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_d9307c5ec788_9 | c4071babde0d428f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/ToMathlib/Polynomial/BivariateDegree.lean | BivariateDegree | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 4 | [
{
"theorem_name": "evalY_eq_evalX_swap",
"depth": 1,
"n_commands": 0,
"n_lines": 21,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n letI : Algebra F[X] F[X] := Polynomial.algebra (R := F) (A := F)\n have eval_eq_aeval : Polynomial.eval ... | [
{
"name": "evalX_eq_map",
"text": "lemma evalX_eq_map (x : F) (f : F[X][Y]) :\n Polynomial.Bivariate.evalX x f = f.map (Polynomial.evalRingHom x) := by\n classical\n ext n\n simp [Polynomial.Bivariate.evalX, Polynomial.toFinsupp_apply]\n\n",
"fan_in": 4,
"n_lines": 7,
"n_chars": 204,
"... | [
{
"name": "descend_evalX",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 1022,
"n_subproofs": 5,
"n_tactics": 16,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import CompPoly.Bivariate.ToPoly
import Aesop
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polyn... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import CompPoly.Bivariate.ToPoly
import Aesop
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polyn... | @@ -208,6 +208,12 @@
variable [CommSemiring F]
+lemma evalX_eq_map (x : F) (f : F[X][Y]) :
+ Polynomial.Bivariate.evalX x f = f.map (Polynomial.evalRingHom x) := by
+ classical
+ ext n
+ simp [Polynomial.Bivariate.evalX, Polynomial.toFinsupp_apply]
+
end CommSemiring
section CommRing
@@ -222,7 +228,22 @@... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_d9307c5ec788_10 | 7f8d809eb9ec9813 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/ToMathlib/Polynomial/BivariateDegree.lean | BivariateDegree | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "exists_x_preserve_natDegreeY",
"depth": 1,
"n_commands": 0,
"n_lines": 30,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n let p : F[X] := leadingCoeffY B\n have hp0 : p ≠ 0 := by\n simpa [p] using (leadingCoeffY_ne... | [
{
"name": "leadingCoeffY_ne_zero",
"text": "/-- The polynomial coefficient of the highest power of `Y` is not `0` if and only if the\nbivariate polynomial is non-zero. -/\n@[simp, grind =]\nlemma leadingCoeffY_ne_zero (f : F[X][Y]) : leadingCoeffY f ≠ 0 ↔ f ≠ 0 := by\n exact not_congr (leadingCoeffY_eq_zer... | [
{
"name": "exists_x_preserve_natDegreeY",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 34,
"n_chars": 1458,
"n_subproofs": 10,
"n_tactics": 30,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 8,
"automation_only": false,... | 4 | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import CompPoly.Bivariate.ToPoly
import Aesop
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polyn... | /-
Copyright (c) 2026 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import CompPoly.Bivariate.ToPoly
import Aesop
import Mathlib.Algebra.BigOperators.Group.Finset.Basic
import Mathlib.Algebra.Polynomial.BigOperators
import Mathlib.Algebra.Polyn... | @@ -52,6 +52,12 @@
theorem leadingCoeffY_eq_zero (f : F[X][Y]) : leadingCoeffY f = 0 ↔ f = 0 := by
simp [leadingCoeffY]
+/-- The polynomial coefficient of the highest power of `Y` is not `0` if and only if the
+bivariate polynomial is non-zero. -/
+@[simp, grind =]
+lemma leadingCoeffY_ne_zero (f : F[X][Y]) : lea... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_939c518928ec_0 | e111246220bd5924 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Factor.lean | Factor | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 1 | [
{
"theorem_name": "divByLinearY_pair_of_one_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let n := natDegreeY Q\n let a : ℕ → CPolynomial R := fun j => CPolynomial.coeff Q j\n let step : CPolynomial... | [
{
"name": "divByLinearY_fold_split",
"text": "private theorem divByLinearY_fold_split [CommRing R] [BEq R] [LawfulBEq R]\n [Nontrivial R] [DecidableEq R] (Q : CBivariate R) (f : CPolynomial R) (h : 1 < natDegreeY Q) :\n let n := natDegreeY Q\n let a : ℕ → CPolynomial R := fun j => CPolynomial.coeff Q j... | [
{
"name": "divByLinearY_pair_of_one_lt",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 33,
"n_chars": 1401,
"n_subproofs": 2,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | @@ -67,6 +67,25 @@
let quotArr : CPolynomial.Raw (CPolynomial R) := coeffs.reverse
(⟨quotArr.trim, CPolynomial.Raw.Trim.isCanonical_trim quotArr⟩, rem)
+private theorem divByLinearY_fold_split [CommRing R] [BEq R] [LawfulBEq R]
+ [Nontrivial R] [DecidableEq R] (Q : CBivariate R) (f : CPolynomial R) (h : ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_939c518928ec_1 | 8e48b5a4abbaaa7b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Factor.lean | Factor | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 1 | [
{
"theorem_name": "divByLinearY_divX_pair_of_one_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 68,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let n := natDegreeY Q\n let a : ℕ → CPolynomial R := fun j => CPolynomial.coeff Q j\n let step : CPolyn... | [
{
"name": "natDegreeY_divX_of_one_lt",
"text": "private theorem natDegreeY_divX_of_one_lt [CommRing R] [BEq R] [LawfulBEq R]\n [Nontrivial R] [DecidableEq R] (Q : CBivariate R) (h : 1 < natDegreeY Q) :\n natDegreeY (CPolynomial.divX Q) = natDegreeY Q - 1 := by\n unfold CBivariate.natDegreeY CPolynomial... | [
{
"name": "divByLinearY_divX_pair_of_one_lt",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 83,
"n_chars": 3644,
"n_subproofs": 10,
"n_tactics": 68,
"cyclomatic": 1,
"n_automation": 10,
"n_rewrites": 4,
"n_structural": 4,
"automation_only": f... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | @@ -67,6 +67,20 @@
let quotArr : CPolynomial.Raw (CPolynomial R) := coeffs.reverse
(⟨quotArr.trim, CPolynomial.Raw.Trim.isCanonical_trim quotArr⟩, rem)
+private theorem natDegreeY_divX_of_one_lt [CommRing R] [BEq R] [LawfulBEq R]
+ [Nontrivial R] [DecidableEq R] (Q : CBivariate R) (h : 1 < natDegreeY Q) ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_939c518928ec_2 | f4b0e8ec505016c6 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Factor.lean | Factor | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "divByLinearY_divX_quot_coeff",
"depth": 1,
"n_commands": 0,
"n_lines": 63,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n change CPolynomial.coeff ((divByLinearY (CPolynomial.divX Q) f).1) j =\n CPolynomial.coeff ((... | [
{
"name": "divByLinearY_const",
"text": "theorem divByLinearY_const [CommRing R] [BEq R] [LawfulBEq R]\n [Nontrivial R] [DecidableEq R] (a f : CPolynomial R) :\n divByLinearY (CPolynomial.C a : CBivariate R) f = (0, a) := by\n unfold divByLinearY\n have hdeg : natDegreeY (CPolynomial.C a : CBivariate ... | [
{
"name": "divByLinearY_divX_quot_coeff",
"fan_in": 1,
"n_deps_direct": 9,
"n_deps_transitive": 11,
"n_lines": 69,
"n_chars": 3632,
"n_subproofs": 7,
"n_tactics": 63,
"cyclomatic": 1,
"n_automation": 8,
"n_rewrites": 6,
"n_structural": 5,
"automation_only": false,... | 11 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | @@ -67,6 +67,19 @@
let quotArr : CPolynomial.Raw (CPolynomial R) := coeffs.reverse
(⟨quotArr.trim, CPolynomial.Raw.Trim.isCanonical_trim quotArr⟩, rem)
+theorem divByLinearY_const [CommRing R] [BEq R] [LawfulBEq R]
+ [Nontrivial R] [DecidableEq R] (a f : CPolynomial R) :
+ divByLinearY (CPolynomial.C a ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_939c518928ec_3 | 46d414bb619467d8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Factor.lean | Factor | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "divByLinearY_divX_quot_coeff",
"depth": 1,
"n_commands": 0,
"n_lines": 63,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n change CPolynomial.coeff ((divByLinearY (CPolynomial.divX Q) f).1) j =\n CPolynomial.coeff ((... | [
{
"name": "divByLinearY_const",
"text": "theorem divByLinearY_const [CommRing R] [BEq R] [LawfulBEq R]\n [Nontrivial R] [DecidableEq R] (a f : CPolynomial R) :\n divByLinearY (CPolynomial.C a : CBivariate R) f = (0, a) := by\n unfold divByLinearY\n have hdeg : natDegreeY (CPolynomial.C a : CBivariate ... | [
{
"name": "divByLinearY_divX_rem",
"fan_in": 1,
"n_deps_direct": 9,
"n_deps_transitive": 11,
"n_lines": 47,
"n_chars": 2404,
"n_subproofs": 6,
"n_tactics": 42,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 5,
"n_structural": 4,
"automation_only": false,
"m... | 11 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | @@ -67,6 +67,19 @@
let quotArr : CPolynomial.Raw (CPolynomial R) := coeffs.reverse
(⟨quotArr.trim, CPolynomial.Raw.Trim.isCanonical_trim quotArr⟩, rem)
+theorem divByLinearY_const [CommRing R] [BEq R] [LawfulBEq R]
+ [Nontrivial R] [DecidableEq R] (a f : CPolynomial R) :
+ divByLinearY (CPolynomial.C a ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_939c518928ec_4 | f162b50e1eed0718 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Factor.lean | Factor | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "divByLinearY_divX_quot_coeff",
"depth": 1,
"n_commands": 0,
"n_lines": 63,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n change CPolynomial.coeff ((divByLinearY (CPolynomial.divX Q) f).1) j =\n CPolynomial.coeff ((... | [
{
"name": "divByLinearY_const",
"text": "theorem divByLinearY_const [CommRing R] [BEq R] [LawfulBEq R]\n [Nontrivial R] [DecidableEq R] (a f : CPolynomial R) :\n divByLinearY (CPolynomial.C a : CBivariate R) f = (0, a) := by\n unfold divByLinearY\n have hdeg : natDegreeY (CPolynomial.C a : CBivariate ... | [
{
"name": "divByLinearY_quot_recurrence",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 15,
"n_lines": 21,
"n_chars": 921,
"n_subproofs": 2,
"n_tactics": 16,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false,
... | 15 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | @@ -67,6 +67,19 @@
let quotArr : CPolynomial.Raw (CPolynomial R) := coeffs.reverse
(⟨quotArr.trim, CPolynomial.Raw.Trim.isCanonical_trim quotArr⟩, rem)
+theorem divByLinearY_const [CommRing R] [BEq R] [LawfulBEq R]
+ [Nontrivial R] [DecidableEq R] (a f : CPolynomial R) :
+ divByLinearY (CPolynomial.C a ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_939c518928ec_5 | a733abca35251ed5 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Factor.lean | Factor | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 2 | [
{
"theorem_name": "divByLinearY_divX_quot_coeff",
"depth": 1,
"n_commands": 0,
"n_lines": 63,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n change CPolynomial.coeff ((divByLinearY (CPolynomial.divX Q) f).1) j =\n CPolynomial.coeff ((... | [
{
"name": "divByLinearY_const",
"text": "theorem divByLinearY_const [CommRing R] [BEq R] [LawfulBEq R]\n [Nontrivial R] [DecidableEq R] (a f : CPolynomial R) :\n divByLinearY (CPolynomial.C a : CBivariate R) f = (0, a) := by\n unfold divByLinearY\n have hdeg : natDegreeY (CPolynomial.C a : CBivariate ... | [
{
"name": "divByLinearY_spec",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 16,
"n_lines": 48,
"n_chars": 2402,
"n_subproofs": 6,
"n_tactics": 35,
"cyclomatic": 2,
"n_automation": 8,
"n_rewrites": 5,
"n_structural": 3,
"automation_only": false,
"max_n... | 16 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | @@ -67,6 +67,19 @@
let quotArr : CPolynomial.Raw (CPolynomial R) := coeffs.reverse
(⟨quotArr.trim, CPolynomial.Raw.Trim.isCanonical_trim quotArr⟩, rem)
+theorem divByLinearY_const [CommRing R] [BEq R] [LawfulBEq R]
+ [Nontrivial R] [DecidableEq R] (a f : CPolynomial R) :
+ divByLinearY (CPolynomial.C a ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_939c518928ec_6 | 02345fd08dcd0b8f | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Factor.lean | Factor | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 1 | [
{
"theorem_name": "divByLinearY_rem_eq_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Evaluate `toPoly Q = toPoly quot * (X - C f.toPoly) + C rem.toPoly` at `Y = f.toPoly`.\n have hspec := divByL... | [
{
"name": "evalYPoly_toPoly",
"text": "/-- Bridge to Mathlib: evaluating `Q` at `f` and mapping to `Polynomial R` agrees\nwith evaluating the mapped `toPoly Q : R[X][Y]` at `f.toPoly`. -/\ntheorem evalYPoly_toPoly [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (f : CPolynomial R) (Q ... | [
{
"name": "divByLinearY_rem_eq_eval",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 18,
"n_lines": 17,
"n_chars": 892,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"... | 18 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | @@ -43,6 +43,21 @@
(Q : CBivariate R) (f : CPolynomial R) : Bool :=
evalYPoly f Q == 0
+/-- Bridge to Mathlib: evaluating `Q` at `f` and mapping to `Polynomial R` agrees
+with evaluating the mapped `toPoly Q : R[X][Y]` at `f.toPoly`. -/
+theorem evalYPoly_toPoly [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_939c518928ec_7 | 8bfc8efe00b0159b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/Factor.lean | Factor | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 20 | 1 | [
{
"theorem_name": "divByLinearY_exact",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [divByLinearY_rem_eq_eval]\n exact (isLinearYFactor_iff Q f).mp h",
"n_chars": 74,
"n_subproofs": 0,
"n_... | [
{
"name": "isLinearYFactor_iff",
"text": "/-- The `isLinearYFactor` boolean test agrees with the proposition `Q(X, f(X)) = 0`. -/\ntheorem isLinearYFactor_iff [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]\n (Q : CBivariate R) (f : CPolynomial R) :\n isLinearYFactor Q f = true ↔ eva... | [
{
"name": "divByLinearY_exact",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 20,
"n_lines": 9,
"n_chars": 378,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nes... | 20 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Dimitris Mitsios
-/
import CompPoly.Bivariate.Basic
import CompPoly.Bivariate.ToPoly
import Mathlib.Data.List.GetD
import Mathlib.Data.List.Range
import Mathlib.Algebra.Polynomial.Coeff
im... | @@ -43,6 +43,12 @@
(Q : CBivariate R) (f : CPolynomial R) : Bool :=
evalYPoly f Q == 0
+/-- The `isLinearYFactor` boolean test agrees with the proposition `Q(X, f(X)) = 0`. -/
+theorem isLinearYFactor_iff [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R] [DecidableEq R]
+ (Q : CBivariate R) (f : CPolynomia... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_0 | 7d64e264e5c08ad8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 1 | [
{
"theorem_name": "hasseDerivative_sub",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff_coeff]\n intro i j\n rw [hasseDerivative_coeff, coeff_sub, coeff_sub, hasseDerivative_coeff,\n hasseDer... | [
{
"name": "coeff_sub",
"text": "theorem coeff_sub {R : Type*}\n [Ring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (P Q : CBivariate R) (i j : Nat) :\n coeff (P - Q) i j = coeff P i j - coeff Q i j := by\n change CPolynomial.coeff (CPolynomial.coeff (P - Q : CBivariate R) j) i =\n CPolynomial.coef... | [
{
"name": "hasseDerivative_sub",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 364,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -16,11 +16,28 @@
namespace CBivariate
+theorem coeff_sub {R : Type*}
+ [Ring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (P Q : CBivariate R) (i j : Nat) :
+ coeff (P - Q) i j = coeff P i j - coeff Q i j := by
+ change CPolynomial.coeff (CPolynomial.coeff (P - Q : CBivariate R) j) i =
+ CPolynomial.c... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_1 | 60d1f0620400442b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 1 | [
{
"theorem_name": "hasseDerivative_CC_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff_coeff]\n intro i j\n rw [hasseDerivative_coeff, coeff_CC_mul, coeff_CC_mul, hasseDerivative_coeff]\n r... | [
{
"name": "coeff_CC_mul",
"text": "theorem coeff_CC_mul {R : Type*}\n [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (c : R) (Q : CBivariate R) (i j : Nat) :\n coeff (CC c * Q) i j = c * coeff Q i j := by\n change CPolynomial.coeff (CPolynomial.coeff (CC c * Q : CBivariate R) j) i =\n c * ... | [
{
"name": "hasseDerivative_CC_mul",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 332,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -16,10 +16,25 @@
namespace CBivariate
+theorem coeff_CC_mul {R : Type*}
+ [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (c : R) (Q : CBivariate R) (i j : Nat) :
+ coeff (CC c * Q) i j = c * coeff Q i j := by
+ change CPolynomial.coeff (CPolynomial.coeff (CC c * Q : CBivariate R) j) i =
+ c * ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_2 | 4ba1d4f096c4ef3b | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 2 | [
{
"theorem_name": "hasseDerivative_X_mul_zero_xOrder",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff_coeff]\n intro i j\n cases i with\n | zero =>\n rw [hasseDerivative_coeff, coeff_X_mu... | [
{
"name": "coeff_X_mul_zero",
"text": "theorem coeff_X_mul_zero {R : Type*}\n [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (Q : CBivariate R) (j : Nat) :\n coeff (X * Q) 0 j = 0 := by\n change CPolynomial.coeff (CPolynomial.coeff (X * Q : CBivariate R) j) 0 = 0\n have houter : CPolynomial.... | [
{
"name": "hasseDerivative_X_mul_zero_xOrder",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 16,
"n_chars": 472,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": fal... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -16,6 +16,16 @@
namespace CBivariate
+theorem coeff_X_mul_zero {R : Type*}
+ [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (Q : CBivariate R) (j : Nat) :
+ coeff (X * Q) 0 j = 0 := by
+ change CPolynomial.coeff (CPolynomial.coeff (X * Q : CBivariate R) j) 0 = 0
+ have houter : CPolynomial.coeff... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_3 | 30b5c7d3f72f61cd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 2 | [
{
"theorem_name": "hasseDerivative_X_mul_zero_xOrder",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff_coeff]\n intro i j\n cases i with\n | zero =>\n rw [hasseDerivative_coeff, coeff_X_mu... | [
{
"name": "coeff_X_mul_zero",
"text": "theorem coeff_X_mul_zero {R : Type*}\n [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (Q : CBivariate R) (j : Nat) :\n coeff (X * Q) 0 j = 0 := by\n change CPolynomial.coeff (CPolynomial.coeff (X * Q : CBivariate R) j) 0 = 0\n have houter : CPolynomial.... | [
{
"name": "hasseDerivative_X_mul_succ_xOrder",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 33,
"n_chars": 1171,
"n_subproofs": 1,
"n_tactics": 27,
"cyclomatic": 2,
"n_automation": 11,
"n_rewrites": 18,
"n_structural": 2,
"automation_only": ... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -16,6 +16,16 @@
namespace CBivariate
+theorem coeff_X_mul_zero {R : Type*}
+ [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (Q : CBivariate R) (j : Nat) :
+ coeff (X * Q) 0 j = 0 := by
+ change CPolynomial.coeff (CPolynomial.coeff (X * Q : CBivariate R) j) 0 = 0
+ have houter : CPolynomial.coeff... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_4 | e8bbec8411bf9c0c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 1 | [
{
"theorem_name": "hasseDerivativeEval_CC_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← hasseDerivative_eval_eq_eval a b x y (CC c * Q)]\n rw [hasseDerivative_CC_mul]\n rw [evalEval_CC_mul]\n ... | [
{
"name": "evalEval_CC_mul",
"text": "theorem evalEval_CC_mul {F : Type*}\n [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]\n (c x y : F) (Q : CBivariate F) :\n evalEval x y (CC c * Q) = c * evalEval x y Q := by\n rw [evalEval_toPoly, evalEval_toPoly, toPoly_mul, CC_toPoly]\n simp [Polynomial.eva... | [
{
"name": "hasseDerivativeEval_CC_mul",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 11,
"n_chars": 394,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 4,
"n_structural": 0,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -27,6 +27,13 @@
exact CPolynomial.coeff_C_mul (p := Q) (c := CPolynomial.C c) j
rw [houter, CPolynomial.coeff_C_mul]
+theorem evalEval_CC_mul {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]
+ (c x y : F) (Q : CBivariate F) :
+ evalEval x y (CC c * Q) = c * evalEval x y Q := by
+ rw ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_5 | bf2da3be207019db | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 1 | [
{
"theorem_name": "hasseDerivativeEval_sub",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← hasseDerivative_eval_eq_eval a b x y (P - Q)]\n rw [hasseDerivative_sub]\n rw [evalEval_sub]\n rw [hasseDe... | [
{
"name": "evalEval_sub",
"text": "theorem evalEval_sub {F : Type*}\n [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]\n (x y : F) (P Q : CBivariate F) :\n evalEval x y (P - Q) = evalEval x y P - evalEval x y Q := by\n rw [evalEval_toPoly, evalEval_toPoly, evalEval_toPoly]\n have hsub : toPoly (P ... | [
{
"name": "hasseDerivativeEval_sub",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 11,
"n_chars": 431,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 4,
"n_structural": 0,
"automation_only": false,
"ma... | 3 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -28,6 +28,16 @@
exact CPolynomial.coeff_sub (p := P) (q := Q) (i := j)
rw [houter, CPolynomial.coeff_sub]
+theorem evalEval_sub {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]
+ (x y : F) (P Q : CBivariate F) :
+ evalEval x y (P - Q) = evalEval x y P - evalEval x y Q := by
+ rw [eva... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_6 | 279d6979db70996c | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 2 | [
{
"theorem_name": "hasseDerivative_X_mul_zero_xOrder",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff_coeff]\n intro i j\n cases i with\n | zero =>\n rw [hasseDerivative_coeff, coeff_X_mu... | [
{
"name": "coeff_X_mul_succ",
"text": "theorem coeff_X_mul_succ {R : Type*}\n [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (Q : CBivariate R) (i j : Nat) :\n coeff (X * Q) (i + 1) j = coeff Q i j := by\n change CPolynomial.coeff (CPolynomial.coeff (X * Q : CBivariate R) j) (i + 1) =\n CP... | [
{
"name": "hasseDerivativeEval_X_mul_zero_xOrder",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 11,
"n_chars": 399,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 4,
"n_structural": 0,
"automation_only": ... | 4 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -26,6 +26,17 @@
exact CPolynomial.coeff_C_mul (p := Q) (c := CPolynomial.X) j
rw [houter, CPolynomial.coeff_X_mul_zero]
+theorem coeff_X_mul_succ {R : Type*}
+ [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (Q : CBivariate R) (i j : Nat) :
+ coeff (X * Q) (i + 1) j = coeff Q i j := by
+ chan... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_7 | 5dae005a23d10fec | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 2 | [
{
"theorem_name": "hasseDerivative_X_mul_zero_xOrder",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [eq_iff_coeff]\n intro i j\n cases i with\n | zero =>\n rw [hasseDerivative_coeff, coeff_X_mu... | [
{
"name": "coeff_X_mul_succ",
"text": "theorem coeff_X_mul_succ {R : Type*}\n [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]\n (Q : CBivariate R) (i j : Nat) :\n coeff (X * Q) (i + 1) j = coeff Q i j := by\n change CPolynomial.coeff (CPolynomial.coeff (X * Q : CBivariate R) j) (i + 1) =\n CP... | [
{
"name": "hasseDerivativeEval_X_mul_succ_xOrder",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 12,
"n_chars": 503,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 4,
"n_structural": 0,
"automation_only": ... | 4 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -26,6 +26,17 @@
exact CPolynomial.coeff_C_mul (p := Q) (c := CPolynomial.X) j
rw [houter, CPolynomial.coeff_X_mul_zero]
+theorem coeff_X_mul_succ {R : Type*}
+ [Semiring R] [BEq R] [LawfulBEq R] [Nontrivial R]
+ (Q : CBivariate R) (i j : Nat) :
+ coeff (X * Q) (i + 1) j = coeff Q i j := by
+ chan... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_8 | 5d11a4282a7f94ec | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 1 | [
{
"theorem_name": "natWeightedDegree_ofYConstant_mul_le",
"depth": 1,
"n_commands": 0,
"n_lines": 25,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CBivariate.natWeightedDegree_le_iff_coeff]\n intro i j hcoeff\n rw [coeff_ofYConstant_mul] at h... | [
{
"name": "cpoly_natDegree_mul_le",
"text": "theorem cpoly_natDegree_mul_le {F : Type*}\n [Field F] [BEq F] [LawfulBEq F] (P Q : CPolynomial F) :\n (P * Q).natDegree ≤ P.natDegree + Q.natDegree := by\n rw [CPolynomial.natDegree_toPoly, CPolynomial.toPoly_mul,\n CPolynomial.natDegree_toPoly, CPolyn... | [
{
"name": "natWeightedDegree_ofYConstant_mul_le",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 31,
"n_chars": 1240,
"n_subproofs": 6,
"n_tactics": 25,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 4,
"automation_only":... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -14,6 +14,13 @@
namespace CompPoly
+theorem cpoly_natDegree_mul_le {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F] (P Q : CPolynomial F) :
+ (P * Q).natDegree ≤ P.natDegree + Q.natDegree := by
+ rw [CPolynomial.natDegree_toPoly, CPolynomial.toPoly_mul,
+ CPolynomial.natDegree_toPoly, CPolynomial.natDegr... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_9 | 17c0bd42065326eb | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 2 | [
{
"theorem_name": "ofYConstant_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CBivariate.eq_iff_coeff]\n intro i j\n rw [coeff_ofYConstant, CBivariate.coeff_zero]\n by_cases hj : j = 0\n · sub... | [
{
"name": "coeff_ofYConstant",
"text": "theorem coeff_ofYConstant {F : Type*}\n [Semiring F] [BEq F] [LawfulBEq F] [Nontrivial F]\n (P : CPolynomial F) (i j : Nat) :\n CBivariate.coeff (CBivariate.ofYConstant P) i j =\n if j = 0 then P.coeff i else 0 := by\n unfold CBivariate.ofYConstant CBiv... | [
{
"name": "ofYConstant_zero",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 327,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -24,9 +24,37 @@
def koetterYCap (params : GSInterpParams) : Nat :=
params.weightedDegreeBound / yWeight params
+theorem coeff_ofYConstant {F : Type*}
+ [Semiring F] [BEq F] [LawfulBEq F] [Nontrivial F]
+ (P : CPolynomial F) (i j : Nat) :
+ CBivariate.coeff (CBivariate.ofYConstant P) i j =
+ if j ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_10 | 14276097e1920988 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 2 | [
{
"theorem_name": "ofYConstant_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CBivariate.eq_iff_coeff]\n intro i j\n rw [coeff_ofYConstant, CBivariate.coeff_zero]\n by_cases hj : j = 0\n · sub... | [
{
"name": "coeff_ofYConstant",
"text": "theorem coeff_ofYConstant {F : Type*}\n [Semiring F] [BEq F] [LawfulBEq F] [Nontrivial F]\n (P : CPolynomial F) (i j : Nat) :\n CBivariate.coeff (CBivariate.ofYConstant P) i j =\n if j = 0 then P.coeff i else 0 := by\n unfold CBivariate.ofYConstant CBiv... | [
{
"name": "ofYConstant_add",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 436,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -24,11 +24,39 @@
def koetterYCap (params : GSInterpParams) : Nat :=
params.weightedDegreeBound / yWeight params
+theorem coeff_ofYConstant {F : Type*}
+ [Semiring F] [BEq F] [LawfulBEq F] [Nontrivial F]
+ (P : CPolynomial F) (i j : Nat) :
+ CBivariate.coeff (CBivariate.ofYConstant P) i j =
+ if j... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_11 | 88d02c85efafe718 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 2 | [
{
"theorem_name": "hasseDerivativeEval_X_mul_zero_xOrder",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← hasseDerivative_eval_eq_eval 0 b x y (X * Q)]\n rw [hasseDerivative_X_mul_zero_xOrder]\n rw [... | [
{
"name": "evalEval_X_mul",
"text": "theorem evalEval_X_mul {F : Type*}\n [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]\n (x y : F) (Q : CBivariate F) :\n evalEval x y (X * Q) = x * evalEval x y Q := by\n rw [evalEval_toPoly, evalEval_toPoly, toPoly_mul, X_toPoly]\n simp [Polynomial.evalEval]\n... | [
{
"name": "hasseDerivativeEval_ofYConstant_mul_eq_eval_mul_of_lower",
"fan_in": 1,
"n_deps_direct": 10,
"n_deps_transitive": 19,
"n_lines": 59,
"n_chars": 2898,
"n_subproofs": 8,
"n_tactics": 51,
"cyclomatic": 3,
"n_automation": 10,
"n_rewrites": 5,
"n_structural": 9,... | 19 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -66,6 +66,13 @@
rw [evalEval_toPoly, evalEval_toPoly, toPoly_mul, CC_toPoly]
simp [Polynomial.evalEval]
+theorem evalEval_X_mul {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]
+ (x y : F) (Q : CBivariate F) :
+ evalEval x y (X * Q) = x * evalEval x y Q := by
+ rw [evalEval_toPoly, eva... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_12 | 39e44086f91c07d8 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 2 | [
{
"theorem_name": "hasseDerivativeEval_X_mul_zero_xOrder",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← hasseDerivative_eval_eq_eval 0 b x y (X * Q)]\n rw [hasseDerivative_X_mul_zero_xOrder]\n rw [... | [
{
"name": "evalEval_X_mul",
"text": "theorem evalEval_X_mul {F : Type*}\n [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]\n (x y : F) (Q : CBivariate F) :\n evalEval x y (X * Q) = x * evalEval x y Q := by\n rw [evalEval_toPoly, evalEval_toPoly, toPoly_mul, X_toPoly]\n simp [Polynomial.evalEval]\n... | [
{
"name": "hasseDerivativeEval_ofYConstant_mul_eq_zero_of_lower",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 20,
"n_lines": 13,
"n_chars": 535,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 2,
"au... | 20 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -66,6 +66,13 @@
rw [evalEval_toPoly, evalEval_toPoly, toPoly_mul, CC_toPoly]
simp [Polynomial.evalEval]
+theorem evalEval_X_mul {F : Type*}
+ [Field F] [BEq F] [LawfulBEq F] [DecidableEq F]
+ (x y : F) (Q : CBivariate F) :
+ evalEval x y (X * Q) = x * evalEval x y Q := by
+ rw [evalEval_toPoly, eva... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_13 | 9dd74c8a4ec05ea3 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 1 | [
{
"theorem_name": "foldl_add_distrib_terms",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa using foldl_add_distrib_terms_aux xs f g (0 : α) (0 : α)",
"n_chars": 70,
"n_subproofs": 0,
"n_ta... | [
{
"name": "foldl_add_distrib_terms_aux",
"text": "theorem foldl_add_distrib_terms_aux {α : Type*} [AddCommMonoid α]\n (xs : List Nat) (f g : Nat → α) (a b : α) :\n xs.foldl (fun out x ↦ out + (f x + g x)) (a + b) =\n xs.foldl (fun out x ↦ out + f x) a +\n xs.foldl (fun out x ↦ out + g x) b... | [
{
"name": "foldl_add_distrib_terms",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 320,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -24,11 +24,25 @@
def koetterYCap (params : GSInterpParams) : Nat :=
params.weightedDegreeBound / yWeight params
+theorem foldl_add_distrib_terms_aux {α : Type*} [AddCommMonoid α]
+ (xs : List Nat) (f g : Nat → α) (a b : α) :
+ xs.foldl (fun out x ↦ out + (f x + g x)) (a + b) =
+ xs.foldl (fun out x ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_14 | caee390e5593fcae | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 1 | [
{
"theorem_name": "foldl_add_single_beq_of_nodup_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 20,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction xs with\n | nil =>\n simp at hmem\n | cons idx xs ih =>\n simp only [List.foldl_co... | [
{
"name": "foldl_add_single_beq_of_not_mem",
"text": "theorem foldl_add_single_beq_of_not_mem {α : Type*} [AddCommMonoid α]\n (xs : List Nat) (target : Nat) (term acc : α)\n (hnot : target ∉ xs) :\n xs.foldl (fun out idx ↦ out + if idx == target then term else 0) acc =\n acc := by\n induction... | [
{
"name": "foldl_add_single_beq_of_nodup_mem",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 26,
"n_chars": 936,
"n_subproofs": 2,
"n_tactics": 20,
"cyclomatic": 4,
"n_automation": 3,
"n_rewrites": 5,
"n_structural": 6,
"automation_only": fal... | 1 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -24,6 +24,24 @@
def koetterYCap (params : GSInterpParams) : Nat :=
params.weightedDegreeBound / yWeight params
+theorem foldl_add_single_beq_of_not_mem {α : Type*} [AddCommMonoid α]
+ (xs : List Nat) (target : Nat) (term acc : α)
+ (hnot : target ∉ xs) :
+ xs.foldl (fun out idx ↦ out + if idx == targe... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_b10a09fe0b33_15 | 8d755915cd07d8c3 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Bivariate/GuruswamiSudan/Interpolation/LeeOSullivan/Correctness/Combinations.lean | Combinations | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 27 | 2 | [
{
"theorem_name": "ofYConstant_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [CBivariate.eq_iff_coeff]\n intro i j\n rw [coeff_ofYConstant, CBivariate.coeff_zero]\n by_cases hj : j = 0\n · sub... | [
{
"name": "coeff_ofYConstant",
"text": "theorem coeff_ofYConstant {F : Type*}\n [Semiring F] [BEq F] [LawfulBEq F] [Nontrivial F]\n (P : CPolynomial F) (i j : Nat) :\n CBivariate.coeff (CBivariate.ofYConstant P) i j =\n if j = 0 then P.coeff i else 0 := by\n unfold CBivariate.ofYConstant CBiv... | [
{
"name": "koetterBasisCombination_eq_zero_of_weights_zero",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 27,
"n_chars": 1046,
"n_subproofs": 2,
"n_tactics": 21,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 3,
"n_structural": 5,
"automa... | 2 | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | /-
Copyright (c) 2026 CompPoly Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Valerii Huhnin
-/
import CompPoly.Bivariate.GuruswamiSudan.Interpolation.LeeOSullivan.Correctness.Common
/-!
# Generic Basis Combination Helpers
Generic finite-Y and basis-co... | @@ -24,9 +24,37 @@
def koetterYCap (params : GSInterpParams) : Nat :=
params.weightedDegreeBound / yWeight params
+theorem coeff_ofYConstant {F : Type*}
+ [Semiring F] [BEq F] [LawfulBEq F] [Nontrivial F]
+ (P : CPolynomial F) (i j : Nat) :
+ CBivariate.coeff (CBivariate.ofYConstant P) i j =
+ if j ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_0 | 78f982237ec9a515 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "ghashTail_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " ghashTail_monic.ne_zero",
"n_chars": 24,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation":... | [
{
"name": "ghashTail_monic",
"text": "/-- The GHASH polynomial is monic. -/\nlemma ghashTail_monic : Monic ghashTail := by\n unfold Monic leadingCoeff\n -- Use our degree lemma to look at the right index\n rw [ghashTail_natDegree]\n unfold ghashTail\n -- coeff (A + B) i = coeff A i + coeff B i\n rw [c... | [
{
"name": "ghashTail_ne_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 3,
"n_chars": 70,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -72,8 +72,25 @@
simp only [natDegree_pow, natDegree_X, mul_one, Nat.reduceLT])]
simp only [natDegree_pow, natDegree_X, mul_one]
-lemma ghashTail_ne_zero : ghashTail ≠ 0 := sorry
+/-- The GHASH polynomial is monic. -/
+lemma ghashTail_monic : Monic ghashTail := by
+ unfold Monic leadingCoeff
+ -- Use our ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_1 | a982da531764a2aa | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "ghashTail_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 1,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " ghashTail_monic.ne_zero",
"n_chars": 24,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation":... | [
{
"name": "ghashTail_monic",
"text": "/-- The GHASH polynomial is monic. -/\nlemma ghashTail_monic : Monic ghashTail := by\n unfold Monic leadingCoeff\n -- Use our degree lemma to look at the right index\n rw [ghashTail_natDegree]\n unfold ghashTail\n -- coeff (A + B) i = coeff A i + coeff B i\n rw [c... | [
{
"name": "ghashTail_degree",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 158,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -72,8 +72,25 @@
simp only [natDegree_pow, natDegree_X, mul_one, Nat.reduceLT])]
simp only [natDegree_pow, natDegree_X, mul_one]
-lemma ghashTail_ne_zero : ghashTail ≠ 0 := sorry
+/-- The GHASH polynomial is monic. -/
+lemma ghashTail_monic : Monic ghashTail := by
+ unfold Monic leadingCoeff
+ -- Use our ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_2 | 15733c6fbdf710ec | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "ghashPoly_monic",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold Monic leadingCoeff\n -- Use our degree lemma to look at the right index\n rw [ghashPoly_natDegree]\n unfold ghas... | [
{
"name": "ghashPoly_natDegree",
"text": "/-- The degree of the GHASH polynomial is 128. -/\nlemma ghashPoly_natDegree : (ghashPoly).natDegree = 128 := by\n unfold ghashPoly\n -- The polynomial is of the form A + B.\n -- If deg(B) < deg(A), then deg(A + B) = deg(A).\n rw [add_assoc, add_assoc, add_assoc... | [
{
"name": "ghashPoly_monic",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 19,
"n_chars": 614,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 9,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -72,8 +72,36 @@
simp only [natDegree_pow, natDegree_X, mul_one, Nat.reduceLT])]
simp only [natDegree_pow, natDegree_X, mul_one]
+/-- The degree of the GHASH polynomial is 128. -/
+lemma ghashPoly_natDegree : (ghashPoly).natDegree = 128 := by
+ unfold ghashPoly
+ -- The polynomial is of the form A + B.
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_3 | 1c330e9aac4952ce | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "ghashPoly_monic",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold Monic leadingCoeff\n -- Use our degree lemma to look at the right index\n rw [ghashPoly_natDegree]\n unfold ghas... | [
{
"name": "ghashPoly_natDegree",
"text": "/-- The degree of the GHASH polynomial is 128. -/\nlemma ghashPoly_natDegree : (ghashPoly).natDegree = 128 := by\n unfold ghashPoly\n -- The polynomial is of the form A + B.\n -- If deg(B) < deg(A), then deg(A + B) = deg(A).\n rw [add_assoc, add_assoc, add_assoc... | [
{
"name": "ghashPoly_ne_zero",
"fan_in": 5,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 4,
"n_chars": 110,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -72,8 +72,36 @@
simp only [natDegree_pow, natDegree_X, mul_one, Nat.reduceLT])]
simp only [natDegree_pow, natDegree_X, mul_one]
+/-- The degree of the GHASH polynomial is 128. -/
+lemma ghashPoly_natDegree : (ghashPoly).natDegree = 128 := by
+ unfold ghashPoly
+ -- The polynomial is of the form A + B.
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_4 | db4847819dec2273 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "ghashPoly_monic",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold Monic leadingCoeff\n -- Use our degree lemma to look at the right index\n rw [ghashPoly_natDegree]\n unfold ghas... | [
{
"name": "ghashPoly_natDegree",
"text": "/-- The degree of the GHASH polynomial is 128. -/\nlemma ghashPoly_natDegree : (ghashPoly).natDegree = 128 := by\n unfold ghashPoly\n -- The polynomial is of the form A + B.\n -- If deg(B) < deg(A), then deg(A + B) = deg(A).\n rw [add_assoc, add_assoc, add_assoc... | [
{
"name": "ghashPoly_degree",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 5,
"n_chars": 169,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 3 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -72,13 +72,43 @@
simp only [natDegree_pow, natDegree_X, mul_one, Nat.reduceLT])]
simp only [natDegree_pow, natDegree_X, mul_one]
+/-- The degree of the GHASH polynomial is 128. -/
+lemma ghashPoly_natDegree : (ghashPoly).natDegree = 128 := by
+ unfold ghashPoly
+ -- The polynomial is of the form A + B.
+... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_5 | 7cb943238c89ae74 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "ghashPoly_monic",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold Monic leadingCoeff\n -- Use our degree lemma to look at the right index\n rw [ghashPoly_natDegree]\n unfold ghas... | [
{
"name": "ghashPoly_natDegree",
"text": "/-- The degree of the GHASH polynomial is 128. -/\nlemma ghashPoly_natDegree : (ghashPoly).natDegree = 128 := by\n unfold ghashPoly\n -- The polynomial is of the form A + B.\n -- If deg(B) < deg(A), then deg(A + B) = deg(A).\n rw [add_assoc, add_assoc, add_assoc... | [
{
"name": "X_mod_ghashPoly",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 5,
"n_chars": 167,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nesting... | 4 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -72,13 +72,43 @@
simp only [natDegree_pow, natDegree_X, mul_one, Nat.reduceLT])]
simp only [natDegree_pow, natDegree_X, mul_one]
+/-- The degree of the GHASH polynomial is 128. -/
+lemma ghashPoly_natDegree : (ghashPoly).natDegree = 128 := by
+ unfold ghashPoly
+ -- The polynomial is of the form A + B.
+... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_6 | fd368d7e67419810 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "ghashTail_degree",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [degree_eq_natDegree (hp := ghashTail_ne_zero)]\n simp only [ghashTail_natDegree, Nat.cast_ofNat]",
"n_chars": 106... | [
{
"name": "ghashTail_ne_zero",
"text": "lemma ghashTail_ne_zero : ghashTail ≠ 0 := ghashTail_monic.ne_zero\n\n",
"fan_in": 1,
"n_lines": 3,
"n_chars": 70,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automa... | [
{
"name": "X_pow_128_mod_ghashPoly",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 9,
"n_lines": 16,
"n_chars": 656,
"n_subproofs": 1,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 8,
"n_structural": 3,
"automation_only": false,
"m... | 7 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -89,8 +89,12 @@
-- 1 + 0 + 0 + 0 + 0 = 1
simp only [add_zero]
-lemma ghashTail_degree : (ghashTail).degree = 7 := sorry
+lemma ghashTail_ne_zero : ghashTail ≠ 0 := ghashTail_monic.ne_zero
+lemma ghashTail_degree : (ghashTail).degree = 7 := by
+ rw [degree_eq_natDegree (hp := ghashTail_ne_zero)]
+ simp on... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_7 | ddd29df8aaa67cd7 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "ghashTail_degree",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [degree_eq_natDegree (hp := ghashTail_ne_zero)]\n simp only [ghashTail_natDegree, Nat.cast_ofNat]",
"n_chars": 106... | [
{
"name": "ghashTail_ne_zero",
"text": "lemma ghashTail_ne_zero : ghashTail ≠ 0 := ghashTail_monic.ne_zero\n\n",
"fan_in": 1,
"n_lines": 3,
"n_chars": 70,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automa... | [
{
"name": "reduce_degree_step",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 10,
"n_lines": 12,
"n_chars": 516,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": false,
"max_ne... | 8 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -89,8 +89,12 @@
-- 1 + 0 + 0 + 0 + 0 = 1
simp only [add_zero]
-lemma ghashTail_degree : (ghashTail).degree = 7 := sorry
+lemma ghashTail_ne_zero : ghashTail ≠ 0 := ghashTail_monic.ne_zero
+lemma ghashTail_degree : (ghashTail).degree = 7 := by
+ rw [degree_eq_natDegree (hp := ghashTail_ne_zero)]
+ simp on... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_8 | f79d6de032377f25 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "ghashPoly_eq_P_val",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold ghashPoly P_val\n repeat rw [toPoly_xor]\n rw [toPoly_one_shiftLeft (h := by omega), toPoly_one_shiftLeft (h :=... | [
{
"name": "toPoly_one_shiftLeft",
"text": "lemma toPoly_one_shiftLeft {w : Nat} (n : Nat) (h : n < w) :\n toPoly (1 <<< n : BitVec w) = X^n := by\n rw [toPoly]\n rw [Finset.sum_eq_single (⟨n, h⟩ : Fin w)]\n -- 1. The Main Term (j = n): Prove it equals X^n\n · simp only\n simp only [BitVec.natCast_... | [
{
"name": "ghashPoly_eq_P_val",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 387,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 2,
"n_automation": 7,
"n_rewrites": 6,
"n_structural": 0,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -82,8 +82,55 @@
(1 <<< 128) ^^^ (1 <<< 7) ^^^ (1 <<< 2) ^^^ (1 <<< 1) ^^^ 1
-- Helper: toPoly (1 <<< n) is just X^n
-lemma ghashPoly_eq_P_val : ghashPoly = toPoly P_val := sorry
+lemma toPoly_one_shiftLeft {w : Nat} (n : Nat) (h : n < w) :
+ toPoly (1 <<< n : BitVec w) = X^n := by
+ rw [toPoly]
+ rw [Fins... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_9 | 2f1b93ec888e58de | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "ghashPoly_monic",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold Monic leadingCoeff\n -- Use our degree lemma to look at the right index\n rw [ghashPoly_natDegree]\n unfold ghas... | [
{
"name": "ghashPoly_natDegree",
"text": "/-- The degree of the GHASH polynomial is 128. -/\nlemma ghashPoly_natDegree : (ghashPoly).natDegree = 128 := by\n unfold ghashPoly\n -- The polynomial is of the form A + B.\n -- If deg(B) < deg(A), then deg(A + B) = deg(A).\n rw [add_assoc, add_assoc, add_assoc... | [
{
"name": "chain_step",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 16,
"n_chars": 993,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 8,
"n_structural": 5,
"automation_only": false,
"max_nesting": ... | 3 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -72,8 +72,36 @@
simp only [natDegree_pow, natDegree_X, mul_one, Nat.reduceLT])]
simp only [natDegree_pow, natDegree_X, mul_one]
+/-- The degree of the GHASH polynomial is 128. -/
+lemma ghashPoly_natDegree : (ghashPoly).natDegree = 128 := by
+ unfold ghashPoly
+ -- The polynomial is of the form A + B.
+ ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_10 | 2bb93cd2cf969e2a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 3 | [
{
"theorem_name": "clMulNat_bv_eq_clMul",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [ clMulNat_bv_eq_fold_range, clMul_eq_fold_range]\n rw [← to256_toNat b, ofNat_toB256]",
"n_chars": 101,
... | [
{
"name": "ofNat_toB256",
"text": "/-- Reinterpret a 256-bit vector's `toNat` back as the original bitvector. -/\nprivate theorem ofNat_toB256 (x : B256) : (BitVec.ofNat 256 x.toNat : B256) = x := by\n simp [BitVec.ofNat_toNat]\n\n",
"fan_in": 3,
"n_lines": 5,
"n_chars": 193,
"n_subproofs":... | [
{
"name": "clMulNat_bv_eq_clMul",
"fan_in": 3,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 300,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_ne... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -126,6 +126,10 @@
let rhs := clMulNat q.toNat b.toNat 256 ^^^ r.toNat
a.toNat == rhs
+/-- Reinterpret a 256-bit vector's `toNat` back as the original bitvector. -/
+private theorem ofNat_toB256 (x : B256) : (BitVec.ofNat 256 x.toNat : B256) = x := by
+ simp [BitVec.ofNat_toNat]
+
/-- `BitVec.ofNat 256` tra... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_11 | 601ee01f3ec237ad | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 3 | [
{
"theorem_name": "to256_truncate_128",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply BitVec.eq_of_toNat_eq\n rw [to256_toNat, toNat_truncate_of_lt v hv]",
"n_chars": 79,
"n_subproofs": 0,
... | [
{
"name": "toNat_truncate_of_lt",
"text": "private theorem toNat_truncate_of_lt {n m : Nat} (v : BitVec n)\n (hv : v.toNat < 2^m) :\n (v.truncate m).toNat = v.toNat := by\n rw [BitVec.truncate_eq_setWidth, BitVec.toNat_setWidth]\n exact Nat.mod_eq_of_lt hv\n\n",
"fan_in": 3,
"n_lines": 7,
... | [
{
"name": "to256_truncate_128",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 177,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -147,8 +147,16 @@
ofNat_shiftLeft_256, BitVec.xor_comm]
· simp [clMulNat, hbit, clMulNat_bv_eq_fold_range a b n]
+private theorem toNat_truncate_of_lt {n m : Nat} (v : BitVec n)
+ (hv : v.toNat < 2^m) :
+ (v.truncate m).toNat = v.toNat := by
+ rw [BitVec.truncate_eq_setWidth, BitVec.toNat_... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_12 | 6062b34c3bd2d0a4 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 3 | [
{
"theorem_name": "to256_truncate_128",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply BitVec.eq_of_toNat_eq\n rw [to256_toNat, toNat_truncate_of_lt v hv]",
"n_chars": 79,
"n_subproofs": 0,
... | [
{
"name": "toNat_truncate_of_lt",
"text": "private theorem toNat_truncate_of_lt {n m : Nat} (v : BitVec n)\n (hv : v.toNat < 2^m) :\n (v.truncate m).toNat = v.toNat := by\n rw [BitVec.truncate_eq_setWidth, BitVec.toNat_setWidth]\n exact Nat.mod_eq_of_lt hv\n\n",
"fan_in": 3,
"n_lines": 7,
... | [
{
"name": "toPoly_truncate_128",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 168,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nes... | 2 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -147,8 +147,16 @@
ofNat_shiftLeft_256, BitVec.xor_comm]
· simp [clMulNat, hbit, clMulNat_bv_eq_fold_range a b n]
+private theorem toNat_truncate_of_lt {n m : Nat} (v : BitVec n)
+ (hv : v.toNat < 2^m) :
+ (v.truncate m).toNat = v.toNat := by
+ rw [BitVec.truncate_eq_setWidth, BitVec.toNat_... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_13 | 3bc1176f901766e3 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 3 | [
{
"theorem_name": "to256_truncate_128",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply BitVec.eq_of_toNat_eq\n rw [to256_toNat, toNat_truncate_of_lt v hv]",
"n_chars": 79,
"n_subproofs": 0,
... | [
{
"name": "toNat_truncate_of_lt",
"text": "private theorem toNat_truncate_of_lt {n m : Nat} (v : BitVec n)\n (hv : v.toNat < 2^m) :\n (v.truncate m).toNat = v.toNat := by\n rw [BitVec.truncate_eq_setWidth, BitVec.toNat_setWidth]\n exact Nat.mod_eq_of_lt hv\n\n",
"fan_in": 3,
"n_lines": 7,
... | [
{
"name": "toPoly_clMul_B256",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 5,
"n_chars": 245,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesti... | 3 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -147,8 +147,16 @@
ofNat_shiftLeft_256, BitVec.xor_comm]
· simp [clMulNat, hbit, clMulNat_bv_eq_fold_range a b n]
+private theorem toNat_truncate_of_lt {n m : Nat} (v : BitVec n)
+ (hv : v.toNat < 2^m) :
+ (v.truncate m).toNat = v.toNat := by
+ rw [BitVec.truncate_eq_setWidth, BitVec.toNat_... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_14 | 745698bed07677d3 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 3 | [
{
"theorem_name": "clMulNat_bv_eq_clMul",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [ clMulNat_bv_eq_fold_range, clMul_eq_fold_range]\n rw [← to256_toNat b, ofNat_toB256]",
"n_chars": 101,
... | [
{
"name": "ofNat_toB256",
"text": "/-- Reinterpret a 256-bit vector's `toNat` back as the original bitvector. -/\nprivate theorem ofNat_toB256 (x : B256) : (BitVec.ofNat 256 x.toNat : B256) = x := by\n simp [BitVec.ofNat_toNat]\n\n",
"fan_in": 3,
"n_lines": 5,
"n_chars": 193,
"n_subproofs":... | [
{
"name": "clSqNat_bv_eq_clSq",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 10,
"n_chars": 333,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_nes... | 3 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -126,6 +126,10 @@
let rhs := clMulNat q.toNat b.toNat 256 ^^^ r.toNat
a.toNat == rhs
+/-- Reinterpret a 256-bit vector's `toNat` back as the original bitvector. -/
+private theorem ofNat_toB256 (x : B256) : (BitVec.ofNat 256 x.toNat : B256) = x := by
+ simp [BitVec.ofNat_toNat]
+
/-- `BitVec.ofNat 256` tra... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_15 | 9e05bc5b1e6ef8dc | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 3 | [
{
"theorem_name": "clMulNat_bv_eq_clMul",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [ clMulNat_bv_eq_fold_range, clMul_eq_fold_range]\n rw [← to256_toNat b, ofNat_toB256]",
"n_chars": 101,
... | [
{
"name": "ofNat_toB256",
"text": "/-- Reinterpret a 256-bit vector's `toNat` back as the original bitvector. -/\nprivate theorem ofNat_toB256 (x : B256) : (BitVec.ofNat 256 x.toNat : B256) = x := by\n simp [BitVec.ofNat_toNat]\n\n",
"fan_in": 3,
"n_lines": 5,
"n_chars": 193,
"n_subproofs":... | [
{
"name": "toPoly_clSqNat_eq_sq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 6,
"n_chars": 249,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_ne... | 4 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -126,6 +126,10 @@
let rhs := clMulNat q.toNat b.toNat 256 ^^^ r.toNat
a.toNat == rhs
+/-- Reinterpret a 256-bit vector's `toNat` back as the original bitvector. -/
+private theorem ofNat_toB256 (x : B256) : (BitVec.ofNat 256 x.toNat : B256) = x := by
+ simp [BitVec.ofNat_toNat]
+
/-- `BitVec.ofNat 256` tra... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_16 | 32f6f42ca0e3cad5 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "toPoly_mulByP_Nat",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold mulByP_Nat\n rw [ofNat_xor_256, ofNat_xor_256, ofNat_xor_256, ofNat_xor_256]\n repeat rw [toPoly_xor]\n rw [of... | [
{
"name": "ghashPoly_eq_P_val",
"text": "lemma ghashPoly_eq_P_val : ghashPoly = toPoly P_val := by\n unfold ghashPoly P_val\n repeat rw [toPoly_xor]\n rw [toPoly_one_shiftLeft (h := by omega), toPoly_one_shiftLeft (h := by omega),\n toPoly_one_shiftLeft (h := by omega), toPoly_one_shiftLeft (h := by o... | [
{
"name": "toPoly_mulByP_Nat",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 5,
"n_lines": 16,
"n_chars": 615,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 10,
"n_structural": 0,
"automation_only": false,
"max_ne... | 5 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -122,6 +122,15 @@
simp at h_absurd -- Finset.univ contains everything
-- Main Proof
+lemma ghashPoly_eq_P_val : ghashPoly = toPoly P_val := by
+ unfold ghashPoly P_val
+ repeat rw [toPoly_xor]
+ rw [toPoly_one_shiftLeft (h := by omega), toPoly_one_shiftLeft (h := by omega),
+ toPoly_one_shiftLeft (h :=... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_17 | bcf9ca7a4bdd0363 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "toPoly_mulByP_Nat",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold mulByP_Nat\n rw [ofNat_xor_256, ofNat_xor_256, ofNat_xor_256, ofNat_xor_256]\n repeat rw [toPoly_xor]\n rw [of... | [
{
"name": "ofNat_to256",
"text": "/-- Reinterpret a bounded `Nat` as the zero-extended 256-bit vector. -/\nprivate theorem ofNat_to256 (x : B128) : (BitVec.ofNat 256 x.toNat : B256) = to256 x := by\n apply BitVec.eq_of_toNat_eq\n rw [to256_toNat]\n exact Nat.mod_eq_of_lt (lt_of_lt_of_le x.isLt (by omega)... | [
{
"name": "verify_square_step_correct",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 10,
"n_lines": 20,
"n_chars": 898,
"n_subproofs": 2,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 6,
"n_structural": 2,
"automation_only": false,
... | 10 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -175,6 +175,12 @@
let rhs := clMulNat q.toNat b.toNat 256 ^^^ r.toNat
a.toNat == rhs
+/-- Reinterpret a bounded `Nat` as the zero-extended 256-bit vector. -/
+private theorem ofNat_to256 (x : B128) : (BitVec.ofNat 256 x.toNat : B256) = to256 x := by
+ apply BitVec.eq_of_toNat_eq
+ rw [to256_toNat]
+ exact... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_18 | c15806630b809c13 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 3 | [
{
"theorem_name": "clMulNat_bv_eq_clMul",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [ clMulNat_bv_eq_fold_range, clMul_eq_fold_range]\n rw [← to256_toNat b, ofNat_toB256]",
"n_chars": 101,
... | [
{
"name": "ofNat_toB256",
"text": "/-- Reinterpret a 256-bit vector's `toNat` back as the original bitvector. -/\nprivate theorem ofNat_toB256 (x : B256) : (BitVec.ofNat 256 x.toNat : B256) = x := by\n simp [BitVec.ofNat_toNat]\n\n",
"fan_in": 3,
"n_lines": 5,
"n_chars": 193,
"n_subproofs":... | [
{
"name": "verify_div_step_bounded",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 8,
"n_lines": 17,
"n_chars": 782,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 2,
"automation_only": false,
"m... | 8 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -126,6 +126,10 @@
let rhs := clMulNat q.toNat b.toNat 256 ^^^ r.toNat
a.toNat == rhs
+/-- Reinterpret a 256-bit vector's `toNat` back as the original bitvector. -/
+private theorem ofNat_toB256 (x : B256) : (BitVec.ofNat 256 x.toNat : B256) = x := by
+ simp [BitVec.ofNat_toNat]
+
/-- `BitVec.ofNat 256` tra... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_9cb8194efa42_19 | 1aa1453e35d8150a | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Fields/Binary/BF128Ghash/Prelude.lean | Prelude | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 3 | [
{
"theorem_name": "clMulNat_bv_eq_clMul",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [ clMulNat_bv_eq_fold_range, clMul_eq_fold_range]\n rw [← to256_toNat b, ofNat_toB256]",
"n_chars": 101,
... | [
{
"name": "ofNat_toB256",
"text": "/-- Reinterpret a 256-bit vector's `toNat` back as the original bitvector. -/\nprivate theorem ofNat_toB256 (x : B256) : (BitVec.ofNat 256 x.toNat : B256) = x := by\n simp [BitVec.ofNat_toNat]\n\n",
"fan_in": 3,
"n_lines": 5,
"n_chars": 193,
"n_subproofs":... | [
{
"name": "verify_div_step",
"fan_in": 0,
"n_deps_direct": 6,
"n_deps_transitive": 9,
"n_lines": 20,
"n_chars": 877,
"n_subproofs": 1,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 6,
"n_structural": 2,
"automation_only": false,
"max_nesti... | 9 | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | /-
Copyright (c) 2024-2025 ArkLib Contributors. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Chung Thai Nguyen, Quang Dao, Dimitris Mitsios
-/
import CompPoly.Fields.Binary.Common
/-! # BinaryField128Ghash Prelude
Define GF(2^128) as a single field extension over ... | @@ -144,6 +144,10 @@
rw [step]; exact ih (by omega)
· simp [show m = k + 1 by omega]
+/-- Reinterpret a 256-bit vector's `toNat` back as the original bitvector. -/
+private theorem ofNat_toB256 (x : B256) : (BitVec.ofNat 256 x.toNat : B256) = x := by
+ simp [BitVec.ofNat_toNat]
+
/-- `BitVec.ofNat 256` ... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_a1638dfeadb3_0 | a2873ec953eaa8de | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multivariate/Operations.lean | Operations | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "bind₁_C",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [bind₁_eq_aeval]\n simpa [show (algebraMap R (CMvPolynomial m R)) c = CMvPolynomial.C (n := m) c from rfl]\n using (aeval_C ... | [
{
"name": "bind₁_eq_aeval",
"text": "/-- The computable substitution `bind₁` agrees with algebraic evaluation. -/\nlemma bind₁_eq_aeval {n m : ℕ} {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R]\n (f : Fin n → CMvPolynomial m R) (p : CMvPolynomial n R) :\n bind₁ f p = aeval (σ := CMvPolynomial m R) ... | [
{
"name": "bind₁_C",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 396,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting": 4
}... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frantisek Silvasi, Julian Sutherland, Andrei Burdușa, Derek Sorensen, Dimitris Mitsios
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import CompPoly.Multivariate.MvPolyEquiv.Instances
/-... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frantisek Silvasi, Julian Sutherland, Andrei Burdușa, Derek Sorensen, Dimitris Mitsios
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import CompPoly.Multivariate.MvPolyEquiv.Instances
/-... | @@ -202,17 +202,35 @@
(fun acc mono c => CMvPolynomial.C (n := m) c * MonoR.evalMonomial f mono + acc)
0 p.1
+/-- The computable substitution `bind₁` agrees with algebraic evaluation. -/
+lemma bind₁_eq_aeval {n m : ℕ} {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R]
+ (f : Fin n → CMvPolynomial m R) (... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_a1638dfeadb3_1 | d9749147ae23f415 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multivariate/Operations.lean | Operations | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "fromCMvPolynomial_X",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [X_eq_monomial, fromCMvPolynomial_monomial, toFinsupp_unitMono]\n rfl",
"n_chars": 78,
"n_subproofs": 0,
... | [
{
"name": "X_eq_monomial",
"text": "lemma X_eq_monomial {k : ℕ} {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R]\n (i : Fin k) :\n CMvPolynomial.X (R := R) i = CMvPolynomial.monomial\n (Vector.ofFn (fun j => if j = i then 1 else 0))\n (1 : R) := by\n unfold CMvPolynomial.X CMvPolynomial.m... | [
{
"name": "fromCMvPolynomial_X",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 8,
"n_chars": 261,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nes... | 3 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frantisek Silvasi, Julian Sutherland, Andrei Burdușa, Derek Sorensen, Dimitris Mitsios
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import CompPoly.Multivariate.MvPolyEquiv.Instances
/-... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frantisek Silvasi, Julian Sutherland, Andrei Burdușa, Derek Sorensen, Dimitris Mitsios
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import CompPoly.Multivariate.MvPolyEquiv.Instances
/-... | @@ -253,6 +253,18 @@
/-! ## Bridge and transport lemmas (technical) -/
+lemma X_eq_monomial {k : ℕ} {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R]
+ (i : Fin k) :
+ CMvPolynomial.X (R := R) i = CMvPolynomial.monomial
+ (Vector.ofFn (fun j => if j = i then 1 else 0))
+ (1 : R) := by
+ unfold CM... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_a1638dfeadb3_2 | 31a112509e24372e | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multivariate/Operations.lean | Operations | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "foldl_add_comm",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [Std.ExtTreeMap.foldl_eq_foldl_toList]\n exact list_foldl_add_comm g t.toList 0",
"n_chars": 95,
"n_subpr... | [
{
"name": "list_foldl_add_comm",
"text": "lemma list_foldl_add_comm {β K V : Type*} [AddCommMonoid β]\n (g : K → V → β) (l : List (K × V)) (init : β) :\n List.foldl (fun acc pair => acc + g pair.1 pair.2) init l =\n List.foldl (fun acc pair => g pair.1 pair.2 + acc) init l := by\n induction l gene... | [
{
"name": "foldl_add_comm",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 391,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frantisek Silvasi, Julian Sutherland, Andrei Burdușa, Derek Sorensen, Dimitris Mitsios
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import CompPoly.Multivariate.MvPolyEquiv.Instances
/-... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frantisek Silvasi, Julian Sutherland, Andrei Burdușa, Derek Sorensen, Dimitris Mitsios
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import CompPoly.Multivariate.MvPolyEquiv.Instances
/-... | @@ -379,11 +379,24 @@
simp [MvPolynomial.eval₂_eta (p := fromCMvPolynomial p)]
_ = CPoly.polyRingEquiv (n := n) (R := R) p := rfl
+lemma list_foldl_add_comm {β K V : Type*} [AddCommMonoid β]
+ (g : K → V → β) (l : List (K × V)) (init : β) :
+ List.foldl (fun acc pair => acc + g pair.1 pair.2) in... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_a1638dfeadb3_3 | 622b361b0e984eb9 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multivariate/Operations.lean | Operations | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "fromCMvPolynomial_X",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [X_eq_monomial, fromCMvPolynomial_monomial, toFinsupp_unitMono]\n rfl",
"n_chars": 78,
"n_subproofs": 0,
... | [
{
"name": "fromCMvPolynomial_monomial",
"text": "lemma fromCMvPolynomial_monomial {k : ℕ} {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R]\n (mono : CMvMonomial k) (c : R) :\n fromCMvPolynomial (CMvPolynomial.monomial mono c) =\n MvPolynomial.monomial (CMvMonomial.toFinsupp mono) c := by\n by_ca... | [
{
"name": "sumToIter_eq",
"fan_in": 4,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 12,
"n_chars": 503,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 6,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 4 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frantisek Silvasi, Julian Sutherland, Andrei Burdușa, Derek Sorensen, Dimitris Mitsios
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import CompPoly.Multivariate.MvPolyEquiv.Instances
/-... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frantisek Silvasi, Julian Sutherland, Andrei Burdușa, Derek Sorensen, Dimitris Mitsios
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import CompPoly.Multivariate.MvPolyEquiv.Instances
/-... | @@ -275,10 +275,39 @@
simp [CMvMonomial.toFinsupp, Vector.get,
Finsupp.single_apply, eq_comm]
+lemma fromCMvPolynomial_monomial {k : ℕ} {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R]
+ (mono : CMvMonomial k) (c : R) :
+ fromCMvPolynomial (CMvPolynomial.monomial mono c) =
+ MvPolynomial.monomial (... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_a1638dfeadb3_4 | 375444a7053702b3 | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multivariate/Operations.lean | Operations | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "fromCMvPolynomial_X",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [X_eq_monomial, fromCMvPolynomial_monomial, toFinsupp_unitMono]\n rfl",
"n_chars": 78,
"n_subproofs": 0,
... | [
{
"name": "fromCMvPolynomial_monomial",
"text": "lemma fromCMvPolynomial_monomial {k : ℕ} {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R]\n (mono : CMvMonomial k) (c : R) :\n fromCMvPolynomial (CMvPolynomial.monomial mono c) =\n MvPolynomial.monomial (CMvMonomial.toFinsupp mono) c := by\n by_ca... | [
{
"name": "coeff_sumToIter",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 6,
"n_chars": 209,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting"... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frantisek Silvasi, Julian Sutherland, Andrei Burdușa, Derek Sorensen, Dimitris Mitsios
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import CompPoly.Multivariate.MvPolyEquiv.Instances
/-... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frantisek Silvasi, Julian Sutherland, Andrei Burdușa, Derek Sorensen, Dimitris Mitsios
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import CompPoly.Multivariate.MvPolyEquiv.Instances
/-... | @@ -275,10 +275,39 @@
simp [CMvMonomial.toFinsupp, Vector.get,
Finsupp.single_apply, eq_comm]
+lemma fromCMvPolynomial_monomial {k : ℕ} {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R]
+ (mono : CMvMonomial k) (c : R) :
+ fromCMvPolynomial (CMvPolynomial.monomial mono c) =
+ MvPolynomial.monomial (... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_a1638dfeadb3_5 | dc7bb787e16588bd | lean | lean | github.com/Verified-zkEVM/CompPoly | e95ba1b1cac21ac3e980725abcfb2a0c707d1062 | CompPoly/Multivariate/Operations.lean | Operations | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "fromCMvPolynomial_X",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [X_eq_monomial, fromCMvPolynomial_monomial, toFinsupp_unitMono]\n rfl",
"n_chars": 78,
"n_subproofs": 0,
... | [
{
"name": "fromCMvPolynomial_monomial",
"text": "lemma fromCMvPolynomial_monomial {k : ℕ} {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R]\n (mono : CMvMonomial k) (c : R) :\n fromCMvPolynomial (CMvPolynomial.monomial mono c) =\n MvPolynomial.monomial (CMvMonomial.toFinsupp mono) c := by\n by_ca... | [
{
"name": "sumToIter_add",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 6,
"n_chars": 192,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": ... | 5 | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frantisek Silvasi, Julian Sutherland, Andrei Burdușa, Derek Sorensen, Dimitris Mitsios
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import CompPoly.Multivariate.MvPolyEquiv.Instances
/-... | /-
Copyright (c) 2025 CompPoly. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frantisek Silvasi, Julian Sutherland, Andrei Burdușa, Derek Sorensen, Dimitris Mitsios
-/
import CompPoly.Multivariate.MvPolyEquiv.Eval
import CompPoly.Multivariate.MvPolyEquiv.Instances
/-... | @@ -275,10 +275,39 @@
simp [CMvMonomial.toFinsupp, Vector.get,
Finsupp.single_apply, eq_comm]
+lemma fromCMvPolynomial_monomial {k : ℕ} {R : Type*} [CommSemiring R] [BEq R] [LawfulBEq R]
+ (mono : CMvMonomial k) (c : R) :
+ fromCMvPolynomial (CMvPolynomial.monomial mono c) =
+ MvPolynomial.monomial (... | {
"repo": "CompPoly",
"git_repo": "github.com/Verified-zkEVM/CompPoly",
"revision": "e95ba1b1cac21ac3e980725abcfb2a0c707d1062",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-dele... |
ablate_0dd4eb57d9bd_0 | ab451f34742004c1 | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LinearAlgebra/Matrix/Spectrum.lean | Spectrum | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "det_eq_prod_eigenvalues",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply mul_left_cancel₀ (det_ne_zero_of_left_inverse\n (Basis.toMatrix_mul_toMatrix_flip (Pi.basisFun 𝕜 n) xs.to... | [
{
"name": "spectral_theorem",
"text": "/-- *Diagonalization theorem*, *spectral theorem* for matrices; A hermitian matrix can be\ndiagonalized by a change of basis using a matrix consisting of eigenvectors. -/\ntheorem spectral_theorem (xs : OrthonormalBasis n 𝕜 (EuclideanSpace 𝕜 n)) (as : n → ℝ)\n (hx... | [
{
"name": "det_eq_prod_eigenvalues",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 423,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max... | 1 | import Mathlib.LinearAlgebra.Matrix.Spectrum
import CvxLean.Lib.Math.Analysis.InnerProductSpace.Spectrum
/-!
Version of the spectral theorem for matrices.
-/
namespace Matrix
variable {𝕜 : Type _} [RCLike 𝕜] [DecidableEq 𝕜]
variable {n : Type _} [Fintype n] [DecidableEq n]
variable {A : Matrix n n 𝕜}
open Matri... | import Mathlib.LinearAlgebra.Matrix.Spectrum
import CvxLean.Lib.Math.Analysis.InnerProductSpace.Spectrum
/-!
Version of the spectral theorem for matrices.
-/
namespace Matrix
variable {𝕜 : Type _} [RCLike 𝕜] [DecidableEq 𝕜]
variable {n : Type _} [Fintype n] [DecidableEq n]
variable {A : Matrix n n 𝕜}
open Matri... | @@ -27,8 +27,45 @@
noncomputable instance : InnerProductSpace 𝕜 (n → 𝕜) :=
PiLp.innerProductSpace (fun _ : n => 𝕜)
+/-- *Diagonalization theorem*, *spectral theorem* for matrices; A hermitian matrix can be
+diagonalized by a change of basis using a matrix consisting of eigenvectors. -/
+theorem spectral_theore... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_55af77dc5403_0 | 035e73dc11626a4f | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/SchurComplement.lean | SchurComplement | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "PosSemidef.fromBlocks₁₁",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [PosSemidef, IsHermitian.fromBlocks₁₁ _ _ hA.1]\n constructor\n { intro h; refine' ⟨h.1, _⟩; intro x\n hav... | [
{
"name": "schur_complement_eq₁₁",
"text": "lemma schur_complement_eq₁₁ [Fintype m] [DecidableEq m] [Fintype n] {A : Matrix m m 𝕜}\n (B : Matrix m n 𝕜) (D : Matrix n n 𝕜) (x : m → 𝕜) (y : n → 𝕜) [Invertible A]\n (hA : A.IsHermitian) :\n vecMul (star (x ⊕ᵥ y)) (fromBlocks A B Bᴴ D) ⬝ᵥ (x ⊕ᵥ y) ... | [
{
"name": "PosSemidef.fromBlocks₁₁",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 19,
"n_chars": 900,
"n_subproofs": 1,
"n_tactics": 20,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 6,
"n_structural": 9,
"automation_only": false,
"m... | 1 | import Mathlib.LinearAlgebra.Matrix.Symmetric
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.Algebra.Star.Pi
/-!
# Schur complement
This file proves properties of the Schur complement `D - C A⁻¹ B` of a block Matrix `[A B; C D]`.
The determinant of a bl... | import Mathlib.LinearAlgebra.Matrix.Symmetric
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.Algebra.Star.Pi
/-!
# Schur complement
This file proves properties of the Schur complement `D - C A⁻¹ B` of a block Matrix `[A B; C D]`.
The determinant of a bl... | @@ -25,6 +25,17 @@
scoped infix:65 " ⊕ᵥ " => Sum.elim
+lemma schur_complement_eq₁₁ [Fintype m] [DecidableEq m] [Fintype n] {A : Matrix m m 𝕜}
+ (B : Matrix m n 𝕜) (D : Matrix n n 𝕜) (x : m → 𝕜) (y : n → 𝕜) [Invertible A]
+ (hA : A.IsHermitian) :
+ vecMul (star (x ⊕ᵥ y)) (fromBlocks A B Bᴴ D) ⬝ᵥ (x ⊕ᵥ... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_55af77dc5403_1 | a3f45d03ebd1395d | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/SchurComplement.lean | SchurComplement | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "PosSemidef.fromBlocks₁₁",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [PosSemidef, IsHermitian.fromBlocks₁₁ _ _ hA.1]\n constructor\n { intro h; refine' ⟨h.1, _⟩; intro x\n hav... | [
{
"name": "schur_complement_eq₁₁",
"text": "lemma schur_complement_eq₁₁ [Fintype m] [DecidableEq m] [Fintype n] {A : Matrix m m 𝕜}\n (B : Matrix m n 𝕜) (D : Matrix n n 𝕜) (x : m → 𝕜) (y : n → 𝕜) [Invertible A]\n (hA : A.IsHermitian) :\n vecMul (star (x ⊕ᵥ y)) (fromBlocks A B Bᴴ D) ⬝ᵥ (x ⊕ᵥ y) ... | [
{
"name": "PosSemidef.fromBlocks₂₂",
"fan_in": 0,
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"n_deps_transitive": 3,
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"max... | 1 | import Mathlib.LinearAlgebra.Matrix.Symmetric
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.Algebra.Star.Pi
/-!
# Schur complement
This file proves properties of the Schur complement `D - C A⁻¹ B` of a block Matrix `[A B; C D]`.
The determinant of a bl... | import Mathlib.LinearAlgebra.Matrix.Symmetric
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.Algebra.Star.Pi
/-!
# Schur complement
This file proves properties of the Schur complement `D - C A⁻¹ B` of a block Matrix `[A B; C D]`.
The determinant of a bl... | @@ -25,6 +25,17 @@
scoped infix:65 " ⊕ᵥ " => Sum.elim
+lemma schur_complement_eq₁₁ [Fintype m] [DecidableEq m] [Fintype n] {A : Matrix m m 𝕜}
+ (B : Matrix m n 𝕜) (D : Matrix n n 𝕜) (x : m → 𝕜) (y : n → 𝕜) [Invertible A]
+ (hA : A.IsHermitian) :
+ vecMul (star (x ⊕ᵥ y)) (fromBlocks A B Bᴴ D) ⬝ᵥ (x ⊕ᵥ... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_ddee381108d4_0 | 290320732ea3ea85 | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LinearAlgebra/Matrix/Block.lean | Block | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "BlockTriangular_blockDiagonal",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rintro ⟨i, i'⟩ ⟨j, j'⟩ h\n rw [blockDiagonal'_eq_blockDiagonal, BlockTriangular_blockDiagonal']\n exact h",... | [
{
"name": "BlockTriangular_blockDiagonal'",
"text": "lemma BlockTriangular_blockDiagonal' [DecidableEq α]\n (d : ∀ (i : α), Matrix (m' i) (m' i) R) :\n BlockTriangular (blockDiagonal' d) Sigma.fst := by\n rintro ⟨i, i'⟩ ⟨j, j'⟩ h\n apply blockDiagonal'_apply_ne d i' j' (fun h' => ne_of_lt h h'.symm... | [
{
"name": "BlockTriangular_blockDiagonal",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
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... | 1 | import Mathlib.LinearAlgebra.Matrix.Block
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
/-!
More results about block matrices (see `Mathlib.LinearAlgebra.Matrix.Block`).
-/
namespace Matrix
open Matrix
open Finset
universe v
variable {α β m n o : Type _} {m' n' : α → Type _}
variable {R : Type v} [CommRi... | import Mathlib.LinearAlgebra.Matrix.Block
import Mathlib.LinearAlgebra.Matrix.NonsingularInverse
/-!
More results about block matrices (see `Mathlib.LinearAlgebra.Matrix.Block`).
-/
namespace Matrix
open Matrix
open Finset
universe v
variable {α β m n o : Type _} {m' n' : α → Type _}
variable {R : Type v} [CommRi... | @@ -26,8 +26,17 @@
variable [Preorder α]
+lemma BlockTriangular_blockDiagonal' [DecidableEq α]
+ (d : ∀ (i : α), Matrix (m' i) (m' i) R) :
+ BlockTriangular (blockDiagonal' d) Sigma.fst := by
+ rintro ⟨i, i'⟩ ⟨j, j'⟩ h
+ apply blockDiagonal'_apply_ne d i' j' (fun h' => ne_of_lt h h'.symm)
+
lemma BlockTr... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_295174d16299_0 | 1fd5363689dfec73 | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/Data/Real.lean | Real | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "inv_eq_pow_neg_one",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [inv_eq_one_div, one_div_eq_pow_neg_one ha]",
"n_chars": 52,
"n_subproofs": 0,
"n_tactics": 2,
"cyclo... | [
{
"name": "one_div_eq_pow_neg_one",
"text": "lemma one_div_eq_pow_neg_one {a : ℝ} (ha : 0 < a) : 1 / a = a ^ (-1 : ℝ) := by\n rw [rpow_neg (le_of_lt ha), rpow_one, div_eq_mul_inv, one_mul]\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 149,
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"cyclomatic... | [
{
"name": "inv_eq_pow_neg_one",
"fan_in": 0,
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"max_nest... | 1 | import Mathlib.Data.Real.Basic
import Mathlib.Data.Complex.Exponential
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
Extra real functions and results. Some are needed to define atoms. There are also some lemmas that
are useful for the pre-DCP rewrite system.
-/
namespace Real
/-- This makes real powers the d... | import Mathlib.Data.Real.Basic
import Mathlib.Data.Complex.Exponential
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
Extra real functions and results. Some are needed to define atoms. There are also some lemmas that
are useful for the pre-DCP rewrite system.
-/
namespace Real
/-- This makes real powers the d... | @@ -59,8 +59,12 @@
/- Lemmas used to prove properties about cones. -/
-lemma inv_eq_pow_neg_one {a : ℝ} (ha : 0 < a) : a⁻¹ = a ^ (-1 : ℝ) := sorry
+lemma one_div_eq_pow_neg_one {a : ℝ} (ha : 0 < a) : 1 / a = a ^ (-1 : ℝ) := by
+ rw [rpow_neg (le_of_lt ha), rpow_one, div_eq_mul_inv, one_mul]
+lemma inv_eq_pow_ne... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
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"proof_assistant": "lean",
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"ablator_flags": [
"--coroll... |
ablate_d7139e7c021d_0 | 7c4ae7fdbf1daba6 | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/CovarianceEstimation.lean | CovarianceEstimation | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "prod_gaussianPdf_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n Finset.prod_pos (fun _ _ => gaussianPdf_pos _ _ h)",
"n_chars": 53,
"n_subproofs": 0,
"n_tactics": 1,
"cy... | [
{
"name": "gaussianPdf_pos",
"text": "lemma gaussianPdf_pos {n : ℕ} (R : Matrix (Fin n) (Fin n) ℝ) (y : Fin n → ℝ) (h : R.PosDef) :\n 0 < gaussianPdf R y := by\n refine' mul_pos (div_pos zero_lt_one (sqrt_pos.2 (mul_pos _ h.det_pos))) (exp_pos _)\n exact (pow_pos (mul_pos (by positivity) pi_pos) n)\n\n... | [
{
"name": "prod_gaussianPdf_pos",
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"automation_only": false,
"max_ne... | 1 | import CvxLean.Lib.Math.LinearAlgebra.Matrix.PosDef
/-!
Definitions needed for `CvxLean/Examples/CovarianceEstimation.lean`.
-/
noncomputable section CovarianceEstimation
open Real
open Matrix
open BigOperators
def Matrix.quadForm {n : ℕ} (R : Matrix (Fin n) (Fin n) ℝ) (x : Fin n → ℝ) : ℝ :=
x ⬝ᵥ R.mulVec x
de... | import CvxLean.Lib.Math.LinearAlgebra.Matrix.PosDef
/-!
Definitions needed for `CvxLean/Examples/CovarianceEstimation.lean`.
-/
noncomputable section CovarianceEstimation
open Real
open Matrix
open BigOperators
def Matrix.quadForm {n : ℕ} (R : Matrix (Fin n) (Fin n) ℝ) (x : Fin n → ℝ) : ℝ :=
x ⬝ᵥ R.mulVec x
de... | @@ -21,8 +21,14 @@
def covarianceMatrix {N n : ℕ} (y : Fin N → Fin n → ℝ) : Matrix (Fin n) (Fin n) ℝ :=
fun i j : Fin n => (∑ k : Fin N, y k i * y k j) / N
+lemma gaussianPdf_pos {n : ℕ} (R : Matrix (Fin n) (Fin n) ℝ) (y : Fin n → ℝ) (h : R.PosDef) :
+ 0 < gaussianPdf R y := by
+ refine' mul_pos (div_pos zero... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_d7139e7c021d_1 | ee8b5b563c4b6f7e | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/CovarianceEstimation.lean | CovarianceEstimation | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "prod_gaussianPdf_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n Finset.prod_pos (fun _ _ => gaussianPdf_pos _ _ h)",
"n_chars": 53,
"n_subproofs": 0,
"n_tactics": 1,
"cy... | [
{
"name": "gaussianPdf_pos",
"text": "lemma gaussianPdf_pos {n : ℕ} (R : Matrix (Fin n) (Fin n) ℝ) (y : Fin n → ℝ) (h : R.PosDef) :\n 0 < gaussianPdf R y := by\n refine' mul_pos (div_pos zero_lt_one (sqrt_pos.2 (mul_pos _ h.det_pos))) (exp_pos _)\n exact (pow_pos (mul_pos (by positivity) pi_pos) n)\n\n... | [
{
"name": "log_prod_gaussianPdf",
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"n_deps_transitive": 1,
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"automation_only": false,
"max... | 1 | import CvxLean.Lib.Math.LinearAlgebra.Matrix.PosDef
/-!
Definitions needed for `CvxLean/Examples/CovarianceEstimation.lean`.
-/
noncomputable section CovarianceEstimation
open Real
open Matrix
open BigOperators
def Matrix.quadForm {n : ℕ} (R : Matrix (Fin n) (Fin n) ℝ) (x : Fin n → ℝ) : ℝ :=
x ⬝ᵥ R.mulVec x
de... | import CvxLean.Lib.Math.LinearAlgebra.Matrix.PosDef
/-!
Definitions needed for `CvxLean/Examples/CovarianceEstimation.lean`.
-/
noncomputable section CovarianceEstimation
open Real
open Matrix
open BigOperators
def Matrix.quadForm {n : ℕ} (R : Matrix (Fin n) (Fin n) ℝ) (x : Fin n → ℝ) : ℝ :=
x ⬝ᵥ R.mulVec x
de... | @@ -21,11 +21,16 @@
def covarianceMatrix {N n : ℕ} (y : Fin N → Fin n → ℝ) : Matrix (Fin n) (Fin n) ℝ :=
fun i j : Fin n => (∑ k : Fin N, y k i * y k j) / N
+lemma gaussianPdf_pos {n : ℕ} (R : Matrix (Fin n) (Fin n) ℝ) (y : Fin n → ℝ) (h : R.PosDef) :
+ 0 < gaussianPdf R y := by
+ refine' mul_pos (div_pos zer... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_e7a6bd47545b_0 | 10338ca6b90d545c | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LinearAlgebra/Eigenspace.lean | Eigenspace | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "has_eigenvector_add",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨eigenspace_add ⟨hf.1, hg.1⟩, hf.2⟩",
"n_chars": 46,
"n_subproofs": 0,
"n_tactics": 1,
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... | [
{
"name": "eigenspace_add",
"text": "lemma eigenspace_add {f g : End R M} {a b : R} :\n eigenspace f a ⊓ eigenspace g b ≤ eigenspace (f + g) (a + b) := by\n rintro x ⟨hf, hg⟩\n simp only [eigenspace, SetLike.mem_coe, LinearMap.mem_ker,\n LinearMap.sub_apply, algebraMap_end_apply] at hf hg\n simp on... | [
{
"name": "has_eigenvector_add",
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"automation_only": false,
"max_nes... | 1 | import Mathlib.LinearAlgebra.Eigenspace.Basic
/-!
Results about the eigenspaces of the sum of two endomorphisms.
-/
universe u v w
namespace Module
namespace End
variable {K R : Type v} {V M : Type w}
variable [CommRing R] [AddCommGroup M] [Module R M]
variable [Field K] [AddCommGroup V] [Module K V]
lemma has_ei... | import Mathlib.LinearAlgebra.Eigenspace.Basic
/-!
Results about the eigenspaces of the sum of two endomorphisms.
-/
universe u v w
namespace Module
namespace End
variable {K R : Type v} {V M : Type w}
variable [CommRing R] [AddCommGroup M] [Module R M]
variable [Field K] [AddCommGroup V] [Module K V]
lemma eigens... | @@ -14,8 +14,18 @@
variable [CommRing R] [AddCommGroup M] [Module R M]
variable [Field K] [AddCommGroup V] [Module K V]
+lemma eigenspace_add {f g : End R M} {a b : R} :
+ eigenspace f a ⊓ eigenspace g b ≤ eigenspace (f + g) (a + b) := by
+ rintro x ⟨hf, hg⟩
+ simp only [eigenspace, SetLike.mem_coe, LinearMap.... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
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ablate_e7a6bd47545b_1 | 75b2be076bbd04a1 | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LinearAlgebra/Eigenspace.lean | Eigenspace | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
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"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨by { rw [eigenspace_one]; apply Submodule.mem_top }, hx⟩",
"n_chars": 64,
"n_subproofs": 0,
"n_tactics": 2,
... | [
{
"name": "eigenspace_one",
"text": "lemma eigenspace_one : eigenspace (1 : End R M) 1 = ⊤ := by\n apply eq_top_iff.2\n intros x _\n simp only [mem_eigenspace_iff, LinearMap.one_apply, one_smul]\n\n",
"fan_in": 1,
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"n_chars": 161,
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"cy... | [
{
"name": "has_eigenvector_one",
"fan_in": 0,
"n_deps_direct": 1,
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"n_lines": 4,
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"n_rewrites": 1,
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"automation_only": false,
"max_nes... | 1 | import Mathlib.LinearAlgebra.Eigenspace.Basic
/-!
Results about the eigenspaces of the sum of two endomorphisms.
-/
universe u v w
namespace Module
namespace End
variable {K R : Type v} {V M : Type w}
variable [CommRing R] [AddCommGroup M] [Module R M]
variable [Field K] [AddCommGroup V] [Module K V]
lemma has_ei... | import Mathlib.LinearAlgebra.Eigenspace.Basic
/-!
Results about the eigenspaces of the sum of two endomorphisms.
-/
universe u v w
namespace Module
namespace End
variable {K R : Type v} {V M : Type w}
variable [CommRing R] [AddCommGroup M] [Module R M]
variable [Field K] [AddCommGroup V] [Module K V]
lemma eigens... | @@ -14,8 +14,13 @@
variable [CommRing R] [AddCommGroup M] [Module R M]
variable [Field K] [AddCommGroup V] [Module K V]
+lemma eigenspace_one : eigenspace (1 : End R M) 1 = ⊤ := by
+ apply eq_top_iff.2
+ intros x _
+ simp only [mem_eigenspace_iff, LinearMap.one_apply, one_smul]
+
lemma has_eigenvector_one {x : ... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
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"ablator_flags": [
"--coroll... |
ablate_ea459e459dbd_0 | cb7de495b7f6fddf | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LinearAlgebra/Matrix/LDL.lean | LDL | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "lowerTriangular_lower",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n lowerTriangular_inv_of_lowerTriangular (lowerTriangular_lowerInv hS)",
"n_chars": 71,
"n_subproofs": 0,
"n_t... | [
{
"name": "lowerTriangular_lowerInv",
"text": "lemma lowerTriangular_lowerInv : lowerTriangular (lowerInv hS) := by\n apply lowerInv_triangular\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 98,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites":... | [
{
"name": "lowerTriangular_lower",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 4,
"n_chars": 132,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_n... | 1 | import Mathlib.LinearAlgebra.Matrix.LDL
import Mathlib.LinearAlgebra.Matrix.Block
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Spectrum
import CvxLean.Lib.Math.Analysis.InnerProductSpace.GramSchmidtOrtho
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
/-!
More results about LDL factorization (see `Mathlib.Line... | import Mathlib.LinearAlgebra.Matrix.LDL
import Mathlib.LinearAlgebra.Matrix.Block
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Spectrum
import CvxLean.Lib.Math.Analysis.InnerProductSpace.GramSchmidtOrtho
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
/-!
More results about LDL factorization (see `Mathlib.Line... | @@ -28,8 +28,12 @@
rw [Basis.coe_mk, ← @repr_gramSchmidt_diagonal 𝕜 (n → 𝕜) _ _ _ n _ _ _ i (Pi.basisFun 𝕜 n)]
simp [Basis.toMatrix]
-lemma lowerTriangular_lower : lowerTriangular (lower hS) := sorry
+lemma lowerTriangular_lowerInv : lowerTriangular (lowerInv hS) := by
+ apply lowerInv_triangular
+lemma l... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_8a1eb5d24c69_0 | 9ed333362bc2a0e5 | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Cones/SOCone.lean | SOCone | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "soCone_add_sub_two_of_nonneg",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h := soCone_add_sub_two_mul_of_nonneg 1 hx hy\n rw [mul_one, one_rpow] at h\n exact h",
"n_chars": ... | [
{
"name": "soCone_add_sub_two_mul_of_nonneg",
"text": "/-- To handle powers, a common trick is to use the fact that for\n`x, y ≥ 0` and `z ∈ ℝ`,\n `((x + y), (x - y, 2z)ᵀ) ∈ 𝒬ⁿ⁺¹ ↔ z ^ 2 ≤ xy`. -/\nlemma soCone_add_sub_two_mul_of_nonneg {x y : ℝ} (z : ℝ)\n (hx : 0 ≤ x) (hy : 0 ≤ y) : soCone (x + y)... | [
{
"name": "soCone_add_sub_two_of_nonneg",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 290,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
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"n_rewrites": 1,
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"automation_only": false,
... | 1 | import Mathlib.Data.Real.Sqrt
import Mathlib.Data.Matrix.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import CvxLean.Lib.Math.Data.Real
import CvxLean.Lib.Math.Data.Vec
/-!
Second-order cones.
We follow the MOSEK modeling cookbook: https://docs.mosek.com/modeling-cookbook/cqo.html
-/
namespace Real
open ... | import Mathlib.Data.Real.Sqrt
import Mathlib.Data.Matrix.Basic
import Mathlib.Analysis.SpecialFunctions.Pow.Real
import CvxLean.Lib.Math.Data.Real
import CvxLean.Lib.Math.Data.Vec
/-!
Second-order cones.
We follow the MOSEK modeling cookbook: https://docs.mosek.com/modeling-cookbook/cqo.html
-/
namespace Real
open ... | @@ -48,9 +48,21 @@
section Lemmas
+/-- To handle powers, a common trick is to use the fact that for
+`x, y ≥ 0` and `z ∈ ℝ`,
+ `((x + y), (x - y, 2z)ᵀ) ∈ 𝒬ⁿ⁺¹ ↔ z ^ 2 ≤ xy`. -/
+lemma soCone_add_sub_two_mul_of_nonneg {x y : ℝ} (z : ℝ)
+ (hx : 0 ≤ x) (hy : 0 ≤ y) : soCone (x + y) ![x - y, 2 * z] ↔ z ^ (2 :... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_1af40f539f2e_0 | 5affdf4afb04821e | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/Subadditivity.lean | Subadditivity | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "PosSemidef.sqrt_mul_sqrt",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n calc\n hA.1.sqrt * hA.1.sqrt =\n hA.1.eigenvectorMatrix * (Matrix.diagonal (fun i => (hA.1.eigenvalues i).sq... | [
{
"name": "conjTranspose_eq_transpose",
"text": "lemma conjTranspose_eq_transpose {m n : Type _} {A : Matrix m n ℝ} : Aᴴ = Aᵀ := rfl\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 91,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_s... | [
{
"name": "PosSemidef.sqrt_mul_sqrt",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 18,
"n_chars": 816,
"n_subproofs": 0,
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"automation_only": false,
"... | 3 | import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.LinearAlgebra.Matrix.Spectrum
import Mathlib.LinearAlgebra.Eigenspace.Basic
import Mathlib.LinearAlgebra.Matrix.LDL
import Mathlib.LinearAlgebra.Matrix.DotProduct
import CvxLean.Lib.Math.LinearAlgebra.Matrix.PosDef
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Sp... | import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.LinearAlgebra.Matrix.Spectrum
import Mathlib.LinearAlgebra.Eigenspace.Basic
import Mathlib.LinearAlgebra.Matrix.LDL
import Mathlib.LinearAlgebra.Matrix.DotProduct
import CvxLean.Lib.Math.LinearAlgebra.Matrix.PosDef
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Sp... | @@ -43,9 +43,24 @@
noncomputable def IsHermitian.sqrt {A : Matrix n n ℝ} (hA : A.IsHermitian) : Matrix n n ℝ :=
hA.eigenvectorMatrix * Matrix.diagonal (fun i => (hA.eigenvalues i).sqrt) * hA.eigenvectorMatrixᵀ
+lemma conjTranspose_eq_transpose {m n : Type _} {A : Matrix m n ℝ} : Aᴴ = Aᵀ := rfl
+
@[simp]
lemma P... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_1af40f539f2e_1 | 9718af79309b82bb | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/Subadditivity.lean | Subadditivity | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "PosSemidef.sqrt_mul_sqrt",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n calc\n hA.1.sqrt * hA.1.sqrt =\n hA.1.eigenvectorMatrix * (Matrix.diagonal (fun i => (hA.1.eigenvalues i).sq... | [
{
"name": "conjTranspose_eq_transpose",
"text": "lemma conjTranspose_eq_transpose {m n : Type _} {A : Matrix m n ℝ} : Aᴴ = Aᵀ := rfl\n\n",
"fan_in": 2,
"n_lines": 3,
"n_chars": 91,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_s... | [
{
"name": "PosSemidef.PosDef_iff_det_ne_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 18,
"n_chars": 828,
"n_subproofs": 1,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 5,
"automation_only": fal... | 1 | import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.LinearAlgebra.Matrix.Spectrum
import Mathlib.LinearAlgebra.Eigenspace.Basic
import Mathlib.LinearAlgebra.Matrix.LDL
import Mathlib.LinearAlgebra.Matrix.DotProduct
import CvxLean.Lib.Math.LinearAlgebra.Matrix.PosDef
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Sp... | import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.LinearAlgebra.Matrix.Spectrum
import Mathlib.LinearAlgebra.Eigenspace.Basic
import Mathlib.LinearAlgebra.Matrix.LDL
import Mathlib.LinearAlgebra.Matrix.DotProduct
import CvxLean.Lib.Math.LinearAlgebra.Matrix.PosDef
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Sp... | @@ -43,9 +43,24 @@
noncomputable def IsHermitian.sqrt {A : Matrix n n ℝ} (hA : A.IsHermitian) : Matrix n n ℝ :=
hA.eigenvectorMatrix * Matrix.diagonal (fun i => (hA.eigenvalues i).sqrt) * hA.eigenvectorMatrixᵀ
+lemma conjTranspose_eq_transpose {m n : Type _} {A : Matrix m n ℝ} : Aᴴ = Aᵀ := rfl
+
@[simp]
lemma P... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_1af40f539f2e_2 | d25bcbfd646d5417 | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/Subadditivity.lean | Subadditivity | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "det_add_det_le_det_add'",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let sqrtA := hA.1.sqrt\n have isUnit_det_sqrtA :=\n isUnit_iff_ne_zero.2 hA.PosDef_sqrt.det_ne_zero\n have : ... | [
{
"name": "one_add_prod_le_prod_one_add",
"text": "lemma one_add_prod_le_prod_one_add {n : Type _} [Fintype n] [Nonempty n]\n (f : n → ℝ) (hf : ∀ i, 0 ≤ f i) : 1 + (∏ i, f i) ≤ ∏ i, (1 + f i) := by\n classical\n calc 1 + (∏ i, f i)\n = (∏ _a : n, 1 : ℝ) * ∏ a : n in univ \\ univ, f a\n + (∏ a :... | [
{
"name": "det_add_det_le_det_add'",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 50,
"n_chars": 2637,
"n_subproofs": 4,
"n_tactics": 44,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 8,
"n_structural": 7,
"automation_only": false,
"... | 1 | import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.LinearAlgebra.Matrix.Spectrum
import Mathlib.LinearAlgebra.Eigenspace.Basic
import Mathlib.LinearAlgebra.Matrix.LDL
import Mathlib.LinearAlgebra.Matrix.DotProduct
import CvxLean.Lib.Math.LinearAlgebra.Matrix.PosDef
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Sp... | import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.LinearAlgebra.Matrix.Spectrum
import Mathlib.LinearAlgebra.Eigenspace.Basic
import Mathlib.LinearAlgebra.Matrix.LDL
import Mathlib.LinearAlgebra.Matrix.DotProduct
import CvxLean.Lib.Math.LinearAlgebra.Matrix.PosDef
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Sp... | @@ -16,6 +16,21 @@
open BigOperators
+lemma one_add_prod_le_prod_one_add {n : Type _} [Fintype n] [Nonempty n]
+ (f : n → ℝ) (hf : ∀ i, 0 ≤ f i) : 1 + (∏ i, f i) ≤ ∏ i, (1 + f i) := by
+ classical
+ calc 1 + (∏ i, f i)
+ = (∏ _a : n, 1 : ℝ) * ∏ a : n in univ \ univ, f a
+ + (∏ a : n in ∅, 1) * ∏ a : n... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_1af40f539f2e_3 | 105a515322c3dcfe | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/Subadditivity.lean | Subadditivity | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "det_add_det_le_det_add",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hA' : A.det = 0\n { by_cases hB' : B.det = 0\n { simp [hA', hB']\n apply (hA.add hB).det_nonneg }\... | [
{
"name": "det_add_det_le_det_add'",
"text": "/-- Subadditivity lemma for positive semidefinite matrices. This version assumes that one of the\nmatrices is positive definite. See `det_add_det_le_det_add` for the more general statement.\n\nThe argument is taken from Andreas Thom's comment on mathoverflow:\nh... | [
{
"name": "det_add_det_le_det_add",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 12,
"n_chars": 530,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max... | 2 | import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.LinearAlgebra.Matrix.Spectrum
import Mathlib.LinearAlgebra.Eigenspace.Basic
import Mathlib.LinearAlgebra.Matrix.LDL
import Mathlib.LinearAlgebra.Matrix.DotProduct
import CvxLean.Lib.Math.LinearAlgebra.Matrix.PosDef
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Sp... | import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.LinearAlgebra.Matrix.Spectrum
import Mathlib.LinearAlgebra.Eigenspace.Basic
import Mathlib.LinearAlgebra.Matrix.LDL
import Mathlib.LinearAlgebra.Matrix.DotProduct
import CvxLean.Lib.Math.LinearAlgebra.Matrix.PosDef
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Sp... | @@ -115,9 +115,65 @@
rw [← hM.sqrt_mul_sqrt, det_mul, sqrtMdet0, mul_zero] at hdet
apply hdet rfl
+/-- Subadditivity lemma for positive semidefinite matrices. This version assumes that one of the
+matrices is positive definite. See `det_add_det_le_det_add` for the more general statement.
+
+The argument is take... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_074ae4d0573d_0 | 03fcf79a99aa540c | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LinearAlgebra/Matrix/PosDef.lean | PosDef | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "PosDef.nonsingular_inv",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine' ⟨hM.1.nonsingular_inv (isUnit_iff_ne_zero.2 hM.det_ne_zero), _⟩\n intros x hx\n have hMMinv := mul_nonsin... | [
{
"name": "conj_symm",
"text": "lemma conj_symm {x : n → 𝕜} {M : Matrix n n 𝕜} (hM : M.IsHermitian) :\n star (star x ⬝ᵥ mulVec M x) = star x ⬝ᵥ mulVec M x := by\n nth_rewrite 1 [star_dotProduct, star_mulVec]\n rw [star_star, dotProduct_mulVec, hM.eq]\n\n",
"fan_in": 1,
"n_lines": 6,
"n_ch... | [
{
"name": "PosDef.nonsingular_inv",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 599,
"n_subproofs": 3,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"ma... | 1 | import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.Algebra.Star.Pi
/-!
More results about positive definite and positive semidefinite matrices (see
`Mathlib.LinearAlgebra.Matrix.PosDef`).
-/
namespace Matrix
variable {m n : Type _} [Fintype m] [Fintype n]
variable {𝕜 : Type _}
variable [NormedField 𝕜] [Part... | import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.Algebra.Star.Pi
/-!
More results about positive definite and positive semidefinite matrices (see
`Mathlib.LinearAlgebra.Matrix.PosDef`).
-/
namespace Matrix
variable {m n : Type _} [Fintype m] [Fintype n]
variable {𝕜 : Type _}
variable [NormedField 𝕜] [Part... | @@ -31,7 +31,21 @@
refine' (Matrix.inv_eq_right_inv _).symm
rw [conjTranspose_nonsing_inv, hM.eq, mul_nonsing_inv _ hMdet]
-lemma PosDef.nonsingular_inv [DecidableEq n] {M : Matrix n n 𝕜} (hM : M.PosDef) : M⁻¹.PosDef := sorry
+lemma conj_symm {x : n → 𝕜} {M : Matrix n n 𝕜} (hM : M.IsHermitian) :
+ star (s... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_074ae4d0573d_1 | 27ec60a4360bd04e | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LinearAlgebra/Matrix/PosDef.lean | PosDef | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "PosDef_inv_iff_PosDef",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n { intros hM\n rw [← Matrix.nonsing_inv_nonsing_inv M (isUnit_det_of_PosDef_inv hM)]\n apply hM.n... | [
{
"name": "isUnit_det_of_PosDef_inv",
"text": "lemma isUnit_det_of_PosDef_inv [DecidableEq n] {M : Matrix n n ℝ} (h : M⁻¹.PosDef) :\n IsUnit M.det := by\n apply isUnit_iff_ne_zero.2\n have := h.isUnit_det\n rw [det_nonsing_inv, isUnit_ring_inverse] at this\n apply IsUnit.ne_zero this\n\n",
"fan_i... | [
{
"name": "PosDef_inv_iff_PosDef",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 281,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 5,
"automation_only": false,
"max_n... | 1 | import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.Algebra.Star.Pi
/-!
More results about positive definite and positive semidefinite matrices (see
`Mathlib.LinearAlgebra.Matrix.PosDef`).
-/
namespace Matrix
variable {m n : Type _} [Fintype m] [Fintype n]
variable {𝕜 : Type _}
variable [NormedField 𝕜] [Part... | import Mathlib.LinearAlgebra.Matrix.PosDef
import Mathlib.Algebra.Star.Pi
/-!
More results about positive definite and positive semidefinite matrices (see
`Mathlib.LinearAlgebra.Matrix.PosDef`).
-/
namespace Matrix
variable {m n : Type _} [Fintype m] [Fintype n]
variable {𝕜 : Type _}
variable [NormedField 𝕜] [Part... | @@ -50,7 +50,20 @@
rw [conj_symm ((@isHermitian_inv _ _ _ _ _ _ M hM.Invertible).2 hM.1)] at hres
exact hres
-lemma PosDef_inv_iff_PosDef [DecidableEq n] (M : Matrix n n ℝ) : M⁻¹.PosDef ↔ M.PosDef := sorry
+lemma isUnit_det_of_PosDef_inv [DecidableEq n] {M : Matrix n n ℝ} (h : M⁻¹.PosDef) :
+ IsUnit M.det :=... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_9b88aec5f36e_0 | d3c23a250e23612a | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LogDet.lean | LogDet | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "LogDetAtom.feasibility_PosDef'",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hY_tri : upperTriangular Y := by\n { rw [hY]\n apply upperTriangular.mul\n apply BlockTriangula... | [
{
"name": "LogDetAtom.feasibility_PosDef",
"text": "lemma LogDetAtom.feasibility_PosDef {D Z : Matrix n n ℝ} (hD : D = LDL.diag hA)\n (hZ : Z = LDL.diag hA * (LDL.lower hA)ᵀ) : (fromBlocks D Z Zᵀ A).PosSemidef := by\n have h_D_eq : D = Z * A⁻¹ * Zᴴ :=\n calc D\n = D * D⁻¹ * D := by\n rw... | [
{
"name": "LogDetAtom.feasibility_PosDef'",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 523,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 5,
"automation_only": false,... | 1 | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | @@ -31,8 +31,36 @@
lemma PosSemidef_zero : PosSemidef (0 : Matrix n n 𝕜) := by
simp [PosSemidef]
+lemma LogDetAtom.feasibility_PosDef {D Z : Matrix n n ℝ} (hD : D = LDL.diag hA)
+ (hZ : Z = LDL.diag hA * (LDL.lower hA)ᵀ) : (fromBlocks D Z Zᵀ A).PosSemidef := by
+ have h_D_eq : D = Z * A⁻¹ * Zᴴ :=
+ calc D... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_9b88aec5f36e_1 | d61022f52a36bbc9 | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LogDet.lean | LogDet | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "LogDetAtom.solution_eq_atom",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n conv => rhs; rw [(LDL.lower_conj_diag hA).symm]\n have heqsum := Real.log_prod Finset.univ (LDL.diagEntries hA... | [
{
"name": "LDL.diagEntries_pos",
"text": "lemma LDL.diagEntries_pos {A : Matrix n n ℝ} (hA: A.PosDef) (i : n) :\n 0 < LDL.diagEntries hA i := by\n have : (LDL.lowerInv hA).det ≠ 0 := by simp [LDL.det_lowerInv hA]\n have : LDL.lowerInv hA i ≠ 0 := fun h =>\n this (Matrix.det_eq_zero_of_row_eq_zero i ... | [
{
"name": "LogDetAtom.solution_eq_atom",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 339,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
... | 1 | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | @@ -31,8 +31,19 @@
lemma PosSemidef_zero : PosSemidef (0 : Matrix n n 𝕜) := by
simp [PosSemidef]
+lemma LDL.diagEntries_pos {A : Matrix n n ℝ} (hA: A.PosDef) (i : n) :
+ 0 < LDL.diagEntries hA i := by
+ have : (LDL.lowerInv hA).det ≠ 0 := by simp [LDL.det_lowerInv hA]
+ have : LDL.lowerInv hA i ≠ 0 := fun h... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_9b88aec5f36e_2 | 7e72fb53bb7b2c85 | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LogDet.lean | LogDet | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "PosSemidef₁₁_of_PosSemidef_toBlock",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨IsHermitian₁₁_of_IsHermitian_toBlock h.1,\n fun x => by simpa [Matrix.fromBlocks_mulVec, star] using h.2... | [
{
"name": "IsHermitian₁₁_of_IsHermitian_toBlock",
"text": "lemma IsHermitian₁₁_of_IsHermitian_toBlock {A B C D : Matrix n n ℝ}\n (h : (fromBlocks A B C D).IsHermitian) : IsHermitian A := by\n ext i j; simpa using congr_fun (congr_fun h (Sum.inl i)) (Sum.inl j)\n\n",
"fan_in": 1,
"n_lines": 5,
... | [
{
"name": "PosSemidef₁₁_of_PosSemidef_toBlock",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 266,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true... | 1 | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | @@ -31,8 +31,14 @@
lemma PosSemidef_zero : PosSemidef (0 : Matrix n n 𝕜) := by
simp [PosSemidef]
+lemma IsHermitian₁₁_of_IsHermitian_toBlock {A B C D : Matrix n n ℝ}
+ (h : (fromBlocks A B C D).IsHermitian) : IsHermitian A := by
+ ext i j; simpa using congr_fun (congr_fun h (Sum.inl i)) (Sum.inl j)
+
lemma ... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_9b88aec5f36e_3 | ac308fe92e45a698 | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LogDet.lean | LogDet | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "PosSemidef₂₂_of_PosSemidef_toBlock",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨IsHermitian₂₂_of_IsHermitian_toBlock h.1,\n fun x => by simpa [Matrix.fromBlocks_mulVec, star] using h.2... | [
{
"name": "IsHermitian₂₂_of_IsHermitian_toBlock",
"text": "lemma IsHermitian₂₂_of_IsHermitian_toBlock {A B C D : Matrix n n ℝ}\n (h : (fromBlocks A B C D).IsHermitian) : IsHermitian D := by\n ext i j; simpa using congr_fun (congr_fun h (Sum.inr i)) (Sum.inr j)\n\n",
"fan_in": 1,
"n_lines": 5,
... | [
{
"name": "PosSemidef₂₂_of_PosSemidef_toBlock",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 270,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true... | 1 | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | @@ -31,9 +31,15 @@
lemma PosSemidef_zero : PosSemidef (0 : Matrix n n 𝕜) := by
simp [PosSemidef]
+lemma IsHermitian₂₂_of_IsHermitian_toBlock {A B C D : Matrix n n ℝ}
+ (h : (fromBlocks A B C D).IsHermitian) : IsHermitian D := by
+ ext i j; simpa using congr_fun (congr_fun h (Sum.inr i)) (Sum.inr j)
+
lemma ... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_9b88aec5f36e_4 | 1d99769405be8e44 | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LogDet.lean | LogDet | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "PosSemidef₁₁_of_PosSemidef_toBlock",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨IsHermitian₁₁_of_IsHermitian_toBlock h.1,\n fun x => by simpa [Matrix.fromBlocks_mulVec, star] using h.2... | [
{
"name": "IsHermitian₁₁_of_IsHermitian_toBlock",
"text": "lemma IsHermitian₁₁_of_IsHermitian_toBlock {A B C D : Matrix n n ℝ}\n (h : (fromBlocks A B C D).IsHermitian) : IsHermitian A := by\n ext i j; simpa using congr_fun (congr_fun h (Sum.inl i)) (Sum.inl j)\n\n",
"fan_in": 1,
"n_lines": 5,
... | [
{
"name": "LogDetAtom.optimality_D_posdef",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 493,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
... | 2 | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | @@ -31,8 +31,14 @@
lemma PosSemidef_zero : PosSemidef (0 : Matrix n n 𝕜) := by
simp [PosSemidef]
+lemma IsHermitian₁₁_of_IsHermitian_toBlock {A B C D : Matrix n n ℝ}
+ (h : (fromBlocks A B C D).IsHermitian) : IsHermitian A := by
+ ext i j; simpa using congr_fun (congr_fun h (Sum.inl i)) (Sum.inl j)
+
lemma ... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_9b88aec5f36e_5 | bdc76738243769b3 | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LogDet.lean | LogDet | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "PosSemidef₁₁_of_PosSemidef_toBlock",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨IsHermitian₁₁_of_IsHermitian_toBlock h.1,\n fun x => by simpa [Matrix.fromBlocks_mulVec, star] using h.2... | [
{
"name": "IsHermitian₁₁_of_IsHermitian_toBlock",
"text": "lemma IsHermitian₁₁_of_IsHermitian_toBlock {A B C D : Matrix n n ℝ}\n (h : (fromBlocks A B C D).IsHermitian) : IsHermitian A := by\n ext i j; simpa using congr_fun (congr_fun h (Sum.inl i)) (Sum.inl j)\n\n",
"fan_in": 1,
"n_lines": 5,
... | [
{
"name": "LogDetAtom.optimality_Ddet_le_Adet",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 20,
"n_chars": 1100,
"n_subproofs": 4,
"n_tactics": 16,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": f... | 3 | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | @@ -31,8 +31,14 @@
lemma PosSemidef_zero : PosSemidef (0 : Matrix n n 𝕜) := by
simp [PosSemidef]
+lemma IsHermitian₁₁_of_IsHermitian_toBlock {A B C D : Matrix n n ℝ}
+ (h : (fromBlocks A B C D).IsHermitian) : IsHermitian A := by
+ ext i j; simpa using congr_fun (congr_fun h (Sum.inl i)) (Sum.inl j)
+
lemma ... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_9b88aec5f36e_6 | d56347b4e5f180c4 | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LogDet.lean | LogDet | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "PosSemidef₂₂_of_PosSemidef_toBlock",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨IsHermitian₂₂_of_IsHermitian_toBlock h.1,\n fun x => by simpa [Matrix.fromBlocks_mulVec, star] using h.2... | [
{
"name": "IsHermitian₂₂_of_IsHermitian_toBlock",
"text": "lemma IsHermitian₂₂_of_IsHermitian_toBlock {A B C D : Matrix n n ℝ}\n (h : (fromBlocks A B C D).IsHermitian) : IsHermitian D := by\n ext i j; simpa using congr_fun (congr_fun h (Sum.inr i)) (Sum.inr j)\n\n",
"fan_in": 1,
"n_lines": 5,
... | [
{
"name": "LogDetAtom.cond_elim",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 11,
"n_chars": 621,
"n_subproofs": 4,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_n... | 6 | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | @@ -35,6 +35,10 @@
(h : (fromBlocks A B C D).IsHermitian) : IsHermitian A := by
ext i j; simpa using congr_fun (congr_fun h (Sum.inl i)) (Sum.inl j)
+lemma IsHermitian₂₂_of_IsHermitian_toBlock {A B C D : Matrix n n ℝ}
+ (h : (fromBlocks A B C D).IsHermitian) : IsHermitian D := by
+ ext i j; simpa using co... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_9b88aec5f36e_7 | 169b52948822339c | lean | lean | github.com/verified-optimization/CvxLean | c62c2f292c6420f31a12e738ebebdfed50f6f840 | CvxLean/Lib/Math/LogDet.lean | LogDet | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "PosSemidef₂₂_of_PosSemidef_toBlock",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨IsHermitian₂₂_of_IsHermitian_toBlock h.1,\n fun x => by simpa [Matrix.fromBlocks_mulVec, star] using h.2... | [
{
"name": "IsHermitian₂₂_of_IsHermitian_toBlock",
"text": "lemma IsHermitian₂₂_of_IsHermitian_toBlock {A B C D : Matrix n n ℝ}\n (h : (fromBlocks A B C D).IsHermitian) : IsHermitian D := by\n ext i j; simpa using congr_fun (congr_fun h (Sum.inr i)) (Sum.inr j)\n\n",
"fan_in": 1,
"n_lines": 5,
... | [
{
"name": "LogDetAtom.optimality",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 7,
"n_lines": 12,
"n_chars": 657,
"n_subproofs": 3,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_... | 7 | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | import Mathlib.LinearAlgebra.Matrix.LDL
import CvxLean.Lib.Math.SchurComplement
import CvxLean.Lib.Math.Subadditivity
import CvxLean.Lib.Math.LinearAlgebra.Matrix.Triangular
import CvxLean.Lib.Math.LinearAlgebra.Matrix.ToUpperTri
import CvxLean.Lib.Math.LinearAlgebra.Matrix.LDL
/-!
In this file we prove properties ne... | @@ -35,6 +35,10 @@
(h : (fromBlocks A B C D).IsHermitian) : IsHermitian A := by
ext i j; simpa using congr_fun (congr_fun h (Sum.inl i)) (Sum.inl j)
+lemma IsHermitian₂₂_of_IsHermitian_toBlock {A B C D : Matrix n n ℝ}
+ (h : (fromBlocks A B C D).IsHermitian) : IsHermitian D := by
+ ext i j; simpa using co... | {
"repo": "CvxLean",
"git_repo": "github.com/verified-optimization/CvxLean",
"revision": "c62c2f292c6420f31a12e738ebebdfed50f6f840",
"lean_toolchain": "leanprover/lean4:v4.8.0-rc1",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--coroll... |
ablate_af10f733b0b6_0 | a9f238a9673d87a7 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 8 | [
{
"theorem_name": "scaled_mantissa_bounded",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases eq_or_ne x 0 with Heq | _\n simp [Heq, scaled_mantissa]\n rcases lt_or_ge (Int.log 2 |x| + 1 - format.pre... | [
{
"name": "mantissa_normal_of_fexp_ne_dexp",
"text": "lemma mantissa_normal_of_fexp_ne_dexp (x : ℝ) :\n let x' := @scaled_mantissa format x\n ¬x = 0 →\n -format.dexp ≤ Int.log 2 |x| + 1 - format.precision →\n 2 ^ (format.precision - 1) ≤ |x'| ∧ |x'| < 2 ^ format.precision := by\n simp\n intros Hx' Hlt... | [
{
"name": "scaled_mantissa_bounded",
"fan_in": 6,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 16,
"n_chars": 522,
"n_subproofs": 3,
"n_tactics": 15,
"cyclomatic": 5,
"n_automation": 7,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"m... | 2 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -21,6 +21,36 @@
noncomputable def scaled_mantissa (x : ℝ) :=
x * 2 ^ (-@fexp_real' format x)
+lemma mantissa_normal_of_fexp_ne_dexp (x : ℝ) :
+ let x' := @scaled_mantissa format x
+ ¬x = 0 →
+ -format.dexp ≤ Int.log 2 |x| + 1 - format.precision →
+ 2 ^ (format.precision - 1) ≤ |x'| ∧ |x'| < 2 ^ format.prec... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_1 | 980e0c48202317a9 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 2 | [
{
"theorem_name": "scaled_mantissa_bounded",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rcases eq_or_ne x 0 with Heq | _\n simp [Heq, scaled_mantissa]\n rcases lt_or_ge (Int.log 2 |x| + 1 - format.pre... | [
{
"name": "mantissa_subnormal_of_fexp_dexp",
"text": "lemma mantissa_subnormal_of_fexp_dexp (x : ℝ) :\n let x' := @scaled_mantissa format x;\n ¬x = 0 →\n Int.log 2 |x| + 1 - format.precision < -format.dexp →\n |x'| < 2 ^ (format.precision - 1) := by\n simp [fexp_real', scaled_mantissa]\n intros\n rw ... | [
{
"name": "valid_round_fp_bounded",
"fan_in": 5,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 56,
"n_chars": 1925,
"n_subproofs": 8,
"n_tactics": 58,
"cyclomatic": 5,
"n_automation": 21,
"n_rewrites": 14,
"n_structural": 11,
"automation_only": false,
... | 5 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -51,8 +51,44 @@
simp
assumption
+lemma mantissa_subnormal_of_fexp_dexp (x : ℝ) :
+ let x' := @scaled_mantissa format x;
+ ¬x = 0 →
+ Int.log 2 |x| + 1 - format.precision < -format.dexp →
+ |x'| < 2 ^ (format.precision - 1) := by
+ simp [fexp_real', scaled_mantissa]
+ intros
+ rw [max_eq_right]
+ rewr... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_2 | a4c17523a64b6052 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 6 | [
{
"theorem_name": "valid_round_fp_bounded",
"depth": 1,
"n_commands": 0,
"n_lines": 52,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [round_fp_ne0]\n split\n .case isTrue heq =>\n constructor\n rw [abs_eq] at heq; rcases heq with heq|h... | [
{
"name": "scaled_mantissa_bounded",
"text": "lemma scaled_mantissa_bounded (x : ℝ) :\n |@scaled_mantissa format x| < 2 ^ format.precision := by\n rcases eq_or_ne x 0 with Heq | _\n simp [Heq, scaled_mantissa]\n rcases lt_or_ge (Int.log 2 |x| + 1 - format.precision) (-format.dexp)\n have _ := @mantissa... | [
{
"name": "valid_round_fp_canonical",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 6,
"n_lines": 163,
"n_chars": 3990,
"n_subproofs": 12,
"n_tactics": 160,
"cyclomatic": 19,
"n_automation": 75,
"n_rewrites": 41,
"n_structural": 21,
"automation_only": fals... | 6 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -75,6 +75,21 @@
simp; apply zpow_pos; linarith
linarith
+lemma scaled_mantissa_bounded (x : ℝ) :
+ |@scaled_mantissa format x| < 2 ^ format.precision := by
+ rcases eq_or_ne x 0 with Heq | _
+ simp [Heq, scaled_mantissa]
+ rcases lt_or_ge (Int.log 2 |x| + 1 - format.precision) (-format.dexp)
+ have _ :=... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_3 | 874ae42b55f2050c | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 14 | [
{
"theorem_name": "round_fp_bounded_self",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro hb\n have ⟨hy, heq⟩ := @canonicalize_correct_all 2 format x ?_ hb\n set y := @canonicalize 2 format x with h... | [
{
"name": "valid_round_simp",
"text": "lemma valid_round_simp (x : ℝ) :\n (@round_fp_ne0 format (rnd := rnd) x : ℝ) = (⟨rnd (@fexp_real' format x) (@scaled_mantissa format x), @fexp_real' format x⟩ : float 2) := by\n simp [round_fp_ne0, to_real]\n split\n simp\n have divide : 2 ∣ (@vnum 2 format : ℤ) :... | [
{
"name": "round_fp_bounded_self",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 47,
"n_chars": 1266,
"n_subproofs": 3,
"n_tactics": 52,
"cyclomatic": 4,
"n_automation": 23,
"n_rewrites": 6,
"n_structural": 10,
"automation_only": false,
"... | 1 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -94,10 +94,91 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma valid_round_simp (x : ℝ) :
+ (@round_fp_ne0 format (rnd := rnd) x : ℝ) = (⟨rnd (@fexp_real' format x) (@scaled_mantissa format x), @fexp_real' format x⟩ : float 2) := by
+ simp [round_fp_ne0, to_real]
+ split
+ simp
+... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_4 | 1d294a7c1c298c5c | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 6 | [
{
"theorem_name": "valid_round_fp_bounded",
"depth": 1,
"n_commands": 0,
"n_lines": 52,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [round_fp_ne0]\n split\n .case isTrue heq =>\n constructor\n rw [abs_eq] at heq; rcases heq with heq|h... | [
{
"name": "scaled_mantissa_bounded",
"text": "lemma scaled_mantissa_bounded (x : ℝ) :\n |@scaled_mantissa format x| < 2 ^ format.precision := by\n rcases eq_or_ne x 0 with Heq | _\n simp [Heq, scaled_mantissa]\n rcases lt_or_ge (Int.log 2 |x| + 1 - format.precision) (-format.dexp)\n have _ := @mantissa... | [
{
"name": "valid_round_monotone_aux",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 5,
"n_lines": 69,
"n_chars": 2369,
"n_subproofs": 7,
"n_tactics": 90,
"cyclomatic": 4,
"n_automation": 39,
"n_rewrites": 24,
"n_structural": 22,
"automation_only": false,
... | 5 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -75,6 +75,21 @@
simp; apply zpow_pos; linarith
linarith
+lemma scaled_mantissa_bounded (x : ℝ) :
+ |@scaled_mantissa format x| < 2 ^ format.precision := by
+ rcases eq_or_ne x 0 with Heq | _
+ simp [Heq, scaled_mantissa]
+ rcases lt_or_ge (Int.log 2 |x| + 1 - format.precision) (-format.dexp)
+ have _ :=... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_5 | b9e0882e8387dd21 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 14 | [
{
"theorem_name": "round_fp_bounded_self",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro hb\n have ⟨hy, heq⟩ := @canonicalize_correct_all 2 format x ?_ hb\n set y := @canonicalize 2 format x with h... | [
{
"name": "valid_round_simp",
"text": "lemma valid_round_simp (x : ℝ) :\n (@round_fp_ne0 format (rnd := rnd) x : ℝ) = (⟨rnd (@fexp_real' format x) (@scaled_mantissa format x), @fexp_real' format x⟩ : float 2) := by\n simp [round_fp_ne0, to_real]\n split\n simp\n have divide : 2 ∣ (@vnum 2 format : ℤ) :... | [
{
"name": "roundup_strict_monotone_aux",
"fan_in": 2,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 91,
"n_chars": 3047,
"n_subproofs": 11,
"n_tactics": 111,
"cyclomatic": 4,
"n_automation": 49,
"n_rewrites": 26,
"n_structural": 23,
"automation_only": fal... | 4 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -138,6 +138,46 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma valid_round_simp (x : ℝ) :
+ (@round_fp_ne0 format (rnd := rnd) x : ℝ) = (⟨rnd (@fexp_real' format x) (@scaled_mantissa format x), @fexp_real' format x⟩ : float 2) := by
+ simp [round_fp_ne0, to_real]
+ split
+ simp
... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_6 | e1636d84d45168d3 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 6 | [
{
"theorem_name": "valid_round_fp_bounded",
"depth": 1,
"n_commands": 0,
"n_lines": 52,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [round_fp_ne0]\n split\n .case isTrue heq =>\n constructor\n rw [abs_eq] at heq; rcases heq with heq|h... | [
{
"name": "scaled_mantissa_bounded",
"text": "lemma scaled_mantissa_bounded (x : ℝ) :\n |@scaled_mantissa format x| < 2 ^ format.precision := by\n rcases eq_or_ne x 0 with Heq | _\n simp [Heq, scaled_mantissa]\n rcases lt_or_ge (Int.log 2 |x| + 1 - format.precision) (-format.dexp)\n have _ := @mantissa... | [
{
"name": "rounddown_strict_monotone_aux",
"fan_in": 2,
"n_deps_direct": 5,
"n_deps_transitive": 7,
"n_lines": 101,
"n_chars": 3500,
"n_subproofs": 13,
"n_tactics": 123,
"cyclomatic": 5,
"n_automation": 51,
"n_rewrites": 33,
"n_structural": 24,
"automation_only": ... | 7 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -89,6 +89,21 @@
simp; apply zpow_pos; linarith
linarith
+lemma scaled_mantissa_bounded (x : ℝ) :
+ |@scaled_mantissa format x| < 2 ^ format.precision := by
+ rcases eq_or_ne x 0 with Heq | _
+ simp [Heq, scaled_mantissa]
+ rcases lt_or_ge (Int.log 2 |x| + 1 - format.precision) (-format.dexp)
+ have _ :=... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_7 | a60712c2fadcd352 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 11 | [
{
"theorem_name": "roundup_strict_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 57,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros\n let rnd : ℝ → ℤ := (⌈.⌉)\n have : rnd (0:ℝ) = 0 := by simp [rnd]\n rcases lt_or_ge (x:ℝ) 0 with hltx|... | [
{
"name": "round_fp_ne0_simp",
"text": "lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :\n @round_fp format rnd x = @round_fp_ne0 format rnd x := by\n simp [round_fp]\n intro; exfalso; apply hne; assumption\n\n",
"fan_in": 11,
"n_lines": 6,
"n_chars": 199,
"n_subproofs":... | [
{
"name": "roundup_strict_monotone",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 10,
"n_lines": 62,
"n_chars": 1625,
"n_subproofs": 4,
"n_tactics": 62,
"cyclomatic": 7,
"n_automation": 38,
"n_rewrites": 6,
"n_structural": 17,
"automation_only": false,
... | 10 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -183,6 +183,11 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :
+ @round_fp format rnd x = @round_fp_ne0 format rnd x := by
+ simp [round_fp]
+ intro; exfalso; apply hne; assumption
+
lemma valid_round_simp (x : ℝ) :
... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_8 | 14feea843362bff0 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 11 | [
{
"theorem_name": "roundup_strict_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 57,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros\n let rnd : ℝ → ℤ := (⌈.⌉)\n have : rnd (0:ℝ) = 0 := by simp [rnd]\n rcases lt_or_ge (x:ℝ) 0 with hltx|... | [
{
"name": "round_fp_ne0_simp",
"text": "lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :\n @round_fp format rnd x = @round_fp_ne0 format rnd x := by\n simp [round_fp]\n intro; exfalso; apply hne; assumption\n\n",
"fan_in": 11,
"n_lines": 6,
"n_chars": 199,
"n_subproofs":... | [
{
"name": "rounddown_strict_monotone",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 10,
"n_lines": 49,
"n_chars": 1462,
"n_subproofs": 4,
"n_tactics": 49,
"cyclomatic": 4,
"n_automation": 32,
"n_rewrites": 7,
"n_structural": 13,
"automation_only": false,
... | 10 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -183,6 +183,11 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :
+ @round_fp format rnd x = @round_fp_ne0 format rnd x := by
+ simp [round_fp]
+ intro; exfalso; apply hne; assumption
+
lemma valid_round_simp (x : ℝ) :
... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_9 | 8eb74a7ef1f7e281 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 11 | [
{
"theorem_name": "roundup_strict_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 57,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros\n let rnd : ℝ → ℤ := (⌈.⌉)\n have : rnd (0:ℝ) = 0 := by simp [rnd]\n rcases lt_or_ge (x:ℝ) 0 with hltx|... | [
{
"name": "round_fp_ne0_simp",
"text": "lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :\n @round_fp format rnd x = @round_fp_ne0 format rnd x := by\n simp [round_fp]\n intro; exfalso; apply hne; assumption\n\n",
"fan_in": 11,
"n_lines": 6,
"n_chars": 199,
"n_subproofs":... | [
{
"name": "round_monotone",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 7,
"n_lines": 83,
"n_chars": 1998,
"n_subproofs": 4,
"n_tactics": 87,
"cyclomatic": 9,
"n_automation": 42,
"n_rewrites": 14,
"n_structural": 26,
"automation_only": false,
"max_ne... | 7 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -163,6 +163,11 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :
+ @round_fp format rnd x = @round_fp_ne0 format rnd x := by
+ simp [round_fp]
+ intro; exfalso; apply hne; assumption
+
lemma valid_round_simp (x : ℝ) :
... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_10 | e8fb9b2a6dc20811 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 11 | [
{
"theorem_name": "roundup_strict_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 57,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros\n let rnd : ℝ → ℤ := (⌈.⌉)\n have : rnd (0:ℝ) = 0 := by simp [rnd]\n rcases lt_or_ge (x:ℝ) 0 with hltx|... | [
{
"name": "round_fp_ne0_simp",
"text": "lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :\n @round_fp format rnd x = @round_fp_ne0 format rnd x := by\n simp [round_fp]\n intro; exfalso; apply hne; assumption\n\n",
"fan_in": 11,
"n_lines": 6,
"n_chars": 199,
"n_subproofs":... | [
{
"name": "weakly_round_le_monotone",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 10,
"n_lines": 12,
"n_chars": 459,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 3,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 4,
"automation_only": false,
"... | 10 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -163,6 +163,11 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :
+ @round_fp format rnd x = @round_fp_ne0 format rnd x := by
+ simp [round_fp]
+ intro; exfalso; apply hne; assumption
+
lemma valid_round_simp (x : ℝ) :
... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_11 | 2aaf1a5ba4f5c6ea | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 11 | [
{
"theorem_name": "roundup_strict_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 57,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros\n let rnd : ℝ → ℤ := (⌈.⌉)\n have : rnd (0:ℝ) = 0 := by simp [rnd]\n rcases lt_or_ge (x:ℝ) 0 with hltx|... | [
{
"name": "round_fp_ne0_simp",
"text": "lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :\n @round_fp format rnd x = @round_fp_ne0 format rnd x := by\n simp [round_fp]\n intro; exfalso; apply hne; assumption\n\n",
"fan_in": 11,
"n_lines": 6,
"n_chars": 199,
"n_subproofs":... | [
{
"name": "weakly_le_round_monotone",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 10,
"n_lines": 12,
"n_chars": 459,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 3,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 4,
"automation_only": false,
"... | 10 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -163,6 +163,11 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :
+ @round_fp format rnd x = @round_fp_ne0 format rnd x := by
+ simp [round_fp]
+ intro; exfalso; apply hne; assumption
+
lemma valid_round_simp (x : ℝ) :
... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_12 | 4ff26551c5d9627f | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 2 | [
{
"theorem_name": "abs_sub_round_choice_abs",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [round_choice_abs]; split\n norm_cast\n . case isTrue Heq =>\n rcases choice_or x e choice (by linarith... | [
{
"name": "choice_or",
"text": "lemma choice_or (x : ℝ) (e : ℤ) (choice : ℤ → ℤ → ℤ) [ValidChoice choice] :\n ¬Int.fract x = 0 →\n let r := if 0 < x then choice e ⌊|x|⌋ else -choice e ⌊|x|⌋\n r = ⌊x⌋ ∨ r = ⌊x⌋+1 := by\n intro hf\n simp\n expose_names\n split\n rw [abs_of_pos (by assumption)]\n rcas... | [
{
"name": "abs_sub_round_choice_abs",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 19,
"n_chars": 543,
"n_subproofs": 2,
"n_tactics": 19,
"cyclomatic": 3,
"n_automation": 7,
"n_rewrites": 8,
"n_structural": 1,
"automation_only": false,
"... | 1 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -618,11 +618,40 @@
noncomputable def round_nearest_all (x : ℝ) [ValidChoice choice] : float 2 :=
@round_fp format (round_choice choice) x
+lemma choice_or (x : ℝ) (e : ℤ) (choice : ℤ → ℤ → ℤ) [ValidChoice choice] :
+ ¬Int.fract x = 0 →
+ let r := if 0 < x then choice e ⌊|x|⌋ else -choice e ⌊|x|⌋
+ r = ⌊x⌋ ∨... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_13 | a684ccca62541692 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 2 | [
{
"theorem_name": "abs_sub_round_choice_abs",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [round_choice_abs]; split\n norm_cast\n . case isTrue Heq =>\n rcases choice_or x e choice (by linarith... | [
{
"name": "choice_or",
"text": "lemma choice_or (x : ℝ) (e : ℤ) (choice : ℤ → ℤ → ℤ) [ValidChoice choice] :\n ¬Int.fract x = 0 →\n let r := if 0 < x then choice e ⌊|x|⌋ else -choice e ⌊|x|⌋\n r = ⌊x⌋ ∨ r = ⌊x⌋+1 := by\n intro hf\n simp\n expose_names\n split\n rw [abs_of_pos (by assumption)]\n rcas... | [
{
"name": "round_choice_abs_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 35,
"n_chars": 949,
"n_subproofs": 4,
"n_tactics": 39,
"cyclomatic": 5,
"n_automation": 18,
"n_rewrites": 9,
"n_structural": 4,
"automation_only": false,
"max_... | 1 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -618,9 +618,60 @@
noncomputable def round_nearest_all (x : ℝ) [ValidChoice choice] : float 2 :=
@round_fp format (round_choice choice) x
+lemma choice_or (x : ℝ) (e : ℤ) (choice : ℤ → ℤ → ℤ) [ValidChoice choice] :
+ ¬Int.fract x = 0 →
+ let r := if 0 < x then choice e ⌊|x|⌋ else -choice e ⌊|x|⌋
+ r = ⌊x⌋ ∨ ... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_14 | 3ddf52e98b0243c7 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 11 | [
{
"theorem_name": "roundup_strict_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 57,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros\n let rnd : ℝ → ℤ := (⌈.⌉)\n have : rnd (0:ℝ) = 0 := by simp [rnd]\n rcases lt_or_ge (x:ℝ) 0 with hltx|... | [
{
"name": "round_fp_ne0_simp",
"text": "lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :\n @round_fp format rnd x = @round_fp_ne0 format rnd x := by\n simp [round_fp]\n intro; exfalso; apply hne; assumption\n\n",
"fan_in": 11,
"n_lines": 6,
"n_chars": 199,
"n_subproofs":... | [
{
"name": "roundup_real_roundup_pos",
"fan_in": 2,
"n_deps_direct": 5,
"n_deps_transitive": 8,
"n_lines": 125,
"n_chars": 3504,
"n_subproofs": 15,
"n_tactics": 139,
"cyclomatic": 5,
"n_automation": 54,
"n_rewrites": 27,
"n_structural": 36,
"automation_only": false... | 8 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -181,6 +181,11 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :
+ @round_fp format rnd x = @round_fp_ne0 format rnd x := by
+ simp [round_fp]
+ intro; exfalso; apply hne; assumption
+
lemma valid_round_fp_bounded [h : F... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_15 | 6ee0560ea8054df0 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 11 | [
{
"theorem_name": "roundup_strict_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 57,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros\n let rnd : ℝ → ℤ := (⌈.⌉)\n have : rnd (0:ℝ) = 0 := by simp [rnd]\n rcases lt_or_ge (x:ℝ) 0 with hltx|... | [
{
"name": "round_fp_ne0_simp",
"text": "lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :\n @round_fp format rnd x = @round_fp_ne0 format rnd x := by\n simp [round_fp]\n intro; exfalso; apply hne; assumption\n\n",
"fan_in": 11,
"n_lines": 6,
"n_chars": 199,
"n_subproofs":... | [
{
"name": "rounddown_real_rounddown_pos",
"fan_in": 2,
"n_deps_direct": 5,
"n_deps_transitive": 8,
"n_lines": 109,
"n_chars": 3432,
"n_subproofs": 12,
"n_tactics": 145,
"cyclomatic": 5,
"n_automation": 56,
"n_rewrites": 32,
"n_structural": 39,
"automation_only": f... | 8 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -181,6 +181,11 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :
+ @round_fp format rnd x = @round_fp_ne0 format rnd x := by
+ simp [round_fp]
+ intro; exfalso; apply hne; assumption
+
lemma valid_round_fp_bounded [h : F... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_16 | 2261940f7a0b8419 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 11 | [
{
"theorem_name": "roundup_strict_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 57,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros\n let rnd : ℝ → ℤ := (⌈.⌉)\n have : rnd (0:ℝ) = 0 := by simp [rnd]\n rcases lt_or_ge (x:ℝ) 0 with hltx|... | [
{
"name": "round_fp_ne0_simp",
"text": "lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :\n @round_fp format rnd x = @round_fp_ne0 format rnd x := by\n simp [round_fp]\n intro; exfalso; apply hne; assumption\n\n",
"fan_in": 11,
"n_lines": 6,
"n_chars": 199,
"n_subproofs":... | [
{
"name": "roundup_real_roundup",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 11,
"n_lines": 42,
"n_chars": 1148,
"n_subproofs": 2,
"n_tactics": 42,
"cyclomatic": 6,
"n_automation": 15,
"n_rewrites": 7,
"n_structural": 14,
"automation_only": false,
"... | 11 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -181,6 +181,11 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :
+ @round_fp format rnd x = @round_fp_ne0 format rnd x := by
+ simp [round_fp]
+ intro; exfalso; apply hne; assumption
+
lemma valid_round_fp_bounded [h : F... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_17 | f6f1ff7ff6c5fece | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 11 | [
{
"theorem_name": "roundup_strict_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 57,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros\n let rnd : ℝ → ℤ := (⌈.⌉)\n have : rnd (0:ℝ) = 0 := by simp [rnd]\n rcases lt_or_ge (x:ℝ) 0 with hltx|... | [
{
"name": "round_fp_ne0_simp",
"text": "lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :\n @round_fp format rnd x = @round_fp_ne0 format rnd x := by\n simp [round_fp]\n intro; exfalso; apply hne; assumption\n\n",
"fan_in": 11,
"n_lines": 6,
"n_chars": 199,
"n_subproofs":... | [
{
"name": "rounddown_real_rounddown",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 11,
"n_lines": 40,
"n_chars": 1245,
"n_subproofs": 2,
"n_tactics": 41,
"cyclomatic": 6,
"n_automation": 16,
"n_rewrites": 6,
"n_structural": 13,
"automation_only": false,
... | 11 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -181,6 +181,11 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :
+ @round_fp format rnd x = @round_fp_ne0 format rnd x := by
+ simp [round_fp]
+ intro; exfalso; apply hne; assumption
+
lemma valid_round_fp_bounded [h : F... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_18 | e3e5dc1ad88ebe22 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 11 | [
{
"theorem_name": "roundup_strict_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 57,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros\n let rnd : ℝ → ℤ := (⌈.⌉)\n have : rnd (0:ℝ) = 0 := by simp [rnd]\n rcases lt_or_ge (x:ℝ) 0 with hltx|... | [
{
"name": "round_fp_ne0_simp",
"text": "lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :\n @round_fp format rnd x = @round_fp_ne0 format rnd x := by\n simp [round_fp]\n intro; exfalso; apply hne; assumption\n\n",
"fan_in": 11,
"n_lines": 6,
"n_chars": 199,
"n_subproofs":... | [
{
"name": "nearest_round_nearest",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 10,
"n_lines": 87,
"n_chars": 3014,
"n_subproofs": 11,
"n_tactics": 113,
"cyclomatic": 5,
"n_automation": 48,
"n_rewrites": 28,
"n_structural": 25,
"automation_only": false,
... | 10 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -181,6 +181,11 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :
+ @round_fp format rnd x = @round_fp_ne0 format rnd x := by
+ simp [round_fp]
+ intro; exfalso; apply hne; assumption
+
lemma valid_round_fp_bounded [h : F... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_19 | 9502990dd2bae88b | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 11 | [
{
"theorem_name": "roundup_strict_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 57,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros\n let rnd : ℝ → ℤ := (⌈.⌉)\n have : rnd (0:ℝ) = 0 := by simp [rnd]\n rcases lt_or_ge (x:ℝ) 0 with hltx|... | [
{
"name": "round_fp_ne0_simp",
"text": "lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :\n @round_fp format rnd x = @round_fp_ne0 format rnd x := by\n simp [round_fp]\n intro; exfalso; apply hne; assumption\n\n",
"fan_in": 11,
"n_lines": 6,
"n_chars": 199,
"n_subproofs":... | [
{
"name": "rne_abs_correct_no_tie_breaking",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 12,
"n_lines": 86,
"n_chars": 3004,
"n_subproofs": 11,
"n_tactics": 112,
"cyclomatic": 5,
"n_automation": 47,
"n_rewrites": 28,
"n_structural": 25,
"automation_only"... | 11 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -181,6 +181,11 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :
+ @round_fp format rnd x = @round_fp_ne0 format rnd x := by
+ simp [round_fp]
+ intro; exfalso; apply hne; assumption
+
lemma valid_round_fp_bounded [h : F... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_20 | a4db1f57a26d0758 | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 2 | [
{
"theorem_name": "rne_symm",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [rne_abs]\n rw [fopp_correct]\n rw [<-round_fp_opp]; simp\n simp_rw [round_choice_abs_symm]",
"n_chars": 102,
"n_s... | [
{
"name": "round_fp_opp",
"text": "lemma round_fp_opp (rnd : ℤ → ℝ → ℤ) (x : ℝ) :\n @round_fp format (round_opp rnd) x = fopp (@round_fp format rnd (-x)) := by\n simp [round_fp]; split\n simp [fopp]\n simp [round_fp_ne0, round_opp]\n simp [scaled_mantissa]\n have hneg (x : ℝ) : @fexp_real' format (-x)... | [
{
"name": "rne_symm",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 173,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 2 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -94,6 +94,30 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_opp (rnd : ℤ → ℝ → ℤ) (x : ℝ) :
+ @round_fp format (round_opp rnd) x = fopp (@round_fp format rnd (-x)) := by
+ simp [round_fp]; split
+ simp [fopp]
+ simp [round_fp_ne0, round_opp]
+ simp [scaled_mantissa]
+... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_21 | d214ba36bc11940d | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 2 | [
{
"theorem_name": "rne_symm",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [rne_abs]\n rw [fopp_correct]\n rw [<-round_fp_opp]; simp\n simp_rw [round_choice_abs_symm]",
"n_chars": 102,
"n_s... | [
{
"name": "round_fp_opp",
"text": "lemma round_fp_opp (rnd : ℤ → ℝ → ℤ) (x : ℝ) :\n @round_fp format (round_opp rnd) x = fopp (@round_fp format rnd (-x)) := by\n simp [round_fp]; split\n simp [fopp]\n simp [round_fp_ne0, round_opp]\n simp [scaled_mantissa]\n have hneg (x : ℝ) : @fexp_real' format (-x)... | [
{
"name": "rto_symm",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 181,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 2 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -94,6 +94,30 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_opp (rnd : ℤ → ℝ → ℤ) (x : ℝ) :
+ @round_fp format (round_opp rnd) x = fopp (@round_fp format rnd (-x)) := by
+ simp [round_fp]; split
+ simp [fopp]
+ simp [round_fp_ne0, round_opp]
+ simp [scaled_mantissa]
+... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
ablate_af10f733b0b6_22 | a1634e0692cf9f9a | lean | lean | github.com/rutgers-apl/FLoPS | 95081ac643663da507115abe23ebd5701433587f | Flops/Core/RoundOp.lean | RoundOp | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 34 | 11 | [
{
"theorem_name": "roundup_strict_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 57,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intros\n let rnd : ℝ → ℤ := (⌈.⌉)\n have : rnd (0:ℝ) = 0 := by simp [rnd]\n rcases lt_or_ge (x:ℝ) 0 with hltx|... | [
{
"name": "round_fp_ne0_simp",
"text": "lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :\n @round_fp format rnd x = @round_fp_ne0 format rnd x := by\n simp [round_fp]\n intro; exfalso; apply hne; assumption\n\n",
"fan_in": 11,
"n_lines": 6,
"n_chars": 199,
"n_subproofs":... | [
{
"name": "rne_abs_correct",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 14,
"n_lines": 169,
"n_chars": 4088,
"n_subproofs": 11,
"n_tactics": 199,
"cyclomatic": 24,
"n_automation": 91,
"n_rewrites": 41,
"n_structural": 21,
"automation_only": false,
"... | 13 | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | import Flops.Core.Defs
import Flops.Core.Rounding
/-
this file defines rounding as a function
that takes a real value and returns a floating point, depending on the specific rounding mode
the rounding mode again is also a function that rounds the significand to integer
it satisfies a type class [ValidRound], which sho... | @@ -181,6 +181,11 @@
if x = 0 then ⟨0, -format.dexp⟩ else
@round_fp_ne0 format rnd x
+lemma round_fp_ne0_simp (rnd : ℤ → ℝ → ℤ) (x : ℝ) (hne : ¬x = 0) :
+ @round_fp format rnd x = @round_fp_ne0 format rnd x := by
+ simp [round_fp]
+ intro; exfalso; apply hne; assumption
+
lemma valid_round_fp_bounded [h : F... | {
"repo": "FLoPS",
"git_repo": "github.com/rutgers-apl/FLoPS",
"revision": "95081ac643663da507115abe23ebd5701433587f",
"lean_toolchain": "leanprover/lean4:v4.28.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-lemmas... |
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