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_d86ab6b5f148_7 | 7fe6c124d5f13609 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DivDirectedRoundingSoundness.lean | DivDirectedRoundingSoundness | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "le_ratUpper",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hdenpos : (0 : ℝ) < (den : ℝ) := by exact_mod_cast Nat.pos_of_ne_zero hden\n have hpowpos : (0 : ℝ) < (2 : ℝ) ^ ratAppro... | [
{
"name": "ratUpperMant_mul_ge",
"text": "private lemma ratUpperMant_mul_ge (num den : Nat) (hden : den ≠ 0) :\n Nat.shiftLeft num ratApproxShift ≤ ratUpperMant num den * den := by\n -- `ratUpperMant` is `ceil( (num*2^K) / den )`.\n simpa [ratUpperMant] using\n (quotCeil_mul_ge (num := Nat.shiftLeft... | [
{
"name": "toEReal_divUp_ge",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 11,
"n_lines": 120,
"n_chars": 6507,
"n_subproofs": 32,
"n_tactics": 113,
"cyclomatic": 15,
"n_automation": 15,
"n_rewrites": 6,
"n_structural": 13,
"automation_only": false,
"... | 11 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | @@ -118,6 +118,12 @@
-- `ratLowerMant = floor( (num*2^K) / den )` so `floor * den ≤ num*2^K`.
simpa [ratLowerMant] using Nat.div_mul_le_self (Nat.shiftLeft num ratApproxShift) den
+private lemma ratUpperMant_mul_ge (num den : Nat) (hden : den ≠ 0) :
+ Nat.shiftLeft num ratApproxShift ≤ ratUpperMant num den *... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_36948b38fc06_0 | a9420ab88f215d50 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/StronglyConvexGD.lean | StronglyConvexGD | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "dist_sq_iterate_le_of_q_nonneg",
"depth": 1,
"n_commands": 0,
"n_lines": 21,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction k with\n | zero =>\n simp\n | succ k ih =>\n have h1 :\n ‖(step η g)^[Nat.su... | [
{
"name": "step_dist_sq_le",
"text": "theorem step_dist_sq_le (η μ : ℝ) (hη : 0 ≤ η) {L : NNReal} (g : E → E)\n (hmono : StrongMonotone (E := E) μ g) (hlip : LipschitzWith L g)\n {xStar x : E} (hxStar : g xStar = 0) :\n ‖step η g x - xStar‖ ^ 2 ≤ q η μ L * ‖x - xStar‖ ^ 2 := by\n -- Apply the two-... | [
{
"name": "dist_sq_iterate_le_of_q_nonneg",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 33,
"n_chars": 1452,
"n_subproofs": 3,
"n_tactics": 17,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.GDLinearConvergence
import Mathlib.Logic.Function.Iterate
import Mathlib.Algebra.Order.GroupWithZero.Basic
import Mathlib.Tactic.Linarith
import Mathli... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.GDLinearConvergence
import Mathlib.Logic.Function.Iterate
import Mathlib.Algebra.Order.GroupWithZero.Basic
import Mathlib.Tactic.Linarith
import Mathli... | @@ -55,6 +55,15 @@
def q (η μ : ℝ) (L : NNReal) : ℝ :=
1 - 2 * η * μ + (η ^ 2) * (L : ℝ) ^ 2
+theorem step_dist_sq_le (η μ : ℝ) (hη : 0 ≤ η) {L : NNReal} (g : E → E)
+ (hmono : StrongMonotone (E := E) μ g) (hlip : LipschitzWith L g)
+ {xStar x : E} (hxStar : g xStar = 0) :
+ ‖step η g x - xStar‖ ^ 2 ≤ q ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_36948b38fc06_1 | ff9aa2d75f48e4f3 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/StronglyConvexGD.lean | StronglyConvexGD | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "dist_sq_iterate_le_of_q_lt_one",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- We use the iterate bound and the fact that `0 ≤ q < 1` implies `q^k ≤ 1`.\n have hpow : (q η μ L) ^ k ≤... | [
{
"name": "dist_sq_iterate_le_of_q_nonneg",
"text": "/--\nIterated contraction bound in squared norm.\n\nIf `q η μ L ≥ 0`, then after `k` steps we have\n\n`‖(step η g)^[k] x - x⋆‖² ≤ (q η μ L)^k * ‖x - x⋆‖²`.\n-/\ntheorem dist_sq_iterate_le_of_q_nonneg (η μ : ℝ) (hη : 0 ≤ η) {L : NNReal} (g : E → E)\n (h... | [
{
"name": "dist_sq_iterate_le_of_q_lt_one",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 25,
"n_chars": 1278,
"n_subproofs": 5,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.GDLinearConvergence
import Mathlib.Logic.Function.Iterate
import Mathlib.Algebra.Order.GroupWithZero.Basic
import Mathlib.Tactic.Linarith
import Mathli... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.GDLinearConvergence
import Mathlib.Logic.Function.Iterate
import Mathlib.Algebra.Order.GroupWithZero.Basic
import Mathlib.Tactic.Linarith
import Mathli... | @@ -65,6 +65,38 @@
hmono hlip x xStar)
/--
+Iterated contraction bound in squared norm.
+
+If `q η μ L ≥ 0`, then after `k` steps we have
+
+`‖(step η g)^[k] x - x⋆‖² ≤ (q η μ L)^k * ‖x - x⋆‖²`.
+-/
+theorem dist_sq_iterate_le_of_q_nonneg (η μ : ℝ) (hη : 0 ≤ η) {L : NNReal} (g : E → E)
+ (hmono : StrongMon... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_36948b38fc06_2 | 0435ad2d0a43e3ec | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/StronglyConvexGD.lean | StronglyConvexGD | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "error_abs_contract_real",
"depth": 1,
"n_commands": 0,
"n_lines": 20,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have herr : step lr target x - target = (1 - lr) * (x - target) :=\n error_after_step (α := ℝ) lr target x\n h... | [
{
"name": "error_after_step",
"text": "/--\nOne scalar quadratic gradient-descent step multiplies the current error by `1 - lr`.\n\nFor ordered fields, this is the usual starting point for contraction proofs when `0 < lr < 2`.\n-/\ntheorem error_after_step {α : Type} [CommRing α] (lr target x : α) :\n st... | [
{
"name": "error_abs_contract_real",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 28,
"n_chars": 1039,
"n_subproofs": 7,
"n_tactics": 20,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.GDLinearConvergence
import Mathlib.Logic.Function.Iterate
import Mathlib.Algebra.Order.GroupWithZero.Basic
import Mathlib.Tactic.Linarith
import Mathli... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.GDLinearConvergence
import Mathlib.Logic.Function.Iterate
import Mathlib.Algebra.Order.GroupWithZero.Basic
import Mathlib.Tactic.Linarith
import Mathli... | @@ -80,6 +80,16 @@
def step {α : Type} [Sub α] [Mul α] (lr target x : α) : α :=
x - lr * quadraticGrad target x
+/--
+One scalar quadratic gradient-descent step multiplies the current error by `1 - lr`.
+
+For ordered fields, this is the usual starting point for contraction proofs when `0 < lr < 2`.
+-/
+theorem ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8a1ddcc93ee0_0 | e1f3b5408d6514c6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Runtime/Link/Accumulation.lean | Accumulation | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "addGradAll_ok_size",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro grads id g grads' h\n simpa [h] using addGradAll_size_preserved (t := t) grads id g",
"n_chars": 95,
"n_s... | [
{
"name": "addGradAll_size_preserved",
"text": "/--\n`Tape.addGradAll` never changes the size of the dense gradient array in the `.ok` case.\n\nThis is a structural property needed to show the runtime reverse loop preserves array sizes.\n-/\ntheorem addGradAll_size_preserved {α : Type} [Add α] [DecidableEq ... | [
{
"name": "addGradAll_ok_size",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 523,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Runtime.Link.Invariants
/-!
# Runtime Gradient Accumulation Link
This file connects the executable dense-gradient array used by the runtime tape to the type... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Runtime.Link.Invariants
/-!
# Runtime Gradient Accumulation Link
This file connects the executable dense-gradient array used by the runtime tape to the type... | @@ -30,13 +30,114 @@
open Runtime
open Runtime.Autograd
+/--
+`Tape.addGradAll` never changes the size of the dense gradient array in the `.ok` case.
+
+This is a structural property needed to show the runtime reverse loop preserves array sizes.
+-/
+theorem addGradAll_size_preserved {α : Type} [Add α] [DecidableEq... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8a1ddcc93ee0_1 | 4e88e9d6f7ff127b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Runtime/Link/Accumulation.lean | Accumulation | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "backwardDenseFromStep_ok_size",
"depth": 1,
"n_commands": 0,
"n_lines": 77,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro acc id acc' h\n -- `foldlM` over `addGradAll` preserves `size` in the `.ok` case.\n have fold_ok_siz... | [
{
"name": "addGradAll_ok_size",
"text": "/-- If `addGradAll` returns `.ok grads'`, then `grads'.size = grads.size`. -/\ntheorem addGradAll_ok_size {α : Type} [Add α] [DecidableEq Shape]\n (t : Runtime.Autograd.Tape α) :\n ∀ {grads : Array (Runtime.AnyTensor α)} {id : Nat} {g : Runtime.AnyTensor α}\n ... | [
{
"name": "backwardDenseFromStep_ok_size",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 90,
"n_chars": 3917,
"n_subproofs": 6,
"n_tactics": 75,
"cyclomatic": 14,
"n_automation": 14,
"n_rewrites": 0,
"n_structural": 15,
"automation_only": fal... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Runtime.Link.Invariants
/-!
# Runtime Gradient Accumulation Link
This file connects the executable dense-gradient array used by the runtime tape to the type... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Runtime.Link.Invariants
/-!
# Runtime Gradient Accumulation Link
This file connects the executable dense-gradient array used by the runtime tape to the type... | @@ -129,6 +129,16 @@
simp [Runtime.Autograd.Tape.addGradAll, hnode, hreq, hshape, throw, throwThe,
MonadExceptOf.throw]
+/-- If `addGradAll` returns `.ok grads'`, then `grads'.size = grads.size`. -/
+theorem addGradAll_ok_size {α : Type} [Add α] [DecidableEq Shape]
+ (t : Runtime.Autograd.T... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_cab86f17d492_0 | b233fcb76c18f740 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/Ops/Elementwise/Unary.lean | Unary | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "approxT_relu_spec",
"depth": 1,
"n_commands": 0,
"n_lines": 150,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro xS xR eps hx\n induction s with\n | scalar =>\n cases xS with\n | scalar x =>\n cases xR wit... | [
{
"name": "abs_max0_sub_max0_le",
"text": "private lemma abs_max0_sub_max0_le (x y : ℝ) : abs (max x 0 - max y 0) ≤ abs (x - y) := by\n simpa using (abs_max_sub_max_le_abs x y (0 : ℝ))\n\n",
"fan_in": 1,
"n_lines": 4,
"n_chars": 149,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1... | [
{
"name": "approxT_relu_spec",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 164,
"n_chars": 9426,
"n_subproofs": 16,
"n_tactics": 146,
"cyclomatic": 6,
"n_automation": 15,
"n_rewrites": 1,
"n_structural": 14,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.Ops.Elementwise.Binary
/-!
# NF Elementwise Bounds: Unary Operations
-/
@[expose] public section
namespace Proofs
namespace RuntimeApprox
open Spe... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.Ops.Elementwise.Binary
/-!
# NF Elementwise Bounds: Unary Operations
-/
@[expose] public section
namespace Proofs
namespace RuntimeApprox
open Spe... | @@ -33,6 +33,9 @@
local notation "R" => TorchLean.Floats.NF β fexp rnd
+private lemma abs_max0_sub_max0_le (x y : ℝ) : abs (max x 0 - max y 0) ≤ abs (x - y) := by
+ simpa using (abs_max_sub_max_le_abs x y (0 : ℝ))
+
/-- Rounded ReLU scalar op for `NF`: apply `max · 0` then round. -/
noncomputable def reluR (x :... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6252f602f05c_0 | 833a5382aaf47190 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundShiftRightEven.lean | RoundShiftRightEven | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 3 | [
{
"theorem_name": "roundShiftRightEven_eq_shiftRight_or_shiftRight_add1",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- This is just `roundShiftRightEven_eq_q_or_q_add1` with `q := n >>> shift`.\n simpa... | [
{
"name": "roundShiftRightEven_eq_q_or_q_add1",
"text": "/--\n`roundShiftRightEven` returns either the floor quotient `q = n >>> shift` or `q+1`.\n\nThis is the core structural fact we use to derive order bounds: nearest-even rounding can only\nmove the quotient by at most one ulp in the shifted domain.\n-/... | [
{
"name": "roundShiftRightEven_eq_shiftRight_or_shiftRight_add1",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 555,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"aut... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.NatLemmas
/-!
# Basic order bounds for `roundShiftRightEven`
`IEEE32Exec.roundShiftRightEven` is the core integer-ro... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.NatLemmas
/-!
# Basic order bounds for `roundShiftRightEven`
`IEEE32Exec.roundShiftRightEven` is the core integer-ro... | @@ -44,6 +44,60 @@
open Nat
/--
+`roundShiftRightEven` returns either the floor quotient `q = n >>> shift` or `q+1`.
+
+This is the core structural fact we use to derive order bounds: nearest-even rounding can only
+move the quotient by at most one ulp in the shifted domain.
+-/
+private lemma roundShiftRightEven_e... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6252f602f05c_1 | fc276a30968a70a0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundShiftRightEven.lean | RoundShiftRightEven | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 3 | [
{
"theorem_name": "roundShiftRightEven_eq_shiftRight_or_shiftRight_add1",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- This is just `roundShiftRightEven_eq_q_or_q_add1` with `q := n >>> shift`.\n simpa... | [
{
"name": "roundShiftRightEven_eq_q_or_q_add1",
"text": "/--\n`roundShiftRightEven` returns either the floor quotient `q = n >>> shift` or `q+1`.\n\nThis is the core structural fact we use to derive order bounds: nearest-even rounding can only\nmove the quotient by at most one ulp in the shifted domain.\n-/... | [
{
"name": "shiftRight_le_roundShiftRightEven",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 506,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": fals... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.NatLemmas
/-!
# Basic order bounds for `roundShiftRightEven`
`IEEE32Exec.roundShiftRightEven` is the core integer-ro... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.NatLemmas
/-!
# Basic order bounds for `roundShiftRightEven`
`IEEE32Exec.roundShiftRightEven` is the core integer-ro... | @@ -43,9 +43,71 @@
open Nat
+/--
+`roundShiftRightEven` returns either the floor quotient `q = n >>> shift` or `q+1`.
+
+This is the core structural fact we use to derive order bounds: nearest-even rounding can only
+move the quotient by at most one ulp in the shifted domain.
+-/
+private lemma roundShiftRightEven... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6252f602f05c_2 | 6b625f43e9825f97 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundShiftRightEven.lean | RoundShiftRightEven | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 3 | [
{
"theorem_name": "roundShiftRightEven_eq_shiftRight_or_shiftRight_add1",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- This is just `roundShiftRightEven_eq_q_or_q_add1` with `q := n >>> shift`.\n simpa... | [
{
"name": "roundShiftRightEven_eq_q_or_q_add1",
"text": "/--\n`roundShiftRightEven` returns either the floor quotient `q = n >>> shift` or `q+1`.\n\nThis is the core structural fact we use to derive order bounds: nearest-even rounding can only\nmove the quotient by at most one ulp in the shifted domain.\n-/... | [
{
"name": "roundShiftRightEven_le_shiftRight_add1",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 506,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.NatLemmas
/-!
# Basic order bounds for `roundShiftRightEven`
`IEEE32Exec.roundShiftRightEven` is the core integer-ro... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.NatLemmas
/-!
# Basic order bounds for `roundShiftRightEven`
`IEEE32Exec.roundShiftRightEven` is the core integer-ro... | @@ -43,9 +43,71 @@
open Nat
+/--
+`roundShiftRightEven` returns either the floor quotient `q = n >>> shift` or `q+1`.
+
+This is the core structural fact we use to derive order bounds: nearest-even rounding can only
+move the quotient by at most one ulp in the shifted domain.
+-/
+private lemma roundShiftRightEven... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6252f602f05c_3 | cc027dc571bfb2b2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundShiftRightEven.lean | RoundShiftRightEven | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "roundShiftRightEven_le_shiftRightCeilPow2",
"depth": 1,
"n_commands": 0,
"n_lines": 34,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n by_cases h0 : (shift == 0) = true\n · have hs : shift = 0 := Eq.mp (Nat.beq_eq_tru... | [
{
"name": "roundShiftRightEven_le_shiftRight_add1",
"text": "/-- Nearest-even rounding is never above `shiftRight n shift + 1`. -/\nlemma roundShiftRightEven_le_shiftRight_add1 (n shift : Nat) :\n roundShiftRightEven n shift ≤ Nat.shiftRight n shift + 1 := by\n classical\n set q : Nat := Nat.shiftRight... | [
{
"name": "roundShiftRightEven_le_shiftRightCeilPow2",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 43,
"n_chars": 2011,
"n_subproofs": 10,
"n_tactics": 35,
"cyclomatic": 4,
"n_automation": 11,
"n_rewrites": 1,
"n_structural": 2,
"automation... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.NatLemmas
/-!
# Basic order bounds for `roundShiftRightEven`
`IEEE32Exec.roundShiftRightEven` is the core integer-ro... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.NatLemmas
/-!
# Basic order bounds for `roundShiftRightEven`
`IEEE32Exec.roundShiftRightEven` is the core integer-ro... | @@ -97,6 +97,18 @@
(directed rounding).
-/
+/-- Nearest-even rounding is never above `shiftRight n shift + 1`. -/
+lemma roundShiftRightEven_le_shiftRight_add1 (n shift : Nat) :
+ roundShiftRightEven n shift ≤ Nat.shiftRight n shift + 1 := by
+ classical
+ set q : Nat := Nat.shiftRight n shift
+ have hor := (... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6252f602f05c_4 | 425e3fdfe2f182fa | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundShiftRightEven.lean | RoundShiftRightEven | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "roundShiftRightEven_le_shiftRightCeilPow2",
"depth": 1,
"n_commands": 0,
"n_lines": 34,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n by_cases h0 : (shift == 0) = true\n · have hs : shift = 0 := Eq.mp (Nat.beq_eq_tru... | [
{
"name": "roundShiftRightEven_le_shiftRight_add1",
"text": "/-- Nearest-even rounding is never above `shiftRight n shift + 1`. -/\nlemma roundShiftRightEven_le_shiftRight_add1 (n shift : Nat) :\n roundShiftRightEven n shift ≤ Nat.shiftRight n shift + 1 := by\n classical\n set q : Nat := Nat.shiftRight... | [
{
"name": "shiftRight_le_roundShiftRightEven_le_shiftRightCeilPow2",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 8,
"n_chars": 444,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"a... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.NatLemmas
/-!
# Basic order bounds for `roundShiftRightEven`
`IEEE32Exec.roundShiftRightEven` is the core integer-ro... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.NatLemmas
/-!
# Basic order bounds for `roundShiftRightEven`
`IEEE32Exec.roundShiftRightEven` is the core integer-ro... | @@ -109,6 +109,18 @@
· simp [hq, q]
· simp [hq, q]
+/-- Nearest-even rounding is never above `shiftRight n shift + 1`. -/
+lemma roundShiftRightEven_le_shiftRight_add1 (n shift : Nat) :
+ roundShiftRightEven n shift ≤ Nat.shiftRight n shift + 1 := by
+ classical
+ set q : Nat := Nat.shiftRight n shift
+ h... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_0257ebf07f28_0 | f8d1f7185189e766 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/ConstantTarget.lean | ConstantTarget | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "gamma_nonempty_of_BoxValid",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨fun i => (B i).lo, ?_⟩\n intro i\n have hv : Interval32.Valid (B i) := hB i\n have hlelo : (B i).lo ≤... | [
{
"name": "le_refl_of_isFinite",
"text": "theorem le_refl_of_isFinite (x : F) (hx : isFinite x = true) : x ≤ x := by\n have hcmp : compare x x = some .eq := by\n have h :=\n (compare_eq_some_eq_iff_toReal_eq_of_isFinite (x := x) (y := x) hx hx)\n exact h.mpr rfl\n change IEEE32Exec.le x x\n si... | [
{
"name": "gamma_nonempty_of_BoxValid",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 315,
"n_subproofs": 2,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.Interval.IEEEExec32
/-!
# Constant ro... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.Interval.IEEEExec32
/-!
# Constant ro... | @@ -99,12 +99,20 @@
IsMaxOn fHat (γ (d := d) B) M ∧
γI (nuInt B) = Icc m M)
+theorem le_refl_of_isFinite (x : F) (hx : isFinite x = true) : x ≤ x := by
+ have hcmp : compare x x = some .eq := by
+ have h :=
+ (compare_eq_some_eq_iff_toReal_eq_of_isFinite (x := x) (y := x) hx hx)
+ ex... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_0257ebf07f28_1 | f346f9ff9600004f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/ConstantTarget.lean | ConstantTarget | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "gamma_nonempty_of_BoxValid",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨fun i => (B i).lo, ?_⟩\n intro i\n have hv : Interval32.Valid (B i) := hB i\n have hlelo : (B i).lo ≤... | [
{
"name": "le_refl_of_isFinite",
"text": "theorem le_refl_of_isFinite (x : F) (hx : isFinite x = true) : x ≤ x := by\n have hcmp : compare x x = some .eq := by\n have h :=\n (compare_eq_some_eq_iff_toReal_eq_of_isFinite (x := x) (y := x) hx hx)\n exact h.mpr rfl\n change IEEE32Exec.le x x\n si... | [
{
"name": "exactIntervalImage_constant",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 37,
"n_chars": 1354,
"n_subproofs": 2,
"n_tactics": 29,
"cyclomatic": 5,
"n_automation": 4,
"n_rewrites": 4,
"n_structural": 14,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.Interval.IEEEExec32
/-!
# Constant ro... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.Interval.IEEEExec32
/-!
# Constant ro... | @@ -99,12 +99,20 @@
IsMaxOn fHat (γ (d := d) B) M ∧
γI (nuInt B) = Icc m M)
+theorem le_refl_of_isFinite (x : F) (hx : isFinite x = true) : x ≤ x := by
+ have hcmp : compare x x = some .eq := by
+ have h :=
+ (compare_eq_some_eq_iff_toReal_eq_of_isFinite (x := x) (y := x) hx hx)
+ ex... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_f68ac8753b3c_0 | 7d4aeca3ecc8587d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/ERealSemantics.lean | ERealSemantics | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 3 | [
{
"theorem_name": "toEReal_eq_coe_toReal_of_isFinite",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hnan : isNaN x = false := isNaN_eq_false_of_isFinite_eq_true (x := x) hx\n have hinf : isInf x = fa... | [
{
"name": "toEReal_eq_ite",
"text": "/--\nConvenient unfolding lemma for `toEReal`.\n\nThis is the form that works best with `simp` once you have established/assumed (non-)NaN and\n(non-)Inf facts.\n-/\ntheorem toEReal_eq_ite (x : IEEE32Exec) :\n toEReal x =\n if isNaN x then\n (0 : EReal)\n ... | [
{
"name": "toEReal_eq_coe_toReal_of_isFinite",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 20,
"n_chars": 668,
"n_subproofs": 2,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": fals... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import NN.Floats.IEEEExec.BridgeERealTotal
/-!
# Total `EReal` semantics helpers for `IEEE32Exec`
`BridgeERealTotal.lean` defines `toEReal? : I... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import NN.Floats.IEEEExec.BridgeERealTotal
/-!
# Total `EReal` semantics helpers for `IEEE32Exec`
`BridgeERealTotal.lean` defines `toEReal? : I... | @@ -72,6 +72,30 @@
toEReal x = (0 : EReal) := by
simp [toEReal, h]
+/--
+Convenient unfolding lemma for `toEReal`.
+
+This is the form that works best with `simp` once you have established/assumed (non-)NaN and
+(non-)Inf facts.
+-/
+theorem toEReal_eq_ite (x : IEEE32Exec) :
+ toEReal x =
+ if isNaN x... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_24e299a3f01a_0 | 26691ff778bd5b3d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Progress.lean | Progress | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 3 | [
{
"theorem_name": "energy_cycleUpdate_le",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n simpa [cycleUpdate] using energy_foldl_le (n := n) (p := p) hsym hdiag (List.finRange n) s",
"n_char... | [
{
"name": "energy_foldl_le",
"text": "private lemma energy_foldl_le\n (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p) :\n ∀ l : List (Fin n), ∀ s : State n,\n energy (α := ℝ) p (l.foldl (fun s u => updateAt (α := ℝ) p s u) s)\n ≤\n energy (α := ℝ) p s := by\n classic... | [
{
"name": "energy_cycleUpdate_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 310,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_ne... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Proofs.Hopfield.Energy
/-!
# Hopfield cyclic sweep progress (tie-handling)
This file proves the key “tie-handling” lemma needed for paper-style Hopfield global-dyn... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Proofs.Hopfield.Energy
/-!
# Hopfield cyclic sweep progress (tie-handling)
This file proves the key “tie-handling” lemma needed for paper-style Hopfield global-dyn... | @@ -42,10 +42,36 @@
variable (p : Params ℝ n)
+private lemma energy_foldl_le
+ (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p) :
+ ∀ l : List (Fin n), ∀ s : State n,
+ energy (α := ℝ) p (l.foldl (fun s u => updateAt (α := ℝ) p s u) s)
+ ≤
+ energy (α := ℝ) p s := by
+ class... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_24e299a3f01a_1 | 41b50507e1c7218e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Progress.lean | Progress | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "pluses_updateAt_ge_of_energy_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n by_cases hchange : updateAt (α := ℝ) p s u = s\n · -- Avoid `simp` here: `updateAt` is a simp... | [
{
"name": "pluses_updateAt_gt_of_energy_eq_of_ne",
"text": "private lemma pluses_updateAt_gt_of_energy_eq_of_ne\n (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)\n (s : State n) (u : Fin n)\n (hE : energy (α := ℝ) p (updateAt (α := ℝ) p s u) = energy (α := ℝ) p s)\n (hchange : u... | [
{
"name": "pluses_updateAt_ge_of_energy_eq",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 700,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Proofs.Hopfield.Energy
/-!
# Hopfield cyclic sweep progress (tie-handling)
This file proves the key “tie-handling” lemma needed for paper-style Hopfield global-dyn... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Proofs.Hopfield.Energy
/-!
# Hopfield cyclic sweep progress (tie-handling)
This file proves the key “tie-handling” lemma needed for paper-style Hopfield global-dyn... | @@ -42,6 +42,46 @@
variable (p : Params ℝ n)
+private lemma pluses_updateAt_gt_of_energy_eq_of_ne
+ (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)
+ (s : State n) (u : Fin n)
+ (hE : energy (α := ℝ) p (updateAt (α := ℝ) p s u) = energy (α := ℝ) p s)
+ (hchange : updateAt (α := ℝ) p s ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_24e299a3f01a_2 | f4a7b2a2abc6dc7e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Progress.lean | Progress | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "pluses_foldl_ge_of_energy_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 29,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n intro l\n induction l with\n | nil =>\n intro s hE\n simp\n | cons u l IH =>\n ... | [
{
"name": "pluses_updateAt_ge_of_energy_eq",
"text": "private lemma pluses_updateAt_ge_of_energy_eq\n (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)\n (s : State n) (u : Fin n)\n (hE : energy (α := ℝ) p (updateAt (α := ℝ) p s u) = energy (α := ℝ) p s) :\n pluses (n := n) (updat... | [
{
"name": "pluses_foldl_ge_of_energy_eq",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 35,
"n_chars": 1662,
"n_subproofs": 8,
"n_tactics": 29,
"cyclomatic": 2,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Proofs.Hopfield.Energy
/-!
# Hopfield cyclic sweep progress (tie-handling)
This file proves the key “tie-handling” lemma needed for paper-style Hopfield global-dyn... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Proofs.Hopfield.Energy
/-!
# Hopfield cyclic sweep progress (tie-handling)
This file proves the key “tie-handling” lemma needed for paper-style Hopfield global-dyn... | @@ -106,6 +106,20 @@
hnet)
exact False.elim (hlt.ne hE)
+private lemma pluses_updateAt_ge_of_energy_eq
+ (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)
+ (s : State n) (u : Fin n)
+ (hE : energy (α := ℝ) p (updateAt (α := ℝ) p s u) = energy (α := ℝ) p s) :
+ pluses (n := n)... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_24e299a3f01a_3 | b5adcc9123e09a50 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Progress.lean | Progress | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "pluses_foldl_gt_of_energy_eq_of_ne",
"depth": 1,
"n_commands": 0,
"n_lines": 95,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n intro l\n induction l with\n | nil =>\n intro s hE hne\n cases hne rfl\n | co... | [
{
"name": "pluses_foldl_ge_of_energy_eq",
"text": "private lemma pluses_foldl_ge_of_energy_eq\n (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p) :\n ∀ l : List (Fin n), ∀ s : State n,\n (energy (α := ℝ) p (l.foldl (fun s u => updateAt (α := ℝ) p s u) s) = energy (α := ℝ) p s) →\n ... | [
{
"name": "pluses_foldl_gt_of_energy_eq_of_ne",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 102,
"n_chars": 5395,
"n_subproofs": 22,
"n_tactics": 87,
"cyclomatic": 3,
"n_automation": 12,
"n_rewrites": 0,
"n_structural": 20,
"automation_only... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Proofs.Hopfield.Energy
/-!
# Hopfield cyclic sweep progress (tie-handling)
This file proves the key “tie-handling” lemma needed for paper-style Hopfield global-dyn... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Proofs.Hopfield.Energy
/-!
# Hopfield cyclic sweep progress (tie-handling)
This file proves the key “tie-handling” lemma needed for paper-style Hopfield global-dyn... | @@ -120,6 +120,40 @@
· exact le_of_lt (pluses_updateAt_gt_of_energy_eq_of_ne (n := n) (p := p) hsym hdiag s u hE
hchange)
+private lemma pluses_foldl_ge_of_energy_eq
+ (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p) :
+ ∀ l : List (Fin n), ∀ s : State n,
+ (energy (α := ℝ) p (l.fol... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_24e299a3f01a_4 | 9fd9e6ac686b0476 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Progress.lean | Progress | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "pluses_foldl_gt_of_energy_eq_of_ne",
"depth": 1,
"n_commands": 0,
"n_lines": 95,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n intro l\n induction l with\n | nil =>\n intro s hE hne\n cases hne rfl\n | co... | [
{
"name": "pluses_foldl_ge_of_energy_eq",
"text": "private lemma pluses_foldl_ge_of_energy_eq\n (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p) :\n ∀ l : List (Fin n), ∀ s : State n,\n (energy (α := ℝ) p (l.foldl (fun s u => updateAt (α := ℝ) p s u) s) = energy (α := ℝ) p s) →\n ... | [
{
"name": "cycleUpdate_progress",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 17,
"n_chars": 861,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_n... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Proofs.Hopfield.Energy
/-!
# Hopfield cyclic sweep progress (tie-handling)
This file proves the key “tie-handling” lemma needed for paper-style Hopfield global-dyn... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Proofs.Hopfield.Energy
/-!
# Hopfield cyclic sweep progress (tie-handling)
This file proves the key “tie-handling” lemma needed for paper-style Hopfield global-dyn... | @@ -127,6 +127,40 @@
· exact le_of_lt (pluses_updateAt_gt_of_energy_eq_of_ne (n := n) (p := p) hsym hdiag s u hE
hchange)
+private lemma pluses_foldl_ge_of_energy_eq
+ (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p) :
+ ∀ l : List (Fin n), ∀ s : State n,
+ (energy (α := ℝ) p (l.fol... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6877a597bb43_0 | 7dd5bda370bdddcb | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/Core.lean | Core | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "signBit_ofBits_xor_signMask",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hSignMask : signMask.toNat = 2 ^ 31 := by decide\n have hmask : Nat.testBit signMask.toNat 31 = true := ... | [
{
"name": "signBit_ofBits_eq_testBit31",
"text": "/-- `signBit (ofBits b)` is literally the 31st bit of `b` (at the nat level). -/\nlemma signBit_ofBits_eq_testBit31 (b : UInt32) :\n signBit (ofBits b) = Nat.testBit b.toNat 31 := by\n classical\n have hSignMask : signMask.toNat = 2 ^ 31 := by decide\n ... | [
{
"name": "signBit_ofBits_xor_signMask",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 790,
"n_subproofs": 5,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Analysis.SpecialFunctions.Log.Base
public import Mathlib.Analysis.SpecialFunctions.Sqrt
public import Mathlib.Data.Nat.Bi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Analysis.SpecialFunctions.Log.Base
public import Mathlib.Analysis.SpecialFunctions.Sqrt
public import Mathlib.Data.Nat.Bi... | @@ -48,9 +48,47 @@
noncomputable def signFactor (s : Bool) : ℝ :=
if s then (-1 : ℝ) else (1 : ℝ)
+/-- `signBit (ofBits b)` is literally the 31st bit of `b` (at the nat level). -/
+lemma signBit_ofBits_eq_testBit31 (b : UInt32) :
+ signBit (ofBits b) = Nat.testBit b.toNat 31 := by
+ classical
+ have hSignMas... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6877a597bb43_1 | 6e5c328cfc404b7f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/Core.lean | Core | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "signBit_ofBits_xor_signMask",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hSignMask : signMask.toNat = 2 ^ 31 := by decide\n have hmask : Nat.testBit signMask.toNat 31 = true := ... | [
{
"name": "signBit_ofBits_eq_testBit31",
"text": "/-- `signBit (ofBits b)` is literally the 31st bit of `b` (at the nat level). -/\nlemma signBit_ofBits_eq_testBit31 (b : UInt32) :\n signBit (ofBits b) = Nat.testBit b.toNat 31 := by\n classical\n have hSignMask : signMask.toNat = 2 ^ 31 := by decide\n ... | [
{
"name": "toDyadic?_neg_of_toDyadic?_some",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 58,
"n_chars": 2730,
"n_subproofs": 17,
"n_tactics": 46,
"cyclomatic": 1,
"n_automation": 16,
"n_rewrites": 3,
"n_structural": 0,
"automation_only": fa... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Analysis.SpecialFunctions.Log.Base
public import Mathlib.Analysis.SpecialFunctions.Sqrt
public import Mathlib.Data.Nat.Bi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Analysis.SpecialFunctions.Log.Base
public import Mathlib.Analysis.SpecialFunctions.Sqrt
public import Mathlib.Data.Nat.Bi... | @@ -48,9 +48,47 @@
noncomputable def signFactor (s : Bool) : ℝ :=
if s then (-1 : ℝ) else (1 : ℝ)
+/-- `signBit (ofBits b)` is literally the 31st bit of `b` (at the nat level). -/
+lemma signBit_ofBits_eq_testBit31 (b : UInt32) :
+ signBit (ofBits b) = Nat.testBit b.toNat 31 := by
+ classical
+ have hSignMas... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6877a597bb43_2 | a90f857f7dd16d3b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/Core.lean | Core | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "signBit_ofBits_xor_signMask",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hSignMask : signMask.toNat = 2 ^ 31 := by decide\n have hmask : Nat.testBit signMask.toNat 31 = true := ... | [
{
"name": "signBit_ofBits_eq_testBit31",
"text": "/-- `signBit (ofBits b)` is literally the 31st bit of `b` (at the nat level). -/\nlemma signBit_ofBits_eq_testBit31 (b : UInt32) :\n signBit (ofBits b) = Nat.testBit b.toNat 31 := by\n classical\n have hSignMask : signMask.toNat = 2 ^ 31 := by decide\n ... | [
{
"name": "toReal_neg_eq_neg",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 12,
"n_chars": 522,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nest... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Analysis.SpecialFunctions.Log.Base
public import Mathlib.Analysis.SpecialFunctions.Sqrt
public import Mathlib.Data.Nat.Bi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Analysis.SpecialFunctions.Log.Base
public import Mathlib.Analysis.SpecialFunctions.Sqrt
public import Mathlib.Data.Nat.Bi... | @@ -55,9 +55,47 @@
dyadicToReal { sign := (!d.sign), mant := d.mant, exp := d.exp } = -dyadicToReal d := by
by_cases hs : d.sign <;> simp [dyadicToReal, hs]
+/-- `signBit (ofBits b)` is literally the 31st bit of `b` (at the nat level). -/
+lemma signBit_ofBits_eq_testBit31 (b : UInt32) :
+ signBit (ofBits ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_a40eaee4aae8_0 | 68f49fc24fc6cb57 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphRunibpEndToEnd.lean | GraphRunibpEndToEnd | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "evalGraphPrefix_succ_get_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n let acc := evalGraphPrefix g ps inputs n\n have haccSz : acc.size = g.nodes.size := by\n s... | [
{
"name": "evalGraphPrefix_size",
"text": "private lemma evalGraphPrefix_size (g : Graph) (ps : ParamStore ℝ) (inputs : Std.HashMap Nat Val) :\n ∀ n, (evalGraphPrefix g ps inputs n).size = g.nodes.size := by\n intro n; induction n with\n | zero => simp [evalGraphPrefix]\n | succ n ih =>\n simp [e... | [
{
"name": "evalGraphPrefix_succ_get_of_lt",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 27,
"n_chars": 1264,
"n_subproofs": 7,
"n_tactics": 20,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | @@ -74,13 +74,21 @@
/-! Prefix size facts. -/
+private lemma evalGraphPrefix_size (g : Graph) (ps : ParamStore ℝ) (inputs : Std.HashMap Nat Val) :
+ ∀ n, (evalGraphPrefix g ps inputs n).size = g.nodes.size := by
+ intro n; induction n with
+ | zero => simp [evalGraphPrefix]
+ | succ n ih =>
+ simp [eval... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_a40eaee4aae8_1 | 2f4659ec5391f070 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphRunibpEndToEnd.lean | GraphRunibpEndToEnd | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "runIBPPrefix_succ_get_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n let acc := runIBPPrefix g ps n\n have haccSz : acc.size = g.nodes.size := by\n simpa [acc] us... | [
{
"name": "runIBPPrefix_size",
"text": "private lemma runIBPPrefix_size (g : Graph) (ps : ParamStore ℝ) :\n ∀ n, (runIBPPrefix g ps n).size = g.nodes.size := by\n intro n; induction n with\n | zero => simp [runIBPPrefix]\n | succ n ih =>\n simp [runIBPPrefix, ih, Array.set!_eq_setIfInBounds]\n\n/... | [
{
"name": "runIBPPrefix_succ_get_of_lt",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 24,
"n_chars": 1081,
"n_subproofs": 7,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | @@ -74,13 +74,23 @@
/-! Prefix size facts. -/
+private lemma runIBPPrefix_size (g : Graph) (ps : ParamStore ℝ) :
+ ∀ n, (runIBPPrefix g ps n).size = g.nodes.size := by
+ intro n; induction n with
+ | zero => simp [runIBPPrefix]
+ | succ n ih =>
+ simp [runIBPPrefix, ih, Array.set!_eq_setIfInBounds]
+
+/... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_a40eaee4aae8_2 | d1526d4af5709e24 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphRunibpEndToEnd.lean | GraphRunibpEndToEnd | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "evalGraphPrefix_get_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n generalizing k with\n | zero =>\n have hk : k = 0 := Nat.eq_zero_of_le_zero hkn\n subst h... | [
{
"name": "evalGraphPrefix_succ_get_of_lt",
"text": "private lemma evalGraphPrefix_succ_get_of_lt\n (g : Graph) (ps : ParamStore ℝ) (inputs : Std.HashMap Nat Val)\n {n i : Nat} (hi : i < n) :\n (evalGraphPrefix g ps inputs (n + 1))[i]! = (evalGraphPrefix g ps inputs n)[i]! := by\n classical\n let... | [
{
"name": "evalGraphPrefix_get_of_lt",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 19,
"n_chars": 711,
"n_subproofs": 3,
"n_tactics": 14,
"cyclomatic": 4,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | @@ -81,6 +81,32 @@
| succ n ih =>
simp [evalGraphPrefix, ih, Array.set!_eq_setIfInBounds]
+private lemma evalGraphPrefix_succ_get_of_lt
+ (g : Graph) (ps : ParamStore ℝ) (inputs : Std.HashMap Nat Val)
+ {n i : Nat} (hi : i < n) :
+ (evalGraphPrefix g ps inputs (n + 1))[i]! = (evalGraphPrefix g ps i... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_a40eaee4aae8_3 | b0cd1414b4d26fd7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphRunibpEndToEnd.lean | GraphRunibpEndToEnd | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "runIBPPrefix_get_of_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction n generalizing k with\n | zero =>\n have hk : k = 0 := Nat.eq_zero_of_le_zero hkn\n subst hk\n... | [
{
"name": "runIBPPrefix_succ_get_of_lt",
"text": "private lemma runIBPPrefix_succ_get_of_lt\n (g : Graph) (ps : ParamStore ℝ)\n {n i : Nat} (hi : i < n) :\n (runIBPPrefix g ps (n + 1))[i]! = (runIBPPrefix g ps n)[i]! := by\n classical\n let acc := runIBPPrefix g ps n\n have haccSz : acc.size = g... | [
{
"name": "runIBPPrefix_get_of_lt",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 25,
"n_chars": 802,
"n_subproofs": 3,
"n_tactics": 13,
"cyclomatic": 4,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
"ma... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | @@ -83,6 +83,29 @@
/-! Prefix stability: later writes do not change earlier entries. -/
+private lemma runIBPPrefix_succ_get_of_lt
+ (g : Graph) (ps : ParamStore ℝ)
+ {n i : Nat} (hi : i < n) :
+ (runIBPPrefix g ps (n + 1))[i]! = (runIBPPrefix g ps n)[i]! := by
+ classical
+ let acc := runIBPPrefix g ps... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_a40eaee4aae8_4 | 4e8c24f191547017 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphRunibpEndToEnd.lean | GraphRunibpEndToEnd | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "evalGraphRec_SemLocalOK",
"depth": 1,
"n_commands": 0,
"n_lines": 67,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n refine ⟨by simpa [evalGraphRec] using (evalGraphPrefix_size (g := g) (ps := ps) (inputs := inputs)\n ... | [
{
"name": "evalNode?_congr_of_parents",
"text": "private lemma evalNode?_congr_of_parents\n (nodes : Array Node) (ps : ParamStore ℝ) (inputs : Std.HashMap Nat Val)\n (vals₁ vals₂ : Array (Option Val))\n {id : Nat} (hid : id < nodes.size)\n (hsize₁ : vals₁.size = nodes.size)\n (hsize₂ : vals₂.... | [
{
"name": "evalGraphRec_SemLocalOK",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 71,
"n_chars": 3652,
"n_subproofs": 15,
"n_tactics": 61,
"cyclomatic": 2,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 7,
"automation_only": false,
... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | @@ -142,6 +142,194 @@
ih (hkn := hkn') hi
· rfl
+private lemma evalNode?_congr_of_parents
+ (nodes : Array Node) (ps : ParamStore ℝ) (inputs : Std.HashMap Nat Val)
+ (vals₁ vals₂ : Array (Option Val))
+ {id : Nat} (hid : id < nodes.size)
+ (hsize₁ : vals₁.size = nodes.size)
+ (hsize₂ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_a40eaee4aae8_5 | 448175eb31b142ac | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphRunibpEndToEnd.lean | GraphRunibpEndToEnd | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "runIBP?_CertLocalOK",
"depth": 1,
"n_commands": 0,
"n_lines": 49,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n refine ⟨by simpa [runIBP?] using (runIBPPrefix_size (g := g) (ps := ps) g.nodes.size), ?_⟩\n intro id hi... | [
{
"name": "certStepNode?_congr_of_parents",
"text": "private lemma certStepNode?_congr_of_parents\n (nodes : Array Node) (ps : ParamStore ℝ)\n (cert₁ cert₂ : Array (Option (FlatBox ℝ)))\n {id : Nat} (hid : id < nodes.size)\n (hsize₁ : cert₁.size = nodes.size)\n (hsize₂ : cert₂.size = nodes.si... | [
{
"name": "runIBP?_CertLocalOK",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 58,
"n_chars": 2475,
"n_subproofs": 14,
"n_tactics": 50,
"cyclomatic": 1,
"n_automation": 8,
"n_rewrites": 0,
"n_structural": 6,
"automation_only": false,
"max... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | @@ -147,6 +147,115 @@
same result.
-/
+private lemma certStepNode?_congr_of_parents
+ (nodes : Array Node) (ps : ParamStore ℝ)
+ (cert₁ cert₂ : Array (Option (FlatBox ℝ)))
+ {id : Nat} (hid : id < nodes.size)
+ (hsize₁ : cert₁.size = nodes.size)
+ (hsize₂ : cert₂.size = nodes.size)
+ (hparsLt : ∀ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_a40eaee4aae8_6 | fd9782040be8e6d4 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphRunibpEndToEnd.lean | GraphRunibpEndToEnd | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "runIBP?_encloses_evalGraphRec",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hcert : CertLocalOK (g := g) (ps := ps) (runIBP? g ps) :=\n runIBP?_CertLocalOK (g := g) (ps := ps) ... | [
{
"name": "runIBP?_CertLocalOK",
"text": "/-- Under topological order, the certificate produced by `runIBP?` satisfies `CertLocalOK`. -/\ntheorem runIBP?_CertLocalOK (g : Graph) (ps : ParamStore ℝ)\n (htopo : TopoSorted g) :\n CertLocalOK (g := g) (ps := ps) (runIBP? g ps) := by\n classical\n refine... | [
{
"name": "runIBP?_encloses_evalGraphRec",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 12,
"n_lines": 26,
"n_chars": 929,
"n_subproofs": 2,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,... | 12 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end IBP soundness (graph dialect, over `ℝ`)
`NN.MLTheory.CROWN.Proofs.GraphCertSoundness` proves:
> If a per-node IBP... | @@ -565,6 +565,63 @@
id := hset
_ = evalNode? g.nodes ps inputs (evalGraphRec g ps inputs) id := hnode
+/-- Under topological order, the certificate produced by `runIBP?` satisfies `CertLocalOK`. -/
+theorem runIBP?_CertLocalOK (g : Graph) (ps : ParamStore ℝ)
+ (htopo : TopoSorted g) :
+ CertLocalOK... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_335648d5fce8_0 | d5654bb76877fc16 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/Semantics.lean | Semantics | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "le_self_of_isNaN_false",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hcmp : IEEE32Exec.compare x x = some .eq := compare_self_of_isNaN_false (x := x) hx\n change IEEE32Exec.le x x... | [
{
"name": "compare_self_of_isNaN_false",
"text": "theorem compare_self_of_isNaN_false (x : F) (hx : IEEE32Exec.isNaN x = false) :\n IEEE32Exec.compare x x = some .eq := by\n classical\n cases hinf : IEEE32Exec.isInf x with\n | true =>\n -- `compare` short-circuits on infinities.\n simp [IEEE... | [
{
"name": "le_self_of_isNaN_false",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 237,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | @@ -91,8 +91,37 @@
open IEEE32Exec
+theorem compare_self_of_isNaN_false (x : F) (hx : IEEE32Exec.isNaN x = false) :
+ IEEE32Exec.compare x x = some .eq := by
+ classical
+ cases hinf : IEEE32Exec.isInf x with
+ | true =>
+ -- `compare` short-circuits on infinities.
+ simp [IEEE32Exec.compare, hx, h... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_335648d5fce8_1 | e47775a31f2ecbd8 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/Semantics.lean | Semantics | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 3 | [
{
"theorem_name": "mem_point_of_isNaN_false",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n dsimp [point]\n -- `x ∈ ⟨x,x⟩` reduces to `x ≤ x ∧ x ≤ x`.\n simp [mem_range_iff, ExecLemmas.le_self_of_isNaN_fa... | [
{
"name": "le_self_of_isNaN_false",
"text": "theorem le_self_of_isNaN_false (x : F) (hx : IEEE32Exec.isNaN x = false) : x ≤ x := by\n have hcmp : IEEE32Exec.compare x x = some .eq := compare_self_of_isNaN_false (x := x) hx\n change IEEE32Exec.le x x\n simp [IEEE32Exec.le, hcmp]\n\n",
"fan_in": 3,
... | [
{
"name": "mem_point_of_isNaN_false",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 6,
"n_chars": 241,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | @@ -120,6 +120,11 @@
rcases hdy with ⟨d, hd⟩
simp [IEEE32Exec.compare, hx, hinf, hd, IEEE32Exec.cmpDyadic]
+theorem le_self_of_isNaN_false (x : F) (hx : IEEE32Exec.isNaN x = false) : x ≤ x := by
+ have hcmp : IEEE32Exec.compare x x = some .eq := compare_self_of_isNaN_false (x := x) hx
+ change IEEE32E... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_335648d5fce8_2 | c68f0e78e74701ef | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/Semantics.lean | Semantics | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "mem_pointBox_of_isNaN_false",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro i\n exact mem_point_of_isNaN_false (x := x i) (hx i)",
"n_chars": 64,
"n_subproofs": 0,
"n_t... | [
{
"name": "mem_point_of_isNaN_false",
"text": "theorem mem_point_of_isNaN_false (x : F) (hx : IEEE32Exec.isNaN x = false) : x ∈ point x := by\n dsimp [point]\n -- `x ∈ ⟨x,x⟩` reduces to `x ≤ x ∧ x ≤ x`.\n simp [mem_range_iff, ExecLemmas.le_self_of_isNaN_false (x := x) hx]\n\n",
"fan_in": 2,
"n_li... | [
{
"name": "mem_pointBox_of_isNaN_false",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 7,
"n_chars": 216,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | @@ -165,12 +165,19 @@
/-- Point interval `⟨x,x⟩`. -/
@[inline] def point (x : F) : I := range x x
+theorem mem_point_of_isNaN_false (x : F) (hx : IEEE32Exec.isNaN x = false) : x ∈ point x := by
+ dsimp [point]
+ -- `x ∈ ⟨x,x⟩` reduces to `x ≤ x ∧ x ≤ x`.
+ simp [mem_range_iff, ExecLemmas.le_self_of_isNaN_false (... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_335648d5fce8_3 | edb6525b5a2a9007 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/Semantics.lean | Semantics | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "mem_hull_of_mem",
"depth": 1,
"n_commands": 0,
"n_lines": 32,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n unfold hull\n by_cases hnan : ∃ z ∈ s, IEEE32Exec.isNaN z = true\n · simp [hnan, I.mem_top]\n · have hs : ... | [
{
"name": "chooseMax_spec",
"text": "theorem chooseMax_spec (s : Finset F) (hs : s.Nonempty) :\n chooseMax s hs ∈ s ∧ toERealTotal (chooseMax s hs) = (s.image toERealTotal).max' (hs.image _) :=\n by\n simpa [chooseMax] using (Classical.choose_spec (exists_chooseMax s hs))\n\n",
"fan_in": 1,
... | [
{
"name": "mem_hull_of_mem",
"fan_in": 3,
"n_deps_direct": 5,
"n_deps_transitive": 7,
"n_lines": 36,
"n_chars": 1806,
"n_subproofs": 12,
"n_tactics": 29,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nes... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | @@ -341,6 +341,11 @@
by
simpa [chooseMin] using (Classical.choose_spec (exists_chooseMin s hs))
+theorem chooseMax_spec (s : Finset F) (hs : s.Nonempty) :
+ chooseMax s hs ∈ s ∧ toERealTotal (chooseMax s hs) = (s.image toERealTotal).max' (hs.image _) :=
+ by
+ simpa [chooseMax] using (Classical.cho... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_335648d5fce8_4 | 1e6531a6f719cc78 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/Semantics.lean | Semantics | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "add_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro x y hx hy\n cases A with\n | top =>\n simp [addSharp, I.mem_top]\n | range a b =>\n cases B with\n | top... | [
{
"name": "mem_γFinsetBox_iff",
"text": "theorem mem_γFinsetBox_iff {d : Nat} (B : I.Box d) (x : Fin d → F) :\n x ∈ γFinsetBox B ↔ ∀ i, x i ∈ B i := by\n classical\n simp [γFinsetBox]\n\n",
"fan_in": 2,
"n_lines": 6,
"n_chars": 159,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic"... | [
{
"name": "add_sound",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 9,
"n_lines": 25,
"n_chars": 973,
"n_subproofs": 2,
"n_tactics": 22,
"cyclomatic": 3,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 7,
"automation_only": false,
"max_nesting": 1... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | @@ -404,6 +404,11 @@
classical
exact Finset.univ.filter (fun x => ∀ i, x i ∈ B i)
+theorem mem_γFinsetBox_iff {d : Nat} (B : I.Box d) (x : Fin d → F) :
+ x ∈ γFinsetBox B ↔ ∀ i, x i ∈ B i := by
+ classical
+ simp [γFinsetBox]
+
/-- Build a 2D box from two intervals (coordinate `0` is `A`, coordinate `1` i... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_335648d5fce8_5 | c1027da6676a4255 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/Semantics.lean | Semantics | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 3 | [
{
"theorem_name": "add_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro x y hx hy\n cases A with\n | top =>\n simp [addSharp, I.mem_top]\n | range a b =>\n cases B with\n | top... | [
{
"name": "mem_hull_of_mem",
"text": "theorem mem_hull_of_mem (s : Finset F) {x : F} (hx : x ∈ s) : x ∈ hull s := by\n classical\n unfold hull\n by_cases hnan : ∃ z ∈ s, IEEE32Exec.isNaN z = true\n · simp [hnan, I.mem_top]\n · have hs : s.Nonempty := ⟨x, hx⟩\n have hn : ∀ z, z ∈ s → IEEE32Exec.isNaN... | [
{
"name": "relu_sound",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 8,
"n_lines": 14,
"n_chars": 423,
"n_subproofs": 2,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": ... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | @@ -359,6 +359,41 @@
else
I.top
+theorem mem_hull_of_mem (s : Finset F) {x : F} (hx : x ∈ s) : x ∈ hull s := by
+ classical
+ unfold hull
+ by_cases hnan : ∃ z ∈ s, IEEE32Exec.isNaN z = true
+ · simp [hnan, I.mem_top]
+ · have hs : s.Nonempty := ⟨x, hx⟩
+ have hn : ∀ z, z ∈ s → IEEE32Exec.isNaN z = fa... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_335648d5fce8_6 | d9fc9364b8e0d1c8 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/Semantics.lean | Semantics | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "add_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro x y hx hy\n cases A with\n | top =>\n simp [addSharp, I.mem_top]\n | range a b =>\n cases B with\n | top... | [
{
"name": "mem_γFinsetBox_iff",
"text": "theorem mem_γFinsetBox_iff {d : Nat} (B : I.Box d) (x : Fin d → F) :\n x ∈ γFinsetBox B ↔ ∀ i, x i ∈ B i := by\n classical\n simp [γFinsetBox]\n\n",
"fan_in": 2,
"n_lines": 6,
"n_chars": 159,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic"... | [
{
"name": "sumSharp_sound",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 12,
"n_lines": 36,
"n_chars": 1855,
"n_subproofs": 5,
"n_tactics": 27,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 5,
"automation_only": false,
"max_nest... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | @@ -438,6 +438,11 @@
classical
exact Finset.univ.filter (fun x => ∀ i, x i ∈ B i)
+theorem mem_γFinsetBox_iff {d : Nat} (B : I.Box d) (x : Fin d → F) :
+ x ∈ γFinsetBox B ↔ ∀ i, x i ∈ B i := by
+ classical
+ simp [γFinsetBox]
+
/-- Build a 2D box from two intervals (coordinate `0` is `A`, coordinate `1` i... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_335648d5fce8_7 | 290bbf8fe0352dae | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/Semantics.lean | Semantics | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 3 | [
{
"theorem_name": "mem_point_of_isNaN_false",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n dsimp [point]\n -- `x ∈ ⟨x,x⟩` reduces to `x ≤ x ∧ x ≤ x`.\n simp [mem_range_iff, ExecLemmas.le_self_of_isNaN_fa... | [
{
"name": "le_self_of_isNaN_false",
"text": "theorem le_self_of_isNaN_false (x : F) (hx : IEEE32Exec.isNaN x = false) : x ≤ x := by\n have hcmp : IEEE32Exec.compare x x = some .eq := compare_self_of_isNaN_false (x := x) hx\n change IEEE32Exec.le x x\n simp [IEEE32Exec.le, hcmp]\n\n",
"fan_in": 3,
... | [
{
"name": "exactIntervalImage_constant",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 27,
"n_chars": 811,
"n_subproofs": 0,
"n_tactics": 23,
"cyclomatic": 5,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 13,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | @@ -120,6 +120,11 @@
rcases hdy with ⟨d, hd⟩
simp [IEEE32Exec.compare, hx, hinf, hd, IEEE32Exec.cmpDyadic]
+theorem le_self_of_isNaN_false (x : F) (hx : IEEE32Exec.isNaN x = false) : x ≤ x := by
+ have hcmp : IEEE32Exec.compare x x = some .eq := compare_self_of_isNaN_false (x := x) hx
+ change IEEE32E... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_335648d5fce8_8 | edaf5f172738c4b7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/Semantics.lean | Semantics | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "add_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro x y hx hy\n cases A with\n | top =>\n simp [addSharp, I.mem_top]\n | range a b =>\n cases B with\n | top... | [
{
"name": "mem_γFinsetBox_iff",
"text": "theorem mem_γFinsetBox_iff {d : Nat} (B : I.Box d) (x : Fin d → F) :\n x ∈ γFinsetBox B ↔ ∀ i, x i ∈ B i := by\n classical\n simp [γFinsetBox]\n\n",
"fan_in": 2,
"n_lines": 6,
"n_chars": 159,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic"... | [
{
"name": "aff_sound",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 15,
"n_lines": 41,
"n_chars": 2071,
"n_subproofs": 7,
"n_tactics": 30,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting":... | 9 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | @@ -443,6 +443,11 @@
classical
exact Finset.univ.filter (fun x => ∀ i, x i ∈ B i)
+theorem mem_γFinsetBox_iff {d : Nat} (B : I.Box d) (x : Fin d → F) :
+ x ∈ γFinsetBox B ↔ ∀ i, x i ∈ B i := by
+ classical
+ simp [γFinsetBox]
+
/-- Build a 2D box from two intervals (coordinate `0` is `A`, coordinate `1` i... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_335648d5fce8_9 | aa8d77aebf4fa6b9 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/Semantics.lean | Semantics | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "add_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro x y hx hy\n cases A with\n | top =>\n simp [addSharp, I.mem_top]\n | range a b =>\n cases B with\n | top... | [
{
"name": "mem_γFinsetBox_iff",
"text": "theorem mem_γFinsetBox_iff {d : Nat} (B : I.Box d) (x : Fin d → F) :\n x ∈ γFinsetBox B ↔ ∀ i, x i ∈ B i := by\n classical\n simp [γFinsetBox]\n\n",
"fan_in": 2,
"n_lines": 6,
"n_chars": 159,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic"... | [
{
"name": "eval_sound",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 17,
"n_lines": 25,
"n_chars": 1328,
"n_subproofs": 3,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nesting"... | 10 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | @@ -443,6 +443,11 @@
classical
exact Finset.univ.filter (fun x => ∀ i, x i ∈ B i)
+theorem mem_γFinsetBox_iff {d : Nat} (B : I.Box d) (x : Fin d → F) :
+ x ∈ γFinsetBox B ↔ ∀ i, x i ∈ B i := by
+ classical
+ simp [γFinsetBox]
+
/-- Build a 2D box from two intervals (coordinate `0` is `A`, coordinate `1` i... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_335648d5fce8_10 | d684c44d9c046440 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/Semantics.lean | Semantics | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "eval_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro x hx\n -- First affine layer.\n have hz1 : aff net.W1 net.b1 x ∈ I.γ (affSharp net.W1 net.b1 B) :=\n aff_sound (W :=... | [
{
"name": "aff_sound",
"text": "theorem aff_sound [OpsExact.Sound] {d m : Nat}\n (W : Fin m → Fin d → F) (b : Fin m → F) (B : I.Box d)\n (hW : ∀ i j, IEEE32Exec.isNaN (W i j) = false)\n (hb : ∀ i, IEEE32Exec.isNaN (b i) = false) :\n ∀ {x : Fin d → F}, x ∈ I.γ B → aff W b x ∈ I.γ (affSharp W b B)... | [
{
"name": "interval_semantics_sound",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 18,
"n_lines": 11,
"n_chars": 498,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"... | 11 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | @@ -687,6 +687,46 @@
let z2 : I.Box 1 := affSharp net.W2 net.b2 a1
z2 0
+theorem aff_sound [OpsExact.Sound] {d m : Nat}
+ (W : Fin m → Fin d → F) (b : Fin m → F) (B : I.Box d)
+ (hW : ∀ i j, IEEE32Exec.isNaN (W i j) = false)
+ (hb : ∀ i, IEEE32Exec.isNaN (b i) = false) :
+ ∀ {x : Fin d → F}, x ∈ I.γ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_335648d5fce8_11 | 9c7ec36cf0134a14 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/Semantics.lean | Semantics | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "eval_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro x hx\n -- First affine layer.\n have hz1 : aff net.W1 net.b1 x ∈ I.γ (affSharp net.W1 net.b1 B) :=\n aff_sound (W :=... | [
{
"name": "aff_sound",
"text": "theorem aff_sound [OpsExact.Sound] {d m : Nat}\n (W : Fin m → Fin d → F) (b : Fin m → F) (B : I.Box d)\n (hW : ∀ i j, IEEE32Exec.isNaN (W i j) = false)\n (hb : ∀ i, IEEE32Exec.isNaN (b i) = false) :\n ∀ {x : Fin d → F}, x ∈ I.γ B → aff W b x ∈ I.γ (affSharp W b B)... | [
{
"name": "eval_sound_pointBox",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 19,
"n_lines": 11,
"n_chars": 612,
"n_subproofs": 1,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_n... | 12 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Fin.Tuple.Basic
public import Mathlib.Data.Set.Image
public import NN.Floats.IEEEExec.BridgeERealTotal
public import NN.Float... | @@ -693,6 +693,46 @@
let z2 : I.Box 1 := affSharp net.W2 net.b2 a1
z2 0
+theorem aff_sound [OpsExact.Sound] {d m : Nat}
+ (W : Fin m → Fin d → F) (b : Fin m → F) (B : I.Box d)
+ (hW : ∀ i j, IEEE32Exec.isNaN (W i j) = false)
+ (hb : ∀ i, IEEE32Exec.isNaN (b i) = false) :
+ ∀ {x : Fin d → F}, x ∈ I.γ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_4924abb8ece0_1 | b578d15ccd20b89b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/BackwardOps/Backend.lean | Backend | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "approxT_fill_one",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro s\n exact\n approxT_fill_const (β := β) (fexp := fexp) (rnd := rnd)\n (cS := (1 : ℝ)) (cR := (1 : R))\n ... | [
{
"name": "approxT_fill_const",
"text": "lemma approxT_fill_const {cS : ℝ} {cR : R} {eps : ℝ} (h : abs (toSpec (β := β) (fexp := fexp) (rnd\n := rnd) cR - cS) ≤ eps) :\n ∀ {s : Shape}, approxT (α := R) (toSpec := toSpec (β := β) (fexp := fexp) (rnd := rnd))\n (Spec.fill cS s) (Spec.fill cR s) eps :... | [
{
"name": "approxT_fill_zero",
"fan_in": 4,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 329,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.BackwardOps.Sparse
/-!
# NF Backward Approximation Backend
Core approximation lemmas for the rounded NF backend: constants, sparse context writes, a... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.BackwardOps.Sparse
/-!
# NF Backward Approximation Backend
Core approximation lemmas for the rounded NF backend: constants, sparse context writes, a... | @@ -38,9 +38,63 @@
-- `toSpec` is already defined in `NN.Proofs.RuntimeApprox.NF.Ops`.
+lemma approxT_fill_const {cS : ℝ} {cR : R} {eps : ℝ} (h : abs (toSpec (β := β) (fexp := fexp) (rnd
+ := rnd) cR - cS) ≤ eps) :
+ ∀ {s : Shape}, approxT (α := R) (toSpec := toSpec (β := β) (fexp := fexp) (rnd := rnd))
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_06ae330ad58d_0 | d8c4cc9edcc57e05 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/FDeriv.lean | FDeriv | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "inner_toVecT_dim",
"depth": 1,
"n_commands": 0,
"n_lines": 75,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n by_cases hm : Shape.size s = 0\n · have hmul : n * Shape.size s = 0 := by simp [hm]\n -- LHS: transport ... | [
{
"name": "toVecT_dim_apply",
"text": "/--\nCoordinate characterization of `toVecT` on a tensor `.dim n s`.\n\nInformally, the vectorization order is the standard product order induced by `finProdFinEquiv`.\n-/\nlemma toVecT_dim_apply {n : Nat} {s : Shape} (hmpos : 0 < Shape.size s)\n (f : Fin n → Tensor... | [
{
"name": "inner_toVecT_dim",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 82,
"n_chars": 3627,
"n_subproofs": 5,
"n_tactics": 74,
"cyclomatic": 1,
"n_automation": 16,
"n_rewrites": 2,
"n_structural": 8,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | @@ -210,6 +210,44 @@
ext i
simp [castVec]
+/--
+Coordinate characterization of `toVecT` on a tensor `.dim n s`.
+
+Informally, the vectorization order is the standard product order induced by `finProdFinEquiv`.
+-/
+lemma toVecT_dim_apply {n : Nat} {s : Shape} (hmpos : 0 < Shape.size s)
+ (f : Fin n → Tensor... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_06ae330ad58d_1 | e60b52c0f2b9cdb0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/FDeriv.lean | FDeriv | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "dot_eq_inner_toVecT",
"depth": 1,
"n_commands": 0,
"n_lines": 48,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n induction s with\n | scalar =>\n cases a with\n | scalar x =>\n cases b with\n ... | [
{
"name": "sum_spec_dim",
"text": "/--\n`sum_spec` over an outer dimension is a sum over slices.\n\nThis tensor-level “Fubini rule” is used to relate `Spec.dot` to Euclidean inner products after\nvectorization.\n-/\nlemma sum_spec_dim {n : Nat} {s : Shape} (values : Fin n → Tensor ℝ s) :\n sumSpec (Tenso... | [
{
"name": "dot_eq_inner_toVecT",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 57,
"n_chars": 2522,
"n_subproofs": 5,
"n_tactics": 48,
"cyclomatic": 6,
"n_automation": 9,
"n_rewrites": 2,
"n_structural": 10,
"automation_only": false,
"max... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | @@ -211,6 +211,113 @@
simp [castVec]
/--
+`sum_spec` over an outer dimension is a sum over slices.
+
+This tensor-level “Fubini rule” is used to relate `Spec.dot` to Euclidean inner products after
+vectorization.
+-/
+lemma sum_spec_dim {n : Nat} {s : Shape} (values : Fin n → Tensor ℝ s) :
+ sumSpec (Tensor.di... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_06ae330ad58d_2 | 2ec39dc83752a71d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/FDeriv.lean | FDeriv | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "dot_eq_inner_toVecT",
"depth": 1,
"n_commands": 0,
"n_lines": 48,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n induction s with\n | scalar =>\n cases a with\n | scalar x =>\n cases b with\n ... | [
{
"name": "inner_toVecT_dim",
"text": "/-- `toVecT` turns dot products on `.dim n s` into sums of Euclidean inner products over slices. -/\nlemma inner_toVecT_dim {n : Nat} {s : Shape} (a b : Fin n → Tensor ℝ s) :\n inner ℝ (toVecT (t := Tensor.dim a)) (toVecT (t := Tensor.dim b))\n =\n ∑ i : Fin... | [
{
"name": "dotList_eq_inner_flattenCtx",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 55,
"n_chars": 2650,
"n_subproofs": 1,
"n_tactics": 41,
"cyclomatic": 6,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 7,
"automation_only": false,
... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | @@ -355,6 +355,87 @@
simp [toVecT, toVecE, Spec.toVec, flattenSpec, m, hfi, hdiv, hmod]
-- Inner product decomposition across an outer dimension.
+/-- `toVecT` turns dot products on `.dim n s` into sums of Euclidean inner products over slices. -/
+lemma inner_toVecT_dim {n : Nat} {s : Shape} (a b : Fin n → Te... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_06ae330ad58d_3 | 0217c4b203ae43c3 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/FDeriv.lean | FDeriv | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "ctxSize_snoc",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `ctxSize [τ] = Shape.size τ`.\n simp [ctxSize, ctxSize_append]",
"n_chars": 73,
"n_subproofs": 0,
"n_tactics":... | [
{
"name": "ctxSize_append",
"text": "/-- `ctxSize` respects list append (sizes add). -/\nlemma ctxSize_append (Γ ss : List Shape) : ctxSize (Γ ++ ss) = ctxSize Γ + ctxSize ss := by\n induction Γ with\n | nil => simp [ctxSize]\n | cons s Γ ih => simp [ctxSize, ih, Nat.add_assoc]\n\n",
"fan_in": 1,
... | [
{
"name": "ctxSize_snoc",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 244,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | @@ -237,9 +237,17 @@
so that the calculus proofs later can use them without redoing shape arithmetic.
-/
+/-- `ctxSize` respects list append (sizes add). -/
+lemma ctxSize_append (Γ ss : List Shape) : ctxSize (Γ ++ ss) = ctxSize Γ + ctxSize ss := by
+ induction Γ with
+ | nil => simp [ctxSize]
+ | cons s Γ ih =>... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_06ae330ad58d_4 | a316c25286a4bcbe | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/FDeriv.lean | FDeriv | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "ctxSize_snoc",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `ctxSize [τ] = Shape.size τ`.\n simp [ctxSize, ctxSize_append]",
"n_chars": 73,
"n_subproofs": 0,
"n_tactics":... | [
{
"name": "ctxSize_append",
"text": "/-- `ctxSize` respects list append (sizes add). -/\nlemma ctxSize_append (Γ ss : List Shape) : ctxSize (Γ ++ ss) = ctxSize Γ + ctxSize ss := by\n induction Γ with\n | nil => simp [ctxSize]\n | cons s Γ ih => simp [ctxSize, ih, Nat.add_assoc]\n\n",
"fan_in": 1,
... | [
{
"name": "snocCtx_unsnocCtx",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 25,
"n_chars": 1188,
"n_subproofs": 2,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | @@ -237,9 +237,17 @@
so that the calculus proofs later can use them without redoing shape arithmetic.
-/
+/-- `ctxSize` respects list append (sizes add). -/
+lemma ctxSize_append (Γ ss : List Shape) : ctxSize (Γ ++ ss) = ctxSize Γ + ctxSize ss := by
+ induction Γ with
+ | nil => simp [ctxSize]
+ | cons s Γ ih =>... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_06ae330ad58d_5 | 59badd78fda2b763 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/FDeriv.lean | FDeriv | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 1 | [
{
"theorem_name": "dot_eq_inner_toVecT",
"depth": 1,
"n_commands": 0,
"n_lines": 48,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n induction s with\n | scalar =>\n cases a with\n | scalar x =>\n cases b with\n ... | [
{
"name": "inner_toVecT_dim",
"text": "/-- `toVecT` turns dot products on `.dim n s` into sums of Euclidean inner products over slices. -/\nlemma inner_toVecT_dim {n : Nat} {s : Shape} (a b : Fin n → Tensor ℝ s) :\n inner ℝ (toVecT (t := Tensor.dim a)) (toVecT (t := Tensor.dim b))\n =\n ∑ i : Fin... | [
{
"name": "correct_inner",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 24,
"n_chars": 1017,
"n_subproofs": 3,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nestin... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | @@ -355,6 +355,87 @@
simp [toVecT, toVecE, Spec.toVec, flattenSpec, m, hfi, hdiv, hmod]
-- Inner product decomposition across an outer dimension.
+/-- `toVecT` turns dot products on `.dim n s` into sums of Euclidean inner products over slices. -/
+lemma inner_toVecT_dim {n : Nat} {s : Shape} (a b : Fin n → Te... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_06ae330ad58d_6 | d92121254c6b6726 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/FDeriv.lean | FDeriv | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 2 | [
{
"theorem_name": "dotList_eq_inner_flattenCtx",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n induction Γ with\n | nil =>\n cases x\n cases y\n simp [TList.dotList, flattenCtx... | [
{
"name": "dot_eq_inner_toVecT",
"text": "/--\nMain agreement lemma: tensor dot equals Euclidean inner product of vectorizations.\n\nThis is the bridge between `soundness.lean` (stated using `Spec.dot`) and the analytic theorems\nhere (stated using Euclidean `inner`).\n-/\ntheorem dot_eq_inner_toVecT {s : S... | [
{
"name": "backprop_correct_inner",
"fan_in": 2,
"n_deps_direct": 6,
"n_deps_transitive": 13,
"n_lines": 98,
"n_chars": 5303,
"n_subproofs": 9,
"n_tactics": 78,
"cyclomatic": 2,
"n_automation": 11,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
... | 11 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | @@ -446,6 +446,62 @@
simpa using (inner_eq_sum_mul (x := toVecT (t := a i)) (y := toVecT (t := b i))).symm
-- Dot product agrees with the Euclidean inner product after vectorization.
+/--
+Main agreement lemma: tensor dot equals Euclidean inner product of vectorizations.
+
+This is the bridge between `sou... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_06ae330ad58d_7 | 44d4ccc59aafe6e8 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/FDeriv.lean | FDeriv | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 2 | [
{
"theorem_name": "jvpVec_eq_fderiv",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro xV dxV\n rcases hasFDerivAt_evalVec_and_jvp (Γ := Γ) (ss := ss) (g := g) hg xV with ⟨D, hD, hJ⟩\n have hfderiv : f... | [
{
"name": "hasFDerivAt_evalVec_and_jvp",
"text": "/--\nMain induction: `evalVec` is differentiable and its derivative agrees with `jvpVec`.\n\nThis is the technical heart of the `jvp = fderiv` theorem.\n-/\ntheorem hasFDerivAt_evalVec_and_jvp\n {ss : List Shape} (g : Graph Γ ss)\n (hg : GraphFDerivCor... | [
{
"name": "jvpVec_eq_fderiv",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 576,
"n_subproofs": 1,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | @@ -454,12 +454,126 @@
(castCLM (h := (ctxSize_snoc Γ τ).symm)).comp (appendCLM (m := ctxSize Γ) (n := Shape.size τ))
-- Main analytic statement: `HasFDerivAt` for `evalVec` and identification of `jvpVec`.
+/--
+Main induction: `evalVec` is differentiable and its derivative agrees with `jvpVec`.
+
+This is the te... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_06ae330ad58d_8 | 2ab3b8b0a1f4eda4 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/FDeriv.lean | FDeriv | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 2 | [
{
"theorem_name": "dotList_eq_inner_flattenCtx",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n induction Γ with\n | nil =>\n cases x\n cases y\n simp [TList.dotList, flattenCtx... | [
{
"name": "dot_eq_inner_toVecT",
"text": "/--\nMain agreement lemma: tensor dot equals Euclidean inner product of vectorizations.\n\nThis is the bridge between `soundness.lean` (stated using `Spec.dot`) and the analytic theorems\nhere (stated using Euclidean `inner`).\n-/\ntheorem dot_eq_inner_toVecT {s : S... | [
{
"name": "backpropVec_eq_adjoint_fderiv",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 15,
"n_lines": 65,
"n_chars": 2782,
"n_subproofs": 9,
"n_tactics": 39,
"cyclomatic": 2,
"n_automation": 8,
"n_rewrites": 0,
"n_structural": 8,
"automation_only": false... | 13 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | @@ -446,6 +446,62 @@
simpa using (inner_eq_sum_mul (x := toVecT (t := a i)) (y := toVecT (t := b i))).symm
-- Dot product agrees with the Euclidean inner product after vectorization.
+/--
+Main agreement lemma: tensor dot equals Euclidean inner product of vectorizations.
+
+This is the bridge between `sou... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_06ae330ad58d_9 | 69fb8b2fe8c1358c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/FDeriv.lean | FDeriv | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 2 | [
{
"theorem_name": "jvpVec_eq_fderiv_at",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro xV dxV hg\n rcases hasFDerivAt_evalVec_and_jvp_at (Γ := Γ) (ss := ss) (g := g) (xV := xV) hg with\n ⟨D, hD, h... | [
{
"name": "hasFDerivAt_evalVec_and_jvp_at",
"text": "/--\nPointwise induction: `evalVec` is differentiable at `xV`, and its derivative agrees with `jvpVec`.\n\nThis is the version used for graphs involving non-smooth or partial primitives, where we only\nassume differentiability at the values encountered du... | [
{
"name": "jvpVec_eq_fderiv_at",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 579,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | @@ -454,6 +454,93 @@
(castCLM (h := (ctxSize_snoc Γ τ).symm)).comp (appendCLM (m := ctxSize Γ) (n := Shape.size τ))
-- Main analytic statement: `HasFDerivAt` for `evalVec` and identification of `jvpVec`.
+/--
+Pointwise induction: `evalVec` is differentiable at `xV`, and its derivative agrees with `jvpVec`.
+
+Th... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_06ae330ad58d_10 | 5a75c3cb2eeec710 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/FDeriv.lean | FDeriv | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 14 | 2 | [
{
"theorem_name": "dotList_eq_inner_flattenCtx",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n induction Γ with\n | nil =>\n cases x\n cases y\n simp [TList.dotList, flattenCtx... | [
{
"name": "dot_eq_inner_toVecT",
"text": "/--\nMain agreement lemma: tensor dot equals Euclidean inner product of vectorizations.\n\nThis is the bridge between `soundness.lean` (stated using `Spec.dot`) and the analytic theorems\nhere (stated using Euclidean `inner`).\n-/\ntheorem dot_eq_inner_toVecT {s : S... | [
{
"name": "backpropVec_eq_adjoint_fderiv_at",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 15,
"n_lines": 54,
"n_chars": 2228,
"n_subproofs": 9,
"n_tactics": 40,
"cyclomatic": 2,
"n_automation": 8,
"n_rewrites": 0,
"n_structural": 8,
"automation_only": fa... | 13 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Tape.Core.Soundness
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Analysis... | @@ -446,6 +446,62 @@
simpa using (inner_eq_sum_mul (x := toVecT (t := a i)) (y := toVecT (t := b i))).symm
-- Dot product agrees with the Euclidean inner product after vectorization.
+/--
+Main agreement lemma: tensor dot equals Euclidean inner product of vectorizations.
+
+This is the bridge between `sou... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_1fa4e535a266_0 | b545db648eef8d12 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/NeuralFloat/Rounding.lean | Rounding | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "neural_round_preserves_generic",
"depth": 1,
"n_commands": 0,
"n_lines": 25,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- This is Flocq's round_generic theorem\n -- The key insight: if x is in generic format, then rounding do... | [
{
"name": "neural_scaled_mantissa_int_of_generic",
"text": "/--\nIf `x` is already in the generic format grid, then `neural_scaled_mantissa β fexp x` is an integer.\n\nIn words: exact representability means “no fractional bits at the chosen exponent scale”.\n-/\nprivate lemma neural_scaled_mantissa_int_of_g... | [
{
"name": "neural_round_preserves_generic",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 37,
"n_chars": 1371,
"n_subproofs": 3,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 3,
"n_structural": 3,
"automation_only": false... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.NeuralFloat.Core
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# Rounding modes and a half-ULP error bound
We use this file as the “rounding” half of the Flo... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.NeuralFloat.Core
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# Rounding modes and a half-ULP error bound
We use this file as the “rounding” half of the Flo... | @@ -364,6 +364,45 @@
-- Proof-only helper: if `x` is in generic format, then its scaled mantissa is an integer.
/--
+If `x` is already in the generic format grid, then `neural_scaled_mantissa β fexp x` is an integer.
+
+In words: exact representability means “no fractional bits at the chosen exponent scale”.
+-/
+p... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_1fa4e535a266_1 | 2ed13c5bf3f4d752 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/NeuralFloat/Rounding.lean | Rounding | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "neural_error_bound_ulp",
"depth": 1,
"n_commands": 0,
"n_lines": 25,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hx : x = 0\n · subst hx\n simp [neuralUlp, neuralRound, neuralScaledMantissa, neuralCexp, neuralMagnit... | [
{
"name": "neural_scaled_mantissa_mul_bpow",
"text": "/--\nScaled mantissa times base power equals the original value.\n\nIn words: `scaled_mantissa(x) * β^{cexp(x)} = x`.\nThis is the algebraic identity that justifies the scaling used before rounding.\n-/\nlemma neural_scaled_mantissa_mul_bpow (x : ℝ) :\n ... | [
{
"name": "neural_error_bound_ulp",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 35,
"n_chars": 1567,
"n_subproofs": 7,
"n_tactics": 25,
"cyclomatic": 1,
"n_automation": 10,
"n_rewrites": 5,
"n_structural": 1,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.NeuralFloat.Core
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# Rounding modes and a half-ULP error bound
We use this file as the “rounding” half of the Flo... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.NeuralFloat.Core
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# Rounding modes and a half-ULP error bound
We use this file as the “rounding” half of the Flo... | @@ -439,6 +439,19 @@
exact hx.symm
/--
+Scaled mantissa times base power equals the original value.
+
+In words: `scaled_mantissa(x) * β^{cexp(x)} = x`.
+This is the algebraic identity that justifies the scaling used before rounding.
+-/
+lemma neural_scaled_mantissa_mul_bpow (x : ℝ) :
+ neuralScaledMantissa β... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8a14d6879e1f_0 | 1dbfdad72189f2f2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Fft.lean | Fft | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "idft_mul_dft",
"depth": 1,
"n_commands": 0,
"n_lines": 120,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hprim : IsPrimitiveRoot (ζ n) n := Complex.isPrimitiveRoot_exp n hn\n have hn0 : (n : ℂ) ≠ 0 := by exact_... | [
{
"name": "geom_sum_eq_zero_of_pow_eq_one",
"text": "/--\nGeometric-sum lemma (specialized): if `r^n = 1` and `r ≠ 1`, then `∑_{j=0}^{n-1} r^j = 0`.\n-/\nprivate lemma geom_sum_eq_zero_of_pow_eq_one {r : ℂ} {n : Nat} (hr : r ≠ 1) (hrn : r ^ n = 1) :\n (∑ j ∈ Finset.range n, r ^ j) = 0 := by\n -- Use `(r... | [
{
"name": "idft_mul_dft",
"fan_in": 3,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 130,
"n_chars": 5724,
"n_subproofs": 20,
"n_tactics": 90,
"cyclomatic": 1,
"n_automation": 30,
"n_rewrites": 1,
"n_structural": 10,
"automation_only": false,
"max_nes... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | @@ -92,6 +92,23 @@
simp [ζ]
/--
+Geometric-sum lemma (specialized): if `r^n = 1` and `r ≠ 1`, then `∑_{j=0}^{n-1} r^j = 0`.
+-/
+private lemma geom_sum_eq_zero_of_pow_eq_one {r : ℂ} {n : Nat} (hr : r ≠ 1) (hrn : r ^ n = 1) :
+ (∑ j ∈ Finset.range n, r ^ j) = 0 := by
+ -- Use `(r - 1) * (∑ r^j) = r^n - 1`.
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8a14d6879e1f_1 | 936bb7d713a983cb | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Fft.lean | Fft | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "star_omega",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `ω = ζ⁻¹` and `star` preserves inverses.\n simp [ω, star_zeta (n := n)]",
"n_chars": 86,
"n_subproofs": 0,
"n_ta... | [
{
"name": "star_zeta",
"text": "private lemma star_zeta (n : Nat) : star (ζ n) = ω n := by\n -- Conjugation sends `exp z` to `exp (conj z)`, and `conj (2π I / n) = -(2π I / n)`.\n -- Then `exp (-z) = (exp z)⁻¹`.\n set x : ℂ := (2 * Real.pi * Complex.I) / n\n have hstar : star (Complex.exp x) = Complex.e... | [
{
"name": "star_omega",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 246,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | @@ -87,8 +87,24 @@
of unity, so the geometric sum is `0`.
-/
+private lemma star_zeta (n : Nat) : star (ζ n) = ω n := by
+ -- Conjugation sends `exp z` to `exp (conj z)`, and `conj (2π I / n) = -(2π I / n)`.
+ -- Then `exp (-z) = (exp z)⁻¹`.
+ set x : ℂ := (2 * Real.pi * Complex.I) / n
+ have hstar : star (Comp... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8a14d6879e1f_2 | 52db68b500f8daa8 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Fft.lean | Fft | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "idftMatrix_eq_invNat_smul_conjTranspose_dftMatrix",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n ext j k\n -- `simp` reduces the RHS to `((1/n) * star (ω^(j*k)))`, and `sta... | [
{
"name": "star_omega",
"text": "/-- Conjugation sends the negative-frequency DFT root `ωₙ` back to the positive root `ζₙ`. -/\nprivate lemma star_omega (n : Nat) : star (ω n) = ζ n := by\n -- `ω = ζ⁻¹` and `star` preserves inverses.\n simp [ω, star_zeta (n := n)]\n\n",
"fan_in": 1,
"n_lines": 6,
... | [
{
"name": "idftMatrix_eq_invNat_smul_conjTranspose_dftMatrix",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 493,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automa... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | @@ -101,13 +101,23 @@
_ = (ζ n)⁻¹ := by simp [ζ, x]
_ = ω n := rfl
+/-- Conjugation sends the negative-frequency DFT root `ωₙ` back to the positive root `ζₙ`. -/
+private lemma star_omega (n : Nat) : star (ω n) = ζ n := by
+ -- `ω = ζ⁻¹` and `star` preserves inverses.
+ simp [ω, star_zeta (n := n)]
+
/--... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8a14d6879e1f_3 | dec9783343d28839 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Fft.lean | Fft | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "conjTranspose_dft_mul_dft",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hn0 : (n : ℂ) ≠ 0 := by exact_mod_cast hn\n have h :\n ((1 / (n : ℂ)) • (dftMatrix n)ᴴ) ... | [
{
"name": "idftMatrix_eq_invNat_smul_conjTranspose_dftMatrix",
"text": "/--\nOn `ℂ`, the inverse DFT matrix is a scaled conjugate transpose of the DFT matrix:\n\n`F⁻¹ = (1/n) • Fᴴ`.\n-/\ntheorem idftMatrix_eq_invNat_smul_conjTranspose_dftMatrix (n : Nat) :\n idftMatrix n = (1 / (n : ℂ)) • (dftMatrix n)ᴴ ... | [
{
"name": "conjTranspose_dft_mul_dft",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 20,
"n_chars": 775,
"n_subproofs": 4,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | @@ -257,6 +257,19 @@
simp [ω, star_zeta (n := n)]
/--
+On `ℂ`, the inverse DFT matrix is a scaled conjugate transpose of the DFT matrix:
+
+`F⁻¹ = (1/n) • Fᴴ`.
+-/
+theorem idftMatrix_eq_invNat_smul_conjTranspose_dftMatrix (n : Nat) :
+ idftMatrix n = (1 / (n : ℂ)) • (dftMatrix n)ᴴ := by
+ classical
+ ext j ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8a14d6879e1f_4 | d8e9fec25ed61a46 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Fft.lean | Fft | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 3 | [
{
"theorem_name": "conjTranspose_dft_mul_dft",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hn0 : (n : ℂ) ≠ 0 := by exact_mod_cast hn\n have h :\n ((1 / (n : ℂ)) • (dftMatrix n)ᴴ) ... | [
{
"name": "idft_mul_dft",
"text": "/--\nMain algebraic identity: `IDFT * DFT = 1` (over `ℂ`), for `n ≠ 0`.\n\nThis is the standard DFT inversion theorem.\n-/\ntheorem idft_mul_dft (n : Nat) (hn : n ≠ 0) :\n idftMatrix n * dftMatrix n = 1 := by\n classical\n have hprim : IsPrimitiveRoot (ζ n) n := Compl... | [
{
"name": "dft_mul_idft",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 10,
"n_chars": 349,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": ... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | @@ -108,9 +108,141 @@
(sub_ne_zero.mpr hr)
hmul
+/--
+Main algebraic identity: `IDFT * DFT = 1` (over `ℂ`), for `n ≠ 0`.
+
+This is the standard DFT inversion theorem.
+-/
+theorem idft_mul_dft (n : Nat) (hn : n ≠ 0) :
+ idftMatrix n * dftMatrix n = 1 := by
+ classical
+ have hprim : IsPrimitiveRoo... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8a14d6879e1f_5 | 7a770cddfb29c84f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Fft.lean | Fft | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 3 | [
{
"theorem_name": "conjTranspose_dft_mul_dft",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hn0 : (n : ℂ) ≠ 0 := by exact_mod_cast hn\n have h :\n ((1 / (n : ℂ)) • (dftMatrix n)ᴴ) ... | [
{
"name": "idft_mul_dft",
"text": "/--\nMain algebraic identity: `IDFT * DFT = 1` (over `ℂ`), for `n ≠ 0`.\n\nThis is the standard DFT inversion theorem.\n-/\ntheorem idft_mul_dft (n : Nat) (hn : n ≠ 0) :\n idftMatrix n * dftMatrix n = 1 := by\n classical\n have hprim : IsPrimitiveRoot (ζ n) n := Compl... | [
{
"name": "idft_dft",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 18,
"n_chars": 754,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": 8
... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | @@ -108,6 +108,135 @@
(sub_ne_zero.mpr hr)
hmul
+/--
+Main algebraic identity: `IDFT * DFT = 1` (over `ℂ`), for `n ≠ 0`.
+
+This is the standard DFT inversion theorem.
+-/
+theorem idft_mul_dft (n : Nat) (hn : n ≠ 0) :
+ idftMatrix n * dftMatrix n = 1 := by
+ classical
+ have hprim : IsPrimitiveRoo... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8a14d6879e1f_6 | 559f8aa301d4ecd1 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Fft.lean | Fft | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "dft_idft",
"depth": 1,
"n_commands": 0,
"n_lines": 11,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hmulVec :\n Matrix.mulVec (dftMatrix n) (Matrix.mulVec (idftMatrix n) x) =\n Matrix.mulVec (dftMatr... | [
{
"name": "dft_mul_idft",
"text": "/-- Right-inverse form: `DFT * IDFT = 1` (for `n ≠ 0`). -/\ntheorem dft_mul_idft (n : Nat) (hn : n ≠ 0) :\n dftMatrix n * idftMatrix n = 1 := by\n -- Square matrices over a commutative semiring are Dedekind-finite, so a right-inverse is also a\n -- left-inverse.\n si... | [
{
"name": "dft_idft",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 17,
"n_chars": 685,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesting": 8
... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Matrix.Basic
public import Mathlib.RingTheory.RootsOfUnity.Complex
public import Mathlib.LinearAlgebra.Matrix.ConjTranspose
import Mathlib.LinearAlgebra.Matrix.Semi... | @@ -237,6 +237,15 @@
/-! ## Orthogonality / unitary form -/
+/-- Right-inverse form: `DFT * IDFT = 1` (for `n ≠ 0`). -/
+theorem dft_mul_idft (n : Nat) (hn : n ≠ 0) :
+ dftMatrix n * idftMatrix n = 1 := by
+ -- Square matrices over a commutative semiring are Dedekind-finite, so a right-inverse is also a
+ -- ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_2f2748aebf96_0 | c1aa607e417b1526 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/CryptoFoundations/FiatShamir/WithAbort/Cost.lean | Cost | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 3 | [
{
"theorem_name": "signAttempt_outputs_withAddCost_eq_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [AddWriterT.outputs, signAttempt_run_withAddCost_eq, Functor.map_map]",
"n_chars": 80,
... | [
{
"name": "signAttempt_run_withAddCost_eq",
"text": "private lemma signAttempt_run_withAddCost_eq {ω : Type} [AddMonoid ω]\n (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M)\n (costFn : M × Commit → ω) :\n WriterT.run\n (HasQuery.Program.withAddCost\n (f... | [
{
"name": "signAttempt_outputs_withAddCost_eq_eval",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 675,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only"... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | @@ -33,6 +33,42 @@
variable {m : Type → Type u} [Monad m] [LawfulMonad m]
[MonadLiftT ProbComp m]
+private lemma signAttempt_run_withAddCost_eq {ω : Type} [AddMonoid ω]
+ (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M)
+ (costFn : M × Commit → ω) :
+ WriterT.run
+ (Ha... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2f2748aebf96_1 | 3b922fb3d945a4c7 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/CryptoFoundations/FiatShamir/WithAbort/Cost.lean | Cost | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 3 | [
{
"theorem_name": "signAttempt_outputs_withAddCost_eq_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [AddWriterT.outputs, signAttempt_run_withAddCost_eq, Functor.map_map]",
"n_chars": 80,
... | [
{
"name": "signAttempt_run_withAddCost_eq",
"text": "private lemma signAttempt_run_withAddCost_eq {ω : Type} [AddMonoid ω]\n (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M)\n (costFn : M × Commit → ω) :\n WriterT.run\n (HasQuery.Program.withAddCost\n (f... | [
{
"name": "signAttempt_costs_withAddCost_eq",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 689,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | @@ -33,6 +33,42 @@
variable {m : Type → Type u} [Monad m] [LawfulMonad m]
[MonadLiftT ProbComp m]
+private lemma signAttempt_run_withAddCost_eq {ω : Type} [AddMonoid ω]
+ (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M)
+ (costFn : M × Commit → ω) :
+ WriterT.run
+ (Ha... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2f2748aebf96_2 | 02329a692f42e05d | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/CryptoFoundations/FiatShamir/WithAbort/Cost.lean | Cost | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 3 | [
{
"theorem_name": "signAttempt_outputs_withAddCost_eq_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [AddWriterT.outputs, signAttempt_run_withAddCost_eq, Functor.map_map]",
"n_chars": 80,
... | [
{
"name": "signAttempt_run_withAddCost_eq",
"text": "private lemma signAttempt_run_withAddCost_eq {ω : Type} [AddMonoid ω]\n (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M)\n (costFn : M × Commit → ω) :\n WriterT.run\n (HasQuery.Program.withAddCost\n (f... | [
{
"name": "signAttempt_run_withUnitCost_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 966,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | @@ -33,6 +33,42 @@
variable {m : Type → Type u} [Monad m] [LawfulMonad m]
[MonadLiftT ProbComp m]
+private lemma signAttempt_run_withAddCost_eq {ω : Type} [AddMonoid ω]
+ (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M)
+ (costFn : M × Commit → ω) :
+ WriterT.run
+ (Ha... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2f2748aebf96_3 | ded9fa65d1712fcb | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/CryptoFoundations/FiatShamir/WithAbort/Cost.lean | Cost | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 3 | [
{
"theorem_name": "signAttempt_outputs_withAddCost_eq_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [AddWriterT.outputs, signAttempt_run_withAddCost_eq, Functor.map_map]",
"n_chars": 80,
... | [
{
"name": "signAttempt_run_withAddCost_eq",
"text": "private lemma signAttempt_run_withAddCost_eq {ω : Type} [AddMonoid ω]\n (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M)\n (costFn : M × Commit → ω) :\n WriterT.run\n (HasQuery.Program.withAddCost\n (f... | [
{
"name": "signAttempt_usesCostAsQueryCost",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 13,
"n_chars": 728,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,... | 3 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | @@ -33,6 +33,42 @@
variable {m : Type → Type u} [Monad m] [LawfulMonad m]
[MonadLiftT ProbComp m]
+private lemma signAttempt_run_withAddCost_eq {ω : Type} [AddMonoid ω]
+ (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M)
+ (costFn : M × Commit → ω) :
+ WriterT.run
+ (Ha... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2f2748aebf96_4 | 8758709a868667c5 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/CryptoFoundations/FiatShamir/WithAbort/Cost.lean | Cost | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 3 | [
{
"theorem_name": "signAttempt_outputs_withAddCost_eq_eval",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [AddWriterT.outputs, signAttempt_run_withAddCost_eq, Functor.map_map]",
"n_chars": 80,
... | [
{
"name": "signAttempt_run_withAddCost_eq",
"text": "private lemma signAttempt_run_withAddCost_eq {ω : Type} [AddMonoid ω]\n (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M)\n (costFn : M × Commit → ω) :\n WriterT.run\n (HasQuery.Program.withAddCost\n (f... | [
{
"name": "signAttempt_expectedQueryCost_eq_outputExpectation",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 35,
"n_chars": 1783,
"n_subproofs": 0,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"aut... | 4 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | @@ -33,6 +33,42 @@
variable {m : Type → Type u} [Monad m] [LawfulMonad m]
[MonadLiftT ProbComp m]
+private lemma signAttempt_run_withAddCost_eq {ω : Type} [AddMonoid ω]
+ (runtime : QueryImpl (M × Commit →ₒ Chal) m) (pk : Stmt) (sk : Wit) (msg : M)
+ (costFn : M × Commit → ω) :
+ WriterT.run
+ (Ha... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2f2748aebf96_5 | a2a797fb7a3ee1cf | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/CryptoFoundations/FiatShamir/WithAbort/Cost.lean | Cost | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "sign_usesAtMostMaxAttemptsQueries",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [nsmul_eq_mul] using\n sign_usesWeightedQueryCostAtMost ids M hr runtime pk sk msg\n (fun _... | [
{
"name": "sign_usesWeightedQueryCostAtMost",
"text": "/-- Signing makes weighted query cost at most `maxAttempts • w` when each query costs at most\n`w`. -/\ntheorem sign_usesWeightedQueryCostAtMost\n {κ : Type} [AddCommMonoid κ] [PartialOrder κ] [IsOrderedAddMonoid κ]\n [CanonicallyOrderedAdd κ]\n ... | [
{
"name": "sign_usesAtMostMaxAttemptsQueries",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 520,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | @@ -188,13 +188,28 @@
variable (hr : GenerableRelation Stmt Wit rel)
+/-- Signing makes weighted query cost at most `maxAttempts • w` when each query costs at most
+`w`. -/
+theorem sign_usesWeightedQueryCostAtMost
+ {κ : Type} [AddCommMonoid κ] [PartialOrder κ] [IsOrderedAddMonoid κ]
+ [CanonicallyOrderedAd... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2f2748aebf96_8 | 2ea601523791d715 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/CryptoFoundations/FiatShamir/WithAbort/Cost.lean | Cost | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "sign_usesAtMostMaxAttemptsQueries",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [nsmul_eq_mul] using\n sign_usesWeightedQueryCostAtMost ids M hr runtime pk sk msg\n (fun _... | [
{
"name": "sign_usesWeightedQueryCostAtMost",
"text": "/-- Signing makes weighted query cost at most `maxAttempts • w` when each query costs at most\n`w`. -/\ntheorem sign_usesWeightedQueryCostAtMost\n {κ : Type} [AddCommMonoid κ] [PartialOrder κ] [IsOrderedAddMonoid κ]\n [CanonicallyOrderedAdd κ]\n ... | [
{
"name": "sign_expectedQueries_le",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 495,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"ma... | 2 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.CryptoFoundations.FiatShamir.WithAbort
import VCVio.OracleComp.QueryTracking.QueryCost
/-!
# Cost accounting for Fiat-Shamir with aborts
Exact per-query-class c... | @@ -188,13 +188,28 @@
variable (hr : GenerableRelation Stmt Wit rel)
+/-- Signing makes weighted query cost at most `maxAttempts • w` when each query costs at most
+`w`. -/
+theorem sign_usesWeightedQueryCostAtMost
+ {κ : Type} [AddCommMonoid κ] [PartialOrder κ] [IsOrderedAddMonoid κ]
+ [CanonicallyOrderedAd... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_0 | e171977556c00546 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTraceBefore",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTraceBefore so traceFn mx, probFailure_map]",
"n_chars": 73,
"n_sub... | [
{
"name": "fst_map_run_withTraceBefore",
"text": "lemma fst_map_run_withTraceBefore [LawfulMonad m]\n (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTraceBefore traceFn) mx).run = simulateQ so mx :=\n proj_simulateQ_preInsert so (fun t... | [
{
"name": "probFailure_run_simulateQ_withTraceBefore",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 554,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_onl... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -84,13 +84,22 @@
lemma withTraceBefore_apply (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (t : spec.Domain) :
so.withTraceBefore traceFn t = (do tell (traceFn t); so t) := rfl
+lemma fst_map_run_withTraceBefore [LawfulMonad m]
+ (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp s... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_1 | 74b7fd866f585345 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "neverFail_run_simulateQ_withTraceBefore_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [neverFail_iff, probFailure_run_simulateQ_withTraceBefore]",
"n_chars": 74,
"... | [
{
"name": "probFailure_run_simulateQ_withTraceBefore",
"text": "/-- A \"before\"-style trace preserves failure probability for any base monad with\n`MonadLiftT m SPMF`: instrumenting with `withTraceBefore` does not change the\nprobability of failure. -/\nlemma probFailure_run_simulateQ_withTraceBefore [Lawf... | [
{
"name": "neverFail_run_simulateQ_withTraceBefore_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 375,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_on... | 2 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -92,10 +92,20 @@
WriterT.fst_map_run_pure WriterT.fst_map_run_bind
(fun t => by simp) mx
+/-- A "before"-style trace preserves failure probability for any base monad with
+`MonadLiftT m SPMF`: instrumenting with `withTraceBefore` does not change the
+probability of failure. -/
+lemma probFailure_run_simu... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_2 | 9b987512c3c7ae69 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTraceBefore",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTraceBefore so traceFn mx, probFailure_map]",
"n_chars": 73,
"n_sub... | [
{
"name": "fst_map_run_withTraceBefore",
"text": "lemma fst_map_run_withTraceBefore [LawfulMonad m]\n (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTraceBefore traceFn) mx).run = simulateQ so mx :=\n proj_simulateQ_preInsert so (fun t... | [
{
"name": "evalDist_fst_run_withTraceBefore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 357,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -84,13 +84,22 @@
lemma withTraceBefore_apply (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (t : spec.Domain) :
so.withTraceBefore traceFn t = (do tell (traceFn t); so t) := rfl
+lemma fst_map_run_withTraceBefore [LawfulMonad m]
+ (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp s... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_3 | ec7ed26738ad447b | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTraceBefore",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTraceBefore so traceFn mx, probFailure_map]",
"n_chars": 73,
"n_sub... | [
{
"name": "fst_map_run_withTraceBefore",
"text": "lemma fst_map_run_withTraceBefore [LawfulMonad m]\n (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTraceBefore traceFn) mx).run = simulateQ so mx :=\n proj_simulateQ_preInsert so (fun t... | [
{
"name": "probOutput_fst_run_withTraceBefore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 354,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": fals... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -84,13 +84,22 @@
lemma withTraceBefore_apply (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (t : spec.Domain) :
so.withTraceBefore traceFn t = (do tell (traceFn t); so t) := rfl
+lemma fst_map_run_withTraceBefore [LawfulMonad m]
+ (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp s... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_4 | 4c6ee35346e3ccfa | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTraceBefore",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTraceBefore so traceFn mx, probFailure_map]",
"n_chars": 73,
"n_sub... | [
{
"name": "fst_map_run_withTraceBefore",
"text": "lemma fst_map_run_withTraceBefore [LawfulMonad m]\n (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTraceBefore traceFn) mx).run = simulateQ so mx :=\n proj_simulateQ_preInsert so (fun t... | [
{
"name": "support_fst_run_withTraceBefore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 312,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -84,13 +84,22 @@
lemma withTraceBefore_apply (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (t : spec.Domain) :
so.withTraceBefore traceFn t = (do tell (traceFn t); so t) := rfl
+lemma fst_map_run_withTraceBefore [LawfulMonad m]
+ (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp s... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_5 | 8415cd3b169eabc7 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTrace",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTrace so traceFn mx, probFailure_map]",
"n_chars": 67,
"n_subproofs": 0,
... | [
{
"name": "fst_map_run_withTrace",
"text": "lemma fst_map_run_withTrace [LawfulMonad m]\n (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)\n (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTrace traceFn) mx).run = simulateQ so mx :=\n proj_simulateQ_postInsert ... | [
{
"name": "probFailure_run_simulateQ_withTrace",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 731,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": fa... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -142,6 +142,15 @@
(t : spec.Domain) :
so.withTrace traceFn t = (do let u ← so t; tell (traceFn t u); return u) := rfl
+lemma fst_map_run_withTrace [LawfulMonad m]
+ (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)
+ (mx : OracleComp spec α) :
+ Prod.fst <$> (simulateQ (so... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_6 | 1b18dd3b8013c25b | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "neverFail_run_simulateQ_withTrace_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [neverFail_iff, probFailure_run_simulateQ_withTrace]",
"n_chars": 68,
"n_subproofs"... | [
{
"name": "probFailure_run_simulateQ_withTrace",
"text": "/-- An \"after\"-style trace preserves failure probability for any base monad with\n`MonadLiftT m SPMF`: instrumenting with `withTrace` does not change the probability\nof failure. When `m = OracleComp spec`, both sides are `0` (trivially true);\nwhe... | [
{
"name": "neverFail_run_simulateQ_withTrace_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 384,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": t... | 2 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -151,11 +151,24 @@
WriterT.fst_map_run_pure WriterT.fst_map_run_bind
(fun t => by simp) mx
+/-- An "after"-style trace preserves failure probability for any base monad with
+`MonadLiftT m SPMF`: instrumenting with `withTrace` does not change the probability
+of failure. When `m = OracleComp spec`, both s... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_7 | 117d24d317b20c75 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTrace",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTrace so traceFn mx, probFailure_map]",
"n_chars": 67,
"n_subproofs": 0,
... | [
{
"name": "fst_map_run_withTrace",
"text": "lemma fst_map_run_withTrace [LawfulMonad m]\n (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)\n (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTrace traceFn) mx).run = simulateQ so mx :=\n proj_simulateQ_postInsert ... | [
{
"name": "evalDist_fst_run_withTrace",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 366,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -142,6 +142,15 @@
(t : spec.Domain) :
so.withTrace traceFn t = (do let u ← so t; tell (traceFn t u); return u) := rfl
+lemma fst_map_run_withTrace [LawfulMonad m]
+ (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)
+ (mx : OracleComp spec α) :
+ Prod.fst <$> (simulateQ (so... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_8 | 03191ad1b1bf4082 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTrace",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTrace so traceFn mx, probFailure_map]",
"n_chars": 67,
"n_subproofs": 0,
... | [
{
"name": "fst_map_run_withTrace",
"text": "lemma fst_map_run_withTrace [LawfulMonad m]\n (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)\n (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTrace traceFn) mx).run = simulateQ so mx :=\n proj_simulateQ_postInsert ... | [
{
"name": "probOutput_fst_run_withTrace",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 359,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -142,6 +142,15 @@
(t : spec.Domain) :
so.withTrace traceFn t = (do let u ← so t; tell (traceFn t u); return u) := rfl
+lemma fst_map_run_withTrace [LawfulMonad m]
+ (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)
+ (mx : OracleComp spec α) :
+ Prod.fst <$> (simulateQ (so... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_9 | 5ef03315e0aa64c4 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTrace",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTrace so traceFn mx, probFailure_map]",
"n_chars": 67,
"n_subproofs": 0,
... | [
{
"name": "fst_map_run_withTrace",
"text": "lemma fst_map_run_withTrace [LawfulMonad m]\n (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)\n (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTrace traceFn) mx).run = simulateQ so mx :=\n proj_simulateQ_postInsert ... | [
{
"name": "support_fst_run_withTrace",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 321,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -142,6 +142,15 @@
(t : spec.Domain) :
so.withTrace traceFn t = (do let u ← so t; tell (traceFn t u); return u) := rfl
+lemma fst_map_run_withTrace [LawfulMonad m]
+ (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)
+ (mx : OracleComp spec α) :
+ Prod.fst <$> (simulateQ (so... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_10 | 076feb5f49e9e939 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTraceAppendBefore",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTraceAppendBefore so traceFn mx, probFailure_map]",
"n_chars": 79... | [
{
"name": "fst_map_run_withTraceAppendBefore",
"text": "lemma fst_map_run_withTraceAppendBefore [LawfulMonad m] [LawfulAppend ω]\n (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTraceAppendBefore traceFn) mx).run = simulateQ so mx :=\n ... | [
{
"name": "probFailure_run_simulateQ_withTraceAppendBefore",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 410,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automatio... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -207,11 +207,20 @@
(t : spec.Domain) :
so.withTraceAppendBefore traceFn t = (do tell (traceFn t); so t) := rfl
+lemma fst_map_run_withTraceAppendBefore [LawfulMonad m] [LawfulAppend ω]
+ (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp spec α) :
+ Prod.fst <$> (simulateQ (so.wit... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_11 | f4a123064af6dcd6 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "neverFail_run_simulateQ_withTraceAppendBefore_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [neverFail_iff, probFailure_run_simulateQ_withTraceAppendBefore]",
"n_chars... | [
{
"name": "probFailure_run_simulateQ_withTraceAppendBefore",
"text": "lemma probFailure_run_simulateQ_withTraceAppendBefore [LawfulMonad m]\n [LawfulAppend ω] [MonadLiftT m SPMF] [LawfulMonadLiftT m SPMF]\n (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp spec α) :\n Pr[⊥ | (sim... | [
{
"name": "neverFail_run_simulateQ_withTraceAppendBefore_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 417,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automat... | 2 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -215,11 +215,19 @@
WriterT.fst_map_run_pure' WriterT.fst_map_run_bind'
(fun t => by simp) mx
+lemma probFailure_run_simulateQ_withTraceAppendBefore [LawfulMonad m]
+ [LawfulAppend ω] [MonadLiftT m SPMF] [LawfulMonadLiftT m SPMF]
+ (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_12 | 86bfe1a78e1a8856 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTraceAppendBefore",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTraceAppendBefore so traceFn mx, probFailure_map]",
"n_chars": 79... | [
{
"name": "fst_map_run_withTraceAppendBefore",
"text": "lemma fst_map_run_withTraceAppendBefore [LawfulMonad m] [LawfulAppend ω]\n (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTraceAppendBefore traceFn) mx).run = simulateQ so mx :=\n ... | [
{
"name": "evalDist_fst_run_withTraceAppendBefore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 397,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": ... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -207,11 +207,20 @@
(t : spec.Domain) :
so.withTraceAppendBefore traceFn t = (do tell (traceFn t); so t) := rfl
+lemma fst_map_run_withTraceAppendBefore [LawfulMonad m] [LawfulAppend ω]
+ (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp spec α) :
+ Prod.fst <$> (simulateQ (so.wit... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_13 | acea75ccf2600116 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTraceAppendBefore",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTraceAppendBefore so traceFn mx, probFailure_map]",
"n_chars": 79... | [
{
"name": "fst_map_run_withTraceAppendBefore",
"text": "lemma fst_map_run_withTraceAppendBefore [LawfulMonad m] [LawfulAppend ω]\n (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTraceAppendBefore traceFn) mx).run = simulateQ so mx :=\n ... | [
{
"name": "probOutput_fst_run_withTraceAppendBefore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 390,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only"... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -207,11 +207,20 @@
(t : spec.Domain) :
so.withTraceAppendBefore traceFn t = (do tell (traceFn t); so t) := rfl
+lemma fst_map_run_withTraceAppendBefore [LawfulMonad m] [LawfulAppend ω]
+ (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp spec α) :
+ Prod.fst <$> (simulateQ (so.wit... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_14 | 00c7dc78e47ae3ed | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTraceAppendBefore",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTraceAppendBefore so traceFn mx, probFailure_map]",
"n_chars": 79... | [
{
"name": "fst_map_run_withTraceAppendBefore",
"text": "lemma fst_map_run_withTraceAppendBefore [LawfulMonad m] [LawfulAppend ω]\n (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTraceAppendBefore traceFn) mx).run = simulateQ so mx :=\n ... | [
{
"name": "support_fst_run_withTraceAppendBefore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 348,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": f... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -207,11 +207,20 @@
(t : spec.Domain) :
so.withTraceAppendBefore traceFn t = (do tell (traceFn t); so t) := rfl
+lemma fst_map_run_withTraceAppendBefore [LawfulMonad m] [LawfulAppend ω]
+ (so : QueryImpl spec m) (traceFn : spec.Domain → ω) (mx : OracleComp spec α) :
+ Prod.fst <$> (simulateQ (so.wit... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_15 | d41fff6ba15106ef | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTraceAppend",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTraceAppend so traceFn mx, probFailure_map]",
"n_chars": 73,
"n_sub... | [
{
"name": "fst_map_run_withTraceAppend",
"text": "lemma fst_map_run_withTraceAppend [LawfulMonad m] [LawfulAppend ω]\n (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)\n (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTraceAppend traceFn) mx).run = simulateQ so ... | [
{
"name": "probFailure_run_simulateQ_withTraceAppend",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 413,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -258,11 +258,21 @@
(t : spec.Domain) :
so.withTraceAppend traceFn t = (do let u ← so t; tell (traceFn t u); return u) := rfl
+lemma fst_map_run_withTraceAppend [LawfulMonad m] [LawfulAppend ω]
+ (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)
+ (mx : OracleComp spec α) :
+ ... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_16 | 8b1fbf82038c4999 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "neverFail_run_simulateQ_withTraceAppend_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [neverFail_iff, probFailure_run_simulateQ_withTraceAppend]",
"n_chars": 74,
"... | [
{
"name": "probFailure_run_simulateQ_withTraceAppend",
"text": "lemma probFailure_run_simulateQ_withTraceAppend [LawfulMonad m]\n [LawfulAppend ω] [MonadLiftT m SPMF] [LawfulMonadLiftT m SPMF]\n (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)\n (mx : OracleComp spec α) :\n ... | [
{
"name": "neverFail_run_simulateQ_withTraceAppend_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 426,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_on... | 2 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -267,12 +267,20 @@
WriterT.fst_map_run_pure' WriterT.fst_map_run_bind'
(fun t => by simp) mx
+lemma probFailure_run_simulateQ_withTraceAppend [LawfulMonad m]
+ [LawfulAppend ω] [MonadLiftT m SPMF] [LawfulMonadLiftT m SPMF]
+ (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)
+... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_17 | 86a95fb70dafba70 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTraceAppend",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTraceAppend so traceFn mx, probFailure_map]",
"n_chars": 73,
"n_sub... | [
{
"name": "fst_map_run_withTraceAppend",
"text": "lemma fst_map_run_withTraceAppend [LawfulMonad m] [LawfulAppend ω]\n (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)\n (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTraceAppend traceFn) mx).run = simulateQ so ... | [
{
"name": "evalDist_fst_run_withTraceAppend",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 406,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -258,11 +258,21 @@
(t : spec.Domain) :
so.withTraceAppend traceFn t = (do let u ← so t; tell (traceFn t u); return u) := rfl
+lemma fst_map_run_withTraceAppend [LawfulMonad m] [LawfulAppend ω]
+ (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)
+ (mx : OracleComp spec α) :
+ ... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_18 | c939175c5f5bf225 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTraceAppend",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTraceAppend so traceFn mx, probFailure_map]",
"n_chars": 73,
"n_sub... | [
{
"name": "fst_map_run_withTraceAppend",
"text": "lemma fst_map_run_withTraceAppend [LawfulMonad m] [LawfulAppend ω]\n (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)\n (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTraceAppend traceFn) mx).run = simulateQ so ... | [
{
"name": "probOutput_fst_run_withTraceAppend",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 399,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": fals... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -258,11 +258,21 @@
(t : spec.Domain) :
so.withTraceAppend traceFn t = (do let u ← so t; tell (traceFn t u); return u) := rfl
+lemma fst_map_run_withTraceAppend [LawfulMonad m] [LawfulAppend ω]
+ (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)
+ (mx : OracleComp spec α) :
+ ... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_cae88f29a5fa_19 | 4ddd9f996862485c | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Tracing.lean | Tracing | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 4 | [
{
"theorem_name": "probFailure_run_simulateQ_withTraceAppend",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [← fst_map_run_withTraceAppend so traceFn mx, probFailure_map]",
"n_chars": 73,
"n_sub... | [
{
"name": "fst_map_run_withTraceAppend",
"text": "lemma fst_map_run_withTraceAppend [LawfulMonad m] [LawfulAppend ω]\n (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)\n (mx : OracleComp spec α) :\n Prod.fst <$> (simulateQ (so.withTraceAppend traceFn) mx).run = simulateQ so ... | [
{
"name": "support_fst_run_withTraceAppend",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 357,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
import VCVio.OracleComp.QueryTracking.Structures
import VCVio.OracleComp.SimSemantics.QueryImpl.Constructions
import VCVio.OracleComp.EvalDist
import VCVio.OracleComp.SimSemant... | @@ -258,11 +258,21 @@
(t : spec.Domain) :
so.withTraceAppend traceFn t = (do let u ← so t; tell (traceFn t u); return u) := rfl
+lemma fst_map_run_withTraceAppend [LawfulMonad m] [LawfulAppend ω]
+ (so : QueryImpl spec m) (traceFn : (t : spec.Domain) → spec.Range t → ω)
+ (mx : OracleComp spec α) :
+ ... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_25170b85f10e_0 | d0b583fd77fe58d5 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | ToMathlib/ProbabilityTheory/OptimalCoupling.lean | OptimalCoupling | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "isCompact_couplings_set",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n letI := Fintype.ofFinite α\n letI := Fintype.ofFinite β\n exact Metric.isCompact_of_isClosed_isBounded (isClosed_... | [
{
"name": "isClosed_couplings_set",
"text": "lemma isClosed_couplings_set (p : SPMF α) (q : SPMF β) :\n IsClosed (couplings_set p q) := by\n letI := Fintype.ofFinite α\n letI := Fintype.ofFinite β\n rw [show couplings_set p q =\n {c | ∀ z, 0 ≤ c z} ∩\n {c | ∀ z, c z ≤ 1} ∩\n {c | ∀ a, ∑... | [
{
"name": "isCompact_couplings_set",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 8,
"n_chars": 271,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max... | 2 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
module
public import Mathlib.Topology.MetricSpace.Basic
public import Mathlib.Topology.MetricSpace.Bounded
public import Mathlib.Topology.Instances.Discrete
public import Math... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
module
public import Mathlib.Topology.MetricSpace.Basic
public import Mathlib.Topology.MetricSpace.Bounded
public import Mathlib.Topology.Instances.Discrete
public import Math... | @@ -77,6 +77,45 @@
c none = 1 - (∑ z, c (some z)) }
-- 2. Prove this set is closed and bounded
+lemma isClosed_couplings_set (p : SPMF α) (q : SPMF β) :
+ IsClosed (couplings_set p q) := by
+ letI := Fintype.ofFinite α
+ letI := Fintype.ofFinite β
+ rw [show couplings_set p q =
+ {c | ∀ z, 0 ≤ c ... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_25170b85f10e_2 | 7af4178d6b9f897e | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | ToMathlib/ProbabilityTheory/OptimalCoupling.lean | OptimalCoupling | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "mem_couplings_set_of_isCoupling",
"depth": 1,
"n_commands": 0,
"n_lines": 31,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n letI := Fintype.ofFinite α\n letI := Fintype.ofFinite β\n simp only [couplings_set, mem_setOf_eq]\n ref... | [
{
"name": "map_fst_eval",
"text": "lemma map_fst_eval (c : SPMF (α × β)) (a : α) :\n letI := Fintype.ofFinite β\n (Prod.fst <$> c) a = ∑ b, c (a, b) := by\n classical\n letI := Fintype.ofFinite α\n letI := Fintype.ofFinite β\n erw [SPMF.fmap_eq_map, PMF.map_apply, tsum_fintype, Fintype.sum_option]... | [
{
"name": "exists_coupling_of_mem_couplings_set",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 75,
"n_chars": 3235,
"n_subproofs": 7,
"n_tactics": 71,
"cyclomatic": 2,
"n_automation": 9,
"n_rewrites": 10,
"n_structural": 17,
"automation_only... | 3 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
module
public import Mathlib.Topology.MetricSpace.Basic
public import Mathlib.Topology.MetricSpace.Bounded
public import Mathlib.Topology.Instances.Discrete
public import Math... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
module
public import Mathlib.Topology.MetricSpace.Basic
public import Mathlib.Topology.MetricSpace.Bounded
public import Mathlib.Topology.Instances.Discrete
public import Math... | @@ -38,6 +38,32 @@
section Topology
+lemma map_fst_eval (c : SPMF (α × β)) (a : α) :
+ letI := Fintype.ofFinite β
+ (Prod.fst <$> c) a = ∑ b, c (a, b) := by
+ classical
+ letI := Fintype.ofFinite α
+ letI := Fintype.ofFinite β
+ erw [SPMF.fmap_eq_map, PMF.map_apply, tsum_fintype, Fintype.sum_option]
+ h... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_25170b85f10e_3 | 512fcb9a3db0ea25 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | ToMathlib/ProbabilityTheory/OptimalCoupling.lean | OptimalCoupling | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "mem_couplings_set_of_isCoupling",
"depth": 1,
"n_commands": 0,
"n_lines": 31,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n letI := Fintype.ofFinite α\n letI := Fintype.ofFinite β\n simp only [couplings_set, mem_setOf_eq]\n ref... | [
{
"name": "map_fst_eval",
"text": "lemma map_fst_eval (c : SPMF (α × β)) (a : α) :\n letI := Fintype.ofFinite β\n (Prod.fst <$> c) a = ∑ b, c (a, b) := by\n classical\n letI := Fintype.ofFinite α\n letI := Fintype.ofFinite β\n erw [SPMF.fmap_eq_map, PMF.map_apply, tsum_fintype, Fintype.sum_option]... | [
{
"name": "SPMF.exists_max_coupling",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 40,
"n_chars": 1919,
"n_subproofs": 10,
"n_tactics": 30,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 11,
"automation_only": false,
... | 6 | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
module
public import Mathlib.Topology.MetricSpace.Basic
public import Mathlib.Topology.MetricSpace.Bounded
public import Mathlib.Topology.Instances.Discrete
public import Math... | /-
Copyright (c) 2026 Quang Dao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Quang Dao
-/
module
public import Mathlib.Topology.MetricSpace.Basic
public import Mathlib.Topology.MetricSpace.Bounded
public import Mathlib.Topology.Instances.Discrete
public import Math... | @@ -38,6 +38,32 @@
section Topology
+lemma map_fst_eval (c : SPMF (α × β)) (a : α) :
+ letI := Fintype.ofFinite β
+ (Prod.fst <$> c) a = ∑ b, c (a, b) := by
+ classical
+ letI := Fintype.ofFinite α
+ letI := Fintype.ofFinite β
+ erw [SPMF.fmap_eq_map, PMF.map_apply, tsum_fintype, Fintype.sum_option]
+ h... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2e66f40b211a_0 | cf909305ccdefe07 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Iter.lean | Iter | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "countingOracle.support_simulate_replicate_const",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro n\n induction n with\n | zero =>\n refine ⟨[], ?_⟩\n simp only [replicat... | [
{
"name": "countingOracle.mem_support_simulate_bind_iff",
"text": "/-- Compositional support characterization for `countingOracle.simulate (oa >>= ob) 0`:\nthe support decomposes as the sum of a path through `oa` and a path through `ob x`. -/\nprivate lemma countingOracle.mem_support_simulate_bind_iff [Deci... | [
{
"name": "countingOracle.support_simulate_replicate_const",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 25,
"n_chars": 1159,
"n_subproofs": 1,
"n_tactics": 19,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 11,
"autom... | 1 | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | @@ -35,6 +35,29 @@
/-! ### Forward `replicate` bounds -/
+/-- Compositional support characterization for `countingOracle.simulate (oa >>= ob) 0`:
+the support decomposes as the sum of a path through `oa` and a path through `ob x`. -/
+private lemma countingOracle.mem_support_simulate_bind_iff [DecidableEq ι]
+ ... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2e66f40b211a_1 | d18946f01fcc38f7 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Iter.lean | Iter | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "isTotalQueryBound_replicate_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n letI : DecidableEq ι := Classical.decEq ι\n letI : Fintype ι := Fintype.ofFinite ι\n refine ⟨fun h => ?_,... | [
{
"name": "countingOracle.support_simulate_replicate_const",
"text": "/-- Every counting-oracle support point of the body `oa` lifts to a counting-oracle\nsupport point of `replicate n oa` whose query count is `n` times the body's. -/\nprivate lemma countingOracle.support_simulate_replicate_const [Decidable... | [
{
"name": "isTotalQueryBound_replicate_iff",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 13,
"n_chars": 628,
"n_subproofs": 1,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,... | 3 | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | @@ -71,9 +71,41 @@
exact ⟨(a, qc1), ha, (z.1, qc2), hsim _ ▸ hb,
Prod.ext rfl (by simp [QueryCount.monoid_mul_def, hsum])⟩
+/-- Every counting-oracle support point of the body `oa` lifts to a counting-oracle
+support point of `replicate n oa` whose query count is `n` times the body's. -/
+private lemma co... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2e66f40b211a_2 | cb5121b9ebfacbf8 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Iter.lean | Iter | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "isTotalQueryBound_replicate_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n letI : DecidableEq ι := Classical.decEq ι\n letI : Fintype ι := Fintype.ofFinite ι\n refine ⟨fun h => ?_,... | [
{
"name": "countingOracle.support_simulate_replicate_const",
"text": "/-- Every counting-oracle support point of the body `oa` lifts to a counting-oracle\nsupport point of `replicate n oa` whose query count is `n` times the body's. -/\nprivate lemma countingOracle.support_simulate_replicate_const [Decidable... | [
{
"name": "isQueryBoundP_replicate_iff",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 15,
"n_chars": 682,
"n_subproofs": 1,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | @@ -69,9 +69,41 @@
exact ⟨(a, qc1), ha, (z.1, qc2), hsim _ ▸ hb,
Prod.ext rfl (by simp [QueryCount.monoid_mul_def, hsum])⟩
+/-- Every counting-oracle support point of the body `oa` lifts to a counting-oracle
+support point of `replicate n oa` whose query count is `n` times the body's. -/
+private lemma co... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2e66f40b211a_3 | b96fc8bbd2cf3867 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Iter.lean | Iter | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "isTotalQueryBound_replicate_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n letI : DecidableEq ι := Classical.decEq ι\n letI : Fintype ι := Fintype.ofFinite ι\n refine ⟨fun h => ?_,... | [
{
"name": "isTotalQueryBound_replicate",
"text": "lemma isTotalQueryBound_replicate {oa : OracleComp spec α} {k : ℕ}\n (h : IsTotalQueryBound oa k) (n : ℕ) :\n IsTotalQueryBound (oa.replicate n) (n * k) := by\n induction n with\n | zero => rw [replicate_zero, Nat.zero_mul]; exact trivial\n | succ n... | [
{
"name": "isTotalQueryBound_replicateTR",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 244,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | @@ -35,9 +35,23 @@
/-! ### Forward `replicate` bounds -/
+lemma isTotalQueryBound_replicate {oa : OracleComp spec α} {k : ℕ}
+ (h : IsTotalQueryBound oa k) (n : ℕ) :
+ IsTotalQueryBound (oa.replicate n) (n * k) := by
+ induction n with
+ | zero => rw [replicate_zero, Nat.zero_mul]; exact trivial
+ | succ ... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2e66f40b211a_4 | 9abb008f0230970c | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Iter.lean | Iter | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 2 | [
{
"theorem_name": "isQueryBoundP_replicate_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n letI : DecidableEq ι := Classical.decEq ι\n letI : Fintype ι := Fintype.ofFinite ι\n refine ⟨fun h => ?_, fun... | [
{
"name": "isQueryBoundP_replicate",
"text": "lemma isQueryBoundP_replicate {oa : OracleComp spec α} {p : ι → Prop}\n [DecidablePred p] {k : ℕ}\n (h : IsQueryBoundP oa p k) (n : ℕ) :\n IsQueryBoundP (oa.replicate n) p (n * k) := by\n induction n with\n | zero => rw [replicate_zero, Nat.zero_mul];... | [
{
"name": "isQueryBoundP_replicateTR",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 272,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | @@ -35,10 +35,22 @@
/-! ### Forward `replicate` bounds -/
+lemma isQueryBoundP_replicate {oa : OracleComp spec α} {p : ι → Prop}
+ [DecidablePred p] {k : ℕ}
+ (h : IsQueryBoundP oa p k) (n : ℕ) :
+ IsQueryBoundP (oa.replicate n) p (n * k) := by
+ induction n with
+ | zero => rw [replicate_zero, Nat.zero... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2e66f40b211a_5 | 35395f36f37f02d6 | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Iter.lean | Iter | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "isPerIndexQueryBound_replicateTR",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [replicateTR_eq_replicate]; exact isPerIndexQueryBound_replicate h n",
"n_chars": 77,
"n_subpro... | [
{
"name": "isPerIndexQueryBound_replicate",
"text": "lemma isPerIndexQueryBound_replicate [DecidableEq ι]\n {oa : OracleComp spec α} {qb : ι → ℕ}\n (h : IsPerIndexQueryBound oa qb) (n : ℕ) :\n IsPerIndexQueryBound (oa.replicate n) (n • qb) := by\n induction n with\n | zero => rw [replicate_zero, ... | [
{
"name": "isPerIndexQueryBound_replicateTR",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 289,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,... | 1 | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | @@ -35,10 +35,28 @@
/-! ### Forward `replicate` bounds -/
+lemma isPerIndexQueryBound_replicate [DecidableEq ι]
+ {oa : OracleComp spec α} {qb : ι → ℕ}
+ (h : IsPerIndexQueryBound oa qb) (n : ℕ) :
+ IsPerIndexQueryBound (oa.replicate n) (n • qb) := by
+ induction n with
+ | zero => rw [replicate_zero, z... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
ablate_2e66f40b211a_6 | 4914ae6dd56a330c | lean | lean | github.com/Verified-zkEVM/VCV-io | 24fe01dbaf899b7bb2b19453ae2ada61b49b4255 | VCVio/OracleComp/QueryTracking/Iter.lean | Iter | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 10 | 1 | [
{
"theorem_name": "isTotalQueryBound_replicateTR_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [replicateTR_eq_replicate]; exact isTotalQueryBound_replicate_iff hn",
"n_chars": 77,
"n_subpr... | [
{
"name": "isTotalQueryBound_replicate_iff",
"text": "theorem isTotalQueryBound_replicate_iff [Finite ι] [IsUniformSpec spec]\n {oa : OracleComp spec α} {n k : ℕ} (hn : 0 < n) :\n IsTotalQueryBound (oa.replicate n) (n * k) ↔ IsTotalQueryBound oa k := by\n letI : DecidableEq ι := Classical.decEq ι\n ... | [
{
"name": "isTotalQueryBound_replicateTR_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 6,
"n_chars": 289,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false... | 4 | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | /-
Copyright (c) 2026 Devon Tuma. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Devon Tuma
-/
import VCVio.OracleComp.QueryTracking.QueryBound
import VCVio.OracleComp.Constructions.Replicate
/-!
# Query Bounds for Iteration Constructs
This file lifts the structural ... | @@ -95,9 +95,22 @@
· funext i; simp
· funext i; simp [Pi.add_apply, add_mul, add_comm]
+theorem isTotalQueryBound_replicate_iff [Finite ι] [IsUniformSpec spec]
+ {oa : OracleComp spec α} {n k : ℕ} (hn : 0 < n) :
+ IsTotalQueryBound (oa.replicate n) (n * k) ↔ IsTotalQueryBound oa k := by
+ letI ... | {
"repo": "VCV-io",
"git_repo": "github.com/Verified-zkEVM/VCV-io",
"revision": "24fe01dbaf899b7bb2b19453ae2ada61b49b4255",
"lean_toolchain": "leanprover/lean4:v4.30.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-l... |
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