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_d5a7e1bd8a5e_19 | 66e1924f55272700 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "toReal_hinge_fun_ieee_eq_fp32_val",
"depth": 1,
"n_commands": 0,
"n_lines": 47,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- First refine the hinge sum.\n have hsum :\n IEEE32Exec.toReal (hingeSumIeee (c := c) (t := t) x... | [
{
"name": "toReal_hinge_sum_ieee_eq_fp32_val",
"text": "/--\nRefine an executable IEEE hinge-term fold to the FP32 rounded-`ℝ` fold with the same order.\n\nFloating-point addition is not associative, so the theorem preserves the exact `List.finRange`\nevaluation order. This is why the proof is fold-based r... | [
{
"name": "reluApproximationIccIEEE32Exec_twoTerm",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 20,
"n_lines": 55,
"n_chars": 2547,
"n_subproofs": 2,
"n_tactics": 14,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_onl... | 20 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Proofs.Approximation.Universal.IEEE32ExecCore
public import NN.MLTheory.Proofs.Approximation.Universal.UniversalApproximationFP32
/-!
# IEEE32 executable ReLU appro... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Proofs.Approximation.Universal.IEEE32ExecCore
public import NN.MLTheory.Proofs.Approximation.Universal.UniversalApproximationFP32
/-!
# IEEE32 executable ReLU appro... | @@ -335,6 +335,55 @@
(this (xs := List.finRange n) (acc32 := (0 : FP32)) (accR := (0 : ℝ)) (err := (0 : ℝ)))
/--
+Refine an executable IEEE hinge-term fold to the FP32 rounded-`ℝ` fold with the same order.
+
+Floating-point addition is not associative, so the theorem preserves the exact `List.finRange`
+evaluat... | {
"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_710f9bcd446f_0 | b28ed4cc0b740c45 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/Floats/IEEE32Exec.lean | IEEE32Exec | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "toReal_tdResidual_eq_fp32Round_chain_of_isFinite",
"depth": 1,
"n_commands": 0,
"n_lines": 31,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- First, refine the discounted backup part.\n have hbackup :\n toReal (discountedB... | [
{
"name": "toReal_discountedBackup_eq_fp32Round_chain_of_isFinite",
"text": "/--\nRefinement theorem for the RL one-step discounted backup in executable float32 semantics.\n\nAssuming the relevant IEEE32Exec intermediates are finite, the decoded real value of the backup\nagrees with the standard “real op + ... | [
{
"name": "toReal_tdResidual_eq_fp32Round_chain_of_isFinite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 59,
"n_chars": 2778,
"n_subproofs": 3,
"n_tactics": 25,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"autom... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.RL.Core
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Proofs.RL.Tactics
/-!
# RL Float32 Semantics (IEEE32Exec)
TorchLean provides multiple “views”... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.RL.Core
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Proofs.RL.Tactics
/-!
# RL Float32 Semantics (IEEE32Exec)
TorchLean provides multiple “views”... | @@ -53,6 +53,43 @@
open TorchLean.Floats.IEEE754.IEEE32Exec
/--
+Refinement theorem for the RL one-step discounted backup in executable float32 semantics.
+
+Assuming the relevant IEEE32Exec intermediates are finite, the decoded real value of the backup
+agrees with the standard “real op + round-to-float32” model (... | {
"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_471c62e83dec_0 | 28690280985a3801 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximation.lean | UniversalApproximation | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "finRange_foldl_add",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n induction n with\n | zero =>\n simp\n | succ n ih =>\n -- Unfold `finRange (n+1)` and compute `fol... | [
{
"name": "foldl_add_init",
"text": "/--\nMove a scalar initial accumulator out of a left fold that only adds terms.\n\nThis is bookkeeping for converting TorchLean's list-fold tensor semantics into Mathlib finite\nsums.\n-/\nlemma foldl_add_init {α : Type} (l : List α) (f : α → ℝ) (a : ℝ) :\n l.foldl (f... | [
{
"name": "finRange_foldl_add",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 30,
"n_chars": 1448,
"n_subproofs": 1,
"n_tactics": 21,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Floor.Semiring
public import Mathlib.Data.Real.Basic
public import NN.Spec.Core.Tensor
public import NN.Runtime.Context
public import NN.Spec.Layers.Activa... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Floor.Semiring
public import Mathlib.Data.Real.Basic
public import NN.Spec.Core.Tensor
public import NN.Runtime.Context
public import NN.Spec.Layers.Activa... | @@ -70,6 +70,27 @@
(l1 : LinearSpec ℝ 1 hidDim) (l2 : LinearSpec ℝ hidDim 1) (x : ℝ) : ℝ :=
extractScalarOutput (Examples.mlpForward l1 l2 (Tensor.singleton x))
+/--
+Move a scalar initial accumulator out of a left fold that only adds terms.
+
+This is bookkeeping for converting TorchLean's list-fold tensor 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_471c62e83dec_1 | 0326918d5e5c70ca | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximation.lean | UniversalApproximation | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "finRange_foldl_add_scalar",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- First, reduce the tensor fold to a scalar fold.\n have h_scalar :\n ∀ s0 : ℝ,\n (Li... | [
{
"name": "finRange_foldl_add",
"text": "/-- Convert the `List.finRange` fold used in `matVecMulSpec` into a `Finset.univ` sum. -/\nlemma finRange_foldl_add (n : ℕ) (f : Fin n → ℝ) :\n (List.finRange n).foldl (fun acc i => acc + f i) 0 = ∑ i : Fin n, f i := by\n classical\n induction n with\n | zero =... | [
{
"name": "finRange_foldl_add_scalar",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 32,
"n_chars": 1078,
"n_subproofs": 1,
"n_tactics": 20,
"cyclomatic": 3,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 2,
"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.Algebra.Order.Floor.Semiring
public import Mathlib.Data.Real.Basic
public import NN.Spec.Core.Tensor
public import NN.Runtime.Context
public import NN.Spec.Layers.Activa... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Floor.Semiring
public import Mathlib.Data.Real.Basic
public import NN.Spec.Core.Tensor
public import NN.Runtime.Context
public import NN.Spec.Layers.Activa... | @@ -91,6 +91,35 @@
-- After rewriting, both sides become `a + f x + foldl ... 0 xs`.
simp [h1, h2, add_assoc]
+/-- Convert the `List.finRange` fold used in `matVecMulSpec` into a `Finset.univ` sum. -/
+lemma finRange_foldl_add (n : ℕ) (f : Fin n → ℝ) :
+ (List.finRange n).foldl (fun acc i => acc + f i) 0... | {
"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_471c62e83dec_2 | 41225ec17e64c040 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximation.lean | UniversalApproximation | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "mlp_eval_1d_hinge",
"depth": 1,
"n_commands": 0,
"n_lines": 409,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Unfold the definition of `mlp_eval_1d` and rewrite `mlp_forward`.\n unfold mlpEval1d hingeFun extractS... | [
{
"name": "mat_vec_mul_spec_matrixMN_singleton",
"text": "/-- Matrix-vector multiply by the all-ones column extracts the scalar input into every hidden unit. -/\nlemma mat_vec_mul_spec_matrixMN_singleton (n : ℕ) (x : ℝ) :\n matVecMulSpec (matrixMN n 1 (fun _ _ => (1 : ℝ))) (Tensor.singleton x) =\n T... | [
{
"name": "mlp_eval_1d_hinge",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 418,
"n_chars": 20722,
"n_subproofs": 134,
"n_tactics": 366,
"cyclomatic": 5,
"n_automation": 83,
"n_rewrites": 13,
"n_structural": 52,
"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.Algebra.Order.Floor.Semiring
public import Mathlib.Data.Real.Basic
public import NN.Spec.Core.Tensor
public import NN.Runtime.Context
public import NN.Spec.Layers.Activa... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Floor.Semiring
public import Mathlib.Data.Real.Basic
public import NN.Spec.Core.Tensor
public import NN.Runtime.Context
public import NN.Spec.Layers.Activa... | @@ -226,6 +226,16 @@
simp
exact hfold.trans (finRange_foldl_add_scalar n (fun j : Fin n => c j * v j))
+/-- Matrix-vector multiply by the all-ones column extracts the scalar input into every hidden unit. -/
+lemma mat_vec_mul_spec_matrixMN_singleton (n : ℕ) (x : ℝ) :
+ matVecMulSpec (matrixMN n 1 (fun _ _ ... | {
"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_89bdc82a73f2_0 | 050de5fdf316725b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/LinearAlgebra.lean | LinearAlgebra | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "get_preserves_inner_shape",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases t with\n | dim f =>\n simp only [get]\n exact shapeOf_eq_shape (f i)",
"n_chars": 84,
"n_sub... | [
{
"name": "shapeOf_eq_shape",
"text": "/--\n`shapeOf` recovers the shape already tracked in the tensor type.\n\nThis is a small bridge for proofs that move between value-level shape computations and type-indexed\ntensor operations.\n-/\ntheorem shapeOf_eq_shape {α : Type} {s : Shape} (t : Tensor α s) :\n s... | [
{
"name": "get_preserves_inner_shape",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 357,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 2,
"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.Proofs.Tensor.Basic.Folds
/-!
Linear-algebra facts for dependent tensors.
The results here cover dot products, matrix-vector structure, and linearity facts used by
autograd... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Folds
/-!
Linear-algebra facts for dependent tensors.
The results here cover dot products, matrix-vector structure, and linearity facts used by
autograd... | @@ -22,12 +22,36 @@
open Tensor
open scoped BigOperators
+/--
+`shapeOf` recovers the shape already tracked in the tensor type.
+
+This is a small bridge for proofs that move between value-level shape computations and type-indexed
+tensor operations.
+-/
+theorem shapeOf_eq_shape {α : Type} {s : Shape} (t : 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_89bdc82a73f2_1 | 72d30d92fce1e237 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/LinearAlgebra.lean | LinearAlgebra | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 3 | [
{
"theorem_name": "matrix_transpose_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Prove equality by `get2`-extensionality on matrix entries.\n apply matrix_ext\n intro j i\n -- Com... | [
{
"name": "get2_matrix_transpose_spec",
"text": "/-- Coordinate rule for `matrix_transpose_spec`: `(Aᵀ)[i,j] = A[j,i]`. -/\nlemma get2_matrix_transpose_spec {m n : Nat}\n (A : Tensor ℝ (.dim m (.dim n .scalar))) (i : Fin n) (j : Fin m) :\n get2 (matrixTransposeSpec A) i j = get2 A j i := by\n cases A wit... | [
{
"name": "matrix_transpose_mul",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 37,
"n_chars": 1585,
"n_subproofs": 0,
"n_tactics": 24,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 7,
"automation_only": false,
"max... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Folds
/-!
Linear-algebra facts for dependent tensors.
The results here cover dot products, matrix-vector structure, and linearity facts used by
autograd... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Folds
/-!
Linear-algebra facts for dependent tensors.
The results here cover dot products, matrix-vector structure, and linearity facts used by
autograd... | @@ -22,6 +22,20 @@
open Tensor
open scoped BigOperators
+/-- Coordinate rule for `matrix_transpose_spec`: `(Aᵀ)[i,j] = A[j,i]`. -/
+lemma get2_matrix_transpose_spec {m n : Nat}
+ (A : Tensor ℝ (.dim m (.dim n .scalar))) (i : Fin n) (j : Fin m) :
+ get2 (matrixTransposeSpec A) i j = get2 A j i := by
+ cases A wit... | {
"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_89bdc82a73f2_2 | f17fc2616bae4499 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/LinearAlgebra.lean | LinearAlgebra | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "dot_mat_eq_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 43,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases A with\n | dim rowsA =>\n cases B with\n | dim rowsB =>\n -- Unfold `dot` to `sum_spec (mul_... | [
{
"name": "sum_spec_vec",
"text": "/-- `sum_spec` on a 1D tensor equals the `Finset` sum of its coordinates (`toVec`). -/\nlemma sum_spec_vec {n : Nat} (v : Tensor ℝ (.dim n .scalar)) :\n sumSpec v = ∑ i : Fin n, toVec v i := by\n classical\n cases v with\n | dim values =>\n -- `sum_spec_dim` reduc... | [
{
"name": "dot_mat_eq_sum",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 48,
"n_chars": 2237,
"n_subproofs": 2,
"n_tactics": 37,
"cyclomatic": 7,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 11,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Folds
/-!
Linear-algebra facts for dependent tensors.
The results here cover dot products, matrix-vector structure, and linearity facts used by
autograd... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Folds
/-!
Linear-algebra facts for dependent tensors.
The results here cover dot products, matrix-vector structure, and linearity facts used by
autograd... | @@ -22,6 +22,24 @@
open Tensor
open scoped BigOperators
+/-- `sum_spec` on a 1D tensor equals the `Finset` sum of its coordinates (`toVec`). -/
+lemma sum_spec_vec {n : Nat} (v : Tensor ℝ (.dim n .scalar)) :
+ sumSpec v = ∑ i : Fin n, toVec v i := by
+ classical
+ cases v with
+ | dim values =>
+ -- `sum_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_89bdc82a73f2_3 | d20467436f627138 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/LinearAlgebra.lean | LinearAlgebra | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "dot_mat_eq_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 43,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases A with\n | dim rowsA =>\n cases B with\n | dim rowsB =>\n -- Unfold `dot` to `sum_spec (mul_... | [
{
"name": "sum_spec_vec",
"text": "/-- `sum_spec` on a 1D tensor equals the `Finset` sum of its coordinates (`toVec`). -/\nlemma sum_spec_vec {n : Nat} (v : Tensor ℝ (.dim n .scalar)) :\n sumSpec v = ∑ i : Fin n, toVec v i := by\n classical\n cases v with\n | dim values =>\n -- `sum_spec_dim` reduc... | [
{
"name": "dot_mat_mul_right_adjoint",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 26,
"n_chars": 1189,
"n_subproofs": 0,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 2,
"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 NN.Proofs.Tensor.Basic.Folds
/-!
Linear-algebra facts for dependent tensors.
The results here cover dot products, matrix-vector structure, and linearity facts used by
autograd... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Folds
/-!
Linear-algebra facts for dependent tensors.
The results here cover dot products, matrix-vector structure, and linearity facts used by
autograd... | @@ -22,6 +22,24 @@
open Tensor
open scoped BigOperators
+/-- `sum_spec` on a 1D tensor equals the `Finset` sum of its coordinates (`toVec`). -/
+lemma sum_spec_vec {n : Nat} (v : Tensor ℝ (.dim n .scalar)) :
+ sumSpec v = ∑ i : Fin n, toVec v i := by
+ classical
+ cases v with
+ | dim values =>
+ -- `sum_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_89bdc82a73f2_4 | 544a6acefdd2fc63 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/LinearAlgebra.lean | LinearAlgebra | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "dot_mat_eq_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 43,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases A with\n | dim rowsA =>\n cases B with\n | dim rowsB =>\n -- Unfold `dot` to `sum_spec (mul_... | [
{
"name": "sum_spec_vec",
"text": "/-- `sum_spec` on a 1D tensor equals the `Finset` sum of its coordinates (`toVec`). -/\nlemma sum_spec_vec {n : Nat} (v : Tensor ℝ (.dim n .scalar)) :\n sumSpec v = ∑ i : Fin n, toVec v i := by\n classical\n cases v with\n | dim values =>\n -- `sum_spec_dim` reduc... | [
{
"name": "dot_mat_transpose",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 16,
"n_chars": 760,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nest... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Folds
/-!
Linear-algebra facts for dependent tensors.
The results here cover dot products, matrix-vector structure, and linearity facts used by
autograd... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Folds
/-!
Linear-algebra facts for dependent tensors.
The results here cover dot products, matrix-vector structure, and linearity facts used by
autograd... | @@ -22,6 +22,24 @@
open Tensor
open scoped BigOperators
+/-- `sum_spec` on a 1D tensor equals the `Finset` sum of its coordinates (`toVec`). -/
+lemma sum_spec_vec {n : Nat} (v : Tensor ℝ (.dim n .scalar)) :
+ sumSpec v = ∑ i : Fin n, toVec v i := by
+ classical
+ cases v with
+ | dim values =>
+ -- `sum_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_89bdc82a73f2_5 | d682bf0d7b620082 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/LinearAlgebra.lean | LinearAlgebra | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "dot_mat_mul_left_adjoint",
"depth": 1,
"n_commands": 0,
"n_lines": 50,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Reduce to the right-adjoint lemma via transpose.\n -- ⟪A·B, C⟫ = ⟪(A·B)ᵀ, Cᵀ⟫ = ⟪Bᵀ·Aᵀ, Cᵀ⟫ = ⟪B... | [
{
"name": "matrix_transpose_involution",
"text": "/-- Matrix transpose is an involution. -/\ntheorem matrix_transpose_involution {m n : Nat}\n (A : Tensor ℝ (.dim m (.dim n .scalar))) :\n matrixTransposeSpec (matrixTransposeSpec A) = A := by\n cases A with\n | dim rows =>\n -- reduce to function exte... | [
{
"name": "dot_mat_mul_left_adjoint",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 8,
"n_lines": 61,
"n_chars": 2802,
"n_subproofs": 7,
"n_tactics": 40,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 8 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Folds
/-!
Linear-algebra facts for dependent tensors.
The results here cover dot products, matrix-vector structure, and linearity facts used by
autograd... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Folds
/-!
Linear-algebra facts for dependent tensors.
The results here cover dot products, matrix-vector structure, and linearity facts used by
autograd... | @@ -40,6 +40,26 @@
simp [get_eq, toVec, sumSpec, tensorFoldlSpec, hval]
-- Pointwise product of vectors under `toVec`.
+/-- Matrix transpose is an involution. -/
+theorem matrix_transpose_involution {m n : Nat}
+ (A : Tensor ℝ (.dim m (.dim n .scalar))) :
+ matrixTransposeSpec (matrixTransposeSpec 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_eb1279fda498_0 | 1d134af0fbda5012 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/ConvForward.lean | ConvForward | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "conv_input_val_eq_padded",
"depth": 1,
"n_commands": 0,
"n_lines": 61,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n by_cases h4 : padding = 0\n · subst h4\n simp [Spec.Private.mkInputIdx?]\n · have hpad :=\n ... | [
{
"name": "mkInputIdx?_2d",
"text": "private lemma mkInputIdx?_2d\n (out_i out_j di dj stride padding : Nat) :\n Spec.Private.mkInputIdx? [out_i, out_j] [di, dj] [stride, stride] [padding, padding] =\n if _ : out_i * stride + di < padding ∨ out_j * stride + dj < padding then\n none\n ... | [
{
"name": "conv_input_val_eq_padded",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 84,
"n_chars": 3904,
"n_subproofs": 7,
"n_tactics": 58,
"cyclomatic": 2,
"n_automation": 9,
"n_rewrites": 2,
"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.Proofs.RuntimeApprox.Graph.ForwardApprox
public import NN.Proofs.RuntimeApprox.NF.Conv
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Utils
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.Graph.ForwardApprox
public import NN.Proofs.RuntimeApprox.NF.Conv
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Utils
/-!
... | @@ -193,6 +193,24 @@
-- Padding reads: relate `pad_multi_channel` branches to the original input approximation.
-- ---------------------------------------------------------------------------
+private lemma mkInputIdx?_2d
+ (out_i out_j di dj stride padding : Nat) :
+ Spec.Private.mkInputIdx? [out_i, out_j] [d... | {
"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_eb1279fda498_1 | 1b752fc0952ceaad | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/ConvForward.lean | ConvForward | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "approx_conv2d_point",
"depth": 1,
"n_commands": 0,
"n_lines": 346,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro layerS layerR\n classical\n\n let paddedR :=\n if h4 : padding = 0 then\n tensorCast\n (Shape.... | [
{
"name": "foldl_finRange3_eq_flat_foldl",
"text": "private lemma foldl_finRange3_eq_flat_foldl\n {γ : Type} [Zero γ] [Add γ] {inC kH kW : Nat} (term : Fin inC × Fin kH × Fin kW → γ) :\n (List.finRange inC).foldl (fun acc in_ch =>\n (List.finRange kH).foldl (fun acc di =>\n (Li... | [
{
"name": "approx_conv2d_point",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 386,
"n_chars": 18385,
"n_subproofs": 23,
"n_tactics": 326,
"cyclomatic": 4,
"n_automation": 19,
"n_rewrites": 3,
"n_structural": 22,
"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.Proofs.RuntimeApprox.Graph.ForwardApprox
public import NN.Proofs.RuntimeApprox.NF.Conv
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Utils
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.Graph.ForwardApprox
public import NN.Proofs.RuntimeApprox.NF.Conv
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Utils
/-!
... | @@ -59,6 +59,111 @@
set_option maxHeartbeats 8000000
+private lemma foldl_finRange3_eq_flat_foldl
+ {γ : Type} [Zero γ] [Add γ] {inC kH kW : Nat} (term : Fin inC × Fin kH × Fin kW → γ) :
+ (List.finRange inC).foldl (fun acc in_ch =>
+ (List.finRange kH).foldl (fun acc di =>
+ (List.fi... | {
"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_eb1279fda498_2 | c0a0723e57257491 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/ConvForward.lean | ConvForward | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "approxT_conv2d_spec",
"depth": 1,
"n_commands": 0,
"n_lines": 134,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro layerS layerR outS outR bT\n classical\n have hε : 0 ≤ linfNorm bT := linf_norm_nonneg (t := bT)\n refine ap... | [
{
"name": "entry_eq_scalar_get_at_or_zero3",
"text": "lemma entry_eq_scalar_get_at_or_zero3\n {α : Type} [Zero α] {n1 n2 n3 : Nat}\n (t : Tensor α (.dim n1 (.dim n2 (.dim n3 .scalar))))\n (i1 : Fin n1) (i2 : Fin n2) (i3 : Fin n3) :\n (match\n match\n match t with\n | .dim f =>... | [
{
"name": "approxT_conv2d_spec",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 170,
"n_chars": 7391,
"n_subproofs": 16,
"n_tactics": 126,
"cyclomatic": 13,
"n_automation": 6,
"n_rewrites": 5,
"n_structural": 14,
"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.RuntimeApprox.Graph.ForwardApprox
public import NN.Proofs.RuntimeApprox.NF.Conv
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Utils
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.Graph.ForwardApprox
public import NN.Proofs.RuntimeApprox.NF.Conv
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Utils
/-!
... | @@ -164,6 +164,35 @@
-- Component selection: relate 3D `Fin` indexing (via `match`) to `get_at_or_zero`.
-- ---------------------------------------------------------------------------
+lemma entry_eq_scalar_get_at_or_zero3
+ {α : Type} [Zero α] {n1 n2 n3 : Nat}
+ (t : Tensor α (.dim n1 (.dim n2 (.dim n3 .scal... | {
"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_078bbb4da4fe_0 | 202656c7cf89c4cc | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Nodes/Matrix.lean | Matrix | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "inner_transposeVec",
"depth": 1,
"n_commands": 0,
"n_lines": 68,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n let x' : Vec (m * n) := castVec (matSize_eq_mul m n) x\n let y' : Vec (n * m) := castVec (matSize_eq_mul ... | [
{
"name": "transposeEquiv_symm",
"text": "/-- The transpose index equivalence is symmetric up to swapping `m` and `n`. -/\nprivate lemma transposeEquiv_symm (m n : Nat) :\n (transposeEquiv m n).symm = transposeEquiv n m := by\n ext k; simp [transposeEquiv, Equiv.prodComm_symm]\n\n",
"fan_in": 1,
... | [
{
"name": "inner_transposeVec",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 74,
"n_chars": 3525,
"n_subproofs": 8,
"n_tactics": 65,
"cyclomatic": 1,
"n_automation": 16,
"n_rewrites": 0,
"n_structural": 7,
"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 NN.Proofs.Autograd.Tape.Nodes.Arithmetic
/-!
# Matrix tape nodes
Matrix multiplication, transpose, row/column broadcasting, and row means, with VJP correctness facts
stated at... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.Arithmetic
/-!
# Matrix tape nodes
Matrix multiplication, transpose, row/column broadcasting, and row means, with VJP correctness facts
stated at... | @@ -487,6 +487,11 @@
def transposeEquiv (m n : Nat) : Fin (m * n) ≃ Fin (n * m) :=
(finProdFinEquiv.symm.trans (Equiv.prodComm (Fin m) (Fin n))).trans finProdFinEquiv
+/-- The transpose index equivalence is symmetric up to swapping `m` and `n`. -/
+private lemma transposeEquiv_symm (m n : Nat) :
+ (transposeEq... | {
"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_7045d8274f8c_0 | 480a495f11a7def0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/GDLinearConvergence.lean | GDLinearConvergence | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "step_norm_sq_le",
"depth": 1,
"n_commands": 0,
"n_lines": 86,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Expand the squared norm of `(x-y) - η (g x - g y)` using inner-product identities.\n have hxy :\n step η g x - st... | [
{
"name": "step_sub_step",
"text": "/-- Expand the difference of two `step` applications. -/\ntheorem step_sub_step (η : ℝ) (g : E → E) (x y : E) :\n step η g x - step η g y = (x - y) - η • (g x - g y) := by\n simp [step, sub_eq_add_neg, add_assoc, add_left_comm, add_comm]\n\n",
"fan_in": 1,
"n_... | [
{
"name": "step_norm_sq_le",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 97,
"n_chars": 5486,
"n_subproofs": 20,
"n_tactics": 54,
"cyclomatic": 1,
"n_automation": 14,
"n_rewrites": 0,
"n_structural": 5,
"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 Mathlib.Analysis.InnerProductSpace.Basic
public import Mathlib.Topology.MetricSpace.Lipschitz
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
import Mathlib.Logic.Fun... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.InnerProductSpace.Basic
public import Mathlib.Topology.MetricSpace.Lipschitz
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
import Mathlib.Logic.Fun... | @@ -57,6 +57,11 @@
def step (η : ℝ) (g : E → E) (x : E) : E :=
x - η • g x
+/-- Expand the difference of two `step` applications. -/
+theorem step_sub_step (η : ℝ) (g : E → E) (x y : E) :
+ step η g x - step η g y = (x - y) - η • (g x - g y) := by
+ simp [step, sub_eq_add_neg, add_assoc, add_left_comm, add_co... | {
"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_af56d6be3398_0 | f7bb744ede7e2028 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Models/Attention/PermutationEquivariance.lean | PermutationEquivariance | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "softmax_vec_spec_reindexOuter",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Reduce to the plain form.\n simpa [softmax_vec_spec_eq_plain] using\n (softmaxVecPlain_reindexOuter (σ... | [
{
"name": "softmax_vec_spec_eq_plain",
"text": "/-- The stabilized spec `softmax_vec_spec` agrees with `softmaxVecPlain` over `ℝ`. -/\nprivate theorem softmax_vec_spec_eq_plain {n : Nat} (t : Tensor ℝ (.dim (Nat.succ n) .scalar)) :\n Activation.softmaxVecSpec (α := ℝ) (n := Nat.succ n) t = softmaxVecPlai... | [
{
"name": "softmax_vec_spec_reindexOuter",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 620,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic
public import NN.Spec.Layers.Attention
/-!
# Permutation Equivariance of Self-Attention (No Positional Encoding)
Self-attention (without positional info... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic
public import NN.Spec.Layers.Attention
/-!
# Permutation Equivariance of Self-Attention (No Positional Encoding)
Self-attention (without positional info... | @@ -116,6 +116,161 @@
let denom : ℝ := ∑ j : Fin n, Real.exp (x j)
.dim (fun i => .scalar (Real.exp (x i) / denom))
+/-- The stabilized spec `softmax_vec_spec` agrees with `softmaxVecPlain` over `ℝ`. -/
+private theorem softmax_vec_spec_eq_plain {n : Nat} (t : Tensor ℝ (.dim (Nat.succ n) .scalar)) :
+ ... | {
"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_af56d6be3398_1 | 66a29ab558de4745 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Models/Attention/PermutationEquivariance.lean | PermutationEquivariance | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "softmax_vec_spec_reindexOuter",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Reduce to the plain form.\n simpa [softmax_vec_spec_eq_plain] using\n (softmaxVecPlain_reindexOuter (σ... | [
{
"name": "softmaxVecPlain_reindexOuter",
"text": "/-- Plain softmax commutes with reindexing (permuting coordinates). -/\nprivate theorem softmaxVecPlain_reindexOuter {n : Nat} (σ : Equiv.Perm (Fin n))\n (t : Tensor ℝ (.dim n .scalar)) :\n softmaxVecPlain (reindexOuter (α := ℝ) (n := n) (s := .scalar... | [
{
"name": "softmax_spec_permMatrix",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 16,
"n_chars": 801,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"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.Proofs.Tensor.Basic
public import NN.Spec.Layers.Attention
/-!
# Permutation Equivariance of Self-Attention (No Positional Encoding)
Self-attention (without positional info... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic
public import NN.Spec.Layers.Attention
/-!
# Permutation Equivariance of Self-Attention (No Positional Encoding)
Self-attention (without positional info... | @@ -271,6 +271,23 @@
-- `simp` has unfolded the tensor combinators, so the goal is a scalar identity.
simpa [scalarVal, scalarElim, MathFunctions.exp] using hgoal'
+/-- Plain softmax commutes with reindexing (permuting coordinates). -/
+private theorem softmaxVecPlain_reindexOuter {n : Nat} (σ :... | {
"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_af56d6be3398_2 | d36beba1b2c6a429 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Models/Attention/PermutationEquivariance.lean | PermutationEquivariance | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "selfAttention_reindexOuter",
"depth": 1,
"n_commands": 0,
"n_lines": 161,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Reduce to `n = succ _` using `h1`.\n cases n with\n | zero =>\n cases (h1 rfl)\n | suc... | [
{
"name": "mat_mul_reindexOuter_reindexCols",
"text": "/--\nMatrix multiplication commutes with independent output-row and output-column reindexing.\n\nThis is the most general bookkeeping lemma used below: reindexing rows of the left factor controls\nthe rows of the product, while reindexing columns of the... | [
{
"name": "selfAttention_reindexOuter",
"fan_in": 0,
"n_deps_direct": 6,
"n_deps_transitive": 10,
"n_lines": 186,
"n_chars": 10234,
"n_subproofs": 8,
"n_tactics": 138,
"cyclomatic": 3,
"n_automation": 15,
"n_rewrites": 3,
"n_structural": 5,
"automation_only": fals... | 9 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic
public import NN.Spec.Layers.Attention
/-!
# Permutation Equivariance of Self-Attention (No Positional Encoding)
Self-attention (without positional info... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic
public import NN.Spec.Layers.Attention
/-!
# Permutation Equivariance of Self-Attention (No Positional Encoding)
Self-attention (without positional info... | @@ -322,6 +322,27 @@
-/
/--
+Matrix multiplication commutes with independent output-row and output-column reindexing.
+
+This is the most general bookkeeping lemma used below: reindexing rows of the left factor controls
+the rows of the product, while reindexing columns of the right factor controls the columns of 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_f3c4bfda7b50_0 | 1bf128059247fe53 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/Core/SpecApprox.lean | SpecApprox | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "approxT_to_approxTTol_absOnly",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [approxTTol] using\n (approx_with_to_approx_with_tol_absOnly (toSpec := toSpec) (norm := linfNorm)\n... | [
{
"name": "approx_with_to_approx_with_tol_absOnly",
"text": "lemma approx_with_to_approx_with_tol_absOnly {α : Type} {s : Shape}\n {toSpec : α → SpecScalar}\n {norm : ∀ {s : Shape}, SpecTensor s → SpecScalar}\n {spec : SpecTensor s} {runtime : Tensor α s} (eps : ℝ)\n (h : approxWith (toSpec := t... | [
{
"name": "approxT_to_approxTTol_absOnly",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 469,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
... | 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
public import NN.MLTheory.LearningTheory.Robustness.Spec
public import NN.Proofs.RuntimeApprox.Core.Tolerance
public import NN.Spec.Core.Scalar
public... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.NeuralFloat.Core
public import NN.MLTheory.LearningTheory.Robustness.Spec
public import NN.Proofs.RuntimeApprox.Core.Tolerance
public import NN.Spec.Core.Scalar
public... | @@ -86,11 +86,27 @@
(tol : ApproxTol) : Prop :=
approxWithTol (toSpec := toSpec) (norm := linfNorm) spec runtime tol
+lemma approx_with_to_approx_with_tol_absOnly {α : Type} {s : Shape}
+ {toSpec : α → SpecScalar}
+ {norm : ∀ {s : Shape}, SpecTensor s → SpecScalar}
+ {spec : SpecTensor s} {runtime : ... | {
"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_4272c02bca04_0 | cef2b02b36245efc | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/ConvBackward/Input.lean | Input | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "approxT_conv2d_input_deriv_spec",
"depth": 1,
"n_commands": 0,
"n_lines": 101,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro layerS layerR outS outR bT\n classical\n have hε : 0 ≤ linfNorm bT := linf_norm_nonneg (t := bT)\... | [
{
"name": "approx_conv2d_input_point",
"text": "/--\nSoundness of the Conv2D **input**-gradient pointwise bound.\n\nGiven `approxT` hypotheses for the kernel and upstream gradient (`grad_output`), this shows the spec\ninput-gradient entry is approximated by the NF runtime entry within `conv2dInputPointBound... | [
{
"name": "approxT_conv2d_input_deriv_spec",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 143,
"n_chars": 6847,
"n_subproofs": 14,
"n_tactics": 97,
"cyclomatic": 19,
"n_automation": 6,
"n_rewrites": 4,
"n_structural": 12,
"automation_only": ... | 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.ConvBackward.BiasKernel
/-!
# NeuralFloat Conv2D Input-Gradient Bounds
This file completes the pointwise approximation argument for Conv2D backward ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.ConvBackward.BiasKernel
/-!
# NeuralFloat Conv2D Input-Gradient Bounds
This file completes the pointwise approximation argument for Conv2D backward ... | @@ -113,6 +113,677 @@
kernelR δR epsK epsδ in_ch i j)))
/--
+Soundness of the Conv2D **input**-gradient pointwise bound.
+
+Given `approxT` hypotheses for the kernel and upstream gradient (`grad_output`), this shows the spec
+input-gradient entry is approximated by the NF runtime entry within `conv2dInp... | {
"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_45ba4b350e33_0 | 43495f62971724ac | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Compiled/IRExec/Correctness/Ops/LinearAlgebra.lean | LinearAlgebra | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "buildFrom_denoteAllFrom_matmul",
"depth": 1,
"n_commands": 0,
"n_lines": 192,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let vals0 : Array (NN.IR.DVal α) :=\n denoteAllState (α := α) inShape (st := (⟨ss, gd⟩ : State α inShap... | [
{
"name": "buildFrom_denoteAllFrom_matmul_bmm_success",
"text": "/--\nCorrectness lemma for the `.matmul` compilation step in the batched-matmul (`bmm`) case.\n\nThis is used when the parent shapes match `Tensor.bmm_spec` with an explicit batch dimension, and\nagain yields the exact one-step equality consum... | [
{
"name": "buildFrom_denoteAllFrom_matmul",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 223,
"n_chars": 14592,
"n_subproofs": 2,
"n_tactics": 192,
"cyclomatic": 47,
"n_automation": 29,
"n_rewrites": 1,
"n_structural": 43,
"automation_only":... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Compiled.IRExec.Correctness.Common
/-!
# Linear Algebra
Linear-algebra correctness lemmas for the IR → compiled runtime bridge.
This file proves the forwa... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Compiled.IRExec.Correctness.Common
/-!
# Linear Algebra
Linear-algebra correctness lemmas for the IR → compiled runtime bridge.
This file proves the forwa... | @@ -176,6 +176,114 @@
hTail hEval hStep
/--
+Correctness lemma for the `.matmul` compilation step in the batched-matmul (`bmm`) case.
+
+This is used when the parent shapes match `Tensor.bmm_spec` with an explicit batch dimension, and
+again yields the exact one-step equality consumed by the semantic equivalenc... | {
"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_12418ae80e5d_0 | b3bf3e01f5cbce25 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Compiled/IRExec/Correctness/SemanticEquivalenceCommon.lean | SemanticEquivalenceCommon | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "shape_beq_refl",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `==` is definitionally `BEq.beq`, and `BEq Shape` is `Shape.areEqual`.\n simpa [BEq.beq] using shape_areEqual_refl (s :=... | [
{
"name": "shape_areEqual_refl",
"text": "/-- Reflexivity of the explicit structural boolean equality test `Shape.areEqual`. -/\ntheorem shape_areEqual_refl (s : Shape) : Shape.areEqual s s = true := by\n induction s with\n | scalar => rfl\n | dim n s ih =>\n simp [Shape.areEqual, ih]\n\n",
"fan... | [
{
"name": "shape_beq_refl",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 231,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Compiled.IRExec.Correctness.Common
/-!
# SemanticEquivalenceCommon
Shared helper lemmas for the semantic equivalence proof in `NN.Runtime.Autograd.Compiled... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Compiled.IRExec.Correctness.Common
/-!
# SemanticEquivalenceCommon
Shared helper lemmas for the semantic equivalence proof in `NN.Runtime.Autograd.Compiled... | @@ -94,8 +94,17 @@
attribute [grind =] applySwapsTensor_eq_foldl_applySwapDepth
+/-- Reflexivity of the explicit structural boolean equality test `Shape.areEqual`. -/
+theorem shape_areEqual_refl (s : Shape) : Shape.areEqual s s = true := by
+ induction s with
+ | scalar => rfl
+ | dim n s ih =>
+ simp [Sh... | {
"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_12418ae80e5d_1 | 731d71009794fc83 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Compiled/IRExec/Correctness/SemanticEquivalenceCommon.lean | SemanticEquivalenceCommon | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "shape_bne_refl",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `!=` is the boolean negation of `==`.\n simp [bne, shape_beq_refl (s := s)]",
"n_chars": 84,
"n_subproofs": 0,
... | [
{
"name": "shape_beq_refl",
"text": "/-- Reflexivity of `BEq Shape` (`==`). -/\ntheorem shape_beq_refl (s : Shape) : (s == s) = true := by\n -- `==` is definitionally `BEq.beq`, and `BEq Shape` is `Shape.areEqual`.\n simpa [BEq.beq] using shape_areEqual_refl (s := s)\n\n",
"fan_in": 1,
"n_lines": ... | [
{
"name": "shape_bne_refl",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 6,
"n_chars": 201,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Compiled.IRExec.Correctness.Common
/-!
# SemanticEquivalenceCommon
Shared helper lemmas for the semantic equivalence proof in `NN.Runtime.Autograd.Compiled... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Compiled.IRExec.Correctness.Common
/-!
# SemanticEquivalenceCommon
Shared helper lemmas for the semantic equivalence proof in `NN.Runtime.Autograd.Compiled... | @@ -101,8 +101,15 @@
| dim n s ih =>
simp [Shape.areEqual, ih]
+/-- Reflexivity of `BEq Shape` (`==`). -/
+theorem shape_beq_refl (s : Shape) : (s == s) = true := by
+ -- `==` is definitionally `BEq.beq`, and `BEq Shape` is `Shape.areEqual`.
+ simpa [BEq.beq] using shape_areEqual_refl (s := s)
+
/-- Refl... | {
"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_12418ae80e5d_2 | d17b80b13fef6de7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Compiled/IRExec/Correctness/SemanticEquivalenceCommon.lean | SemanticEquivalenceCommon | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "shape_bne_eq_false_of_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases h\n simpa using shape_bne_refl (s := s)",
"n_chars": 51,
"n_subproofs": 0,
"n_tactics": 3,
... | [
{
"name": "shape_bne_refl",
"text": "/-- Reflexivity of boolean inequality (`!=`) on shapes. -/\ntheorem shape_bne_refl (s : Shape) : (s != s) = false := by\n -- `!=` is the boolean negation of `==`.\n simp [bne, shape_beq_refl (s := s)]\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 201,
"n_... | [
{
"name": "shape_bne_eq_false_of_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 6,
"n_chars": 225,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"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.Runtime.Autograd.Compiled.IRExec.Correctness.Common
/-!
# SemanticEquivalenceCommon
Shared helper lemmas for the semantic equivalence proof in `NN.Runtime.Autograd.Compiled... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Compiled.IRExec.Correctness.Common
/-!
# SemanticEquivalenceCommon
Shared helper lemmas for the semantic equivalence proof in `NN.Runtime.Autograd.Compiled... | @@ -106,8 +106,15 @@
-- `==` is definitionally `BEq.beq`, and `BEq Shape` is `Shape.areEqual`.
simpa [BEq.beq] using shape_areEqual_refl (s := s)
+/-- Reflexivity of boolean inequality (`!=`) on shapes. -/
+theorem shape_bne_refl (s : Shape) : (s != s) = false := by
+ -- `!=` is the boolean negation of `==`.
+... | {
"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_98f12aa8a757_0 | c17191f736fe3288 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/Folds.lean | Folds | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "tensor_foldl_spec_add_init",
"depth": 1,
"n_commands": 0,
"n_lines": 105,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction s generalizing acc with\n | scalar =>\n cases t with\n | scalar x =>\n simp [tensorFoldl... | [
{
"name": "tensor_foldl_spec_go_of_not_lt",
"text": "/--\nOne-step unfolding of the internal tail-recursive helper `tensor_foldl_spec.go` when the loop\ncondition fails (`¬ k < n`), i.e. the loop terminates and returns the accumulator.\n-/\nlemma tensor_foldl_spec_go_of_not_lt {α β : Type} (f : β → α → β)\n... | [
{
"name": "tensor_foldl_spec_add_init",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 116,
"n_chars": 5622,
"n_subproofs": 14,
"n_tactics": 87,
"cyclomatic": 5,
"n_automation": 15,
"n_rewrites": 3,
"n_structural": 9,
"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.Proofs.Tensor.Basic.Core
/-!
Fold and reduction lemmas for dependent tensors.
This module packages the algebra needed to reason about tensor reductions, finite sums, and
sh... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Core
/-!
Fold and reduction lemmas for dependent tensors.
This module packages the algebra needed to reason about tensor reductions, finite sums, and
sh... | @@ -50,6 +50,16 @@
simp [hk]
/--
+One-step unfolding of the internal tail-recursive helper `tensor_foldl_spec.go` when the loop
+condition fails (`¬ k < n`), i.e. the loop terminates and returns the accumulator.
+-/
+lemma tensor_foldl_spec_go_of_not_lt {α β : Type} (f : β → α → β)
+ {n : Nat} {s : Shape} (val... | {
"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_98f12aa8a757_1 | 8cdfdc24da258a90 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/Folds.lean | Folds | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "dot_mul_reassoc",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hAssoc := mul_spec_assoc (a := dLdy) (b := m) (c := dx)\n have hComm := mul_spec_comm (a := dLdy) (b := m)\n -- `mul... | [
{
"name": "mul_spec_comm",
"text": "/-- Elementwise multiplication is commutative (`mul_spec` is pointwise `(*)`). -/\ntheorem mul_spec_comm {s : Shape}\n (a b : Tensor ℝ s) : mulSpec a b = mulSpec b a := by\n induction s with\n | scalar =>\n cases a\n cases b\n simp [mulSpec, map2Spec, mu... | [
{
"name": "dot_mul_reassoc",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 12,
"n_chars": 515,
"n_subproofs": 2,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Core
/-!
Fold and reduction lemmas for dependent tensors.
This module packages the algebra needed to reason about tensor reductions, finite sums, and
sh... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Core
/-!
Fold and reduction lemmas for dependent tensors.
This module packages the algebra needed to reason about tensor reductions, finite sums, and
sh... | @@ -42,6 +42,23 @@
funext i
simpa [mulSpec, map2Spec] using ih (a := fa i) (b := fb i) (c := fc i)
+/-- Elementwise multiplication is commutative (`mul_spec` is pointwise `(*)`). -/
+theorem mul_spec_comm {s : Shape}
+ (a b : Tensor ℝ s) : mulSpec a b = mulSpec b a := by
+ induction s with... | {
"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_98f12aa8a757_2 | ae70e27465764bdb | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/Folds.lean | Folds | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "tensor_foldl_spec_add_init",
"depth": 1,
"n_commands": 0,
"n_lines": 105,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction s generalizing acc with\n | scalar =>\n cases t with\n | scalar x =>\n simp [tensorFoldl... | [
{
"name": "tensor_foldl_spec_go_of_not_lt",
"text": "/--\nOne-step unfolding of the internal tail-recursive helper `tensor_foldl_spec.go` when the loop\ncondition fails (`¬ k < n`), i.e. the loop terminates and returns the accumulator.\n-/\nlemma tensor_foldl_spec_go_of_not_lt {α β : Type} (f : β → α → β)\n... | [
{
"name": "sum_spec_dim",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 118,
"n_chars": 5416,
"n_subproofs": 23,
"n_tactics": 109,
"cyclomatic": 6,
"n_automation": 25,
"n_rewrites": 3,
"n_structural": 19,
"automation_only": false,
"max_ne... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Core
/-!
Fold and reduction lemmas for dependent tensors.
This module packages the algebra needed to reason about tensor reductions, finite sums, and
sh... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Core
/-!
Fold and reduction lemmas for dependent tensors.
This module packages the algebra needed to reason about tensor reductions, finite sums, and
sh... | @@ -50,6 +50,16 @@
simp [hk]
/--
+One-step unfolding of the internal tail-recursive helper `tensor_foldl_spec.go` when the loop
+condition fails (`¬ k < n`), i.e. the loop terminates and returns the accumulator.
+-/
+lemma tensor_foldl_spec_go_of_not_lt {α β : Type} (f : β → α → β)
+ {n : Nat} {s : Shape} (val... | {
"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_98f12aa8a757_3 | 542216d56a1f1bc7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/Folds.lean | Folds | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "sum_spec_dim",
"depth": 1,
"n_commands": 0,
"n_lines": 110,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases t with\n | dim values =>\n let f : Fin n → ℝ := fun i => sumSpec (values i)\n have go_eq :\n ... | [
{
"name": "tensor_foldl_spec_add_init",
"text": "/--\nAccumulator lemma for `tensor_foldl_spec` specialized to addition.\n\nInformally: folding with `(+)` over a tensor adds `sum_spec t` to the initial accumulator.\nThis is frequently used to move between “fold-style” specs and “sum-style” algebra.\n-/\nlem... | [
{
"name": "dot_eq_tensorAlgebra_dot",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 50,
"n_chars": 2394,
"n_subproofs": 4,
"n_tactics": 39,
"cyclomatic": 6,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 8,
"automation_only": false,
... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Core
/-!
Fold and reduction lemmas for dependent tensors.
This module packages the algebra needed to reason about tensor reductions, finite sums, and
sh... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.Core
/-!
Fold and reduction lemmas for dependent tensors.
This module packages the algebra needed to reason about tensor reductions, finite sums, and
sh... | @@ -59,6 +59,120 @@
rw [tensorFoldlSpec.go.eq_1]
simp [hk]
+/--
+Accumulator lemma for `tensor_foldl_spec` specialized to addition.
+
+Informally: folding with `(+)` over a tensor adds `sum_spec t` to the initial accumulator.
+This is frequently used to move between “fold-style” specs and “sum-style” algebra.
+... | {
"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_2931786bed5d_0 | 32736fd345ced350 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/Conv.lean | Conv | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "approx_fold_add",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have h0 : abs (toSpec (β := β) (fexp := fexp) (rnd := rnd) (0 : R) - (0 : ℝ)) ≤ (0 : ℝ) := by\n simp [toSpec_zero (β := ... | [
{
"name": "approx_fold_add_state",
"text": "lemma approx_fold_add_state {ι : Type} (l : List ι)\n (termS : ι → ℝ) (termR : ι → R) (epsTerm : ι → ℝ) :\n ∀ (accS : ℝ) (st : R × ℝ),\n abs (toSpec (β := β) (fexp := fexp) (rnd := rnd) st.1 - accS) ≤ st.2 →\n (∀ i ∈ l, abs (toSpec (β := β) (fexp :... | [
{
"name": "approx_fold_add",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 19,
"n_chars": 941,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 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
public import NN.Proofs.RuntimeApprox.NF.Ops
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Conv
/-!
# Conv2... | /-
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
public import NN.Proofs.RuntimeApprox.NF.Ops
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Conv
/-!
# Conv2... | @@ -96,6 +96,53 @@
def foldAddState {ι : Type} (l : List ι) (termR : ι → R) (epsTerm : ι → ℝ) : R × ℝ :=
foldAddStateFrom (β := β) (fexp := fexp) (rnd := rnd) l termR epsTerm ((0 : R), (0 : ℝ))
+lemma approx_fold_add_state {ι : Type} (l : List ι)
+ (termS : ι → ℝ) (termR : ι → R) (epsTerm : ι → ℝ) :
+ ∀ (ac... | {
"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_2931786bed5d_1 | 39312b153450ef8c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/Conv.lean | Conv | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "approx_padded_input_read",
"depth": 1,
"n_commands": 0,
"n_lines": 34,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n by_cases h4 : padding = 0\n · subst h4\n simpa using\n (approx_get_at_or_zero (β := β) (fex... | [
{
"name": "approx_get_at_or_zero",
"text": "lemma approx_get_at_or_zero {s : Shape} :\n ∀ {xS : SpecTensor s} {xR : Tensor R s} {eps : ℝ} (_hx :\n approxT (α := R) (toSpec := toSpec (β := β) (fexp := fexp) (rnd := rnd)) xS xR eps)\n (idx : List Nat),\n abs (toSpec (β := β) (fexp := fexp)... | [
{
"name": "approx_padded_input_read",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 72,
"n_chars": 2873,
"n_subproofs": 9,
"n_tactics": 34,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 6,
"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.Proofs.RuntimeApprox.NF.BackwardOps
public import NN.Proofs.RuntimeApprox.NF.Ops
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Conv
/-!
# Conv2... | /-
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
public import NN.Proofs.RuntimeApprox.NF.Ops
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Conv
/-!
# Conv2... | @@ -96,6 +96,65 @@
def foldAddState {ι : Type} (l : List ι) (termR : ι → R) (epsTerm : ι → ℝ) : R × ℝ :=
foldAddStateFrom (β := β) (fexp := fexp) (rnd := rnd) l termR epsTerm ((0 : R), (0 : ℝ))
+lemma approx_get_at_or_zero {s : Shape} :
+ ∀ {xS : SpecTensor s} {xR : Tensor R s} {eps : ℝ} (_hx :
+ approx... | {
"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_200b9b47b4f5_0 | c12c94f0ce3b5963 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/TorchLean/Fno1d.lean | Fno1d | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "model_paramShapes",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [model, Seq.paramShapes, blocksSeq_paramShapes, paramShapes_comp,\n reshapeVectorToMatrix, reshapeMatrixToVector,... | [
{
"name": "paramShapes_comp",
"text": "/-- `Seq.comp` preserves parameter order by list append. -/\ntheorem paramShapes_comp {σ τ υ : Shape} (f : Seq σ τ) (g : Seq τ υ) :\n Seq.paramShapes (f >>> g) = Seq.paramShapes f ++ Seq.paramShapes g := by\n induction f with\n | id s =>\n simp [Seq.comp, Seq... | [
{
"name": "model_paramShapes",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 18,
"n_chars": 813,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesti... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.TorchLean.Fft
import Mathlib.Algebra.Order.Algebra
/-!
# FNO1D
1D Fourier Neural Operator (FNO) blocks based on an explicit FFT/IFFT transform.
Important... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.TorchLean.Fft
import Mathlib.Algebra.Order.Algebra
/-!
# FNO1D
1D Fourier Neural Operator (FNO) blocks based on an explicit FFT/IFFT transform.
Important... | @@ -285,6 +285,15 @@
/-! ## Model constructor -/
+/-- `Seq.comp` preserves parameter order by list append. -/
+theorem paramShapes_comp {σ τ υ : Shape} (f : Seq σ τ) (g : Seq τ υ) :
+ Seq.paramShapes (f >>> g) = Seq.paramShapes f ++ Seq.paramShapes g := by
+ induction f with
+ | id s =>
+ simp [Seq.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_1d26f59dd04c_0 | f261a89ac0563cb2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "payloadBridgeCoverageTags_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h\n simp [payloadBridgeCoverageTags, payloadBridgeCoverageWitnesses, OpKind.tag] a... | [
{
"name": "payloadBridgeCoverageTags_complete",
"text": "/-- Every current payload-backed IR constructor family appears in the bridge checklist. -/\ntheorem payloadBridgeCoverageTags_complete\n (kind : OpKind) (h : opKindUsesPayloadBridge kind = true) :\n kind.tag ∈ payloadBridgeCoverageTags := by\n ... | [
{
"name": "payloadBridgeCoverageTags_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 919,
"n_subproofs": 0,
"n_tactics": 15,
"cyclomatic": 4,
"n_automation": 6,
"n_rewrites": 4,
"n_structural": 9,
"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.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -77,6 +77,13 @@
| .batchNorm2dNchwEval .. => true
| _ => false
+/-- Every current payload-backed IR constructor family appears in the bridge checklist. -/
+theorem payloadBridgeCoverageTags_complete
+ (kind : OpKind) (h : opKindUsesPayloadBridge kind = true) :
+ kind.tag ∈ payloadBridgeCoverageTags := ... | {
"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_1d26f59dd04c_1 | 0eac5f6f93ea087e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "payloadOfParamStore_const?_some",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [payloadOfParamStore_const?_eq, h]\n rfl",
"n_chars": 49,
"n_subproofs": 0,
"n_tactics": 3,... | [
{
"name": "payloadOfParamStore_const?_eq",
"text": "/-- Constants are forwarded from `ParamStore.constVals` to `Payload.const?` without changing data. -/\ntheorem payloadOfParamStore_const?_eq\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :\n (payloadOfParamStore... | [
{
"name": "payloadOfParamStore_const?_some",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 438,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"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 NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -77,6 +77,14 @@
| .batchNorm2dNchwEval .. => true
| _ => false
+/-- Constants are forwarded from `ParamStore.constVals` to `Payload.const?` without changing data. -/
+theorem payloadOfParamStore_const?_eq
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :
+ (payloadO... | {
"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_1d26f59dd04c_2 | 0a5879106a72fc15 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "payloadOfParamStore_const?_some",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [payloadOfParamStore_const?_eq, h]\n rfl",
"n_chars": 49,
"n_subproofs": 0,
"n_tactics": 3,... | [
{
"name": "payloadOfParamStore_const?_eq",
"text": "/-- Constants are forwarded from `ParamStore.constVals` to `Payload.const?` without changing data. -/\ntheorem payloadOfParamStore_const?_eq\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :\n (payloadOfParamStore... | [
{
"name": "payloadOfParamStore_const?_none",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 361,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"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 NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -77,12 +77,22 @@
| .batchNorm2dNchwEval .. => true
| _ => false
+/-- Constants are forwarded from `ParamStore.constVals` to `Payload.const?` without changing data. -/
+theorem payloadOfParamStore_const?_eq
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :
+ (payload... | {
"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_1d26f59dd04c_3 | 6f43ba2bc4abf808 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "payloadOfParamStore_linear?_some",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [payloadOfParamStore_linear?_eq, h]\n rfl",
"n_chars": 50,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "payloadOfParamStore_linear?_eq",
"text": "/-- Linear weights are forwarded from `ParamStore.linearWB` to `Payload.linear?`. -/\ntheorem payloadOfParamStore_linear?_eq\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :\n (payloadOfParamStore (α := α) ps).l... | [
{
"name": "payloadOfParamStore_linear?_some",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 441,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"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 NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -77,6 +77,14 @@
| .batchNorm2dNchwEval .. => true
| _ => false
+/-- Linear weights are forwarded from `ParamStore.linearWB` to `Payload.linear?`. -/
+theorem payloadOfParamStore_linear?_eq
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :
+ (payloadOfParamStore (α :... | {
"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_1d26f59dd04c_4 | 8301d880055a63f8 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "payloadOfParamStore_linear?_some",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [payloadOfParamStore_linear?_eq, h]\n rfl",
"n_chars": 50,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "payloadOfParamStore_linear?_eq",
"text": "/-- Linear weights are forwarded from `ParamStore.linearWB` to `Payload.linear?`. -/\ntheorem payloadOfParamStore_linear?_eq\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :\n (payloadOfParamStore (α := α) ps).l... | [
{
"name": "payloadOfParamStore_linear?_none",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 361,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"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 NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -77,12 +77,22 @@
| .batchNorm2dNchwEval .. => true
| _ => false
+/-- Linear weights are forwarded from `ParamStore.linearWB` to `Payload.linear?`. -/
+theorem payloadOfParamStore_linear?_eq
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :
+ (payloadOfParamStore (α ... | {
"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_1d26f59dd04c_5 | e85e700c583899cc | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "payloadOfParamStore_conv2d?_some",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [payloadOfParamStore_conv2d?_eq, h]\n rfl",
"n_chars": 50,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "payloadOfParamStore_conv2d?_eq",
"text": "/-- Convolution parameters are forwarded from `ParamStore.conv2dCfg` to `Payload.conv2d?`. -/\ntheorem payloadOfParamStore_conv2d?_eq\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :\n (payloadOfParamStore (α :=... | [
{
"name": "payloadOfParamStore_conv2d?_some",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 463,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"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 NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -77,6 +77,14 @@
| .batchNorm2dNchwEval .. => true
| _ => false
+/-- Convolution parameters are forwarded from `ParamStore.conv2dCfg` to `Payload.conv2d?`. -/
+theorem payloadOfParamStore_conv2d?_eq
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :
+ (payloadOfParamS... | {
"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_1d26f59dd04c_6 | 698b464b87e6bc7d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "payloadOfParamStore_conv2d?_some",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [payloadOfParamStore_conv2d?_eq, h]\n rfl",
"n_chars": 50,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "payloadOfParamStore_conv2d?_eq",
"text": "/-- Convolution parameters are forwarded from `ParamStore.conv2dCfg` to `Payload.conv2d?`. -/\ntheorem payloadOfParamStore_conv2d?_eq\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :\n (payloadOfParamStore (α :=... | [
{
"name": "payloadOfParamStore_conv2d?_none",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 367,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"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 NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -77,12 +77,22 @@
| .batchNorm2dNchwEval .. => true
| _ => false
+/-- Convolution parameters are forwarded from `ParamStore.conv2dCfg` to `Payload.conv2d?`. -/
+theorem payloadOfParamStore_conv2d?_eq
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :
+ (payloadOfParam... | {
"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_1d26f59dd04c_7 | 978bb6ce27f3291e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "payloadOfParamStore_batchNorm2dNchwEval?_some",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [payloadOfParamStore_batchNorm2dNchwEval?_eq, h]\n rfl",
"n_chars": 63,
"n_subpro... | [
{
"name": "payloadOfParamStore_batchNorm2dNchwEval?_eq",
"text": "/-- BatchNorm parameters are forwarded from `ParamStore.batchNorm2dNchwEval` to the IR payload. -/\ntheorem payloadOfParamStore_batchNorm2dNchwEval?_eq\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :\... | [
{
"name": "payloadOfParamStore_batchNorm2dNchwEval?_some",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 528,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -77,6 +77,15 @@
| .batchNorm2dNchwEval .. => true
| _ => false
+/-- BatchNorm parameters are forwarded from `ParamStore.batchNorm2dNchwEval` to the IR payload. -/
+theorem payloadOfParamStore_batchNorm2dNchwEval?_eq
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :
+ ... | {
"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_1d26f59dd04c_8 | 683e8054d528aa21 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "payloadOfParamStore_batchNorm2dNchwEval?_some",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [payloadOfParamStore_batchNorm2dNchwEval?_eq, h]\n rfl",
"n_chars": 63,
"n_subpro... | [
{
"name": "payloadOfParamStore_batchNorm2dNchwEval?_eq",
"text": "/-- BatchNorm parameters are forwarded from `ParamStore.batchNorm2dNchwEval` to the IR payload. -/\ntheorem payloadOfParamStore_batchNorm2dNchwEval?_eq\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :\... | [
{
"name": "payloadOfParamStore_batchNorm2dNchwEval?_none",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 472,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -77,12 +77,23 @@
| .batchNorm2dNchwEval .. => true
| _ => false
+/-- BatchNorm parameters are forwarded from `ParamStore.batchNorm2dNchwEval` to the IR payload. -/
+theorem payloadOfParamStore_batchNorm2dNchwEval?_eq
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat) :
+ ... | {
"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_1d26f59dd04c_9 | f3f18c9385fea2b8 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "evalConst_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalConst,\n payloadOfParamStore_const?_some (ps := ps) (id := id)\n ({ n := Shape.size s, v ... | [
{
"name": "payloadOfParamStore_const?_some",
"text": "/-- A present constant entry becomes the matching IR constant payload. -/\ntheorem payloadOfParamStore_const?_some\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (c : NN.MLTheory.CROWN.Graph.FlatVec α)\n (... | [
{
"name": "evalConst_from_paramStore",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 19,
"n_chars": 826,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"m... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -85,6 +85,17 @@
(ps.constVals.get? id).map (irConstOfFlatVec (α := α)) := by
rfl
+/-- A present constant entry becomes the matching IR constant payload. -/
+theorem payloadOfParamStore_const?_some
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ (c : NN.MLTheor... | {
"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_1d26f59dd04c_10 | 74f0c9dbccbd1e68 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "evalConst_missing_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalConst, payloadOfParamStore_const?_none (ps := ps) (id := id) hMissing]\n rfl",
"n_ch... | [
{
"name": "payloadOfParamStore_const?_none",
"text": "/-- Missing constant entries remain missing after converting to an IR payload. -/\ntheorem payloadOfParamStore_const?_none\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (h : ps.constVals.get? id = none) :\n ... | [
{
"name": "evalConst_missing_from_paramStore",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 574,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -85,6 +85,15 @@
(ps.constVals.get? id).map (irConstOfFlatVec (α := α)) := by
rfl
+/-- Missing constant entries remain missing after converting to an IR payload. -/
+theorem payloadOfParamStore_const?_none
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ (h : 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_1d26f59dd04c_11 | 2ed265e7466bd64e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "evalLinear_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalLinear,\n payloadOfParamStore_linear?_some (ps := ps) (id := id)\n ({ m := outDim, n := ... | [
{
"name": "payloadOfParamStore_linear?_some",
"text": "/-- A present linear entry becomes the matching IR linear payload. -/\ntheorem payloadOfParamStore_linear?_some\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (p : NN.MLTheory.CROWN.Graph.LinParams α)\n (... | [
{
"name": "evalLinear_from_paramStore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 27,
"n_chars": 1220,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -85,6 +85,17 @@
(ps.linearWB.get? id).map (irLinearOfLinParams (α := α)) := by
rfl
+/-- A present linear entry becomes the matching IR linear payload. -/
+theorem payloadOfParamStore_linear?_some
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ (p : NN.MLTheory... | {
"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_1d26f59dd04c_12 | 2fd1eb4d6f2e244a | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "evalLinear_missing_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalLinear,\n payloadOfParamStore_linear?_none (ps := ps) (id := id) hMissing]\n rfl",
... | [
{
"name": "payloadOfParamStore_linear?_none",
"text": "/-- Missing linear entries remain missing after converting to an IR payload. -/\ntheorem payloadOfParamStore_linear?_none\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (h : ps.linearWB.get? id = none) :\n ... | [
{
"name": "evalLinear_missing_from_paramStore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 726,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": tru... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -85,6 +85,15 @@
(ps.linearWB.get? id).map (irLinearOfLinParams (α := α)) := by
rfl
+/-- Missing linear entries remain missing after converting to an IR payload. -/
+theorem payloadOfParamStore_linear?_none
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ (h : 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_1d26f59dd04c_13 | 6449065b68767d59 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "evalConv2D_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hInfer :\n OpContracts.inferConv2dCHWOutShape cfg.inC cfg.outC cfg.kH cfg.kW cfg.stride\n cf... | [
{
"name": "payloadOfParamStore_conv2d?_some",
"text": "/-- A present convolution entry becomes the matching IR convolution payload. -/\ntheorem payloadOfParamStore_conv2d?_some\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (cfg : NN.MLTheory.CROWN.Graph.Conv2DP... | [
{
"name": "evalConv2D_from_paramStore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 37,
"n_chars": 1980,
"n_subproofs": 1,
"n_tactics": 16,
"cyclomatic": 1,
"n_automation": 2,
"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.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -85,6 +85,17 @@
(ps.conv2dCfg.get? id).map (irConv2DOfGraphParams (α := α)) := by
rfl
+/-- A present convolution entry becomes the matching IR convolution payload. -/
+theorem payloadOfParamStore_conv2d?_some
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ (cf... | {
"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_1d26f59dd04c_14 | 0e3f6ae888d79f43 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "evalConv2D_missing_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalConv2D,\n payloadOfParamStore_conv2d?_none (ps := ps) (id := id) hMissing]\n rfl",
... | [
{
"name": "payloadOfParamStore_conv2d?_none",
"text": "/-- Missing convolution entries remain missing after converting to an IR payload. -/\ntheorem payloadOfParamStore_conv2d?_none\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (h : ps.conv2dCfg.get? id = none)... | [
{
"name": "evalConv2D_missing_from_paramStore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 789,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": tru... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -85,6 +85,15 @@
(ps.conv2dCfg.get? id).map (irConv2DOfGraphParams (α := α)) := by
rfl
+/-- Missing convolution entries remain missing after converting to an IR payload. -/
+theorem payloadOfParamStore_conv2d?_none
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ ... | {
"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_1d26f59dd04c_15 | 0d924dbabea3065e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "evalBatchNorm2DNchwEval_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalBatchNorm2DNchwEval,\n payloadOfParamStore_batchNorm2dNchwEval?_some (ps := ps) ... | [
{
"name": "payloadOfParamStore_batchNorm2dNchwEval?_some",
"text": "/-- A present BatchNorm entry becomes the matching IR BatchNorm payload. -/\ntheorem payloadOfParamStore_batchNorm2dNchwEval?_some\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (p : NN.MLTheory... | [
{
"name": "evalBatchNorm2DNchwEval_from_paramStore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 32,
"n_chars": 1456,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -86,6 +86,17 @@
(irBatchNorm2DNchwEvalOfGraphParams (α := α)) := by
rfl
+/-- A present BatchNorm entry becomes the matching IR BatchNorm payload. -/
+theorem payloadOfParamStore_batchNorm2dNchwEval?_some
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ (p : 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_1d26f59dd04c_16 | 60ff56a2c7945716 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "evalBatchNorm2DNchwEval_missing_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalBatchNorm2DNchwEval,\n payloadOfParamStore_batchNorm2dNchwEval?_none (ps... | [
{
"name": "payloadOfParamStore_batchNorm2dNchwEval?_none",
"text": "/-- Missing BatchNorm entries remain missing after converting to an IR payload. -/\ntheorem payloadOfParamStore_batchNorm2dNchwEval?_none\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (h : ps.b... | [
{
"name": "evalBatchNorm2DNchwEval_missing_from_paramStore",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 19,
"n_chars": 878,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automati... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -86,6 +86,17 @@
(irBatchNorm2DNchwEvalOfGraphParams (α := α)) := by
rfl
+/-- Missing BatchNorm entries remain missing after converting to an IR payload. -/
+theorem payloadOfParamStore_batchNorm2dNchwEval?_none
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ ... | {
"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_1d26f59dd04c_17 | e65d03c4372649d1 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "evalAt_const_from_paramStore_of_getNode",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalAt, hNode,\n evalConst_from_paramStore (ps := ps) (id := id) (s := s) (v := v) h... | [
{
"name": "evalConst_from_paramStore",
"text": "/-- `Graph.evalConst` reads flat constants through the `ParamStore` bridge at any node id. -/\ntheorem evalConst_from_paramStore\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α)\n (id : Nat) (s : Shape)\n (v : Tensor α (.dim (... | [
{
"name": "evalAt_const_from_paramStore_of_getNode",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 24,
"n_chars": 1075,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -96,6 +96,24 @@
rw [payloadOfParamStore_const?_eq, h]
rfl
+/-- `Graph.evalConst` reads flat constants through the `ParamStore` bridge at any node id. -/
+theorem evalConst_from_paramStore
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α)
+ (id : Nat) (s : Shape)
+ (v : 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_1d26f59dd04c_18 | 574949f0763cb203 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 1 | [
{
"theorem_name": "evalAt_const_missing_from_paramStore_of_getNode",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalAt, hNode,\n evalConst_missing_from_paramStore (ps := ps) (id := id) (s ... | [
{
"name": "evalConst_missing_from_paramStore",
"text": "/-- Missing `ParamStore.constVals` entries are rejected by `Graph.evalConst` at any node id. -/\ntheorem evalConst_missing_from_paramStore\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α)\n (id : Nat) (s : Shape)\n (hM... | [
{
"name": "evalAt_const_missing_from_paramStore_of_getNode",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 21,
"n_chars": 921,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automati... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -94,6 +94,19 @@
rw [payloadOfParamStore_const?_eq, h]
rfl
+/-- Missing `ParamStore.constVals` entries are rejected by `Graph.evalConst` at any node id. -/
+theorem evalConst_missing_from_paramStore
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α)
+ (id : Nat) (s : Shape)
+ (... | {
"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_1d26f59dd04c_19 | 8d1851247b9bd9f7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "evalLinear_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalLinear,\n payloadOfParamStore_linear?_some (ps := ps) (id := id)\n ({ m := outDim, n := ... | [
{
"name": "payloadOfParamStore_linear?_some",
"text": "/-- A present linear entry becomes the matching IR linear payload. -/\ntheorem payloadOfParamStore_linear?_some\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (p : NN.MLTheory.CROWN.Graph.LinParams α)\n (... | [
{
"name": "evalAt_linear_from_paramStore_of_getNode",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 38,
"n_chars": 1611,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_onl... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -85,6 +85,17 @@
(ps.linearWB.get? id).map (irLinearOfLinParams (α := α)) := by
rfl
+/-- A present linear entry becomes the matching IR linear payload. -/
+theorem payloadOfParamStore_linear?_some
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ (p : NN.MLTheory... | {
"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_1d26f59dd04c_20 | 77f326bbd3e8ac96 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "evalLinear_missing_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalLinear,\n payloadOfParamStore_linear?_none (ps := ps) (id := id) hMissing]\n rfl",
... | [
{
"name": "payloadOfParamStore_linear?_none",
"text": "/-- Missing linear entries remain missing after converting to an IR payload. -/\ntheorem payloadOfParamStore_linear?_none\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (h : ps.linearWB.get? id = none) :\n ... | [
{
"name": "evalAt_linear_missing_from_paramStore_of_getNode",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 24,
"n_chars": 989,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automat... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -85,6 +85,15 @@
(ps.linearWB.get? id).map (irLinearOfLinParams (α := α)) := by
rfl
+/-- Missing linear entries remain missing after converting to an IR payload. -/
+theorem payloadOfParamStore_linear?_none
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ (h : 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_1d26f59dd04c_21 | facea7dae23f9bb0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "evalConv2D_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 16,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hInfer :\n OpContracts.inferConv2dCHWOutShape cfg.inC cfg.outC cfg.kH cfg.kW cfg.stride\n cf... | [
{
"name": "payloadOfParamStore_conv2d?_some",
"text": "/-- A present convolution entry becomes the matching IR convolution payload. -/\ntheorem payloadOfParamStore_conv2d?_some\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (cfg : NN.MLTheory.CROWN.Graph.Conv2DP... | [
{
"name": "evalAt_conv2d_from_paramStore_of_getNode",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 67,
"n_chars": 3276,
"n_subproofs": 2,
"n_tactics": 29,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 2,
"n_structural": 0,
"automation_on... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -85,6 +85,17 @@
(ps.conv2dCfg.get? id).map (irConv2DOfGraphParams (α := α)) := by
rfl
+/-- A present convolution entry becomes the matching IR convolution payload. -/
+theorem payloadOfParamStore_conv2d?_some
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ (cf... | {
"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_1d26f59dd04c_22 | 4a2d0d55d6750fbd | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "evalConv2D_missing_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalConv2D,\n payloadOfParamStore_conv2d?_none (ps := ps) (id := id) hMissing]\n rfl",
... | [
{
"name": "payloadOfParamStore_conv2d?_none",
"text": "/-- Missing convolution entries remain missing after converting to an IR payload. -/\ntheorem payloadOfParamStore_conv2d?_none\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (h : ps.conv2dCfg.get? id = none)... | [
{
"name": "evalAt_conv2d_missing_from_paramStore_of_getNode",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 30,
"n_chars": 1287,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automa... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -85,6 +85,15 @@
(ps.conv2dCfg.get? id).map (irConv2DOfGraphParams (α := α)) := by
rfl
+/-- Missing convolution entries remain missing after converting to an IR payload. -/
+theorem payloadOfParamStore_conv2d?_none
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ ... | {
"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_1d26f59dd04c_23 | bfd0dbc90bbddd7d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 23 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "evalBatchNorm2DNchwEval_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalBatchNorm2DNchwEval,\n payloadOfParamStore_batchNorm2dNchwEval?_some (ps := ps) ... | [
{
"name": "payloadOfParamStore_batchNorm2dNchwEval?_some",
"text": "/-- A present BatchNorm entry becomes the matching IR BatchNorm payload. -/\ntheorem payloadOfParamStore_batchNorm2dNchwEval?_some\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (p : NN.MLTheory... | [
{
"name": "evalAt_batchNorm2dNchwEval_from_paramStore_of_getNode",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 47,
"n_chars": 2234,
"n_subproofs": 1,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -86,6 +86,17 @@
(irBatchNorm2DNchwEvalOfGraphParams (α := α)) := by
rfl
+/-- A present BatchNorm entry becomes the matching IR BatchNorm payload. -/
+theorem payloadOfParamStore_batchNorm2dNchwEval?_some
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ (p : 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_1d26f59dd04c_24 | 7263c9bd25333147 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/PayloadBridge.lean | PayloadBridge | 24 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 15 | 2 | [
{
"theorem_name": "evalBatchNorm2DNchwEval_missing_from_paramStore",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [Graph.evalBatchNorm2DNchwEval,\n payloadOfParamStore_batchNorm2dNchwEval?_none (ps... | [
{
"name": "payloadOfParamStore_batchNorm2dNchwEval?_none",
"text": "/-- Missing BatchNorm entries remain missing after converting to an IR payload. -/\ntheorem payloadOfParamStore_batchNorm2dNchwEval?_none\n {α : Type} [Context α]\n (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)\n (h : ps.b... | [
{
"name": "evalAt_batchNorm2dNchwEval_missing_from_paramStore_of_getNode",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 24,
"n_chars": 1125,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.PayloadOps
/-!
# ParamStore to IR Payload Bridge
Th... | @@ -86,6 +86,17 @@
(irBatchNorm2DNchwEvalOfGraphParams (α := α)) := by
rfl
+/-- Missing BatchNorm entries remain missing after converting to an IR payload. -/
+theorem payloadOfParamStore_batchNorm2dNchwEval?_none
+ {α : Type} [Context α]
+ (ps : NN.MLTheory.CROWN.Graph.ParamStore α) (id : Nat)
+ ... | {
"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_1baf7070de6d_10 | 64e8ab14d85b2b40 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/ReLU/Approximation/CompactSet.lean | CompactSet | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 30 | 1 | [
{
"theorem_name": "approx_pow_linFormC",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro ε hε\n let R : ℝ := max 1 ‖linFormC K w‖\n have hR : 0 < R := lt_of_lt_of_le zero_lt_one (le_max_left 1 ‖linFo... | [
{
"name": "relu_universal_approximation_pow_Icc",
"text": "/--\nUniform approximation of the power function on a bounded interval by a 1D ReLU MLP.\n\nThis packages the 1D Lipschitz ReLU approximation theorem for the specific function\n`x ↦ x^d` on `[-R,R]`.\n-/\ntheorem relu_universal_approximation_pow_Icc... | [
{
"name": "approx_pow_linFormC",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 31,
"n_chars": 1418,
"n_subproofs": 7,
"n_tactics": 25,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 5,
"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 Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | @@ -681,6 +681,42 @@
_ = ((Nat.succ d) * R ^ (Nat.succ d - 1)) * |x - y| := by
simp
+/--
+Uniform approximation of the power function on a bounded interval by a 1D ReLU MLP.
+
+This packages the 1D Lipschitz ReLU approximation theorem for the specific function
+`x ↦ x^d` on `[-R,R]`.
+-/
+theorem relu... | {
"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_1baf7070de6d_11 | 7f9df3a76d23c6a4 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/ReLU/Approximation/CompactSet.lean | CompactSet | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 30 | 1 | [
{
"theorem_name": "approx_coordProd_fin",
"depth": 1,
"n_commands": 0,
"n_lines": 70,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Rewrite the product using the polarization identity, then approximate that RHS.\n let C : ℝ := (2 : ... | [
{
"name": "sum_fintype",
"text": "/-- Finite sums preserve `ApproxOnC` (Fintype-indexed). -/\ntheorem sum_fintype {n : Nat} {K : Set (ReLUMlpBridge.TensorVec n)}\n {ι : Type} [Fintype ι] (f : ι → C(K, ℝ)) (hf : ∀ i : ι, ApproxOnC (n := n) K (f i)) :\n ApproxOnC (n := n) K (∑ i : ι, f i) := by\n class... | [
{
"name": "approx_coordProd_fin",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 10,
"n_lines": 82,
"n_chars": 3999,
"n_subproofs": 14,
"n_tactics": 49,
"cyclomatic": 1,
"n_automation": 10,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | @@ -333,6 +333,16 @@
simpa [Finset.sum_insert ha, add_comm, add_left_comm, add_assoc] using
(add (n := n) (K := K) (f := f a) (g := ∑ i ∈ s, f i) ha' ih')
+/-- Finite sums preserve `ApproxOnC` (Fintype-indexed). -/
+theorem sum_fintype {n : Nat} {K : Set (ReLUMlpBridge.TensorVec n)}
+ {ι : Type} [F... | {
"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_1baf7070de6d_12 | f89407c25ae98e57 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/ReLU/Approximation/CompactSet.lean | CompactSet | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 30 | 1 | [
{
"theorem_name": "relu_universal_approximation_pow_Icc",
"depth": 1,
"n_commands": 0,
"n_lines": 23,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro ε hε\n have hR0 : 0 ≤ R := le_of_lt hR\n have hab : (-R) < R := by nlinarith\n let L : ℝ := ... | [
{
"name": "pow_lipschitz_Icc",
"text": "/--\nLipschitz bound for the power function on a bounded interval.\n\nFor `x,y ∈ [-R,R]`, the map `u ↦ u^d` is Lipschitz with constant `d * R^(d-1)` (with the\nconvention that the `d=0` case is constant).\n-/\nlemma pow_lipschitz_Icc {R : ℝ} (hR : 0 ≤ R) :\n ∀ d : ... | [
{
"name": "approx_coordProd",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 11,
"n_lines": 26,
"n_chars": 1096,
"n_subproofs": 2,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_ne... | 8 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | @@ -852,6 +852,87 @@
fun k => stdBasis (n := n) i k - stdBasis (n := n) j k
/--
+Lipschitz bound for the power function on a bounded interval.
+
+For `x,y ∈ [-R,R]`, the map `u ↦ u^d` is Lipschitz with constant `d * R^(d-1)` (with the
+convention that the `d=0` case is constant).
+-/
+lemma pow_lipschitz_Icc {R :... | {
"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_1baf7070de6d_14 | 4effb58731362af7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/ReLU/Approximation/CompactSet.lean | CompactSet | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 30 | 1 | [
{
"theorem_name": "approx_pow_linFormC",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro ε hε\n let R : ℝ := max 1 ‖linFormC K w‖\n have hR : 0 < R := lt_of_lt_of_le zero_lt_one (le_max_left 1 ‖linFo... | [
{
"name": "relu_universal_approximation_pow_Icc",
"text": "/--\nUniform approximation of the power function on a bounded interval by a 1D ReLU MLP.\n\nThis packages the 1D Lipschitz ReLU approximation theorem for the specific function\n`x ↦ x^d` on `[-R,R]`.\n-/\ntheorem relu_universal_approximation_pow_Icc... | [
{
"name": "approx_aeval_coord_monomial",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 14,
"n_lines": 42,
"n_chars": 2205,
"n_subproofs": 3,
"n_tactics": 31,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 1,
"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.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | @@ -932,6 +932,42 @@
_ = ((Nat.succ d) * R ^ (Nat.succ d - 1)) * |x - y| := by
simp
+/--
+Uniform approximation of the power function on a bounded interval by a 1D ReLU MLP.
+
+This packages the 1D Lipschitz ReLU approximation theorem for the specific function
+`x ↦ x^d` on `[-R,R]`.
+-/
+theorem relu... | {
"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_1baf7070de6d_15 | 56fecd3a07b0f0b2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/ReLU/Approximation/CompactSet.lean | CompactSet | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 30 | 1 | [
{
"theorem_name": "approx_pow_linFormC",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro ε hε\n let R : ℝ := max 1 ‖linFormC K w‖\n have hR : 0 < R := lt_of_lt_of_le zero_lt_one (le_max_left 1 ‖linFo... | [
{
"name": "relu_universal_approximation_pow_Icc",
"text": "/--\nUniform approximation of the power function on a bounded interval by a 1D ReLU MLP.\n\nThis packages the 1D Lipschitz ReLU approximation theorem for the specific function\n`x ↦ x^d` on `[-R,R]`.\n-/\ntheorem relu_universal_approximation_pow_Icc... | [
{
"name": "approx_aeval_coord",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 15,
"n_lines": 47,
"n_chars": 2172,
"n_subproofs": 3,
"n_tactics": 36,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_... | 12 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | @@ -932,6 +932,42 @@
_ = ((Nat.succ d) * R ^ (Nat.succ d - 1)) * |x - y| := by
simp
+/--
+Uniform approximation of the power function on a bounded interval by a 1D ReLU MLP.
+
+This packages the 1D Lipschitz ReLU approximation theorem for the specific function
+`x ↦ x^d` on `[-R,R]`.
+-/
+theorem relu... | {
"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_1baf7070de6d_16 | af0931116dec74d2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/ReLU/Approximation/CompactSet.lean | CompactSet | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 30 | 1 | [
{
"theorem_name": "relu_universal_approximation_pow_Icc",
"depth": 1,
"n_commands": 0,
"n_lines": 23,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro ε hε\n have hR0 : 0 ≤ R := le_of_lt hR\n have hab : (-R) < R := by nlinarith\n let L : ℝ := ... | [
{
"name": "pow_lipschitz_Icc",
"text": "/--\nLipschitz bound for the power function on a bounded interval.\n\nFor `x,y ∈ [-R,R]`, the map `u ↦ u^d` is Lipschitz with constant `d * R^(d-1)` (with the\nconvention that the `d=0` case is constant).\n-/\nlemma pow_lipschitz_Icc {R : ℝ} (hR : 0 ≤ R) :\n ∀ d : ... | [
{
"name": "approxOnC_of_mem_coordSubalg",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 17,
"n_lines": 20,
"n_chars": 803,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 14 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | @@ -872,6 +872,87 @@
fun k => stdBasis (n := n) i k - stdBasis (n := n) j k
/--
+Lipschitz bound for the power function on a bounded interval.
+
+For `x,y ∈ [-R,R]`, the map `u ↦ u^d` is Lipschitz with constant `d * R^(d-1)` (with the
+convention that the `d=0` case is constant).
+-/
+lemma pow_lipschitz_Icc {R :... | {
"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_1baf7070de6d_17 | 593fb55149488386 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/ReLU/Approximation/CompactSet.lean | CompactSet | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 30 | 1 | [
{
"theorem_name": "relu_universal_approximation_pow_Icc",
"depth": 1,
"n_commands": 0,
"n_lines": 23,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro ε hε\n have hR0 : 0 ≤ R := le_of_lt hR\n have hab : (-R) < R := by nlinarith\n let L : ℝ := ... | [
{
"name": "pow_lipschitz_Icc",
"text": "/--\nLipschitz bound for the power function on a bounded interval.\n\nFor `x,y ∈ [-R,R]`, the map `u ↦ u^d` is Lipschitz with constant `d * R^(d-1)` (with the\nconvention that the `d=0` case is constant).\n-/\nlemma pow_lipschitz_Icc {R : ℝ} (hR : 0 ≤ R) :\n ∀ d : ... | [
{
"name": "relu_universal_approximation_compact",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 17,
"n_lines": 106,
"n_chars": 5321,
"n_subproofs": 16,
"n_tactics": 80,
"cyclomatic": 4,
"n_automation": 11,
"n_rewrites": 0,
"n_structural": 10,
"automation_o... | 14 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.MvPolynomial.Eval
public import Mathlib.Algebra.Ring.GeomSum
public import Mathlib.Data.Finsupp.Multiset
p... | @@ -872,6 +872,87 @@
fun k => stdBasis (n := n) i k - stdBasis (n := n) j k
/--
+Lipschitz bound for the power function on a bounded interval.
+
+For `x,y ∈ [-R,R]`, the map `u ↦ u^d` is Lipschitz with constant `d * R^(d-1)` (with the
+convention that the `d=0` case is constant).
+-/
+lemma pow_lipschitz_Icc {R :... | {
"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_550946849b63_0 | 835ae1dbda02c7e1 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/StateSpace/MambaCausality.lean | MambaCausality | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "selectiveMamba_runList_append_outputs_prefix",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [Models.SelectiveMambaBlockSpec.runList] using\n selectiveMamba_runListAux_append_out... | [
{
"name": "selectiveMamba_runListAux_append_outputs_prefix",
"text": "/--\nFull selective Mamba prefix causality for the internal runner.\n\nThe internal runner carries a newest-first causal convolution history. Even with that extra state,\nfuture input tokens only affect future outputs.\n-/\ntheorem selec... | [
{
"name": "selectiveMamba_runList_append_outputs_prefix",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 631,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Models.Mamba
public import NN.Spec.Models.S4
/-!
# Causality of S4/Mamba-style recurrent blocks
This file proves the sequence-causality property expected of state-spac... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Models.Mamba
public import NN.Spec.Models.S4
/-!
# Causality of S4/Mamba-style recurrent blocks
This file proves the sequence-causality property expected of state-spac... | @@ -38,6 +38,25 @@
variable {inputDim stateDim outputDim innerDim convWidth : Nat}
/--
+Full selective Mamba prefix causality for the internal runner.
+
+The internal runner carries a newest-first causal convolution history. Even with that extra state,
+future input tokens only affect future outputs.
+-/
+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_b43e8c5fefa5_0 | 05246de5053dfb32 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_exact_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact exact_certified_step_of_... | [
{
"name": "exact_certified_step_of_direction",
"text": "/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/\ntheorem exact_certified_step_of_direction {m n : Nat}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : MatrixTensor α m n)\n (... | [
{
"name": "update_has_exact_certified_step",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 15,
"n_chars": 729,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"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.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -518,6 +518,18 @@
refine ⟨rfl, ?_⟩
exact horth buffer
+/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/
+theorem exact_certified_step_of_direction {m n : Nat}
+ (state : State α (.dim m (.dim n .scalar)))
+ (params grads direction : MatrixTensor α m n)
+ (hd... | {
"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_b43e8c5fefa5_1 | 2c5e8bef0498ba1f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_exact_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact exact_certified_step_of_... | [
{
"name": "exact_certified_step_of_direction",
"text": "/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/\ntheorem exact_certified_step_of_direction {m n : Nat}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : MatrixTensor α m n)\n (... | [
{
"name": "update_has_exact_certified_step_of_backend",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 16,
"n_chars": 793,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_on... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -518,6 +518,18 @@
refine ⟨rfl, ?_⟩
exact horth buffer
+/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/
+theorem exact_certified_step_of_direction {m n : Nat}
+ (state : State α (.dim m (.dim n .scalar)))
+ (params grads direction : MatrixTensor α m n)
+ (hd... | {
"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_b43e8c5fefa5_2 | 3c59aa8c5d582fc5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_exact_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact exact_certified_step_of_... | [
{
"name": "exact_certified_step_of_direction",
"text": "/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/\ntheorem exact_certified_step_of_direction {m n : Nat}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : MatrixTensor α m n)\n (... | [
{
"name": "update_has_exact_certified_step_of_buffer",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 587,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_onl... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -509,6 +509,18 @@
params_eq :
(update state params grads).2 = subSpec params (scaleSpec direction state.lr)
+/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/
+theorem exact_certified_step_of_direction {m n : Nat}
+ (state : State α (.dim m (.dim n .scalar)))
+ ... | {
"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_b43e8c5fefa5_3 | 3bf0266b0af8b253 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_exact_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact exact_certified_step_of_... | [
{
"name": "exact_certified_step_of_direction",
"text": "/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/\ntheorem exact_certified_step_of_direction {m n : Nat}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : MatrixTensor α m n)\n (... | [
{
"name": "update_has_exact_certified_step_of_checked_backend",
"fan_in": 4,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 27,
"n_chars": 1169,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"auto... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -509,6 +509,18 @@
params_eq :
(update state params grads).2 = subSpec params (scaleSpec direction state.lr)
+/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/
+theorem exact_certified_step_of_direction {m n : Nat}
+ (state : State α (.dim m (.dim n .scalar)))
+ ... | {
"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_b43e8c5fefa5_4 | 384fac7bab4547e5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_exact_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact exact_certified_step_of_... | [
{
"name": "exact_certified_step_of_direction",
"text": "/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/\ntheorem exact_certified_step_of_direction {m n : Nat}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : MatrixTensor α m n)\n (... | [
{
"name": "init_has_exact_certified_step_of_checked_backend",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 20,
"n_chars": 852,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automat... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -509,6 +509,18 @@
params_eq :
(update state params grads).2 = subSpec params (scaleSpec direction state.lr)
+/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/
+theorem exact_certified_step_of_direction {m n : Nat}
+ (state : State α (.dim m (.dim n .scalar)))
+ ... | {
"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_b43e8c5fefa5_5 | cb7e62d91446c4ac | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_exact_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact exact_certified_step_of_... | [
{
"name": "exact_certified_step_of_direction",
"text": "/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/\ntheorem exact_certified_step_of_direction {m n : Nat}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : MatrixTensor α m n)\n (... | [
{
"name": "update_has_exact_certified_step_newtonSchulz_fixed_checked",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 28,
"n_chars": 1233,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -509,6 +509,18 @@
params_eq :
(update state params grads).2 = subSpec params (scaleSpec direction state.lr)
+/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/
+theorem exact_certified_step_of_direction {m n : Nat}
+ (state : State α (.dim m (.dim n .scalar)))
+ ... | {
"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_b43e8c5fefa5_6 | 95a038de22998899 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_exact_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact exact_certified_step_of_... | [
{
"name": "exact_certified_step_of_direction",
"text": "/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/\ntheorem exact_certified_step_of_direction {m n : Nat}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : MatrixTensor α m n)\n (... | [
{
"name": "init_has_exact_certified_step_newtonSchulz_fixed_checked",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 26,
"n_chars": 1032,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -509,6 +509,18 @@
params_eq :
(update state params grads).2 = subSpec params (scaleSpec direction state.lr)
+/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/
+theorem exact_certified_step_of_direction {m n : Nat}
+ (state : State α (.dim m (.dim n .scalar)))
+ ... | {
"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_b43e8c5fefa5_7 | 328a72f08ab6ec04 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_approx_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact approx_certified_step_o... | [
{
"name": "approx_certified_step_of_direction",
"text": "/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/\ntheorem approx_certified_step_of_direction {m n : Nat} {eps : α}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : Ma... | [
{
"name": "update_has_approx_certified_step",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 15,
"n_chars": 693,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"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.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -518,6 +518,18 @@
refine ⟨rfl, ?_⟩
exact horth buffer
+/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/
+theorem approx_certified_step_of_direction {m n : Nat} {eps : α}
+ (state : State α (.dim m (.dim n .scalar)))
+ (params grads direction : Matri... | {
"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_b43e8c5fefa5_8 | daab5b3bf9f830a0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_approx_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact approx_certified_step_o... | [
{
"name": "approx_certified_step_of_direction",
"text": "/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/\ntheorem approx_certified_step_of_direction {m n : Nat} {eps : α}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : Ma... | [
{
"name": "update_has_approx_certified_step_of_backend",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 16,
"n_chars": 817,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_o... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -518,6 +518,18 @@
refine ⟨rfl, ?_⟩
exact horth buffer
+/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/
+theorem approx_certified_step_of_direction {m n : Nat} {eps : α}
+ (state : State α (.dim m (.dim n .scalar)))
+ (params grads direction : Matri... | {
"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_b43e8c5fefa5_9 | 1cea930dbf5f748a | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_approx_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact approx_certified_step_o... | [
{
"name": "approx_certified_step_of_direction",
"text": "/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/\ntheorem approx_certified_step_of_direction {m n : Nat} {eps : α}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : Ma... | [
{
"name": "update_has_approx_certified_step_of_buffer",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 616,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_on... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -509,6 +509,18 @@
params_eq :
(update state params grads).2 = subSpec params (scaleSpec direction state.lr)
+/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/
+theorem approx_certified_step_of_direction {m n : Nat} {eps : α}
+ (state : State α (.dim m... | {
"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_b43e8c5fefa5_10 | af5513dfd3974977 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_approx_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact approx_certified_step_o... | [
{
"name": "approx_certified_step_of_direction",
"text": "/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/\ntheorem approx_certified_step_of_direction {m n : Nat} {eps : α}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : Ma... | [
{
"name": "update_has_approx_certified_step_of_checked_backend",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 27,
"n_chars": 1201,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"aut... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -509,6 +509,18 @@
params_eq :
(update state params grads).2 = subSpec params (scaleSpec direction state.lr)
+/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/
+theorem approx_certified_step_of_direction {m n : Nat} {eps : α}
+ (state : State α (.dim m... | {
"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_b43e8c5fefa5_11 | 06ab5138da2475f4 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_approx_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact approx_certified_step_o... | [
{
"name": "approx_certified_step_of_direction",
"text": "/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/\ntheorem approx_certified_step_of_direction {m n : Nat} {eps : α}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : Ma... | [
{
"name": "init_has_approx_certified_step_of_checked_backend",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 20,
"n_chars": 887,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automa... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -509,6 +509,18 @@
params_eq :
(update state params grads).2 = subSpec params (scaleSpec direction state.lr)
+/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/
+theorem approx_certified_step_of_direction {m n : Nat} {eps : α}
+ (state : State α (.dim m... | {
"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_b43e8c5fefa5_12 | 9218989c9d40086f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_approx_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact approx_certified_step_o... | [
{
"name": "approx_certified_step_of_direction",
"text": "/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/\ntheorem approx_certified_step_of_direction {m n : Nat} {eps : α}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : Ma... | [
{
"name": "update_has_approx_certified_step_newtonSchulz_checked",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 30,
"n_chars": 1395,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"a... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -509,6 +509,18 @@
params_eq :
(update state params grads).2 = subSpec params (scaleSpec direction state.lr)
+/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/
+theorem approx_certified_step_of_direction {m n : Nat} {eps : α}
+ (state : State α (.dim m... | {
"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_b43e8c5fefa5_13 | b5cc9971961b6c52 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_approx_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact approx_certified_step_o... | [
{
"name": "approx_certified_step_of_direction",
"text": "/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/\ntheorem approx_certified_step_of_direction {m n : Nat} {eps : α}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : Ma... | [
{
"name": "init_has_approx_certified_step_newtonSchulz_checked",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 28,
"n_chars": 1183,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"aut... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -509,6 +509,18 @@
params_eq :
(update state params grads).2 = subSpec params (scaleSpec direction state.lr)
+/-- A certified approximate direction for the fresh buffer gives a certified approximate Muon step. -/
+theorem approx_certified_step_of_direction {m n : Nat} {eps : α}
+ (state : State α (.dim m... | {
"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_b43e8c5fefa5_14 | eac553c25717604b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 3 | [
{
"theorem_name": "matMul_right_identity_real",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n apply matrix_ext\n intro i j\n calc\n get2 (matMulSpec A (identityTensorSpec (α := ℝ) n)) i j... | [
{
"name": "get2_identityTensorSpec_real",
"text": "lemma get2_identityTensorSpec_real {n : Nat} (i j : Fin n) :\n get2 (identityTensorSpec (α := ℝ) n) i j = if i = j then 1 else 0 := by\n cases n with\n | zero => exact Fin.elim0 i\n | succ n =>\n by_cases h : i = j\n · subst j\n simp ... | [
{
"name": "matMul_right_identity_real",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 19,
"n_chars": 756,
"n_subproofs": 0,
"n_tactics": 15,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 5,
"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.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -518,9 +518,36 @@
def HasPositiveQRPivots {m n : Nat} (buffer : MatrixTensor ℝ m n) : Prop :=
∀ j : Fin n, 0 < get2 (qrRSpec buffer) j j
+lemma get2_identityTensorSpec_real {n : Nat} (i j : Fin n) :
+ get2 (identityTensorSpec (α := ℝ) n) i j = if i = j then 1 else 0 := by
+ cases n with
+ | zero => exact ... | {
"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_b43e8c5fefa5_15 | 5adfb1d70719d428 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "add_scaled_three_eq_scale_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply matrix_ext\n intro i j\n calc\n get2 (addSpec (addSpec (scaleSpec Q a) (scaleSpec Q b)) (scaleSpe... | [
{
"name": "get2_scaleSpec_real",
"text": "/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/\nlemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)\n (i : Fin m) (j : Fin n) :\n get2 (scaleSpec A c) i j = get2 A i j * c := by\n cases A with\n | dim rows =>\n cases hrow ... | [
{
"name": "add_scaled_three_eq_scale_sum",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 21,
"n_chars": 772,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 3,
"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.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -548,6 +548,18 @@
| scalar b =>
simp [addSpec, map2Spec, get2_eq, get_eq, hA, hB, hAj, hBj]
+/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/
+lemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)
+ (i : Fin m) (j : Fin n) :
+ get2 (scaleSpec A c) i 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_b43e8c5fefa5_16 | f912d7dd50302670 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "add_scaled_three_eq_scale_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply matrix_ext\n intro i j\n calc\n get2 (addSpec (addSpec (scaleSpec Q a) (scaleSpec Q b)) (scaleSpe... | [
{
"name": "get2_scaleSpec_real",
"text": "/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/\nlemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)\n (i : Fin m) (j : Fin n) :\n get2 (scaleSpec A c) i j = get2 A i j * c := by\n cases A with\n | dim rows =>\n cases hrow ... | [
{
"name": "add_scaled_three_eq_self_of_coeff_sum_one",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 19,
"n_chars": 596,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 3,
"n_structural": 3,
"automation_on... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -548,6 +548,18 @@
| scalar b =>
simp [addSpec, map2Spec, get2_eq, get_eq, hA, hB, hAj, hBj]
+/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/
+lemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)
+ (i : Fin m) (j : Fin n) :
+ get2 (scaleSpec A c) i 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_b43e8c5fefa5_17 | b813ed84e422ebdf | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "add_scaled_three_eq_scale_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply matrix_ext\n intro i j\n calc\n get2 (addSpec (addSpec (scaleSpec Q a) (scaleSpec Q b)) (scaleSpe... | [
{
"name": "get2_scaleSpec_real",
"text": "/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/\nlemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)\n (i : Fin m) (j : Fin n) :\n get2 (scaleSpec A c) i j = get2 A i j * c := by\n cases A with\n | dim rows =>\n cases hrow ... | [
{
"name": "scale_hasExactColumnGram_of_square_eq_one",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 60,
"n_chars": 2557,
"n_subproofs": 2,
"n_tactics": 51,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 6,
"n_structural": 12,
"automation_... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -531,6 +531,18 @@
exact h (Fin.ext hv)
simp [identityTensorSpec, get2_eq, get_eq, h, hval]
+/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/
+lemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)
+ (i : Fin m) (j : Fin n) :
+ get2 (scaleSpec A c) i j = get2 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_b43e8c5fefa5_18 | 7bc228b40ee134ee | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "add_scaled_three_eq_scale_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply matrix_ext\n intro i j\n calc\n get2 (addSpec (addSpec (scaleSpec Q a) (scaleSpec Q b)) (scaleSpe... | [
{
"name": "get2_scaleSpec_real",
"text": "/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/\nlemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)\n (i : Fin m) (j : Fin n) :\n get2 (scaleSpec A c) i j = get2 A i j * c := by\n cases A with\n | dim rows =>\n cases hrow ... | [
{
"name": "scale_hasApproxColumnGram_of_exact_column_gram_of_square_error",
"fan_in": 2,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 83,
"n_chars": 3577,
"n_subproofs": 5,
"n_tactics": 72,
"cyclomatic": 1,
"n_automation": 12,
"n_rewrites": 8,
"n_structural"... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -531,6 +531,18 @@
exact h (Fin.ext hv)
simp [identityTensorSpec, get2_eq, get_eq, h, hval]
+/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/
+lemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)
+ (i : Fin m) (j : Fin n) :
+ get2 (scaleSpec A c) i j = get2 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_b43e8c5fefa5_19 | aa49d0cc27dd1af0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "add_scaled_three_eq_scale_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply matrix_ext\n intro i j\n calc\n get2 (addSpec (addSpec (scaleSpec Q a) (scaleSpec Q b)) (scaleSpe... | [
{
"name": "get2_scaleSpec_real",
"text": "/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/\nlemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)\n (i : Fin m) (j : Fin n) :\n get2 (scaleSpec A c) i j = get2 A i j * c := by\n cases A with\n | dim rows =>\n cases hrow ... | [
{
"name": "newtonSchulzStep_eq_scale_sum_of_exact_column_gram",
"fan_in": 4,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 22,
"n_chars": 875,
"n_subproofs": 3,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 2,
"auto... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -548,6 +548,18 @@
| scalar b =>
simp [addSpec, map2Spec, get2_eq, get_eq, hA, hB, hAj, hBj]
+/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/
+lemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)
+ (i : Fin m) (j : Fin n) :
+ get2 (scaleSpec A c) i 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_b43e8c5fefa5_20 | bd2c006c6559c30e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "add_scaled_three_eq_scale_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply matrix_ext\n intro i j\n calc\n get2 (addSpec (addSpec (scaleSpec Q a) (scaleSpec Q b)) (scaleSpe... | [
{
"name": "get2_scaleSpec_real",
"text": "/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/\nlemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)\n (i : Fin m) (j : Fin n) :\n get2 (scaleSpec A c) i j = get2 A i j * c := by\n cases A with\n | dim rows =>\n cases hrow ... | [
{
"name": "newtonSchulzFixedPoint_of_exact_column_gram_of_coeff_sum_one",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 21,
"n_chars": 689,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 3,... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -548,6 +548,18 @@
| scalar b =>
simp [addSpec, map2Spec, get2_eq, get_eq, hA, hB, hAj, hBj]
+/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/
+lemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)
+ (i : Fin m) (j : Fin n) :
+ get2 (scaleSpec A c) i 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_b43e8c5fefa5_21 | 0fef270425948d43 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "add_scaled_three_eq_scale_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply matrix_ext\n intro i j\n calc\n get2 (addSpec (addSpec (scaleSpec Q a) (scaleSpec Q b)) (scaleSpe... | [
{
"name": "get2_scaleSpec_real",
"text": "/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/\nlemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)\n (i : Fin m) (j : Fin n) :\n get2 (scaleSpec A c) i j = get2 A i j * c := by\n cases A with\n | dim rows =>\n cases hrow ... | [
{
"name": "newtonSchulzStep_hasExactColumnGram_of_exact_column_gram_of_sum_square_one",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 7,
"n_lines": 13,
"n_chars": 635,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_st... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -548,6 +548,18 @@
| scalar b =>
simp [addSpec, map2Spec, get2_eq, get_eq, hA, hB, hAj, hBj]
+/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/
+lemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)
+ (i : Fin m) (j : Fin n) :
+ get2 (scaleSpec A c) i 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_b43e8c5fefa5_22 | 7e5089759f6298d9 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "add_scaled_three_eq_scale_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply matrix_ext\n intro i j\n calc\n get2 (addSpec (addSpec (scaleSpec Q a) (scaleSpec Q b)) (scaleSpe... | [
{
"name": "get2_scaleSpec_real",
"text": "/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/\nlemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)\n (i : Fin m) (j : Fin n) :\n get2 (scaleSpec A c) i j = get2 A i j * c := by\n cases A with\n | dim rows =>\n cases hrow ... | [
{
"name": "newtonSchulzStep_hasApproxColumnGram_of_exact_column_gram_of_sum_square_error",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 17,
"n_chars": 775,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -548,6 +548,18 @@
| scalar b =>
simp [addSpec, map2Spec, get2_eq, get_eq, hA, hB, hAj, hBj]
+/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/
+lemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)
+ (i : Fin m) (j : Fin n) :
+ get2 (scaleSpec A c) i 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_b43e8c5fefa5_23 | 573b220caef133d7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 23 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "add_scaled_three_eq_scale_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply matrix_ext\n intro i j\n calc\n get2 (addSpec (addSpec (scaleSpec Q a) (scaleSpec Q b)) (scaleSpe... | [
{
"name": "get2_scaleSpec_real",
"text": "/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/\nlemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)\n (i : Fin m) (j : Fin n) :\n get2 (scaleSpec A c) i j = get2 A i j * c := by\n cases A with\n | dim rows =>\n cases hrow ... | [
{
"name": "newtonSchulzFixedPointCheckedExact_success_of_coeff_sum_one",
"fan_in": 4,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 13,
"n_chars": 630,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -548,6 +548,18 @@
| scalar b =>
simp [addSpec, map2Spec, get2_eq, get_eq, hA, hB, hAj, hBj]
+/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/
+lemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)
+ (i : Fin m) (j : Fin n) :
+ get2 (scaleSpec A c) i 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_b43e8c5fefa5_24 | d667a8636168d2d7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 24 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "add_scaled_three_eq_scale_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply matrix_ext\n intro i j\n calc\n get2 (addSpec (addSpec (scaleSpec Q a) (scaleSpec Q b)) (scaleSpe... | [
{
"name": "get2_scaleSpec_real",
"text": "/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/\nlemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)\n (i : Fin m) (j : Fin n) :\n get2 (scaleSpec A c) i j = get2 A i j * c := by\n cases A with\n | dim rows =>\n cases hrow ... | [
{
"name": "update_has_exact_certified_step_newtonSchulz_exact_gram_checked",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 12,
"n_lines": 36,
"n_chars": 1589,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -624,6 +624,18 @@
| scalar b =>
simp [addSpec, map2Spec, get2_eq, get_eq, hA, hB, hAj, hBj]
+/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/
+lemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)
+ (i : Fin m) (j : Fin n) :
+ get2 (scaleSpec A c) i 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_b43e8c5fefa5_25 | 0bc20df74ef1de1f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 25 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "add_scaled_three_eq_scale_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply matrix_ext\n intro i j\n calc\n get2 (addSpec (addSpec (scaleSpec Q a) (scaleSpec Q b)) (scaleSpe... | [
{
"name": "get2_scaleSpec_real",
"text": "/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/\nlemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)\n (i : Fin m) (j : Fin n) :\n get2 (scaleSpec A c) i j = get2 A i j * c := by\n cases A with\n | dim rows =>\n cases hrow ... | [
{
"name": "update_newtonSchulz_exact_gram_direction_has_exact_column_gram_checked",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 10,
"n_lines": 37,
"n_chars": 1675,
"n_subproofs": 0,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_str... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -598,6 +598,18 @@
| scalar b =>
simp [addSpec, map2Spec, get2_eq, get_eq, hA, hB, hAj, hBj]
+/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/
+lemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)
+ (i : Fin m) (j : Fin n) :
+ get2 (scaleSpec A c) i 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_b43e8c5fefa5_26 | 7bd7da048d3981af | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 26 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 5 | [
{
"theorem_name": "add_scaled_three_eq_scale_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply matrix_ext\n intro i j\n calc\n get2 (addSpec (addSpec (scaleSpec Q a) (scaleSpec Q b)) (scaleSpe... | [
{
"name": "get2_scaleSpec_real",
"text": "/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/\nlemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)\n (i : Fin m) (j : Fin n) :\n get2 (scaleSpec A c) i j = get2 A i j * c := by\n cases A with\n | dim rows =>\n cases hrow ... | [
{
"name": "init_has_exact_certified_step_newtonSchulz_exact_gram_checked",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 13,
"n_lines": 33,
"n_chars": 1289,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural":... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -641,6 +641,18 @@
| scalar b =>
simp [addSpec, map2Spec, get2_eq, get_eq, hA, hB, hAj, hBj]
+/-- Entry rule for matrix-shaped tensor scaling over `ℝ`. -/
+lemma get2_scaleSpec_real {m n : Nat} (A : MatrixTensor ℝ m n) (c : ℝ)
+ (i : Fin m) (j : Fin n) :
+ get2 (scaleSpec A c) i 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_b43e8c5fefa5_27 | 3e35b2bdc9ea63aa | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 27 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 3 | [
{
"theorem_name": "matMul_right_identity_real",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n apply matrix_ext\n intro i j\n calc\n get2 (matMulSpec A (identityTensorSpec (α := ℝ) n)) i j... | [
{
"name": "get2_identityTensorSpec_real",
"text": "lemma get2_identityTensorSpec_real {n : Nat} (i j : Fin n) :\n get2 (identityTensorSpec (α := ℝ) n) i j = if i = j then 1 else 0 := by\n cases n with\n | zero => exact Fin.elim0 i\n | succ n =>\n by_cases h : i = j\n · subst j\n simp ... | [
{
"name": "qrOrthogonalizer_exact_of_positive_pivots",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 29,
"n_chars": 1301,
"n_subproofs": 0,
"n_tactics": 20,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 3,
"n_structural": 6,
"automation_o... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -518,6 +518,19 @@
def HasPositiveQRPivots {m n : Nat} (buffer : MatrixTensor ℝ m n) : Prop :=
∀ j : Fin n, 0 < get2 (qrRSpec buffer) j j
+lemma get2_identityTensorSpec_real {n : Nat} (i j : Fin n) :
+ get2 (identityTensorSpec (α := ℝ) n) i j = if i = j then 1 else 0 := by
+ cases n with
+ | zero => exact ... | {
"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_b43e8c5fefa5_28 | 8d9ead4f4dbf234b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 28 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_exact_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact exact_certified_step_of_... | [
{
"name": "exact_certified_step_of_direction",
"text": "/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/\ntheorem exact_certified_step_of_direction {m n : Nat}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : MatrixTensor α m n)\n (... | [
{
"name": "update_has_exact_certified_step_qr",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 25,
"n_chars": 1037,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": fa... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -509,6 +509,18 @@
params_eq :
(update state params grads).2 = subSpec params (scaleSpec direction state.lr)
+/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/
+theorem exact_certified_step_of_direction {m n : Nat}
+ (state : State α (.dim m (.dim n .scalar)))
+ ... | {
"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_b43e8c5fefa5_29 | a19b73faef496a9e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/Muon.lean | Muon | 29 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "update_has_exact_certified_step",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine ⟨state.orthogonalizer.apply (update state params grads).1.buf, ?_⟩\n exact exact_certified_step_of_... | [
{
"name": "exact_certified_step_of_direction",
"text": "/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/\ntheorem exact_certified_step_of_direction {m n : Nat}\n (state : State α (.dim m (.dim n .scalar)))\n (params grads direction : MatrixTensor α m n)\n (... | [
{
"name": "init_has_exact_certified_step_qr",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 21,
"n_chars": 830,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"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.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.Optimization.OptimizerLaws
public import NN.Proofs.Tensor.Basic.FactorizationsOrthonormal
public import NN.Proofs.Tensor.Basic.LinearAlgebra
/-!
# Muon Orthogonaliz... | @@ -509,6 +509,18 @@
params_eq :
(update state params grads).2 = subSpec params (scaleSpec direction state.lr)
+/-- A certified exact direction for the fresh buffer gives a certified exact Muon step. -/
+theorem exact_certified_step_of_direction {m n : Nat}
+ (state : State α (.dim m (.dim n .scalar)))
+ ... | {
"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_555cf1ddf563_0 | e7b20dafaeb297e3 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphAlphaCrownTransferSoundness/Common.lean | Common | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 2 | [
{
"theorem_name": "castDimScalar_self",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n exact castDimScalar_proof_irrel h rfl t",
"n_chars": 45,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic":... | [
{
"name": "castDimScalar_proof_irrel",
"text": "/-- `castDimScalar` is proof-irrelevant in its equality argument. -/\nlemma castDimScalar_proof_irrel {n n' : Nat}\n (h₁ h₂ : n = n') (t : Tensor ℝ (.dim n .scalar)) :\n castDimScalar (α := ℝ) h₁ t = castDimScalar (α := ℝ) h₂ t := by\n have : h₁ = h₂ :=... | [
{
"name": "castDimScalar_self",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 6,
"n_chars": 182,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | @@ -95,9 +95,18 @@
@[simp] lemma real_one_one : (One.one : ℝ) = (1 : ℝ) := rfl
@[simp] lemma real_zero_zero : (Zero.zero : ℝ) = (0 : ℝ) := rfl
+/-- `castDimScalar` is proof-irrelevant in its equality argument. -/
+lemma castDimScalar_proof_irrel {n n' : Nat}
+ (h₁ h₂ : n = n') (t : Tensor ℝ (.dim n .scalar)) :
+... | {
"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_555cf1ddf563_1 | 0fd413d6ad6674ad | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphAlphaCrownTransferSoundness/Common.lean | Common | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "enclosesAtInput_castOut",
"depth": 1,
"n_commands": 0,
"n_lines": 81,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro hpar\n rcases hpar with ⟨hinDim, hvec⟩\n refine ⟨hinDim, ?_⟩\n -- The `x'` used to evaluate `xin` and the... | [
{
"name": "affineEvalAt_castAffineOut",
"text": "/-- `affineEvalAt` commutes with casting the output dimension of an affine form. -/\nlemma affineEvalAt_castAffineOut {inDim outDim outDim' : Nat}\n (h : outDim = outDim') (aff : AffineVec ℝ inDim outDim) (x : Tensor ℝ (.dim inDim .scalar)) :\n CrownCer... | [
{
"name": "enclosesAtInput_castOut",
"fan_in": 0,
"n_deps_direct": 6,
"n_deps_transitive": 6,
"n_lines": 98,
"n_chars": 4969,
"n_subproofs": 10,
"n_tactics": 65,
"cyclomatic": 4,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 13,
"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.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | @@ -149,6 +149,18 @@
castDimScalar (α := ℝ) h t = t := by
exact castDimScalar_proof_irrel h rfl t
+/-- `affineEvalAt` commutes with casting the output dimension of an affine form. -/
+lemma affineEvalAt_castAffineOut {inDim outDim outDim' : Nat}
+ (h : outDim = outDim') (aff : AffineVec ℝ inDim outDim) (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_555cf1ddf563_2 | 7688545fa71ce494 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphAlphaCrownTransferSoundness/Common.lean | Common | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "encloses_linear_signSplit",
"depth": 1,
"n_commands": 0,
"n_lines": 190,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hx' := (encloses_iff_toVec (lo := lo) (hi := hi) (x := x)).1 hx\n refine (encloses_iff_toVec... | [
{
"name": "get2_mat_neg",
"text": "lemma get2_mat_neg {m n : Nat}\n (W : Tensor ℝ (.dim m (.dim n .scalar))) (i : Fin m) (j : Fin n) :\n Spec.get2 (NN.MLTheory.CROWN.IBP.matNeg (α := ℝ) (m := m) (n := n) W) i j =\n (if Spec.get2 W i j > 0 then 0 else Spec.get2 W i j) := by\n cases W with\n | di... | [
{
"name": "encloses_linear_signSplit",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 5,
"n_lines": 217,
"n_chars": 10121,
"n_subproofs": 28,
"n_tactics": 180,
"cyclomatic": 1,
"n_automation": 19,
"n_rewrites": 0,
"n_structural": 5,
"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.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | @@ -152,6 +152,18 @@
| scalar w =>
simp [NN.MLTheory.CROWN.IBP.matPos, Spec.get2_eq, Spec.get_eq, hrow, hcol]
+lemma get2_mat_neg {m n : Nat}
+ (W : Tensor ℝ (.dim m (.dim n .scalar))) (i : Fin m) (j : Fin n) :
+ Spec.get2 (NN.MLTheory.CROWN.IBP.matNeg (α := ℝ) (m := m) (n := n) W) i 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_555cf1ddf563_3 | 8c7a8c78256f7ab3 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphAlphaCrownTransferSoundness/Common.lean | Common | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "alphaRelaxLowerScalar_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold alphaRelaxLowerScalar\n by_cases hu : u > 0\n · by_cases hlpos : l > 0\n · have hxpos : 0 < x := l... | [
{
"name": "relu_ge_alpha_mul",
"text": "lemma relu_ge_alpha_mul (a z : ℝ) (ha0 : 0 ≤ a) (ha1 : a ≤ 1) :\n a * z ≤ Activation.Math.reluSpec (α := ℝ) z := by\n by_cases hz : z ≤ 0\n · have : a * z ≤ 0 := mul_nonpos_of_nonneg_of_nonpos ha0 hz\n simpa [Activation.Math.reluSpec, max_eq_right hz] using th... | [
{
"name": "alphaRelaxLowerScalar_sound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 692,
"n_subproofs": 3,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"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 NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | @@ -108,6 +108,15 @@
castDimScalar (α := ℝ) h t = t := by
exact castDimScalar_proof_irrel h rfl t
+lemma relu_ge_alpha_mul (a z : ℝ) (ha0 : 0 ≤ a) (ha1 : a ≤ 1) :
+ a * z ≤ Activation.Math.reluSpec (α := ℝ) z := by
+ by_cases hz : z ≤ 0
+ · have : a * z ≤ 0 := mul_nonpos_of_nonneg_of_nonpos ha0 hz
+ 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_555cf1ddf563_4 | aef5ba3b0afc436b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphAlphaCrownTransferSoundness/Common.lean | Common | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 23 | 1 | [
{
"theorem_name": "phaseRelaxUpperScalar_slope_nonneg",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases ph <;> simp [phaseRelaxUpperScalar, relax_scalar_slope_nonneg]",
"n_chars": 74,
"n_subproo... | [
{
"name": "relax_scalar_slope_nonneg",
"text": "lemma relax_scalar_slope_nonneg (l u : ℝ) :\n 0 ≤ (NN.MLTheory.CROWN.Runtime.Ops.ReLU.relaxScalar (α := ℝ) l u).slope := by\n unfold NN.MLTheory.CROWN.Runtime.Ops.ReLU.relaxScalar\n by_cases hu : u > 0\n · by_cases hlpos : l > 0\n · simp [hu, hlpos]\n... | [
{
"name": "phaseRelaxUpperScalar_slope_nonneg",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 209,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 3,
"n_automation": 1,
"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.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Cert.AlphaBetaCROWN
public import NN.MLTheory.CROWN.Cert.AlphaCROWN
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
public import NN.MLTheory.CROWN.P... | @@ -108,8 +108,24 @@
castDimScalar (α := ℝ) h t = t := by
exact castDimScalar_proof_irrel h rfl t
+lemma relax_scalar_slope_nonneg (l u : ℝ) :
+ 0 ≤ (NN.MLTheory.CROWN.Runtime.Ops.ReLU.relaxScalar (α := ℝ) l u).slope := by
+ unfold NN.MLTheory.CROWN.Runtime.Ops.ReLU.relaxScalar
+ by_cases hu : u > 0
+ ·... | {
"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-... |
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