi : i < n), bits[i] = 0 ∨ bits[i] = 1)
+ (hk :... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c9854e24f23c_6 | 3f725197edcd8abe | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Circomlib/CompConstantLemmas.lean | CompConstantLemmas | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 60 | 1 | [
{
"theorem_name": "high_parts_eq_of_pairs_eq_above",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply Nat.eq_of_testBit_eq\n intro i\n simp only [Nat.testBit, Nat.shiftRight_eq_div_pow]\n rw [Nat.div... | [
{
"name": "div_pow_eq_zero_of_lt",
"text": "/-- Division by power larger than bound equals zero -/\nlemma div_pow_eq_zero_of_lt (x n bound : ℕ) (hx : x < 2^bound) (hn : bound ≤ n) :\n x / 2^n = 0 := by\n apply Nat.div_eq_zero_iff.mpr\n right\n calc x < 2^bound := hx\n _ ≤ 2^n := Nat.pow_le_pow_righ... | [
{
"name": "high_parts_eq_of_pairs_eq_above",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 7,
"n_lines": 39,
"n_chars": 1809,
"n_subproofs": 11,
"n_tactics": 33,
"cyclomatic": 1,
"n_automation": 12,
"n_rewrites": 10,
"n_structural": 2,
"automation_only": f... | 7 | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Circomlib.Bitify
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime] [Fact (p < 2^254)] [Fact (p > 2^253)]
namespace CompConstant
/-! ## Helper Definitions -/
/-- The b coefficient for iteration i: b_i = 2^128 - 2^i -/
@[reducible] def bCoeff... | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Circomlib.Bitify
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime] [Fact (p < 2^254)] [Fact (p > 2^253)]
namespace CompConstant
/-! ## Helper Definitions -/
/-- The b coefficient for iteration i: b_i = 2^128 - 2^i -/
@[reducible] def bCoeff... | @@ -80,11 +80,52 @@
_ = y / 2 ^ (pos * 2 + 1) % 2 := by rw [hpow]
omit [Fact (Nat.Prime p)] [Fact (p < 2 ^ 254)] [Fact (p > 2 ^ 253)] in
+/-- Division by power larger than bound equals zero -/
+lemma div_pow_eq_zero_of_lt (x n bound : ℕ) (hx : x < 2^bound) (hn : bound ≤ n) :
+ x / 2^n = 0 := by
+ apply Nat.... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c9854e24f23c_7 | af441b34f519d7bc | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Circomlib/CompConstantLemmas.lean | CompConstantLemmas | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 60 | 2 | [
{
"theorem_name": "mod_four_pow_succ",
"depth": 1,
"n_commands": 0,
"n_lines": 23,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h41 : (4:ℕ)^(k+1) = 4 * 4^k := by ring\n rw [h41]\n have h_4k_pos : 0 < 4^k := four_pow_pos k\n have h_rem : x %... | [
{
"name": "four_pow_pos",
"text": "/-- 4^k is always positive -/\nlemma four_pow_pos (k : ℕ) : 0 < 4^k := Nat.pow_pos (by omega : 0 < 4)\n\n",
"fan_in": 2,
"n_lines": 4,
"n_chars": 104,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
... | [
{
"name": "mod_four_pow_succ",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 26,
"n_chars": 1256,
"n_subproofs": 12,
"n_tactics": 24,
"cyclomatic": 1,
"n_automation": 10,
"n_rewrites": 5,
"n_structural": 1,
"automation_only": false,
"max_... | 2 | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Circomlib.Bitify
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime] [Fact (p < 2^254)] [Fact (p > 2^253)]
namespace CompConstant
/-! ## Helper Definitions -/
/-- The b coefficient for iteration i: b_i = 2^128 - 2^i -/
@[reducible] def bCoeff... | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Circomlib.Bitify
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime] [Fact (p < 2^254)] [Fact (p > 2^253)]
namespace CompConstant
/-! ## Helper Definitions -/
/-- The b coefficient for iteration i: b_i = 2^128 - 2^i -/
@[reducible] def bCoeff... | @@ -46,11 +46,14 @@
have := Nat.div_add_mod n d; linarith
omit [Fact (Nat.Prime p)] [Fact (p < 2 ^ 254)] [Fact (p > 2 ^ 253)] in
+/-- 4^k is always positive -/
+lemma four_pow_pos (k : ℕ) : 0 < 4^k := Nat.pow_pos (by omega : 0 < 4)
+
/-- Helper: x % (4 * 4^k) = (x / 4^k % 4) * 4^k + x % 4^k -/
lemma mod_four_po... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c9854e24f23c_8 | 1eb74792375880e9 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Circomlib/CompConstantLemmas.lean | CompConstantLemmas | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 60 | 1 | [
{
"theorem_name": "lt_of_high_eq_and_pair_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [Nat.shiftRight_eq_div_pow] at h_pair_lt\n have h4k : (4:ℕ)^k = 2^(k*2) := by rw [four_pow_eq_two_pow... | [
{
"name": "mod_four_pow_succ",
"text": "/-- Helper: x % (4 * 4^k) = (x / 4^k % 4) * 4^k + x % 4^k -/\nlemma mod_four_pow_succ (x k : ℕ) : x % 4^(k+1) = (x / 4^k % 4) * 4^k + x % 4^k := by\n have h41 : (4:ℕ)^(k+1) = 4 * 4^k := by ring\n rw [h41]\n have h_4k_pos : 0 < 4^k := four_pow_pos k\n have h_rem : ... | [
{
"name": "lt_of_high_eq_and_pair_lt",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 31,
"n_chars": 1218,
"n_subproofs": 10,
"n_tactics": 22,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
... | 4 | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Circomlib.Bitify
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime] [Fact (p < 2^254)] [Fact (p > 2^253)]
namespace CompConstant
/-! ## Helper Definitions -/
/-- The b coefficient for iteration i: b_i = 2^128 - 2^i -/
@[reducible] def bCoeff... | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Circomlib.Bitify
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime] [Fact (p < 2^254)] [Fact (p > 2^253)]
namespace CompConstant
/-! ## Helper Definitions -/
/-- The b coefficient for iteration i: b_i = 2^128 - 2^i -/
@[reducible] def bCoeff... | @@ -55,13 +55,61 @@
/-- 4^k is always positive -/
lemma four_pow_pos (k : ℕ) : 0 < 4^k := Nat.pow_pos (by omega : 0 < 4)
+/-- Helper: x % (4 * 4^k) = (x / 4^k % 4) * 4^k + x % 4^k -/
+lemma mod_four_pow_succ (x k : ℕ) : x % 4^(k+1) = (x / 4^k % 4) * 4^k + x % 4^k := by
+ have h41 : (4:ℕ)^(k+1) = 4 * 4^k := by ring... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_49fb3b8cf00f_0 | beb8589e8e347f0f | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/Keccak/ThetaXor.lean | ThetaXor | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "soundness",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n circuit_proof_start [Xor64.circuit, Xor64.Assumptions, Xor64.Spec]\n obtain ⟨state_norm, d_norm⟩ := h_assumptions\n\n -- rewri... | [
{
"name": "thetaXor_loop",
"text": "lemma thetaXor_loop (state : Vector ℕ 25) (d : Vector ℕ 5) :\n Specs.Keccak256.thetaXor state d = .mapFinRange 25 fun i => state[i.val] ^^^ d[i.val / 5] := by\n simp [Specs.Keccak256.thetaXor, circuit_norm, Vector.mapFinRange_succ, Vector.mapFinRange_zero]\n\n",
"... | [
{
"name": "soundness",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 18,
"n_chars": 643,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,
"max_nesting": 2... | 1 | import Clean.Circuit.Loops
import Clean.Gadgets.Xor.Xor64
import Clean.Gadgets.Keccak.KeccakState
import Clean.Specs.Keccak256
namespace Gadgets.Keccak256.ThetaXor
variable {p : ℕ} [Fact p.Prime] [Fact (p > 512)]
structure Inputs (F : Type) where
state : KeccakState F
d : KeccakRow F
deriving ProvableStruct
def ... | import Clean.Circuit.Loops
import Clean.Gadgets.Xor.Xor64
import Clean.Gadgets.Keccak.KeccakState
import Clean.Specs.Keccak256
namespace Gadgets.Keccak256.ThetaXor
variable {p : ℕ} [Fact p.Prime] [Fact (p > 512)]
structure Inputs (F : Type) where
state : KeccakState F
d : KeccakRow F
deriving ProvableStruct
def ... | @@ -28,8 +28,27 @@
∧ out.value = Specs.Keccak256.thetaXor state.value d.value
-- rewrite thetaXor as a loop
-theorem soundness : Soundness (F p) main Assumptions Spec := sorry
+lemma thetaXor_loop (state : Vector ℕ 25) (d : Vector ℕ 5) :
+ Specs.Keccak256.thetaXor state d = .mapFinRange 25 fun i => state[i.val... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_0b58fe073ee1_0 | d6a1f5f3db4a2e97 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Circomlib/Mux1.lean | Mux1 | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "Vector.getElem_map_singleton_flatten",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Vector.getElem_flatten_singleton (v.map (fun x => #v[f x])) i hi]\n simp only [Vector.getElem_map... | [
{
"name": "Vector.getElem_flatten_singleton",
"text": "lemma Vector.getElem_flatten_singleton {α : Type} {n : ℕ} (v : Vector (Vector α 1) n) (i : ℕ) (hi : i < n) :\n v.flatten[i] = (v[i])[0] := by\n simp only [Vector.getElem_flatten, Nat.div_one]\n congr\n omega\n\n",
"fan_in": 1,
"n_lines": 7... | [
{
"name": "Vector.getElem_map_singleton_flatten",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 400,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": fa... | 1 | import Clean.Circuit
import Clean.Utils.Field
import Clean.Utils.Tactics
import Clean.Gadgets.Equality
import Clean.Gadgets.Boolean
namespace Circomlib
open Circuit
variable {p : ℕ} [Fact p.Prime] [Fact (p > 2)]
/-
Original source code:
https://github.com/iden3/circomlib/blob/master/circuits/mux1.circom
-/
namespace... | import Clean.Circuit
import Clean.Utils.Field
import Clean.Utils.Tactics
import Clean.Gadgets.Equality
import Clean.Gadgets.Boolean
namespace Circomlib
open Circuit
variable {p : ℕ} [Fact p.Prime] [Fact (p > 2)]
/-
Original source code:
https://github.com/iden3/circomlib/blob/master/circuits/mux1.circom
-/
namespace... | @@ -38,8 +38,17 @@
(c1 - c0) * s + c0
return out
+lemma Vector.getElem_flatten_singleton {α : Type} {n : ℕ} (v : Vector (Vector α 1) n) (i : ℕ) (hi : i < n) :
+ v.flatten[i] = (v[i])[0] := by
+ simp only [Vector.getElem_flatten, Nat.div_one]
+ congr
+ omega
+
lemma Vector.getElem_map_singleton_flatten ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7d3512816689_1 | 32747738da9a3d2e | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Tables/Fibonacci32.lean | Fibonacci32 | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "boundary_vars",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro env\n dsimp only [env, windowEnv]\n have h_offset : (boundary (p:=p)).finalAssignment.offset = 8 := rfl\n simp only... | [
{
"name": "boundary_assignment",
"text": "lemma boundary_assignment : (boundary (p:=p)).finalAssignment.vars =\n #v[.input ⟨0, 0⟩, .input ⟨0, 1⟩, .input ⟨0, 2⟩, .input ⟨0, 3⟩, .input ⟨0, 4⟩, .input ⟨0, 5⟩, .input ⟨0, 6⟩,\n .input ⟨0, 7⟩] := by\n dsimp only [table_assignment_norm, circuit_norm, bou... | [
{
"name": "boundary_vars",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 729,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting... | 1 | import Clean.Utils.Vector
import Clean.Circuit.Basic
import Clean.Table.Theorems
import Clean.Gadgets.Addition32.Addition32
import Clean.Gadgets.Equality
import Clean.Types.U32
namespace Tables.Fibonacci32
variable {p : ℕ} [Fact p.Prime] [p_large_enough: Fact (p > 512)]
def fib32 : ℕ -> ℕ
| 0 => 0
| 1 => 1
| (n... | import Clean.Utils.Vector
import Clean.Circuit.Basic
import Clean.Table.Theorems
import Clean.Gadgets.Addition32.Addition32
import Clean.Gadgets.Equality
import Clean.Types.U32
namespace Tables.Fibonacci32
variable {p : ℕ} [Fact p.Prime] [p_large_enough: Fact (p > 512)]
def fib32 : ℕ -> ℕ
| 0 => 0
| 1 => 1
| (n... | @@ -173,10 +173,29 @@
exact ⟨h_add_mod, h_norm_next_y⟩
omit p_large_enough in
+lemma boundary_assignment : (boundary (p:=p)).finalAssignment.vars =
+ #v[.input ⟨0, 0⟩, .input ⟨0, 1⟩, .input ⟨0, 2⟩, .input ⟨0, 3⟩, .input ⟨0, 4⟩, .input ⟨0, 5⟩, .input ⟨0, 6⟩,
+ .input ⟨0, 7⟩] := by
+ dsimp only [table_ass... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f60dc022760e_0 | 199613bc895fc058 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/SHA256/UpperSigma1.lean | UpperSigma1 | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "soundness",
"depth": 1,
"n_commands": 0,
"n_lines": 45,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n circuit_proof_start [upperSigma1, xor32]\n obtain ⟨h_holds1, h_holds2⟩ := h_holds\n have ha : ∀ i : Fin 32, input[i] = 0 ∨ inp... | [
{
"name": "spec_of_constraint",
"text": "private lemma spec_of_constraint\n (input z : fields 32 (F p))\n (hx : Normalized input)\n (h_z : ∀ i : Fin 32, z[i] =\n (input[(i + 6).val] + input[(i + 11).val] -\n 2 * input[(i + 6).val] * input[(i + 11).val])\n + input[(i + 25).val]\n ... | [
{
"name": "soundness",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 47,
"n_chars": 2524,
"n_subproofs": 13,
"n_tactics": 51,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 10,
"automation_only": false,
"max_nesting"... | 1 | import Clean.Gadgets.SHA256.LowerSigma0
section
variable {p : ℕ} [Fact p.Prime]
namespace Gadgets.SHA256
/-!
# Σ₁ (upper sigma 1) for SHA-256
Σ₁(x) = ROTR6(x) XOR ROTR11(x) XOR ROTR25(x)
Two xor32 calls = 64 witnesses total.
Mirrors `UpperSigma0` with constants 6, 11, 25 instead of 2, 13, 22.
Reuses the helper le... | import Clean.Gadgets.SHA256.LowerSigma0
section
variable {p : ℕ} [Fact p.Prime]
namespace Gadgets.SHA256
/-!
# Σ₁ (upper sigma 1) for SHA-256
Σ₁(x) = ROTR6(x) XOR ROTR11(x) XOR ROTR25(x)
Two xor32 calls = 64 witnesses total.
Mirrors `UpperSigma0` with constants 6, 11, 25 instead of 2, 13, 22.
Reuses the helper le... | @@ -36,10 +36,128 @@
/-! ## Spec proof factored out to avoid kernel deep recursion -/
+private lemma spec_of_constraint
+ (input z : fields 32 (F p))
+ (hx : Normalized input)
+ (h_z : ∀ i : Fin 32, z[i] =
+ (input[(i + 6).val] + input[(i + 11).val] -
+ 2 * input[(i + 6).val] * input[(i + 11).... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_de893445c837_0 | 9b178357d056008e | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/Addition8/Theorems.lean | Theorems | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "soundness",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros hx hy hout carry_in_bool carry_out_bool h\n have carry_in_bound := IsBool.val_lt_two carry_in_bool\n\n rcases carry_out... | [
{
"name": "soundness_zero_carry",
"text": "theorem soundness_zero_carry (x y out carry_in : F p):\n x.val < 256 -> y.val < 256 -> out.val < 256 -> carry_in.val < 2 ->\n (carry_in + x + y - out = 0 -> (out.val = (carry_in.val + x.val + y.val) % 256\n ∧ (carry_in.val + x.val + y.val) / 256 = 0)) := ... | [
{
"name": "soundness",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 62,
"n_chars": 2253,
"n_subproofs": 7,
"n_tactics": 39,
"cyclomatic": 4,
"n_automation": 8,
"n_rewrites": 11,
"n_structural": 8,
"automation_only": false,
"max_nesting":... | 2 | import Clean.Utils.Field
import Clean.Gadgets.Boolean
namespace Gadgets.Addition8.Theorems
variable {p : ℕ} [Fact p.Prime]
variable [p_large_enough: Fact (p > 512)]
/-
First part of the soundness direction: case of zero carry
-/
theorem soundness_one_carry (x y out carry_in : F p):
x.val < 256 -> y.val < 256 ->... | import Clean.Utils.Field
import Clean.Gadgets.Boolean
namespace Gadgets.Addition8.Theorems
variable {p : ℕ} [Fact p.Prime]
variable [p_large_enough: Fact (p > 512)]
/-
First part of the soundness direction: case of zero carry
-/
theorem soundness_zero_carry (x y out carry_in : F p):
x.val < 256 -> y.val < 256 -... | @@ -8,6 +8,24 @@
/-
First part of the soundness direction: case of zero carry
-/
+theorem soundness_zero_carry (x y out carry_in : F p):
+ x.val < 256 -> y.val < 256 -> out.val < 256 -> carry_in.val < 2 ->
+ (carry_in + x + y - out = 0 -> (out.val = (carry_in.val + x.val + y.val) % 256
+ ∧ (carry_in.val ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_0ea10fd31518_1 | dcf3748d7f5ad4e7 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/BLAKE3/FinalizeChunk.lean | FinalizeChunk | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "completeness",
"depth": 1,
"n_commands": 0,
"n_lines": 66,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n circuit_proof_start\n apply And.intro\n · trivial\n rcases h_env with ⟨h_iszero, h_env⟩\n specialize h_iszero trivial\n ... | [
{
"name": "ZMod_val_chunkEnd",
"text": "private lemma ZMod_val_chunkEnd :\n ZMod.val (n:=p) ↑chunkEnd = 2 := by\n have := p_large_enough.elim\n simp only [ZMod.val_natCast, chunkEnd, pow_one]\n rw [Nat.mod_eq_of_lt]; omega\n\nomit p_large_enough in\n",
"fan_in": 1,
"n_lines": 8,
"n_chars":... | [
{
"name": "completeness",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 68,
"n_chars": 1791,
"n_subproofs": 0,
"n_tactics": 66,
"cyclomatic": 12,
"n_automation": 38,
"n_rewrites": 4,
"n_structural": 19,
"automation_only": false,
"max_nest... | 2 | import Clean.Gadgets.BLAKE3.Compress
import Clean.Gadgets.BLAKE3.ApplyRounds
import Clean.Gadgets.BLAKE3.BLAKE3State
import Clean.Gadgets.Or.Or32
import Clean.Gadgets.IsZero
import Clean.Specs.BLAKE3
import Clean.Tables.BLAKE3.ProcessBlocksInductive
import Clean.Circuit.Provable
import Clean.Utils.Tactics
namespace Ga... | import Clean.Gadgets.BLAKE3.Compress
import Clean.Gadgets.BLAKE3.ApplyRounds
import Clean.Gadgets.BLAKE3.BLAKE3State
import Clean.Gadgets.Or.Or32
import Clean.Gadgets.IsZero
import Clean.Specs.BLAKE3
import Clean.Tables.BLAKE3.ProcessBlocksInductive
import Clean.Circuit.Provable
import Clean.Utils.Tactics
namespace Ga... | @@ -108,6 +108,13 @@
output.map U32.value = Specs.BLAKE3.finalizeChunk chunk_state input.base_flags.value ∧
(∀ i : Fin 8, output[i].Normalized)
+private lemma ZMod_val_chunkEnd :
+ ZMod.val (n:=p) ↑chunkEnd = 2 := by
+ have := p_large_enough.elim
+ simp only [ZMod.val_natCast, chunkEnd, pow_one]
+ rw [Nat... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_6f2f9bcaab78_0 | 9a5cce1ece457f4e | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Circuit/WitnessIR.lean | WitnessIR | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "FExpr.eval_getElem",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eval_fields', Vector.getElem_map]",
"n_chars": 43,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1... | [
{
"name": "eval_fields'",
"text": "/-- `Witgen.eval` on `fields n` is elementwise evaluation (the witgen analogue of\n`ProvableType.eval_fields`). -/\ntheorem eval_fields' [FiniteField F] {n : ℕ} (ctx : Ctx F) (xs : Vector (FExpr F) n) :\n Witgen.eval (M := fields n) ctx xs = xs.map (FExpr.eval ctx) := r... | [
{
"name": "FExpr.eval_getElem",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 710,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nes... | 1 | import Clean.Circuit.Expression
import Clean.Utils.Field
import Clean.Utils.FiniteField
import Clean.Utils.Vector
import Clean.Circuit.Provable
/-!
# Witness-generation IR
A deep-embedded IR for witness-generation callbacks
## Design
A witness program (`WitgenIR F m`) is either
- `native f` — an arbitrary Lean clos... | import Clean.Circuit.Expression
import Clean.Utils.Field
import Clean.Utils.FiniteField
import Clean.Utils.Vector
import Clean.Circuit.Provable
/-!
# Witness-generation IR
A deep-embedded IR for witness-generation callbacks
## Design
A witness program (`WitgenIR F m`) is either
- `native f` — an arbitrary Lean clos... | @@ -302,6 +302,11 @@
(compute : ProverEnvironment F → value F) : WitgenIR F (size value) :=
.native fun env => compute env |> toElements
+/-- `Witgen.eval` on `fields n` is elementwise evaluation (the witgen analogue of
+`ProvableType.eval_fields`). -/
+theorem eval_fields' [FiniteField F] {n : ℕ} (ctx : Ctx ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_0 | bdaf2ed67cd9d3ff | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 6 | [
{
"theorem_name": "ext_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor; simp_all; apply ext",
"n_chars": 38,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automat... | [
{
"name": "ext",
"text": "theorem ext {x y : F p} (h : x.val = y.val) : x = y := by\n cases p; cases p_ne_zero rfl\n exact Fin.ext h\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 108,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"... | [
{
"name": "ext_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 4,
"n_chars": 96,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting": 2
}
... | 1 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -25,8 +25,13 @@
theorem p_ne_zero : p ≠ 0 := p_prime.elim.ne_zero
-theorem ext_iff {x y : F p} : x = y ↔ x.val = y.val := sorry
+theorem ext {x y : F p} (h : x.val = y.val) : x = y := by
+ cases p; cases p_ne_zero rfl
+ exact Fin.ext h
+theorem ext_iff {x y : F p} : x = y ↔ x.val = y.val := by
+ constructo... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_1 | 1b10472ab8ce4b05 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 3 | [
{
"theorem_name": "val_eq_256",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " val_lt_p 256 (by linarith [p_large_enough.elim])",
"n_chars": 49,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "val_lt_p",
"text": "theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by\n intro x_lt_p\n have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x_lt_p\n have x_mod_is_x : x % p = x := (Nat.mod_eq_iff_lt p_ne_zero).mpr x_lt_p\n rw [ZMod.val_natCast, x_mod_is_x]\n\n",
"fan_in": 3,
... | [
{
"name": "val_eq_256",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 3,
"n_chars": 127,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 1
... | 1 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -25,8 +25,14 @@
theorem p_ne_zero : p ≠ 0 := p_prime.elim.ne_zero
-lemma val_eq_256 [p_large_enough: Fact (p > 512)] : (256 : F p).val = 256 := sorry
+theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by
+ intro x_lt_p
+ have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x_lt_p
+ have x_mod_is_x : x... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_2 | 3ba309fd134548ad | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 6 | [
{
"theorem_name": "ext_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor; simp_all; apply ext",
"n_chars": 38,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automat... | [
{
"name": "ext",
"text": "theorem ext {x y : F p} (h : x.val = y.val) : x = y := by\n cases p; cases p_ne_zero rfl\n exact Fin.ext h\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 108,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"... | [
{
"name": "natToField_eq_natCast",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 5,
"n_chars": 150,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_n... | 3 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -25,6 +25,10 @@
theorem p_ne_zero : p ≠ 0 := p_prime.elim.ne_zero
+theorem ext {x y : F p} (h : x.val = y.val) : x = y := by
+ cases p; cases p_ne_zero rfl
+ exact Fin.ext h
+
theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by
intro x_lt_p
have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_3 | c84b89dd751ff094 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "mod_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [mod_val]\n exact Nat.mod_lt x.val (by norm_num)",
"n_chars": 57,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic"... | [
{
"name": "mod_val",
"text": "lemma mod_val {x : F p} {c : ℕ+} {lt : c < p} : (mod x c lt).val = x.val % c := by\n rw [mod, ZMod.val_natCast_of_lt]\n grw [Nat.mod_lt x.val c.pos]\n exact lt\n\n",
"fan_in": 2,
"n_lines": 6,
"n_chars": 163,
"n_subproofs": 0,
"n_tactics": 4,
"cycloma... | [
{
"name": "mod_lt",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 133,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2
}
... | 1 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -93,8 +93,15 @@
def floorDiv (x : F p) (c : ℕ+) : F p := (x.val / c : ℕ)
-theorem mod_lt {x : F p} {c : ℕ+} {lt : c < p} : (mod x c lt).val < c := sorry
+lemma mod_val {x : F p} {c : ℕ+} {lt : c < p} : (mod x c lt).val = x.val % c := by
+ rw [mod, ZMod.val_natCast_of_lt]
+ grw [Nat.mod_lt x.val c.pos]
+ exac... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_4 | a18864ff0e4a9295 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 3 | [
{
"theorem_name": "floorDiv_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [floorDiv_val]\n exact Nat.div_lt_of_lt_mul h",
"n_chars": 54,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomati... | [
{
"name": "floorDiv_val",
"text": "lemma floorDiv_val {x : F p} {c : ℕ+} : (floorDiv x c).val = x.val / c := by\n rw [floorDiv, ZMod.val_natCast_of_lt]\n grw [Nat.div_le_self]\n apply ZMod.val_lt\n\n",
"fan_in": 3,
"n_lines": 6,
"n_chars": 164,
"n_subproofs": 0,
"n_tactics": 4,
"c... | [
{
"name": "floorDiv_lt",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 154,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2... | 1 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -98,11 +98,18 @@
grw [Nat.mod_lt x.val c.pos]
exact lt
+lemma floorDiv_val {x : F p} {c : ℕ+} : (floorDiv x c).val = x.val / c := by
+ rw [floorDiv, ZMod.val_natCast_of_lt]
+ grw [Nat.div_le_self]
+ apply ZMod.val_lt
+
theorem mod_lt {x : F p} {c : ℕ+} {lt : c < p} : (mod x c lt).val < c := by
rw [mod... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_5 | f4b4d705464e4f88 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 3 | [
{
"theorem_name": "floorDiv_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [floorDiv_val]\n exact Nat.div_lt_of_lt_mul h",
"n_chars": 54,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomati... | [
{
"name": "floorDiv_val",
"text": "lemma floorDiv_val {x : F p} {c : ℕ+} : (floorDiv x c).val = x.val / c := by\n rw [floorDiv, ZMod.val_natCast_of_lt]\n grw [Nat.div_le_self]\n apply ZMod.val_lt\n\n",
"fan_in": 3,
"n_lines": 6,
"n_chars": 164,
"n_subproofs": 0,
"n_tactics": 4,
"c... | [
{
"name": "val_mul_floorDiv_self",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 358,
"n_subproofs": 2,
"n_tactics": 7,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_n... | 1 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -98,11 +98,21 @@
grw [Nat.mod_lt x.val c.pos]
exact lt
+lemma floorDiv_val {x : F p} {c : ℕ+} : (floorDiv x c).val = x.val / c := by
+ rw [floorDiv, ZMod.val_natCast_of_lt]
+ grw [Nat.div_le_self]
+ apply ZMod.val_lt
+
theorem mod_lt {x : F p} {c : ℕ+} {lt : c < p} : (mod x c lt).val < c := by
rw [mod... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_6 | 427dd9e7a6cba0cd | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 6 | [
{
"theorem_name": "ext_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor; simp_all; apply ext",
"n_chars": 38,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automat... | [
{
"name": "ext",
"text": "theorem ext {x y : F p} (h : x.val = y.val) : x = y := by\n cases p; cases p_ne_zero rfl\n exact Fin.ext h\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 108,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"... | [
{
"name": "mod_add_floorDiv",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 12,
"n_chars": 399,
"n_subproofs": 2,
"n_tactics": 10,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,
"max_nest... | 4 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -25,6 +25,10 @@
theorem p_ne_zero : p ≠ 0 := p_prime.elim.ne_zero
+theorem ext {x y : F p} (h : x.val = y.val) : x = y := by
+ cases p; cases p_ne_zero rfl
+ exact Fin.ext h
+
theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by
intro x_lt_p
have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_7 | 07c930d0db284784 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 6 | [
{
"theorem_name": "ext_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor; simp_all; apply ext",
"n_chars": 38,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automat... | [
{
"name": "ext",
"text": "theorem ext {x y : F p} (h : x.val = y.val) : x = y := by\n cases p; cases p_ne_zero rfl\n exact Fin.ext h\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 108,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"... | [
{
"name": "mul_val_of_dvd",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 26,
"n_chars": 823,
"n_subproofs": 6,
"n_tactics": 24,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 7,
"n_structural": 8,
"automation_only": false,
"max_nestin... | 2 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -25,6 +25,10 @@
theorem p_ne_zero : p ≠ 0 := p_prime.elim.ne_zero
+theorem ext {x y : F p} (h : x.val = y.val) : x = y := by
+ cases p; cases p_ne_zero rfl
+ exact Fin.ext h
+
theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by
intro x_lt_p
have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_8 | fbf7cb84bb5c71e6 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 6 | [
{
"theorem_name": "ext_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor; simp_all; apply ext",
"n_chars": 38,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automat... | [
{
"name": "ext",
"text": "theorem ext {x y : F p} (h : x.val = y.val) : x = y := by\n cases p; cases p_ne_zero rfl\n exact Fin.ext h\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 108,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"... | [
{
"name": "mul_nat_val_of_dvd",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 8,
"n_chars": 297,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_nest... | 3 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -25,6 +25,10 @@
theorem p_ne_zero : p ≠ 0 := p_prime.elim.ne_zero
+theorem ext {x y : F p} (h : x.val = y.val) : x = y := by
+ cases p; cases p_ne_zero rfl
+ exact Fin.ext h
+
theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by
intro x_lt_p
have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_9 | 5bec2e56bb3d6cc9 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 6 | [
{
"theorem_name": "ext_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor; simp_all; apply ext",
"n_chars": 38,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automat... | [
{
"name": "ext",
"text": "theorem ext {x y : F p} (h : x.val = y.val) : x = y := by\n cases p; cases p_ne_zero rfl\n exact Fin.ext h\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 108,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"... | [
{
"name": "mul_nat_val_eq_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 18,
"n_chars": 658,
"n_subproofs": 1,
"n_tactics": 13,
"cyclomatic": 3,
"n_automation": 0,
"n_rewrites": 5,
"n_structural": 7,
"automation_only": false,
"max_ne... | 4 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -25,6 +25,10 @@
theorem p_ne_zero : p ≠ 0 := p_prime.elim.ne_zero
+theorem ext {x y : F p} (h : x.val = y.val) : x = y := by
+ cases p; cases p_ne_zero rfl
+ exact Fin.ext h
+
theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by
intro x_lt_p
have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_10 | 7422eedc01d0c9ee | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 3 | [
{
"theorem_name": "val_eq_256",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " val_lt_p 256 (by linarith [p_large_enough.elim])",
"n_chars": 49,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "val_lt_p",
"text": "theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by\n intro x_lt_p\n have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x_lt_p\n have x_mod_is_x : x % p = x := (Nat.mod_eq_iff_lt p_ne_zero).mpr x_lt_p\n rw [ZMod.val_natCast, x_mod_is_x]\n\n",
"fan_in": 3,
... | [
{
"name": "two_val",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 85,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
}
... | 1 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -25,8 +25,14 @@
theorem p_ne_zero : p ≠ 0 := p_prime.elim.ne_zero
-lemma val_eq_256 [p_large_enough: Fact (p > 512)] : (256 : F p).val = 256 := sorry
+theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by
+ intro x_lt_p
+ have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x_lt_p
+ have x_mod_is_x : x... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_11 | 3c40ac00e989aaea | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 3 | [
{
"theorem_name": "val_eq_256",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " val_lt_p 256 (by linarith [p_large_enough.elim])",
"n_chars": 49,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
... | [
{
"name": "val_lt_p",
"text": "theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by\n intro x_lt_p\n have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x_lt_p\n have x_mod_is_x : x % p = x := (Nat.mod_eq_iff_lt p_ne_zero).mpr x_lt_p\n rw [ZMod.val_natCast, x_mod_is_x]\n\n",
"fan_in": 3,
... | [
{
"name": "two_pow_val",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 5,
"n_chars": 141,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2... | 3 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -25,8 +25,14 @@
theorem p_ne_zero : p ≠ 0 := p_prime.elim.ne_zero
-lemma val_eq_256 [p_large_enough: Fact (p > 512)] : (256 : F p).val = 256 := sorry
+theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by
+ intro x_lt_p
+ have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x_lt_p
+ have x_mod_is_x : x... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_12 | fe8b128fb421a7c5 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "mod_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [mod_val]\n exact Nat.mod_lt x.val (by norm_num)",
"n_chars": 57,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic"... | [
{
"name": "mod_val",
"text": "lemma mod_val {x : F p} {c : ℕ+} {lt : c < p} : (mod x c lt).val = x.val % c := by\n rw [mod, ZMod.val_natCast_of_lt]\n grw [Nat.mod_lt x.val c.pos]\n exact lt\n\n",
"fan_in": 2,
"n_lines": 6,
"n_chars": 163,
"n_subproofs": 0,
"n_tactics": 4,
"cycloma... | [
{
"name": "mod256_lt",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 3,
"n_chars": 79,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 1
... | 1 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -93,8 +93,15 @@
def floorDiv (x : F p) (c : ℕ+) : F p := (x.val / c : ℕ)
-theorem mod_lt {x : F p} {c : ℕ+} {lt : c < p} : (mod x c lt).val < c := sorry
+lemma mod_val {x : F p} {c : ℕ+} {lt : c < p} : (mod x c lt).val = x.val % c := by
+ rw [mod, ZMod.val_natCast_of_lt]
+ grw [Nat.mod_lt x.val c.pos]
+ exac... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_13 | a1041ce8c1fcd6b9 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 6 | [
{
"theorem_name": "ext_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor; simp_all; apply ext",
"n_chars": 38,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automat... | [
{
"name": "ext",
"text": "theorem ext {x y : F p} (h : x.val = y.val) : x = y := by\n cases p; cases p_ne_zero rfl\n exact Fin.ext h\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 108,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"... | [
{
"name": "floorDiv256_bool",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 12,
"n_chars": 465,
"n_subproofs": 1,
"n_tactics": 16,
"cyclomatic": 4,
"n_automation": 3,
"n_rewrites": 3,
"n_structural": 8,
"automation_only": false,
"max_nest... | 2 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -25,6 +25,10 @@
theorem p_ne_zero : p ≠ 0 := p_prime.elim.ne_zero
+theorem ext {x y : F p} (h : x.val = y.val) : x = y := by
+ cases p; cases p_ne_zero rfl
+ exact Fin.ext h
+
theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by
intro x_lt_p
have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_14 | 5631943f4a942a7c | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 6 | [
{
"theorem_name": "ext_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor; simp_all; apply ext",
"n_chars": 38,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automat... | [
{
"name": "ext",
"text": "theorem ext {x y : F p} (h : x.val = y.val) : x = y := by\n cases p; cases p_ne_zero rfl\n exact Fin.ext h\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 108,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"... | [
{
"name": "mod_add_div256",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 4,
"n_chars": 140,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting"... | 5 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -25,6 +25,10 @@
theorem p_ne_zero : p ≠ 0 := p_prime.elim.ne_zero
+theorem ext {x y : F p} (h : x.val = y.val) : x = y := by
+ cases p; cases p_ne_zero rfl
+ exact Fin.ext h
+
theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by
intro x_lt_p
have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_15 | 0cc3ae2a1f99f57b | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 6 | [
{
"theorem_name": "ext_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor; simp_all; apply ext",
"n_chars": 38,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automat... | [
{
"name": "ext",
"text": "theorem ext {x y : F p} (h : x.val = y.val) : x = y := by\n cases p; cases p_ne_zero rfl\n exact Fin.ext h\n\n",
"fan_in": 6,
"n_lines": 5,
"n_chars": 108,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"... | [
{
"name": "splitTwoBytes_concatTwoBytes",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 304,
"n_subproofs": 1,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
... | 1 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -25,6 +25,10 @@
theorem p_ne_zero : p ≠ 0 := p_prime.elim.ne_zero
+theorem ext {x y : F p} (h : x.val = y.val) : x = y := by
+ cases p; cases p_ne_zero rfl
+ exact Fin.ext h
+
theorem val_lt_p {p : ℕ} (x : ℕ) : (x < p) → (x : F p).val = x := by
intro x_lt_p
have p_ne_zero : p ≠ 0 := Nat.ne_zero_of_lt x... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_16 | 9a2b2dab23fb00fc | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "fromByte_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n dsimp [fromByte]\n rw [natToField_val]\n exact x.is_lt",
"n_chars": 60,
"n_subproofs": 0,
"n_tactics": 4,
"cy... | [
{
"name": "natToField_val",
"text": "theorem natToField_val {n : ℕ} (lt : n < p) : (natToField n lt).val = n := by\n cases p\n · exact False.elim (Nat.not_lt_zero n lt)\n · rfl\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 145,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
... | [
{
"name": "fromByte_lt",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 128,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2... | 1 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -72,6 +72,11 @@
| 0 => False.elim (Nat.not_lt_zero n lt)
| _ + 1 => ⟨ n, lt ⟩
+theorem natToField_val {n : ℕ} (lt : n < p) : (natToField n lt).val = n := by
+ cases p
+ · exact False.elim (Nat.not_lt_zero n lt)
+ · rfl
+
def less_than_p (x : F p) : x.val < p := by
rcases p with _ | n; cases p_ne_zero ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_2a02ca99776f_17 | 876f687af03ca4e0 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/Field.lean | Field | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "fromByte_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n dsimp [fromByte]\n apply FieldUtils.natToField_of_val_eq_iff",
"n_chars": 66,
"n_subproofs": 0,
"n_tactics": 3,
... | [
{
"name": "natToField_of_val_eq_iff",
"text": "theorem natToField_of_val_eq_iff {x : F p} {lt : x.val < p} : natToField (x.val) lt = x := by\n cases p\n · exact False.elim (Nat.not_lt_zero x.val lt)\n · dsimp only [natToField]; rfl\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 188,
"n_subpr... | [
{
"name": "fromByte_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 154,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": 2... | 1 | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | import Mathlib.Algebra.Field.ZMod
import Mathlib.Algebra.Order.Star.Basic
import Mathlib.Analysis.Normed.Ring.Lemmas
import Clean.Circuit.SimpGadget
-- main field definition
abbrev F p := ZMod p
instance (p : ℕ) [Fact p.Prime]: Field (F p) := ZMod.instField p
instance (p : ℕ) [Fact p.Prime] : Fintype (F p) := ZMod.fin... | @@ -72,6 +72,11 @@
| 0 => False.elim (Nat.not_lt_zero n lt)
| _ + 1 => ⟨ n, lt ⟩
+theorem natToField_of_val_eq_iff {x : F p} {lt : x.val < p} : natToField (x.val) lt = x := by
+ cases p
+ · exact False.elim (Nat.not_lt_zero x.val lt)
+ · dsimp only [natToField]; rfl
+
def less_than_p (x : F p) : x.val < p :... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c75dbe5c8b75_0 | 19141dcec6e07f6a | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Circomlib/BinSub.lean | BinSub | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "foldl_explicit",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction m with\n | zero => simp_all +arith [Expression.eval]\n | succ m' ihm' =>\n specialize (ihm' (Nat.le_of_add_r... | [
{
"name": "foldl_acc1_powerof2",
"text": "lemma foldl_acc1_powerof2 {n : ℕ} (env : Environment (F p)) (f : Expression (F p) × Expression (F p) → ℕ → Expression (F p)) :\n Expression.eval env (Fin.foldl n (fun acc i ↦ (f acc i, acc.2 + acc.2)) (0, 1)).2 = (2^n : F p) := by\n induction n with\n | zero => s... | [
{
"name": "foldl_explicit",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 1051,
"n_subproofs": 0,
"n_tactics": 14,
"cyclomatic": 3,
"n_automation": 3,
"n_rewrites": 5,
"n_structural": 3,
"automation_only": false,
"max_nesti... | 1 | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Gadgets.Bits
import Clean.Gadgets.Boolean
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime]
-- Define a 2D vector type for BinSub inputs
-- Represents 2 operands, each with n bits
-- This is a vector of 2 elements, where each element is a vec... | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Gadgets.Bits
import Clean.Gadgets.Boolean
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime]
-- Define a 2D vector type for BinSub inputs
-- Represents 2 operands, each with n bits
-- This is a vector of 2 elements, where each element is a vec... | @@ -46,6 +46,13 @@
simp [fieldFromBits_as_sum]
-- Lemma: (Left) folding `n` times over an accumulator that starts as `(0, 1)`, and doubling each time the right element of the accumulator, results in having `2^n` as the right element of the pair
+lemma foldl_acc1_powerof2 {n : ℕ} (env : Environment (F p)) (f : Exp... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c75dbe5c8b75_1 | 437bf5cdaf216e51 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Circomlib/BinSub.lean | BinSub | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "lin_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [lin_val_eq in0 in1 h0 h1 h_p]; omega",
"n_chars": 46,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
... | [
{
"name": "lin_val_eq",
"text": "lemma lin_val_eq {p : ℕ} [Fact p.Prime] {n : ℕ} (in0 in1 : F p)\n (h0 : in0.val < 2^n) (h1 : in1.val < 2^n) (h_p : 2^(n+1) < p) :\n (in0 + 2^n - in1).val = in0.val + 2^n - in1.val := by\n have h_sub_eq : (in0 + 2^n - in1 : F p).val = (in0.val + 2^n - in1.val) % p := b... | [
{
"name": "lin_bound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 274,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 1 | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Gadgets.Bits
import Clean.Gadgets.Boolean
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime]
-- Define a 2D vector type for BinSub inputs
-- Represents 2 operands, each with n bits
-- This is a vector of 2 elements, where each element is a vec... | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Gadgets.Bits
import Clean.Gadgets.Boolean
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime]
-- Define a 2D vector type for BinSub inputs
-- Represents 2 operands, each with n bits
-- This is a vector of 2 elements, where each element is a vec... | @@ -68,8 +68,19 @@
| inr h1 => rw [h1]; left; rw [foldl_acc1_powerof2 env (n:=m') (fun acc i => acc.1 + var { index := offset + ↑i } * acc.2)]
-- Lemma: The value of `in0 + 2^n - in1` in the field is equal to the integer arithmetic result `in0.val + 2^n - in1.val`, provided inputs are small enough (`< 2^n`) and... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c75dbe5c8b75_2 | 842b92edcb529594 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Circomlib/BinSub.lean | BinSub | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "soundness_lhs_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply inputLinearSub_eval_eq_sub; assumption",
"n_chars": 50,
"n_subproofs": 0,
"n_tactics": 3,
"cycloma... | [
{
"name": "inputLinearSub_eval_eq_sub",
"text": "lemma inputLinearSub_eval_eq_sub {n : ℕ} [NeZero n] (env : Environment (F p))\n (input : Var (BinSubInput n) (F p)) (input_val : BinSubInput n (F p)) (h_eval : eval env input = input_val) :\n Expression.eval env (inputLinearSub n input) =\n fieldFrom... | [
{
"name": "soundness_lhs_eval",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 394,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nest... | 1 | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Gadgets.Bits
import Clean.Gadgets.Boolean
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime]
-- Define a 2D vector type for BinSub inputs
-- Represents 2 operands, each with n bits
-- This is a vector of 2 elements, where each element is a vec... | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Gadgets.Bits
import Clean.Gadgets.Boolean
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime]
-- Define a 2D vector type for BinSub inputs
-- Represents 2 operands, each with n bits
-- This is a vector of 2 elements, where each element is a vec... | @@ -35,6 +35,17 @@
Fin.foldl n (fun lin k => lin + inp[0][k] * (2^k.val : F p) - (inp[1][k] * (2^k.val : F p))) (2^n : F p)
-- Lemma: evaluating `inputLinearSub` corresponds to the circuit's desired output
+lemma inputLinearSub_eval_eq_sub {n : ℕ} [NeZero n] (env : Environment (F p))
+ (input : Var (BinSubInput ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c75dbe5c8b75_3 | bc993a7339684156 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Circomlib/BinSub.lean | BinSub | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "input_fieldFromBits_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply fieldFromBits_bound\n intro i\n exact h_assumptions j i (by fin_cases j <;> decide) i.isLt",
"n_chars... | [
{
"name": "fieldFromBits_bound",
"text": "lemma fieldFromBits_bound {n : ℕ} (bits : Vector (F p) n) (h_bool : ∀ i : Fin n, IsBool bits[i]) :\n (fieldFromBits bits).val < 2^n := by\n apply fieldFromBits_lt\n intro i hi\n exact h_bool ⟨i, hi⟩\n\n-- Lemma: fieldFromBits of input bits is bounded\n",
"... | [
{
"name": "input_fieldFromBits_bound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 349,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"m... | 1 | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Gadgets.Bits
import Clean.Gadgets.Boolean
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime]
-- Define a 2D vector type for BinSub inputs
-- Represents 2 operands, each with n bits
-- This is a vector of 2 elements, where each element is a vec... | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Gadgets.Bits
import Clean.Gadgets.Boolean
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime]
-- Define a 2D vector type for BinSub inputs
-- Represents 2 operands, each with n bits
-- This is a vector of 2 elements, where each element is a vec... | @@ -89,8 +89,18 @@
apply inputLinearSub_eval_eq_sub; assumption
-- Lemma: Boolean property from fieldToBits
+lemma fieldFromBits_bound {n : ℕ} (bits : Vector (F p) n) (h_bool : ∀ i : Fin n, IsBool bits[i]) :
+ (fieldFromBits bits).val < 2^n := by
+ apply fieldFromBits_lt
+ intro i hi
+ exact h_bool ⟨i, hi⟩
... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c75dbe5c8b75_4 | 2c92b4267395fb49 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Circomlib/BinSub.lean | BinSub | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "completeness_aux_div",
"depth": 1,
"n_commands": 0,
"n_lines": 29,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [h_env_aux]\n split_ifs with h_if\n · -- Case: Bit is 1\n convert h_if using 1\n · convert h_if.symm using... | [
{
"name": "input_fieldFromBits_bound",
"text": "lemma input_fieldFromBits_bound {n : ℕ} [NeZero n] (input : BinSubInput n (F p)) (h_assumptions : ∀ j i (hj : j < 2) (hi : i < n), IsBool input[j][i]) (j : Fin 2) :\n (fieldFromBits input[j]).val < 2^n := by\n apply fieldFromBits_bound\n intro i\n exact ... | [
{
"name": "completeness_aux_div",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 36,
"n_chars": 2062,
"n_subproofs": 4,
"n_tactics": 29,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 5,
"n_structural": 9,
"automation_only": false,
"max... | 5 | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Gadgets.Bits
import Clean.Gadgets.Boolean
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime]
-- Define a 2D vector type for BinSub inputs
-- Represents 2 operands, each with n bits
-- This is a vector of 2 elements, where each element is a vec... | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Gadgets.Bits
import Clean.Gadgets.Boolean
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime]
-- Define a 2D vector type for BinSub inputs
-- Represents 2 operands, each with n bits
-- This is a vector of 2 elements, where each element is a vec... | @@ -96,6 +96,13 @@
exact h_bool ⟨i, hi⟩
-- Lemma: fieldFromBits of input bits is bounded
+lemma input_fieldFromBits_bound {n : ℕ} [NeZero n] (input : BinSubInput n (F p)) (h_assumptions : ∀ j i (hj : j < 2) (hi : i < n), IsBool input[j][i]) (j : Fin 2) :
+ (fieldFromBits input[j]).val < 2^n := by
+ apply fiel... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_c75dbe5c8b75_5 | 7c303cddd64a7d4f | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Circomlib/BinSub.lean | BinSub | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "completeness_reconstruction",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- 1. Convert Circuit Fold to Summation\n rw [←foldl_explicit (le_refl n) env i₀ h_out_binary]\n -- We verif... | [
{
"name": "completeness_aux_div",
"text": "lemma completeness_aux_div {n : ℕ} [NeZero n] (hnout : 2^(n+1) < p) (env : Environment (F p)) (i₀ : ℕ)\n (input : BinSubInput n (F p)) (h_assumptions : ∀ j i (hj : j < 2) (hi : i < n), IsBool input[j][i])\n (input_var : Var (BinSubInput n) (F p)) (h_input : e... | [
{
"name": "completeness_reconstruction",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 10,
"n_lines": 68,
"n_chars": 2610,
"n_subproofs": 4,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 7,
"n_structural": 2,
"automation_only": false,
... | 8 | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Gadgets.Bits
import Clean.Gadgets.Boolean
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime]
-- Define a 2D vector type for BinSub inputs
-- Represents 2 operands, each with n bits
-- This is a vector of 2 elements, where each element is a vec... | import Clean.Circuit
import Clean.Utils.Bits
import Clean.Gadgets.Bits
import Clean.Gadgets.Boolean
namespace Circomlib
open Utils.Bits
variable {p : ℕ} [Fact p.Prime]
-- Define a 2D vector type for BinSub inputs
-- Represents 2 operands, each with n bits
-- This is a vector of 2 elements, where each element is a vec... | @@ -121,6 +121,41 @@
exact lt_of_le_of_lt (Nat.mod_le _ _) (Nat.lt_of_lt_of_le (ZMod.val_lt _) (by linarith [pow_succ' 2 n]))
-- Lemma: Aux bit equals lin divided by 2^n
+lemma completeness_aux_div {n : ℕ} [NeZero n] (hnout : 2^(n+1) < p) (env : Environment (F p)) (i₀ : ℕ)
+ (input : BinSubInput n (F p)) (h_as... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f596df8e7407_5 | 93c7ccaf1203b5e9 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Examples/FemtoCairo/SpecLemmas.lean | SpecLemmas | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "fetchInstruction_rawInstrType_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [fetchInstruction_rawInstrType_eq_program program pc raw h h_bound]\n aesop",
"n_chars": 84,
... | [
{
"name": "fetchInstruction_rawInstrType_eq_program",
"text": "/-- If fetchInstruction succeeds, rawInstrType is a valid program memory value -/\nlemma fetchInstruction_rawInstrType_eq_program\n {programSize : ℕ} (program : Fin programSize → F p)\n (pc : F p) (raw : Types.RawInstruction (F p))\n (h... | [
{
"name": "fetchInstruction_rawInstrType_bound",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 485,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": fa... | 1 | import Clean.Examples.FemtoCairo.Spec
/-!
# Helper lemmas for FemtoCairo completeness proofs
This file contains lemmas about the FemtoCairo specification that are used
in proving completeness of the circuit.
-/
namespace Examples.FemtoCairo.Spec
open Utils.Bits
open Examples.FemtoCairo.Types
variable {p : ℕ} [Fact p... | import Clean.Examples.FemtoCairo.Spec
/-!
# Helper lemmas for FemtoCairo completeness proofs
This file contains lemmas about the FemtoCairo specification that are used
in proving completeness of the circuit.
-/
namespace Examples.FemtoCairo.Spec
open Utils.Bits
open Examples.FemtoCairo.Types
variable {p : ℕ} [Fact p... | @@ -13,6 +13,34 @@
variable {p : ℕ} [Fact p.Prime] [p_large_enough: Fact (p > 512)]
omit p_large_enough in
+/-- If fetchInstruction succeeds, rawInstrType is a valid program memory value -/
+lemma fetchInstruction_rawInstrType_eq_program
+ {programSize : ℕ} (program : Fin programSize → F p)
+ (pc : F p) (raw ... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_ed30f415d3b3_0 | 28ff36bbcb5dba21 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/IsZero.lean | IsZero | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "soundness",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n circuit_proof_start [IsZeroField.circuit]\n simp only [explicit_provable_type, ProvableType.fromElements_eq_iff] at h_input\n ... | [
{
"name": "foldl_isZero_eq_one_iff",
"text": "/--\nlemma for soundness. Separate because the statement is optimized for induction.\n-/\nlemma foldl_isZero_eq_one_iff {n : ℕ} {vars : Vector (Expression F) n} {vals : Vector F n}\n {env : Environment F} {i₀ : ℕ}\n (h_eval : Vector.map (Expression.eval en... | [
{
"name": "soundness",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 493,
"n_subproofs": 0,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 3,
"n_structural": 3,
"automation_only": false,
"max_nesting": 4... | 1 | import Clean.Circuit.Basic
import Clean.Circuit.Provable
import Clean.Circuit.Theorems
import Clean.Circuit.Loops
import Clean.Gadgets.IsZeroField
import Clean.Utils.Field
import Clean.Utils.Tactics
namespace Gadgets.IsZero
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {M : TypeMap} [ProvableType M]
/... | import Clean.Circuit.Basic
import Clean.Circuit.Provable
import Clean.Circuit.Theorems
import Clean.Circuit.Loops
import Clean.Gadgets.IsZeroField
import Clean.Utils.Field
import Clean.Utils.Tactics
namespace Gadgets.IsZero
variable {F : Type} [FiniteField F] [DecidableEq F]
variable {M : TypeMap} [ProvableType M]
/... | @@ -37,8 +37,81 @@
def Spec [DecidableEq (M F)] (input : M F) (output : F) : Prop :=
output = if input = 0 then 1 else 0
-theorem soundness [DecidableEq (M F)] : Soundness F (main (M:=M)) Assumptions Spec := sorry
+/--
+lemma for soundness. Separate because the statement is optimized for induction.
+-/
+lemma fol... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_8d156a2f7186_0 | e1f4142515383e4c | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/Addition32/Theorems.lean | Theorems | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "add32_soundness",
"depth": 1,
"n_commands": 0,
"n_lines": 90,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n\n apply_fun ZMod.val at h0 h1 h2 h3\n rw [lift_val1 x0_byte y0_byte carry_in_bool, lift_val2 z0_byte c0_bool] at h0\n rw... | [
{
"name": "lift_val2",
"text": "lemma lift_val2 {x b : (F p)} (x_byte : x.val < 256) (b_bool : IsBool b) :\n (b * 256 + x).val = (b.val * 256 + x.val) := by\n have b_lt_2 := IsBool.val_lt_two b_bool\n field_to_nat\n\nomit p_large_enough in\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 208,
... | [
{
"name": "add32_soundness",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 111,
"n_chars": 4819,
"n_subproofs": 21,
"n_tactics": 80,
"cyclomatic": 3,
"n_automation": 18,
"n_rewrites": 12,
"n_structural": 15,
"automation_only": false,
"max... | 3 | import Clean.Gadgets.Addition8.Addition8FullCarry
import Clean.Types.U32
import Clean.Utils.Field
import Clean.Gadgets.Boolean
variable {p : ℕ} [Fact p.Prime]
variable [p_large_enough: Fact (p > 512)]
namespace Gadgets.Addition32.Theorems
lemma lift_val1 {x y b : (F p)} (x_byte : x.val < 256) (y_byte : y.val < 256) ... | import Clean.Gadgets.Addition8.Addition8FullCarry
import Clean.Types.U32
import Clean.Utils.Field
import Clean.Gadgets.Boolean
variable {p : ℕ} [Fact p.Prime]
variable [p_large_enough: Fact (p > 512)]
namespace Gadgets.Addition32.Theorems
lemma lift_val1 {x y b : (F p)} (x_byte : x.val < 256) (y_byte : y.val < 256) ... | @@ -13,6 +13,12 @@
have b_lt_2 := IsBool.val_lt_two b_bool
field_to_nat
+lemma lift_val2 {x b : (F p)} (x_byte : x.val < 256) (b_bool : IsBool b) :
+ (b * 256 + x).val = (b.val * 256 + x.val) := by
+ have b_lt_2 := IsBool.val_lt_two b_bool
+ field_to_nat
+
+omit p_large_enough in
lemma zify_bool {b : (F p... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7fe17188af14_0 | 0b93c47ed88330a3 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/Boolean.lean | Boolean | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "land_inherit_left",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases h with h_l0 | h_l1\n · -- Case: l = 0\n left\n rw [h_l0]\n simp only [HAnd.hAnd, AndOp.and]\n have :... | [
{
"name": "nat_of_lt_two",
"text": "/-- If a natural number is less than 2, then it is boolean (0 or 1) -/\ntheorem nat_of_lt_two {x : ℕ} (h : x < 2) : IsBool x := by\n cases x with\n | zero => exact IsBool.zero\n | succ n =>\n cases n with\n | zero => exact IsBool.one\n | succ m =>\n -- Th... | [
{
"name": "land_inherit_left",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 18,
"n_chars": 429,
"n_subproofs": 1,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 3,
"n_structural": 3,
"automation_only": false,
"max_nes... | 1 | import Clean.Circuit.Basic
import Clean.Utils.Field
import Clean.Utils.Tactics.CircuitProofStart
import Mathlib.Data.Nat.Bitwise
/-- A predicate stating that an element is boolean (0 or 1) for any type with 0 and 1 -/
def IsBool {α : Type*} [Zero α] [One α] (x : α) : Prop := x = 0 ∨ x = 1
/-- IsBool is decidable for ... | import Clean.Circuit.Basic
import Clean.Utils.Field
import Clean.Utils.Tactics.CircuitProofStart
import Mathlib.Data.Nat.Bitwise
/-- A predicate stating that an element is boolean (0 or 1) for any type with 0 and 1 -/
def IsBool {α : Type*} [Zero α] [One α] (x : α) : Prop := x = 0 ∨ x = 1
/-- IsBool is decidable for ... | @@ -24,6 +24,20 @@
IsBool x ↔ x * (x - 1) = 0 := by
rw [mul_eq_zero, sub_eq_zero, IsBool]
+/-- If a natural number is less than 2, then it is boolean (0 or 1) -/
+theorem nat_of_lt_two {x : ℕ} (h : x < 2) : IsBool x := by
+ cases x with
+ | zero => exact IsBool.zero
+ | succ n =>
+ cases n with
+ | z... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_7fe17188af14_1 | 5fd5199695236130 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/Boolean.lean | Boolean | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "one_land_of_IsBool",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Nat.land_comm]\n exact land_one_of_IsBool a h",
"n_chars": 55,
"n_subproofs": 0,
"n_tactics": 3,
"c... | [
{
"name": "land_one_of_IsBool",
"text": "/-- If a is boolean (0 or 1), then a &&& 1 = a -/\ntheorem land_one_of_IsBool (a : ℕ) (h : IsBool a) : a &&& 1 = a := by\n rcases h with h0 | h1\n · rw [h0]; norm_num\n · rw [h1]; norm_num\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 193,
"n_subproo... | [
{
"name": "one_land_of_IsBool",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 175,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nest... | 1 | import Clean.Circuit.Basic
import Clean.Utils.Field
import Clean.Utils.Tactics.CircuitProofStart
import Mathlib.Data.Nat.Bitwise
/-- A predicate stating that an element is boolean (0 or 1) for any type with 0 and 1 -/
def IsBool {α : Type*} [Zero α] [One α] (x : α) : Prop := x = 0 ∨ x = 1
/-- IsBool is decidable for ... | import Clean.Circuit.Basic
import Clean.Utils.Field
import Clean.Utils.Tactics.CircuitProofStart
import Mathlib.Data.Nat.Bitwise
/-- A predicate stating that an element is boolean (0 or 1) for any type with 0 and 1 -/
def IsBool {α : Type*} [Zero α] [One α] (x : α) : Prop := x = 0 ∨ x = 1
/-- IsBool is decidable for ... | @@ -24,8 +24,16 @@
IsBool x ↔ x * (x - 1) = 0 := by
rw [mul_eq_zero, sub_eq_zero, IsBool]
+/-- If a is boolean (0 or 1), then a &&& 1 = a -/
+theorem land_one_of_IsBool (a : ℕ) (h : IsBool a) : a &&& 1 = a := by
+ rcases h with h0 | h1
+ · rw [h0]; norm_num
+ · rw [h1]; norm_num
+
/-- If a is boolean (0 o... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_2 | 77e4ff45c2658483 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "drop_take_cycle_same_endpoints",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_n_lt_len : n.val < path.length := n.isLt\n have h_m_lt_len : m.val < path.length := m.isLt\n have ... | [
{
"name": "getLast_drop_take",
"text": "/-- The last element of (path.drop n).take k is path[n + k - 1] when n + k - 1 < path.length. -/\nlemma getLast_drop_take {α : Type*} (path : List α) (n k : ℕ)\n (h_n_lt : n < path.length)\n (h_bound : n + k ≤ path.length)\n (h_k_pos : k > 0) :\n ((path.dr... | [
{
"name": "drop_take_cycle_same_endpoints",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 25,
"n_chars": 1107,
"n_subproofs": 7,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 8,
"n_rewrites": 4,
"n_structural": 0,
"automation_only": false... | 1 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -115,6 +115,23 @@
-- Helper lemmas for sums and finsets
+/-- The last element of (path.drop n).take k is path[n + k - 1] when n + k - 1 < path.length. -/
+lemma getLast_drop_take {α : Type*} (path : List α) (n k : ℕ)
+ (h_n_lt : n < path.length)
+ (h_bound : n + k ≤ path.length)
+ (h_k_pos : k > 0) :
+... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_5 | a045583c8f4351f4 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "head_pair_not_in_tail_zip",
"depth": 1,
"n_commands": 0,
"n_lines": 25,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro h2\n cases t with\n | nil => simp\n | cons h2' t2 =>\n intro h_contra\n cases t2 with\n | nil ... | [
{
"name": "mem_of_mem_zip_fst",
"text": "/-- If a pair is in a zip, its first component is in the first list. -/\nlemma mem_of_mem_zip_fst {α β : Type*} (l1 : List α) (l2 : List β) (a : α) (b : β) :\n (a, b) ∈ l1.zip l2 → a ∈ l1 := by\n intro h_mem\n induction l1 generalizing l2 with\n | nil => simp a... | [
{
"name": "head_pair_not_in_tail_zip",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 29,
"n_chars": 1093,
"n_subproofs": 3,
"n_tactics": 20,
"cyclomatic": 4,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 5,
"automation_only": false,
... | 1 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -115,6 +115,26 @@
-- Helper lemmas for sums and finsets
+/-- If a pair is in a zip, its first component is in the first list. -/
+lemma mem_of_mem_zip_fst {α β : Type*} (l1 : List α) (l2 : List β) (a : α) (b : β) :
+ (a, b) ∈ l1.zip l2 → a ∈ l1 := by
+ intro h_mem
+ induction l1 generalizing l2 with
+ | n... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_6 | ada15b3b2e662a04 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "head_pair_not_in_tail_zip",
"depth": 1,
"n_commands": 0,
"n_lines": 25,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro h2\n cases t with\n | nil => simp\n | cons h2' t2 =>\n intro h_contra\n cases t2 with\n | nil ... | [
{
"name": "mem_of_mem_zip_fst",
"text": "/-- If a pair is in a zip, its first component is in the first list. -/\nlemma mem_of_mem_zip_fst {α β : Type*} (l1 : List α) (l2 : List β) (a : α) (b : β) :\n (a, b) ∈ l1.zip l2 → a ∈ l1 := by\n intro h_mem\n induction l1 generalizing l2 with\n | nil => simp a... | [
{
"name": "nodup_zip_tail",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 18,
"n_chars": 591,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 4,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 5,
"automation_only": false,
"max_nestin... | 2 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -115,6 +115,26 @@
-- Helper lemmas for sums and finsets
+/-- If a pair is in a zip, its first component is in the first list. -/
+lemma mem_of_mem_zip_fst {α β : Type*} (l1 : List α) (l2 : List β) (a : α) (b : β) :
+ (a, b) ∈ l1.zip l2 → a ∈ l1 := by
+ intro h_mem
+ induction l1 generalizing l2 with
+ | n... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_7 | 3d29730440c3f2b2 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "head_pair_not_in_tail_zip",
"depth": 1,
"n_commands": 0,
"n_lines": 25,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro h2\n cases t with\n | nil => simp\n | cons h2' t2 =>\n intro h_contra\n cases t2 with\n | nil ... | [
{
"name": "mem_of_mem_zip_fst",
"text": "/-- If a pair is in a zip, its first component is in the first list. -/\nlemma mem_of_mem_zip_fst {α β : Type*} (l1 : List α) (l2 : List β) (a : α) (b : β) :\n (a, b) ∈ l1.zip l2 → a ∈ l1 := by\n intro h_mem\n induction l1 generalizing l2 with\n | nil => simp a... | [
{
"name": "nodup_transition_count_le_one",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 16,
"n_chars": 641,
"n_subproofs": 3,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
... | 3 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -115,6 +115,26 @@
-- Helper lemmas for sums and finsets
+/-- If a pair is in a zip, its first component is in the first list. -/
+lemma mem_of_mem_zip_fst {α β : Type*} (l1 : List α) (l2 : List β) (a : α) (b : β) :
+ (a, b) ∈ l1.zip l2 → a ∈ l1 := by
+ intro h_mem
+ induction l1 generalizing l2 with
+ | n... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_8 | 90fafc481d61a187 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "sum_countTransitionInPath_fst",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold countAsFirst countTransitionInPath Transition\n -- Goal: ∑ y, ↑(List.count (x, y) (cycle.zip cycle.t... | [
{
"name": "sum_count_pairs_fst",
"text": "/-- Sum of counts of specific pairs equals count of pairs with fixed first component -/\nlemma sum_count_pairs_fst (xs : List (S × S)) (a : S) :\n ∑ b : S, List.count (a, b) xs = List.countP (fun p => p.1 = a) xs := by\n -- Key: each pair (a, b') in xs contribut... | [
{
"name": "sum_countTransitionInPath_fst",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 872,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
... | 1 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -193,9 +193,36 @@
-- So countFirst = countSecond
aesop
+/-- Sum of counts of specific pairs equals count of pairs with fixed first component -/
+lemma sum_count_pairs_fst (xs : List (S × S)) (a : S) :
+ ∑ b : S, List.count (a, b) xs = List.countP (fun p => p.1 = a) xs := by
+ -- Key: each pair (a, b') in... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_9 | 738a90c9f38137d3 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "sum_countTransitionInPath_snd",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold countAsSecond countTransitionInPath Transition\n -- Goal: ∑ y, ↑(List.count (y, x) (cycle.zip cycle.... | [
{
"name": "sum_count_pairs_snd",
"text": "/-- Sum of counts of specific pairs equals count of pairs with fixed second component -/\nlemma sum_count_pairs_snd (xs : List (S × S)) (b : S) :\n ∑ a : S, List.count (a, b) xs = List.countP (fun p => p.2 = b) xs := by\n -- Symmetric to sum_count_pairs_fst\n i... | [
{
"name": "sum_countTransitionInPath_snd",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 875,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
... | 1 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -193,9 +193,36 @@
-- So countFirst = countSecond
aesop
+/-- Sum of counts of specific pairs equals count of pairs with fixed second component -/
+lemma sum_count_pairs_snd (xs : List (S × S)) (b : S) :
+ ∑ a : S, List.count (a, b) xs = List.countP (fun p => p.2 = b) xs := by
+ -- Symmetric to sum_count_p... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_10 | 8547dc452d672fc9 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "sum_countTransitionInPath_fst",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold countAsFirst countTransitionInPath Transition\n -- Goal: ∑ y, ↑(List.count (x, y) (cycle.zip cycle.t... | [
{
"name": "sum_count_pairs_fst",
"text": "/-- Sum of counts of specific pairs equals count of pairs with fixed first component -/\nlemma sum_count_pairs_fst (xs : List (S × S)) (a : S) :\n ∑ b : S, List.count (a, b) xs = List.countP (fun p => p.1 = a) xs := by\n -- Key: each pair (a, b') in xs contribut... | [
{
"name": "cycle_netFlow_zero",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 19,
"n_chars": 688,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 0,
"automation_only": false,
"max_nes... | 4 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -193,6 +193,24 @@
-- So countFirst = countSecond
aesop
+/-- Sum of counts of specific pairs equals count of pairs with fixed first component -/
+lemma sum_count_pairs_fst (xs : List (S × S)) (a : S) :
+ ∑ b : S, List.count (a, b) xs = List.countP (fun p => p.1 = a) xs := by
+ -- Key: each pair (a, b') in... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_11 | 9e2be9ee14dd498d | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "sum_countTransitionInPath_fst",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold countAsFirst countTransitionInPath Transition\n -- Goal: ∑ y, ↑(List.count (x, y) (cycle.zip cycle.t... | [
{
"name": "sum_count_pairs_fst",
"text": "/-- Sum of counts of specific pairs equals count of pairs with fixed first component -/\nlemma sum_count_pairs_fst (xs : List (S × S)) (a : S) :\n ∑ b : S, List.count (a, b) xs = List.countP (fun p => p.1 = a) xs := by\n -- Key: each pair (a, b') in xs contribut... | [
{
"name": "netFlow_removeCycle_eq",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 14,
"n_chars": 565,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max... | 6 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -193,6 +193,24 @@
-- So countFirst = countSecond
aesop
+/-- Sum of counts of specific pairs equals count of pairs with fixed first component -/
+lemma sum_count_pairs_fst (xs : List (S × S)) (a : S) :
+ ∑ b : S, List.count (a, b) xs = List.countP (fun p => p.1 = a) xs := by
+ -- Key: each pair (a, b') in... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_22 | 23256939bf11f78d | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "sum_pos_of_pos_element",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_a_in_sum : f a ≤ ∑ x : α, f x := single_le_sum_of_nonneg f a h_nonneg\n omega",
"n_chars": 95,
"n_su... | [
{
"name": "single_le_sum_of_nonneg",
"text": "/-- A single element is at most the sum of all elements when all are nonnegative. -/\nlemma single_le_sum_of_nonneg {α : Type*} [Fintype α] (f : α → ℤ) (a : α)\n (h_nonneg : ∀ x, f x ≥ 0) :\n f a ≤ ∑ x : α, f x := by\n calc f a\n = ∑ x ∈ ({a} : Finset ... | [
{
"name": "sum_pos_of_pos_element",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 360,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_... | 1 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -193,12 +193,23 @@
-- So countFirst = countSecond
aesop
+/-- A single element is at most the sum of all elements when all are nonnegative. -/
+lemma single_le_sum_of_nonneg {α : Type*} [Fintype α] (f : α → ℤ) (a : α)
+ (h_nonneg : ∀ x, f x ≥ 0) :
+ f a ≤ ∑ x : α, f x := by
+ calc f a
+ = ∑ x ∈ ({a}... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_23 | 65ae7a632a91aadb | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 23 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "sum_pos_of_pos_element",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_a_in_sum : f a ≤ ∑ x : α, f x := single_le_sum_of_nonneg f a h_nonneg\n omega",
"n_chars": 95,
"n_su... | [
{
"name": "single_le_sum_of_nonneg",
"text": "/-- A single element is at most the sum of all elements when all are nonnegative. -/\nlemma single_le_sum_of_nonneg {α : Type*} [Fintype α] (f : α → ℤ) (a : α)\n (h_nonneg : ∀ x, f x ≥ 0) :\n f a ≤ ∑ x : α, f x := by\n calc f a\n = ∑ x ∈ ({a} : Finset ... | [
{
"name": "sum_nat_cast_pos",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 10,
"n_chars": 317,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesti... | 2 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -193,12 +193,23 @@
-- So countFirst = countSecond
aesop
+/-- A single element is at most the sum of all elements when all are nonnegative. -/
+lemma single_le_sum_of_nonneg {α : Type*} [Fintype α] (f : α → ℤ) (a : α)
+ (h_nonneg : ∀ x, f x ≥ 0) :
+ f a ≤ ∑ x : α, f x := by
+ calc f a
+ = ∑ x ∈ ({a}... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_24 | a93abb57e7b4a530 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 24 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "sum_pos_of_pos_element",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h_a_in_sum : f a ≤ ∑ x : α, f x := single_le_sum_of_nonneg f a h_nonneg\n omega",
"n_chars": 95,
"n_su... | [
{
"name": "single_le_sum_of_nonneg",
"text": "/-- A single element is at most the sum of all elements when all are nonnegative. -/\nlemma single_le_sum_of_nonneg {α : Type*} [Fintype α] (f : α → ℤ) (a : α)\n (h_nonneg : ∀ x, f x ≥ 0) :\n f a ≤ ∑ x : α, f x := by\n calc f a\n = ∑ x ∈ ({a} : Finset ... | [
{
"name": "leaf_has_negative_netFlow",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 22,
"n_chars": 781,
"n_subproofs": 4,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
... | 3 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -193,12 +193,23 @@
-- So countFirst = countSecond
aesop
+/-- A single element is at most the sum of all elements when all are nonnegative. -/
+lemma single_le_sum_of_nonneg {α : Type*} [Fintype α] (f : α → ℤ) (a : α)
+ (h_nonneg : ∀ x, f x ≥ 0) :
+ f a ≤ ∑ x : α, f x := by
+ calc f a
+ = ∑ x ∈ ({a}... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_25 | f3e4af15eea2f8b8 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 25 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "sum_nat_cast_zero_of_not_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply sum_zero_of_all_zero\n intro y\n have h_le := h y\n omega",
"n_chars": 69,
"n_subproofs": 1,
... | [
{
"name": "sum_zero_of_all_zero",
"text": "/-- If all elements of a function are zero, then the sum is zero. -/\nlemma sum_zero_of_all_zero {α : Type*} [Fintype α] (f : α → ℕ) (h : ∀ x, f x = 0) :\n ∑ x : α, (f x : ℤ) = 0 := by\n simp [h]\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 212,
... | [
{
"name": "sum_nat_cast_zero_of_not_pos",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 296,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
... | 1 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -193,10 +193,19 @@
-- So countFirst = countSecond
aesop
+/-- If all elements of a function are zero, then the sum is zero. -/
+lemma sum_zero_of_all_zero {α : Type*} [Fintype α] (f : α → ℕ) (h : ∀ x, f x = 0) :
+ ∑ x : α, (f x : ℤ) = 0 := by
+ simp [h]
+
/-- Sum of natural numbers cast to integers is ze... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_26 | 018a6ea12c2c919d | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 26 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "sum_nat_cast_zero_of_not_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply sum_zero_of_all_zero\n intro y\n have h_le := h y\n omega",
"n_chars": 69,
"n_subproofs": 1,
... | [
{
"name": "sum_zero_of_all_zero",
"text": "/-- If all elements of a function are zero, then the sum is zero. -/\nlemma sum_zero_of_all_zero {α : Type*} [Fintype α] (f : α → ℕ) (h : ∀ x, f x = 0) :\n ∑ x : α, (f x : ℤ) = 0 := by\n simp [h]\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 212,
... | [
{
"name": "positive_netFlow_has_outgoing_edge",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 21,
"n_chars": 732,
"n_subproofs": 3,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": fa... | 3 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -193,6 +193,11 @@
-- So countFirst = countSecond
aesop
+/-- If all elements of a function are zero, then the sum is zero. -/
+lemma sum_zero_of_all_zero {α : Type*} [Fintype α] (f : α → ℕ) (h : ∀ x, f x = 0) :
+ ∑ x : α, (f x : ℤ) = 0 := by
+ simp [h]
+
/-- A sum of natural numbers cast to integers is n... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_46c1e99539c1_30 | ca84632bca99a70c | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Utils/SourceSinkPath.lean | SourceSinkPath | 30 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 55 | 1 | [
{
"theorem_name": "acyclic_has_leaf_aux",
"depth": 1,
"n_commands": 0,
"n_lines": 75,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Get a successor not in path\n obtain ⟨y, h_y_not_in_path, h_edge⟩ := h_has_out\n\n -- Check if y has any outgoin... | [
{
"name": "finset_ssubset_univ_of_not_mem",
"text": "/-- If an element is not in a finset, the finset is a strict subset of univ. -/\nlemma finset_ssubset_univ_of_not_mem {α : Type*} [Fintype α] (s : Finset α) (x : α)\n (h : x ∉ s) :\n s ⊂ Finset.univ := by\n rw [Finset.ssubset_univ_iff]\n intro h_e... | [
{
"name": "exists_path_from_source_to_sink",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 51,
"n_lines": 35,
"n_chars": 1559,
"n_subproofs": 4,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 8,
"automation_only": fal... | 51 | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | import Mathlib.Data.Finset.Basic
import Mathlib.Data.Fintype.Basic
import Mathlib.Data.Fintype.Prod
import Mathlib.Data.List.Basic
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Order.BigOperators.Group.Finset
import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
import Mathlib.Algeb... | @@ -115,6 +115,16 @@
-- Helper lemmas for sums and finsets
+/-- If an element is not in a finset, the finset is a strict subset of univ. -/
+lemma finset_ssubset_univ_of_not_mem {α : Type*} [Fintype α] (s : Finset α) (x : α)
+ (h : x ∉ s) :
+ s ⊂ Finset.univ := by
+ rw [Finset.ssubset_univ_iff]
+ intro h_e... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f87c42644526_0 | 5d66b51ce2f7a8e5 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/FlatEnsemble.lean | FlatEnsemble | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "channel_eq_of_mem_interactionsWith",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [mem_interactionsWith]\n intro h_mem\n rcases h_mem with ⟨ table, h_table, h_mem_table ⟩\n apply t... | [
{
"name": "mem_interactionsWith",
"text": "lemma mem_interactionsWith {witness : EnsembleWitness ens}\n {channel : RawChannel F} {i : Interaction F} :\n i ∈ witness.interactionsWith channel ↔\n ∃ table ∈ witness.allTables, i ∈ table.interactionsWith channel := by\n simp only [interactionsWith, List.... | [
{
"name": "channel_eq_of_mem_interactionsWith",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 355,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": fals... | 1 | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | @@ -173,9 +173,19 @@
(witness : EnsembleWitness ens) (channel : RawChannel F) :
witness.allTablesWitness.interactionsWith channel = witness.interactionsWith channel := rfl
+lemma mem_interactionsWith {witness : EnsembleWitness ens}
+ {channel : RawChannel F} {i : Interaction F} :
+ i ∈ witness.interaction... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f87c42644526_1 | 8fc63e642f3883ef | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/FlatEnsemble.lean | FlatEnsemble | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "verifierConstraints_iff_verifierTable_constraints",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [Ensemble.VerifierConstraints, Table.Constraints]\n simp only [circuit_norm, E... | [
{
"name": "verifierTable_constraints",
"text": "lemma verifierTable_constraints :\n ens.verifierTable.operations.constraints = ens.verifierOperations.constraints := by\n rw [Component.constraints_eq]\n simp only [circuit_norm, Component.rowOperations]\n rfl\n\n",
"fan_in": 1,
"n_lines": 7,
"... | [
{
"name": "verifierConstraints_iff_verifierTable_constraints",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 355,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automat... | 2 | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | @@ -84,6 +84,12 @@
def VerifierSpec (ens : Ensemble F PublicIO) (publicInput : PublicIO F) (data : ProverData F) : Prop :=
ens.verifier.Spec publicInput () data
+lemma verifierTable_constraints :
+ ens.verifierTable.operations.constraints = ens.verifierOperations.constraints := by
+ rw [Component.constraints_eq... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f87c42644526_2 | f08c9942e609bf83 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/FlatEnsemble.lean | FlatEnsemble | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "verifierGuarantees_iff_verifierTable_guarantees",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [Ensemble.VerifierGuarantees, Table.Guarantees]\n simp only [circuit_norm, Ensem... | [
{
"name": "verifierTable_interactions",
"text": "lemma verifierTable_interactions :\n ens.verifierTable.operations.interactions = ens.verifierOperations.interactions := by\n rw [Component.interactions_eq]\n simp only [circuit_norm, Component.rowOperations]\n rfl\n\n",
"fan_in": 2,
"n_lines": 7,
... | [
{
"name": "verifierGuarantees_iff_verifierTable_guarantees",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 318,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automatio... | 1 | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | @@ -84,6 +84,12 @@
def VerifierSpec (ens : Ensemble F PublicIO) (publicInput : PublicIO F) (data : ProverData F) : Prop :=
ens.verifier.Spec publicInput () data
+lemma verifierTable_interactions :
+ ens.verifierTable.operations.interactions = ens.verifierOperations.interactions := by
+ rw [Component.interaction... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f87c42644526_3 | 529a2cf60b5855a3 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/FlatEnsemble.lean | FlatEnsemble | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "verifierGuarantees_iff_verifierTable_guarantees",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [Ensemble.VerifierGuarantees, Table.Guarantees]\n simp only [circuit_norm, Ensem... | [
{
"name": "verifierTable_interactions",
"text": "lemma verifierTable_interactions :\n ens.verifierTable.operations.interactions = ens.verifierOperations.interactions := by\n rw [Component.interactions_eq]\n simp only [circuit_norm, Component.rowOperations]\n rfl\n\n",
"fan_in": 2,
"n_lines": 7,
... | [
{
"name": "verifierChannelRequirements_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 352,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
... | 1 | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | @@ -84,6 +84,12 @@
def VerifierSpec (ens : Ensemble F PublicIO) (publicInput : PublicIO F) (data : ProverData F) : Prop :=
ens.verifier.Spec publicInput () data
+lemma verifierTable_interactions :
+ ens.verifierTable.operations.interactions = ens.verifierOperations.interactions := by
+ rw [Component.interaction... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f87c42644526_4 | 0196a746b9ec7f1b | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/FlatEnsemble.lean | FlatEnsemble | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "verifierConstraints_iff_verifierTable_constraints",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [Ensemble.VerifierConstraints, Table.Constraints]\n simp only [circuit_norm, E... | [
{
"name": "verifierTable_lookups",
"text": "lemma verifierTable_lookups :\n ens.verifierTable.operations.lookups = ens.verifierOperations.lookups := by\n rw [Component.lookups_eq]\n simp only [circuit_norm, Component.rowOperations]\n rfl\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 195,
"... | [
{
"name": "verifierConstraints_of_constraints",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 7,
"n_chars": 320,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": fals... | 4 | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | @@ -90,6 +90,12 @@
simp only [circuit_norm, Component.rowOperations]
rfl
+lemma verifierTable_lookups :
+ ens.verifierTable.operations.lookups = ens.verifierOperations.lookups := by
+ rw [Component.lookups_eq]
+ simp only [circuit_norm, Component.rowOperations]
+ rfl
+
def channelsWithGuarantees (ens : Ens... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f87c42644526_5 | 6cbf19356112c207 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/FlatEnsemble.lean | FlatEnsemble | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "verifierConstraints_of_constraints",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [verifierConstraints_iff_verifierTable_constraints, Constraints, EnsembleWitness.forall_mem_allTables... | [
{
"name": "forall_mem_allTables_iff",
"text": "lemma forall_mem_allTables_iff (witness : EnsembleWitness ens)\n (motive : Table F → Prop) :\n (∀ table ∈ witness.allTables, motive table) ↔\n motive witness.verifierTable ∧ (∀ table ∈ witness.tables, motive table) := by\n simp [allTables]\n\n",
"fa... | [
{
"name": "verifierAssumptions_of_assumptions",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 305,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": fals... | 2 | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | @@ -127,6 +127,12 @@
witness.verifierTable ∈ witness.allTables := by
simp [allTables]
+lemma forall_mem_allTables_iff (witness : EnsembleWitness ens)
+ (motive : Table F → Prop) :
+ (∀ table ∈ witness.allTables, motive table) ↔
+ motive witness.verifierTable ∧ (∀ table ∈ witness.tables, motive table) :... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f87c42644526_6 | 16a7b9c0c903d0a9 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/FlatEnsemble.lean | FlatEnsemble | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "interactionsWith_of_verifier_empty",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [interactionsWith, allTables, Table.interactionsWith,\n Ensemble.verifierTable_interactionsWith,... | [
{
"name": "verifierTable_interactionsWith",
"text": "lemma verifierTable_interactionsWith {channel : RawChannel F} :\n ens.verifierTable.operations.interactionsWith channel =\n ens.verifierOperations.interactionsWith channel := by\n rw [Component.interactionsWith_eq]\n simp only [circuit_norm, Compone... | [
{
"name": "interactionsWith_of_verifier_empty",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 421,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true... | 1 | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | @@ -84,6 +84,13 @@
def VerifierSpec (ens : Ensemble F PublicIO) (publicInput : PublicIO F) (data : ProverData F) : Prop :=
ens.verifier.Spec publicInput () data
+lemma verifierTable_interactionsWith {channel : RawChannel F} :
+ ens.verifierTable.operations.interactionsWith channel =
+ ens.verifierOperations.i... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f87c42644526_7 | 7331a8bd16838470 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/FlatEnsemble.lean | FlatEnsemble | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "verifierConstraints_iff_verifierTable_constraints",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [Ensemble.VerifierConstraints, Table.Constraints]\n simp only [circuit_norm, E... | [
{
"name": "verifierTable_lookups",
"text": "lemma verifierTable_lookups :\n ens.verifierTable.operations.lookups = ens.verifierOperations.lookups := by\n rw [Component.lookups_eq]\n simp only [circuit_norm, Component.rowOperations]\n rfl\n\n",
"fan_in": 1,
"n_lines": 7,
"n_chars": 195,
"... | [
{
"name": "verifierTable_constraints_of_verifier_empty",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 349,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_on... | 3 | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | @@ -90,6 +90,12 @@
simp only [circuit_norm, Component.rowOperations]
rfl
+lemma verifierTable_lookups :
+ ens.verifierTable.operations.lookups = ens.verifierOperations.lookups := by
+ rw [Component.lookups_eq]
+ simp only [circuit_norm, Component.rowOperations]
+ rfl
+
def channelsWithGuarantees (ens : Ens... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_f87c42644526_8 | 8be1c845a58dc21c | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Air/FlatEnsemble.lean | FlatEnsemble | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "verifierAssumptions_of_assumptions",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [verifierAssumptions_iff_verifierTable_assumptions, Assumptions, forall_mem_allTables_iff]\n simp_al... | [
{
"name": "verifierAssumptions_iff_verifierTable_assumptions",
"text": "lemma verifierAssumptions_iff_verifierTable_assumptions {witness : EnsembleWitness ens} :\n ens.verifier.Assumptions witness.publicInput witness.data ↔\n witness.verifierTable.Assumptions := by\n simp +instances only [circuit_norm,... | [
{
"name": "verifierTable_assumptions_of_verifier_empty",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 319,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_on... | 1 | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | /-
This file defines flat AIR ensembles and what soundness and completeness mean for them.
-/
import Clean.Air.FlatComponent
import Clean.Air.Balance
namespace Air.Flat
variable {F : Type} [FiniteField F]
variable {PublicIO : TypeMap} [ProvableType PublicIO]
structure Ensemble (F : Type) [FiniteField F] (PublicIO : T... | @@ -190,9 +190,17 @@
witness.verifierTable.environment (toElements publicInput).toArray =
Environment.fromInput publicInput witness.data := rfl
+lemma verifierAssumptions_iff_verifierTable_assumptions {witness : EnsembleWitness ens} :
+ ens.verifier.Assumptions witness.publicInput witness.data ↔
+ wit... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_1b66b4719329_0 | 36765d11f9f02029 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Gadgets/ByteDecomposition/Theorems.lean | Theorems | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "soundness",
"depth": 1,
"n_commands": 0,
"n_lines": 99,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n\n have two_power_lt : 2^offset.val < 2^8 := Nat.pow_lt_pow_of_lt (by linarith) offset.is_lt\n have two_power_val : ((2 : F p)^o... | [
{
"name": "byteDecomposition_lift",
"text": "theorem byteDecomposition_lift {low high two_power : F p}\n (h_low : low.val < 2^8) (h_high : high.val < 2^8) (h_two_power : two_power.val ≤ 2^8) :\n (low + high * two_power).val = low.val + high.val * two_power.val := by\n field_to_nat\n suffices high.val ... | [
{
"name": "soundness",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 104,
"n_chars": 3802,
"n_subproofs": 17,
"n_tactics": 78,
"cyclomatic": 2,
"n_automation": 33,
"n_rewrites": 19,
"n_structural": 4,
"automation_only": false,
"max_nestin... | 1 | import Clean.Utils.Field
import Clean.Utils.Bitwise
import Clean.Types.U64
import Clean.Types.U32
namespace Gadgets.ByteDecomposition.Theorems
variable {p : ℕ} [Fact p.Prime] [p_large_enough: Fact (p > 2^16 + 2^8)]
instance : Fact (p > 512) := .mk (by linarith [p_large_enough.elim])
open FieldUtils (two_val two_pow_v... | import Clean.Utils.Field
import Clean.Utils.Bitwise
import Clean.Types.U64
import Clean.Types.U32
namespace Gadgets.ByteDecomposition.Theorems
variable {p : ℕ} [Fact p.Prime] [p_large_enough: Fact (p > 2^16 + 2^8)]
instance : Fact (p > 512) := .mk (by linarith [p_large_enough.elim])
open FieldUtils (two_val two_pow_v... | @@ -9,10 +9,118 @@
open FieldUtils (two_val two_pow_val)
+theorem byteDecomposition_lift {low high two_power : F p}
+ (h_low : low.val < 2^8) (h_high : high.val < 2^8) (h_two_power : two_power.val ≤ 2^8) :
+ (low + high * two_power).val = low.val + high.val * two_power.val := by
+ field_to_nat
+ suffices hig... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
ablate_773c3a26d3a0_0 | 2d21a4eff3e75e58 | lean | lean | github.com/Verified-zkEVM/clean | 1e563b9c27991b3795eb440c1ee0757edb4ce8b1 | Clean/Tables/KeccakInductive.lean | KeccakInductive | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "tableStatement",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro n hn trace env\n use (InductiveTable.traceInputs trace.tail).map KeccakBlock.value\n intro Spec\n simp only [formal... | [
{
"name": "initialState_value",
"text": "lemma initialState_value : (initialState (p:=p)).value = .fill 25 0 := by\n ext i hi\n simp only [initialState, KeccakState.value]\n rw [Vector.getElem_map, Vector.getElem_fill, Vector.getElem_fill, U64.fromByte_value, Fin.val_zero]\n\n",
"fan_in": 1,
"n_l... | [
{
"name": "tableStatement",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 12,
"n_chars": 673,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_nesting... | 2 | /- Simple Keccak example using `InductiveTable` -/
import Clean.Table.Inductive
import Clean.Circuit.Extensions
import Clean.Gadgets.Keccak.AbsorbBlock
import Clean.Specs.Keccak256
open Specs.Keccak256
variable {p : ℕ} [Fact p.Prime] [Fact (p > 2 ^ 16 + 2 ^ 8)]
namespace Tables.KeccakInductive
open Gadgets.Keccak256
... | /- Simple Keccak example using `InductiveTable` -/
import Clean.Table.Inductive
import Clean.Circuit.Extensions
import Clean.Gadgets.Keccak.AbsorbBlock
import Clean.Specs.Keccak256
open Specs.Keccak256
variable {p : ℕ} [Fact p.Prime] [Fact (p > 2 ^ 16 + 2 ^ 8)]
namespace Tables.KeccakInductive
open Gadgets.Keccak256
... | @@ -34,6 +34,11 @@
-- the input is hard-coded to the initial keccak state of all zeros
def initialState : KeccakState (F p) := .fill 25 (U64.fromByte 0)
+lemma initialState_value : (initialState (p:=p)).value = .fill 25 0 := by
+ ext i hi
+ simp only [initialState, KeccakState.value]
+ rw [Vector.getElem_map, Ve... | {
"repo": "clean",
"git_repo": "github.com/Verified-zkEVM/clean",
"revision": "1e563b9c27991b3795eb440c1ee0757edb4ce8b1",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lem... |
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