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_e67ae8ef18fd_2 | d9c9d04b768fcc92 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/API/SelfSupervised/Core.lean | Core | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "vectorMaeMask_hidden_get_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hbool : vectorMaeHiddenMask dataDim period offset j = true := by\n simpa [NN.MLTheory.SelfSupervis... | [
{
"name": "vectorMaeMask_get_eq_if_selected_hidden",
"text": "/--\nCoordinate-level bridge from the executable tensor mask to the finite mask used in the\nself-supervised theory files.\n\nFor every batch row and feature coordinate, `vectorMaeMask` returns exactly zero on hidden\ncoordinates and the original... | [
{
"name": "vectorMaeSample_input_hidden_get_eq_zero",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 16,
"n_chars": 746,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"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.API.Core
public import NN.API.Public.TensorPack
public import NN.API.Tensor.Views
public import NN.MLTheory.SelfSupervised.PredictiveView
/-!
# Self-Supervised Training API
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Core
public import NN.API.Public.TensorPack
public import NN.API.Tensor.Views
public import NN.MLTheory.SelfSupervised.PredictiveView
/-!
# Self-Supervised Training API
... | @@ -76,13 +76,46 @@
j.val % period ≠ offset % period
Spec.Tensor.scalar (if keep then v else 0.0)))
+/--
+Coordinate-level bridge from the executable tensor mask to the finite mask used in the
+self-supervised theory files.
+
+For every batch row and feature coordinate, `vectorMaeMask` returns 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_e67ae8ef18fd_3 | 0bfc5c3d3a47d342 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/API/SelfSupervised/Core.lean | Core | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "imagePatchMask_hidden_pixel_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [hHidden] using\n imagePatchMask_pixel_eq_if_hidden batch c h w patchH patchW period offset x ... | [
{
"name": "imagePatchMask_pixel_eq_if_hidden",
"text": "/--\nCoordinate-level behavior of the executable image MAE mask.\n\nThis is the main implementation certificate for image masking: every scalar pixel in the output\nmasked image is either the original scalar (visible patch) or exactly zero (hidden patc... | [
{
"name": "imagePatchMask_hidden_pixel_eq_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 773,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": tr... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Core
public import NN.API.Public.TensorPack
public import NN.API.Tensor.Views
public import NN.MLTheory.SelfSupervised.PredictiveView
/-!
# Self-Supervised Training API
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Core
public import NN.API.Public.TensorPack
public import NN.API.Tensor.Views
public import NN.MLTheory.SelfSupervised.PredictiveView
/-!
# Self-Supervised Training API
... | @@ -195,6 +195,29 @@
Spec.Tensor.scalar (if keep then v else 0.0)))))
/--
+Coordinate-level behavior of the executable image MAE mask.
+
+This is the main implementation certificate for image masking: every scalar pixel in the output
+masked image is either the original scalar (visible patch) or exactly z... | {
"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_e67ae8ef18fd_4 | d8abcbcd63f4e6ae | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/API/SelfSupervised/Core.lean | Core | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "imagePatchMask_hidden_pixel_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [hHidden] using\n imagePatchMask_pixel_eq_if_hidden batch c h w patchH patchW period offset x ... | [
{
"name": "imagePatchMask_pixel_eq_if_hidden",
"text": "/--\nCoordinate-level behavior of the executable image MAE mask.\n\nThis is the main implementation certificate for image masking: every scalar pixel in the output\nmasked image is either the original scalar (visible patch) or exactly zero (hidden patc... | [
{
"name": "imagePatchMask_visible_pixel_eq_input",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 19,
"n_chars": 893,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": ... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Core
public import NN.API.Public.TensorPack
public import NN.API.Tensor.Views
public import NN.MLTheory.SelfSupervised.PredictiveView
/-!
# Self-Supervised Training API
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Core
public import NN.API.Public.TensorPack
public import NN.API.Tensor.Views
public import NN.MLTheory.SelfSupervised.PredictiveView
/-!
# Self-Supervised Training API
... | @@ -195,6 +195,29 @@
Spec.Tensor.scalar (if keep then v else 0.0)))))
/--
+Coordinate-level behavior of the executable image MAE mask.
+
+This is the main implementation certificate for image masking: every scalar pixel in the output
+masked image is either the original scalar (visible patch) or exactly z... | {
"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_e67ae8ef18fd_5 | 5b4d9cbbf739bfb0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/API/SelfSupervised/Core.lean | Core | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "imagePatchMask_hidden_pixel_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [hHidden] using\n imagePatchMask_pixel_eq_if_hidden batch c h w patchH patchW period offset x ... | [
{
"name": "imagePatchMask_pixel_eq_if_hidden",
"text": "/--\nCoordinate-level behavior of the executable image MAE mask.\n\nThis is the main implementation certificate for image masking: every scalar pixel in the output\nmasked image is either the original scalar (visible patch) or exactly zero (hidden patc... | [
{
"name": "imagePatchMaeSample_input_hidden_pixel_eq_zero",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 21,
"n_chars": 1072,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"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.API.Core
public import NN.API.Public.TensorPack
public import NN.API.Tensor.Views
public import NN.MLTheory.SelfSupervised.PredictiveView
/-!
# Self-Supervised Training API
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Core
public import NN.API.Public.TensorPack
public import NN.API.Tensor.Views
public import NN.MLTheory.SelfSupervised.PredictiveView
/-!
# Self-Supervised Training API
... | @@ -195,6 +195,29 @@
Spec.Tensor.scalar (if keep then v else 0.0)))))
/--
+Coordinate-level behavior of the executable image MAE mask.
+
+This is the main implementation certificate for image masking: every scalar pixel in the output
+masked image is either the original scalar (visible patch) or exactly z... | {
"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_e67ae8ef18fd_6 | b0568ed68d94b16d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/API/SelfSupervised/Core.lean | Core | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 2 | [
{
"theorem_name": "imagePatchMask_hidden_pixel_eq_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [hHidden] using\n imagePatchMask_pixel_eq_if_hidden batch c h w patchH patchW period offset x ... | [
{
"name": "imagePatchMask_pixel_eq_if_hidden",
"text": "/--\nCoordinate-level behavior of the executable image MAE mask.\n\nThis is the main implementation certificate for image masking: every scalar pixel in the output\nmasked image is either the original scalar (visible patch) or exactly zero (hidden patc... | [
{
"name": "imagePatchMaeSample_input_visible_pixel_eq_source",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 21,
"n_chars": 1016,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"autom... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Core
public import NN.API.Public.TensorPack
public import NN.API.Tensor.Views
public import NN.MLTheory.SelfSupervised.PredictiveView
/-!
# Self-Supervised Training API
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Core
public import NN.API.Public.TensorPack
public import NN.API.Tensor.Views
public import NN.MLTheory.SelfSupervised.PredictiveView
/-!
# Self-Supervised Training API
... | @@ -195,6 +195,29 @@
Spec.Tensor.scalar (if keep then v else 0.0)))))
/--
+Coordinate-level behavior of the executable image MAE mask.
+
+This is the main implementation certificate for image masking: every scalar pixel in the output
+masked image is either the original scalar (visible patch) or exactly z... | {
"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_76b60c02aa9c_0 | 4a6ba6810c912d42 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/Ops/Sum.lean | Sum | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "approxT_sum_spec",
"depth": 1,
"n_commands": 0,
"n_lines": 30,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro xS xR eps hx\n -- Start from accumulator 0 with a conservative rounding bound.\n let initEps : ℝ := neuralUlp β f... | [
{
"name": "approx_sum_fold_state",
"text": "/--\nCore summation induction: `sum_fold_state` preserves a forward bound.\n\nIn words: if the current accumulator `st.1` approximates a spec value `accS` within\n `st.2`,\nand each tensor entry is approximated within `epsElem`, then folding `sum_fold_state` over... | [
{
"name": "approxT_sum_spec",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 45,
"n_chars": 2366,
"n_subproofs": 5,
"n_tactics": 27,
"cyclomatic": 1,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nes... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.Ops.Scalar
public import NN.Proofs.Tensor.Basic.Folds
/-!
# NF Sum Reduction Bounds
Forward-error bounds for rounded sum reductions. The accumulato... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.Ops.Scalar
public import NN.Proofs.Tensor.Basic.Folds
/-!
# NF Sum Reduction Bounds
Forward-error bounds for rounded sum reductions. The accumulato... | @@ -139,6 +139,102 @@
simpa [sumFoldState, tensorFoldlSpec] using h0
/--
+Core summation induction: `sum_fold_state` preserves a forward bound.
+
+In words: if the current accumulator `st.1` approximates a spec value `accS` within
+ `st.2`,
+and each tensor entry is approximated within `epsElem`, then fo... | {
"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_32149c1c6166_0 | 4e4dc7a798cf17f7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/NearestEven.lean | NearestEven | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "neural_nearest_even_neg_div_eq_roundQuotEven",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hpos :=\n neural_nearest_even_div_eq_roundQuotEven (num := num) (den := den) hden\n -... | [
{
"name": "neural_nearest_even_neg",
"text": "/-- Nearest-even integer rounding commutes with negation. -/\nlemma neural_nearest_even_neg (x : ℝ) :\n TorchLean.Floats.neuralNearestEven (-x) = -TorchLean.Floats.neuralNearestEven x := by\n classical\n -- Use `r = x - ⌊x⌋` for the case split (integer vs n... | [
{
"name": "neural_nearest_even_neg_div_eq_roundQuotEven",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 517,
"n_subproofs": 2,
"n_tactics": 6,
"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.Floats.IEEEExec.BridgeFP32.DyadicRounding
/-!
# IEEE32Exec and FP32: Nearest-Even Quotient Lemmas
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open Torc... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.DyadicRounding
/-!
# IEEE32Exec and FP32: Nearest-Even Quotient Lemmas
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open Torc... | @@ -30,9 +30,169 @@
later when relating the `IEEE32Exec` rounding code to `fp32Round`.
-/
+/-- Nearest-even integer rounding commutes with negation. -/
+lemma neural_nearest_even_neg (x : ℝ) :
+ TorchLean.Floats.neuralNearestEven (-x) = -TorchLean.Floats.neuralNearestEven x := by
+ classical
+ -- Use `r = 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_32149c1c6166_1 | 8dac2b1416b4717f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/NearestEven.lean | NearestEven | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "neural_nearest_even_div_pow2_eq_roundShiftRightEven",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hden : pow2 shift ≠ 0 := by\n have : 0 < pow2 shift := by\n simp [pow2_eq... | [
{
"name": "roundShiftRightEven_eq_roundQuotEven_pow2",
"text": "lemma roundShiftRightEven_eq_roundQuotEven_pow2 (n shift : Nat) :\n roundShiftRightEven n shift = roundQuotEven n (pow2 shift) := by\n classical\n cases shift with\n | zero =>\n -- `pow2 0 = 1`, and `roundQuotEven n 1 = n`.\n si... | [
{
"name": "neural_nearest_even_div_pow2_eq_roundShiftRightEven",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 625,
"n_subproofs": 3,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 2,
"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.Floats.IEEEExec.BridgeFP32.DyadicRounding
/-!
# IEEE32Exec and FP32: Nearest-Even Quotient Lemmas
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open Torc... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.DyadicRounding
/-!
# IEEE32Exec and FP32: Nearest-Even Quotient Lemmas
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open Torc... | @@ -30,9 +30,127 @@
later when relating the `IEEE32Exec` rounding code to `fp32Round`.
-/
+lemma roundShiftRightEven_eq_roundQuotEven_pow2 (n shift : Nat) :
+ roundShiftRightEven n shift = roundQuotEven n (pow2 shift) := by
+ classical
+ cases shift with
+ | zero =>
+ -- `pow2 0 = 1`, and `roundQuotEven ... | {
"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_12943a760202_0 | 7c7c740f0f75e2c5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/Core.lean | Core | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 3 | [
{
"theorem_name": "toVecE_add_spec",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext i\n simp [toVecE_ofLp, toVec_add_spec_apply]",
"n_chars": 54,
"n_subproofs": 0,
"n_tactics": 3,
"cyclo... | [
{
"name": "toVecE_ofLp",
"text": "/-- Coordinate evaluation of `toVecE`. -/\n@[simp] lemma toVecE_ofLp {n : Nat} (t : Tensor ℝ (.dim n .scalar)) (i : Fin n) :\n (toVecE t).ofLp i = Spec.toVec t i := by\n -- `toVecE` is `toLp` and `.ofLp` is the inverse coercion back to functions.\n simp [toVecE, Euclid... | [
{
"name": "toVecE_add_spec",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 7,
"n_chars": 227,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Notation
public import NN.Proofs.Gradients.Activatio... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Notation
public import NN.Proofs.Gradients.Activatio... | @@ -76,6 +76,12 @@
simpa [toVecE, euclideanEquiv] using
(ContinuousLinearEquiv.apply_symm_apply (euclideanEquiv n) (Spec.toVec t))
+/-- Coordinate evaluation of `toVecE`. -/
+@[simp] lemma toVecE_ofLp {n : Nat} (t : Tensor ℝ (.dim n .scalar)) (i : Fin n) :
+ (toVecE t).ofLp i = Spec.toVec t i := by
+ -- `... | {
"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_12943a760202_1 | 5cf93302cdfdb2c1 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/Core.lean | Core | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 3 | [
{
"theorem_name": "toVecE_add_spec",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext i\n simp [toVecE_ofLp, toVec_add_spec_apply]",
"n_chars": 54,
"n_subproofs": 0,
"n_tactics": 3,
"cyclo... | [
{
"name": "toVecE_ofLp",
"text": "/-- Coordinate evaluation of `toVecE`. -/\n@[simp] lemma toVecE_ofLp {n : Nat} (t : Tensor ℝ (.dim n .scalar)) (i : Fin n) :\n (toVecE t).ofLp i = Spec.toVec t i := by\n -- `toVecE` is `toLp` and `.ofLp` is the inverse coercion back to functions.\n simp [toVecE, Euclid... | [
{
"name": "toVecE_map_spec",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 484,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"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.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Notation
public import NN.Proofs.Gradients.Activatio... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Notation
public import NN.Proofs.Gradients.Activatio... | @@ -76,6 +76,12 @@
simpa [toVecE, euclideanEquiv] using
(ContinuousLinearEquiv.apply_symm_apply (euclideanEquiv n) (Spec.toVec t))
+/-- Coordinate evaluation of `toVecE`. -/
+@[simp] lemma toVecE_ofLp {n : Nat} (t : Tensor ℝ (.dim n .scalar)) (i : Fin n) :
+ (toVecE t).ofLp i = Spec.toVec t i := by
+ -- `... | {
"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_12943a760202_2 | a71047a90900c177 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/Core.lean | Core | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 3 | [
{
"theorem_name": "toVecE_add_spec",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext i\n simp [toVecE_ofLp, toVec_add_spec_apply]",
"n_chars": 54,
"n_subproofs": 0,
"n_tactics": 3,
"cyclo... | [
{
"name": "toVecE_ofLp",
"text": "/-- Coordinate evaluation of `toVecE`. -/\n@[simp] lemma toVecE_ofLp {n : Nat} (t : Tensor ℝ (.dim n .scalar)) (i : Fin n) :\n (toVecE t).ofLp i = Spec.toVec t i := by\n -- `toVecE` is `toLp` and `.ofLp` is the inverse coercion back to functions.\n simp [toVecE, Euclid... | [
{
"name": "toVecE_relu_deriv_spec",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 16,
"n_chars": 665,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Notation
public import NN.Proofs.Gradients.Activatio... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Notation
public import NN.Proofs.Gradients.Activatio... | @@ -76,6 +76,12 @@
simpa [toVecE, euclideanEquiv] using
(ContinuousLinearEquiv.apply_symm_apply (euclideanEquiv n) (Spec.toVec t))
+/-- Coordinate evaluation of `toVecE`. -/
+@[simp] lemma toVecE_ofLp {n : Nat} (t : Tensor ℝ (.dim n .scalar)) (i : Fin n) :
+ (toVecE t).ofLp i = Spec.toVec t i := by
+ -- `... | {
"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_12943a760202_3 | 1c053a09721fe549 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/Core.lean | Core | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "toVecE_mat_vec_mul_spec",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n apply (euclideanEquiv m).injective\n funext i\n -- Both sides are equal as `Fin m → ℝ`; match them v... | [
{
"name": "euclideanEquiv_toVecE",
"text": "/-- `toVecE` is defined via `EuclideanSpace.equiv`; this lemma exposes the underlying coordinates.\n -/\n@[simp] lemma euclideanEquiv_toVecE {n : Nat} (t : Tensor ℝ (.dim n .scalar)) :\n euclideanEquiv n (toVecE t) = Spec.toVec t := by\n simpa [toVecE, euclid... | [
{
"name": "toVecE_mat_vec_mul_spec",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 18,
"n_chars": 713,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Notation
public import NN.Proofs.Gradients.Activatio... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Notation
public import NN.Proofs.Gradients.Activatio... | @@ -69,6 +69,13 @@
with Euclidean inner products), we prove that `Spec.dot` agrees with `inner` after vectorization.
-/
+/-- `toVecE` is defined via `EuclideanSpace.equiv`; this lemma exposes the underlying coordinates.
+ -/
+@[simp] lemma euclideanEquiv_toVecE {n : Nat} (t : Tensor ℝ (.dim n .scalar)) :
+ eucl... | {
"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_12943a760202_5 | 747bd5efe1dff108 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/Core.lean | Core | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "hasFDerivAt_mlpVec",
"depth": 1,
"n_commands": 0,
"n_lines": 32,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n dsimp [mlpVec, mlpDeriv]\n let W1 := tensorToMatrix (m := hidDim) (n := inDim) l1.weights\n let b1 : Vec hidDim := to... | [
{
"name": "hasFDerivAt_affine",
"text": "/-- `affine` is Fréchet-differentiable with derivative `W` (as a CLM), since it is linear +\n constant. -/\nlemma hasFDerivAt_affine {inDim outDim : Nat}\n (W : Matrix (Fin outDim) (Fin inDim) ℝ) (b : Vec outDim) (x : Vec inDim) :\n HasFDerivAt (affine (inDim ... | [
{
"name": "hasFDerivAt_mlpVec",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 52,
"n_chars": 2334,
"n_subproofs": 5,
"n_tactics": 28,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false,
"max_n... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Notation
public import NN.Proofs.Gradients.Activatio... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Notation
public import NN.Proofs.Gradients.Activatio... | @@ -114,6 +114,21 @@
Vec inDim → Vec outDim :=
fun x => (matCLM (m := outDim) (n := inDim) W) x + b
+/-- `affine` is Fréchet-differentiable with derivative `W` (as a CLM), since it is linear +
+ constant. -/
+lemma hasFDerivAt_affine {inDim outDim : Nat}
+ (W : Matrix (Fin outDim) (Fin inDim) ℝ) (b : Vec ... | {
"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_12943a760202_7 | f4d428d83fdd01c8 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/Core.lean | Core | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "mlp_backward_eq_adjoint_fderiv",
"depth": 1,
"n_commands": 0,
"n_lines": 129,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro δ\n classical\n let f := mlpVec (inDim := inDim) (hidDim := hidDim) (outDim := outDim) l1 l2\n le... | [
{
"name": "dot_eq_inner_vec",
"text": "/--\nFor 1D scalar tensors, `Spec.dot` agrees with the Euclidean inner product on `Vec n`\nafter converting via `toVecE`.\n-/\nlemma dot_eq_inner_vec {n : Nat} (a b : Tensor ℝ (.dim n .scalar)) :\n Spec.dot a b = inner ℝ (toVecE a) (toVecE b) := by\n classical\n h... | [
{
"name": "mlp_backward_eq_adjoint_fderiv",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 13,
"n_lines": 152,
"n_chars": 7147,
"n_subproofs": 17,
"n_tactics": 105,
"cyclomatic": 1,
"n_automation": 10,
"n_rewrites": 2,
"n_structural": 8,
"automation_only": ... | 13 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Notation
public import NN.Proofs.Gradients.Activatio... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Core.Vectorization
public import NN.Proofs.Autograd.Notation
public import NN.Proofs.Gradients.Activatio... | @@ -82,6 +82,23 @@
-- `toVecE` is `toLp` and `.ofLp` is the inverse coercion back to functions.
simp [toVecE, EuclideanSpace.equiv]
+/--
+For 1D scalar tensors, `Spec.dot` agrees with the Euclidean inner product on `Vec n`
+after converting via `toVecE`.
+-/
+lemma dot_eq_inner_vec {n : Nat} (a b : Tensor ℝ (.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_167a910762a7_0 | 21dbc59fd7a47400 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphCrownCertSoundness.lean | GraphCrownCertSoundness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "crown_checker_encloses_semantics",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro id hid b v hcertId hvalId\n have hmatch :=\n crown_checker_encloses_semantics_match\n (g :=... | [
{
"name": "crown_checker_encloses_semantics_match",
"text": "theorem crown_checker_encloses_semantics_match\n (g : Graph) (ps : ParamStore ℝ)\n (step : Array (Option (FlatAffineBounds ℝ)) → Nat → Option (FlatAffineBounds ℝ))\n (cert : Array (Option (FlatAffineBounds ℝ)))\n (inputs : Std.HashMap ... | [
{
"name": "crown_checker_encloses_semantics",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 34,
"n_chars": 1468,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 1,
"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.Floats.IEEEExec.Exec32
public import NN.MLTheory.CROWN.Graph
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end CROWN certificate-checking framework ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
public import NN.MLTheory.CROWN.Graph
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end CROWN certificate-checking framework ... | @@ -195,6 +195,59 @@
through `step` and `CrownTransferSound`.
-/
+theorem crown_checker_encloses_semantics_match
+ (g : Graph) (ps : ParamStore ℝ)
+ (step : Array (Option (FlatAffineBounds ℝ)) → Nat → Option (FlatAffineBounds ℝ))
+ (cert : Array (Option (FlatAffineBounds ℝ)))
+ (inputs : Std.HashMap 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_167a910762a7_1 | d762c89eb3bb0610 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphCrownCertSoundness.lean | GraphCrownCertSoundness | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "crown_checker_encloses_semantics_ieee32exec",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro id hid b v hcertId hvalId\n have hmatch :=\n crown_checker_encloses_semantics_ieee32e... | [
{
"name": "crown_checker_encloses_semantics_ieee32exec_match",
"text": "theorem crown_checker_encloses_semantics_ieee32exec_match\n (g : Graph) (_ps : ParamStore TorchLean.Floats.IEEE754.IEEE32Exec)\n (step : Array (Option (FlatAffineBounds TorchLean.Floats.IEEE754.IEEE32Exec)) → Nat →\n Option... | [
{
"name": "crown_checker_encloses_semantics_ieee32exec",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 39,
"n_chars": 1909,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
public import NN.MLTheory.CROWN.Graph
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end CROWN certificate-checking framework ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
public import NN.MLTheory.CROWN.Graph
public import NN.MLTheory.CROWN.Proofs.GraphCertSoundness
/-!
# End-to-end CROWN certificate-checking framework ... | @@ -227,6 +227,74 @@
∀ id : Nat, id < g.nodes.size →
vals[id]! = evalNode? g.nodes ps inputs vals id
+theorem crown_checker_encloses_semantics_ieee32exec_match
+ (g : Graph) (_ps : ParamStore TorchLean.Floats.IEEE754.IEEE32Exec)
+ (step : Array (Option (FlatAffineBounds TorchLean.Floats.IEEE754.IEEE... | {
"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_3ec8d1c8df27_0 | 4fcc6de5274e3332 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundQuotEvenBounds.lean | RoundQuotEvenBounds | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 3 | [
{
"theorem_name": "roundQuotEven_eq_div_or_div_add1",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Wrapper around the `q`-based statement used by downstream bounds.\n simpa using (roundQuotEven_eq_q_or... | [
{
"name": "roundQuotEven_eq_q_or_q_add1",
"text": "private lemma roundQuotEven_eq_q_or_q_add1 (num den : Nat) :\n let q := num / den\n roundQuotEven num den = q ∨ roundQuotEven num den = q + 1 := by\n classical\n by_cases hden : den = 0\n · subst hden\n -- Totalized behavior: `num/0 = 0`, `num%0... | [
{
"name": "roundQuotEven_eq_div_or_div_add1",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
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"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.IEEEExec.Exec32
/-!
# Order bounds for `roundQuotEven`
`IEEE32Exec.roundRatToIEEE32` rounds an *exact rational* `num/den` to binary32 using
round-to-nearest, ties-to... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
/-!
# Order bounds for `roundQuotEven`
`IEEE32Exec.roundRatToIEEE32` rounds an *exact rational* `num/den` to binary32 using
round-to-nearest, ties-to... | @@ -35,9 +35,45 @@
open Nat
+private lemma roundQuotEven_eq_q_or_q_add1 (num den : Nat) :
+ let q := num / den
+ roundQuotEven num den = q ∨ roundQuotEven num den = q + 1 := by
+ classical
+ by_cases hden : den = 0
+ · subst hden
+ -- Totalized behavior: `num/0 = 0`, `num%0 = num`.
+ -- The comparis... | {
"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_3ec8d1c8df27_1 | 60e96319ef609896 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundQuotEvenBounds.lean | RoundQuotEvenBounds | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 3 | [
{
"theorem_name": "roundQuotEven_eq_div_or_div_add1",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Wrapper around the `q`-based statement used by downstream bounds.\n simpa using (roundQuotEven_eq_q_or... | [
{
"name": "roundQuotEven_eq_q_or_q_add1",
"text": "private lemma roundQuotEven_eq_q_or_q_add1 (num den : Nat) :\n let q := num / den\n roundQuotEven num den = q ∨ roundQuotEven num den = q + 1 := by\n classical\n by_cases hden : den = 0\n · subst hden\n -- Totalized behavior: `num/0 = 0`, `num%0... | [
{
"name": "div_le_roundQuotEven",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 437,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"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 NN.Floats.IEEEExec.Exec32
/-!
# Order bounds for `roundQuotEven`
`IEEE32Exec.roundRatToIEEE32` rounds an *exact rational* `num/den` to binary32 using
round-to-nearest, ties-to... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
/-!
# Order bounds for `roundQuotEven`
`IEEE32Exec.roundRatToIEEE32` rounds an *exact rational* `num/den` to binary32 using
round-to-nearest, ties-to... | @@ -35,9 +35,51 @@
open Nat
+private lemma roundQuotEven_eq_q_or_q_add1 (num den : Nat) :
+ let q := num / den
+ roundQuotEven num den = q ∨ roundQuotEven num den = q + 1 := by
+ classical
+ by_cases hden : den = 0
+ · subst hden
+ -- Totalized behavior: `num/0 = 0`, `num%0 = num`.
+ -- The comparis... | {
"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_3ec8d1c8df27_2 | 2bf745f78a0ac3c3 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/RoundQuotEvenBounds.lean | RoundQuotEvenBounds | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 3 | [
{
"theorem_name": "roundQuotEven_eq_div_or_div_add1",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Wrapper around the `q`-based statement used by downstream bounds.\n simpa using (roundQuotEven_eq_q_or... | [
{
"name": "roundQuotEven_eq_q_or_q_add1",
"text": "private lemma roundQuotEven_eq_q_or_q_add1 (num den : Nat) :\n let q := num / den\n roundQuotEven num den = q ∨ roundQuotEven num den = q + 1 := by\n classical\n by_cases hden : den = 0\n · subst hden\n -- Totalized behavior: `num/0 = 0`, `num%0... | [
{
"name": "roundQuotEven_le_div_add1",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 455,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 3,
"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.Floats.IEEEExec.Exec32
/-!
# Order bounds for `roundQuotEven`
`IEEE32Exec.roundRatToIEEE32` rounds an *exact rational* `num/den` to binary32 using
round-to-nearest, ties-to... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.Exec32
/-!
# Order bounds for `roundQuotEven`
`IEEE32Exec.roundRatToIEEE32` rounds an *exact rational* `num/den` to binary32 using
round-to-nearest, ties-to... | @@ -35,9 +35,51 @@
open Nat
+private lemma roundQuotEven_eq_q_or_q_add1 (num den : Nat) :
+ let q := num / den
+ roundQuotEven num den = q ∨ roundQuotEven num den = q + 1 := by
+ classical
+ by_cases hden : den = 0
+ · subst hden
+ -- Totalized behavior: `num/0 = 0`, `num%0 = num`.
+ -- The comparis... | {
"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_776b5fd84738_0 | 40e8e5cee0ddc0d0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MDP.lean | MDP | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "stateActionValue_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let out := mdp.step state action\n have hMask : 0 ≤ continueMask (α := ℝ) out.terminated :=\n continueMask_n... | [
{
"name": "continueMask_nonneg",
"text": "/-- `continueMask` is always nonnegative. -/\ntheorem continueMask_nonneg (done : Bool) :\n 0 ≤ (continueMask (α := ℝ) done : ℝ) := by\n cases done <;> norm_num [continueMask]\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 185,
"n_subproofs": 0,
... | [
{
"name": "stateActionValue_monotone",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 25,
"n_chars": 1171,
"n_subproofs": 4,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 1,
"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 Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | @@ -70,6 +70,11 @@
out.reward + mdp.discount * continueMask (α := ℝ) out.terminated * valueAt values out.state := by
rfl
+/-- `continueMask` is always nonnegative. -/
+theorem continueMask_nonneg (done : Bool) :
+ 0 ≤ (continueMask (α := ℝ) done : ℝ) := by
+ cases done <;> norm_num [continueMask]
+
/--... | {
"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_776b5fd84738_1 | 1231dad768b1e69b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MDP.lean | MDP | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "stateActionValue_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let out := mdp.step state action\n have hMask : 0 ≤ continueMask (α := ℝ) out.terminated :=\n continueMask_n... | [
{
"name": "continueMask_nonneg",
"text": "/-- `continueMask` is always nonnegative. -/\ntheorem continueMask_nonneg (done : Bool) :\n 0 ≤ (continueMask (α := ℝ) done : ℝ) := by\n cases done <;> norm_num [continueMask]\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 185,
"n_subproofs": 0,
... | [
{
"name": "bellmanPolicy_monotone",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 14,
"n_chars": 635,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | @@ -80,6 +80,11 @@
stateActionValue mdp values state (policy state) := by
rfl
+/-- `continueMask` is always nonnegative. -/
+theorem continueMask_nonneg (done : Bool) :
+ 0 ≤ (continueMask (α := ℝ) done : ℝ) := by
+ cases done <;> norm_num [continueMask]
+
/-- A Bellman state-action value is monotone i... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_776b5fd84738_2 | 716825b463c9e398 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MDP.lean | MDP | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "bellmanPolicy_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [valueAt_bellmanPolicy] using\n stateActionValue_monotone mdp values₁ values₂ hγ hValues state (policy stat... | [
{
"name": "valueAt_bellmanPolicy",
"text": "/-- Policy Bellman operators read back exactly the selected state-action value. -/\ntheorem valueAt_bellmanPolicy\n (mdp : FiniteMDP ℝ nStates nActions)\n (policy : Policy nStates nActions)\n (values : ValueFunction ℝ nStates)\n (state : Fin nStates) :... | [
{
"name": "bellmanPolicy_le_bellmanOptimality",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 533,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"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 Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | @@ -59,6 +59,16 @@
(Finset.univ : Finset (Fin nStates)).sup' Finset.univ_nonempty
(fun state => |valueAt values₁ state - valueAt values₂ state|)
+/-- Policy Bellman operators read back exactly the selected state-action value. -/
+theorem valueAt_bellmanPolicy
+ (mdp : FiniteMDP ℝ nStates nActions)
+ (po... | {
"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_776b5fd84738_3 | 4bcf064db1d462ed | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MDP.lean | MDP | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "bellmanPolicy_monotone",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [valueAt_bellmanPolicy] using\n stateActionValue_monotone mdp values₁ values₂ hγ hValues state (policy stat... | [
{
"name": "stateActionValue_monotone",
"text": "/-- A Bellman state-action value is monotone in the candidate value function when `γ ≥ 0`. -/\ntheorem stateActionValue_monotone\n (mdp : FiniteMDP ℝ nStates nActions)\n (values₁ values₂ : ValueFunction ℝ nStates)\n (hγ : 0 ≤ mdp.discount)\n (hValu... | [
{
"name": "bellmanOptimality_monotone",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 27,
"n_chars": 1198,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | @@ -75,6 +75,30 @@
0 ≤ (continueMask (α := ℝ) done : ℝ) := by
cases done <;> norm_num [continueMask]
+/-- A Bellman state-action value is monotone in the candidate value function when `γ ≥ 0`. -/
+theorem stateActionValue_monotone
+ (mdp : FiniteMDP ℝ nStates nActions)
+ (values₁ values₂ : ValueFunction... | {
"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_776b5fd84738_4 | 7ec372989bc43f0e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MDP.lean | MDP | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "stateActionValue_abs_sub_le",
"depth": 1,
"n_commands": 0,
"n_lines": 29,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let out := mdp.step state action\n by_cases hdone : out.terminated\n · have hnonneg :\n 0 ≤ mdp.disco... | [
{
"name": "abs_sub_valueAt_le_valueSupDist",
"text": "/-- Every pointwise absolute difference is bounded by the sup distance. -/\ntheorem abs_sub_valueAt_le_valueSupDist [Fact (0 < nStates)]\n (values₁ values₂ : ValueFunction ℝ nStates)\n (state : Fin nStates) :\n |valueAt values₁ state - valueAt v... | [
{
"name": "stateActionValue_abs_sub_le",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 40,
"n_chars": 1974,
"n_subproofs": 4,
"n_tactics": 29,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 3,
"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.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | @@ -73,6 +73,14 @@
(Finset.mem_univ ⟨0, Fact.out⟩)
exact hcoord.trans hle
+/-- Every pointwise absolute difference is bounded by the sup distance. -/
+theorem abs_sub_valueAt_le_valueSupDist [Fact (0 < nStates)]
+ (values₁ values₂ : ValueFunction ℝ nStates)
+ (state : Fin nStates) :
+ |valueAt valu... | {
"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_776b5fd84738_5 | 7cd66ea5e32d975c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MDP.lean | MDP | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "bellmanPolicy_contraction",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let _ : Nonempty (Fin nStates) := ⟨⟨0, Fact.out⟩⟩\n unfold valueSupDist\n refine Finset.sup'_le (s := (Finset.... | [
{
"name": "stateActionValue_abs_sub_le",
"text": "/-- Deterministic state-action Bellman values are Lipschitz with constant `γ`. -/\ntheorem stateActionValue_abs_sub_le\n [Fact (0 < nStates)]\n (mdp : FiniteMDP ℝ nStates nActions)\n (values₁ values₂ : ValueFunction ℝ nStates)\n (hγ₀ : 0 ≤ mdp.di... | [
{
"name": "bellmanPolicy_contraction",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 23,
"n_chars": 1099,
"n_subproofs": 0,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 3,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | @@ -81,6 +81,45 @@
unfold valueSupDist
exact Finset.le_sup' (fun s => |valueAt values₁ s - valueAt values₂ s|) (Finset.mem_univ state)
+/-- Deterministic state-action Bellman values are Lipschitz with constant `γ`. -/
+theorem stateActionValue_abs_sub_le
+ [Fact (0 < nStates)]
+ (mdp : FiniteMDP ℝ nStates... | {
"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_776b5fd84738_6 | 92f9f0232290c434 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MDP.lean | MDP | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "bellmanPolicy_contraction",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let _ : Nonempty (Fin nStates) := ⟨⟨0, Fact.out⟩⟩\n unfold valueSupDist\n refine Finset.sup'_le (s := (Finset.... | [
{
"name": "stateActionValue_abs_sub_le",
"text": "/-- Deterministic state-action Bellman values are Lipschitz with constant `γ`. -/\ntheorem stateActionValue_abs_sub_le\n [Fact (0 < nStates)]\n (mdp : FiniteMDP ℝ nStates nActions)\n (values₁ values₂ : ValueFunction ℝ nStates)\n (hγ₀ : 0 ≤ mdp.di... | [
{
"name": "bellmanOptimality_abs_sub_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 41,
"n_chars": 2249,
"n_subproofs": 7,
"n_tactics": 30,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | @@ -81,6 +81,45 @@
unfold valueSupDist
exact Finset.le_sup' (fun s => |valueAt values₁ s - valueAt values₂ s|) (Finset.mem_univ state)
+/-- Deterministic state-action Bellman values are Lipschitz with constant `γ`. -/
+theorem stateActionValue_abs_sub_le
+ [Fact (0 < nStates)]
+ (mdp : FiniteMDP ℝ nStates... | {
"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_776b5fd84738_7 | a3caf44247ca988f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/MDP.lean | MDP | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 2 | [
{
"theorem_name": "bellmanPolicy_contraction",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let _ : Nonempty (Fin nStates) := ⟨⟨0, Fact.out⟩⟩\n unfold valueSupDist\n refine Finset.sup'_le (s := (Finset.... | [
{
"name": "stateActionValue_abs_sub_le",
"text": "/-- Deterministic state-action Bellman values are Lipschitz with constant `γ`. -/\ntheorem stateActionValue_abs_sub_le\n [Fact (0 < nStates)]\n (mdp : FiniteMDP ℝ nStates nActions)\n (values₁ values₂ : ValueFunction ℝ nStates)\n (hγ₀ : 0 ≤ mdp.di... | [
{
"name": "bellmanOptimality_contraction",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 18,
"n_chars": 846,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import Mathlib.Logic.Function.Iterate
public import NN.Proofs.RL.FinsetSup
public import NN.Proofs.Tensor.Basic
public import NN.Spec.RL.MDP
/-!
... | @@ -81,6 +81,45 @@
unfold valueSupDist
exact Finset.le_sup' (fun s => |valueAt values₁ s - valueAt values₂ s|) (Finset.mem_univ state)
+/-- Deterministic state-action Bellman values are Lipschitz with constant `γ`. -/
+theorem stateActionValue_abs_sub_le
+ [Fact (0 < nStates)]
+ (mdp : FiniteMDP ℝ nStates... | {
"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_e2d7664366f8_0 | 8256764ad788e8c9 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/Positive.lean | Positive | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 3 | [
{
"theorem_name": "pow2_mul",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n (pow2_add a b).symm",
"n_chars": 22,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n... | [
{
"name": "pow2_add",
"text": "lemma pow2_add (a b : Nat) : pow2 (a + b) = pow2 a * pow2 b := by\n -- `pow2 k = 2^k`, so this is `2^(a+b) = 2^a * 2^b`.\n simp [pow2_eq_two_pow, Nat.pow_add]\n\n",
"fan_in": 3,
"n_lines": 5,
"n_chars": 160,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomat... | [
{
"name": "pow2_mul",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 156,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Nat.Bitwise.Lemmas
public import Mathlib.Data.Nat.Log
public import NN.Floats.IEEEExec.ERealSemantics
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Fl... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Nat.Bitwise.Lemmas
public import Mathlib.Data.Nat.Log
public import NN.Floats.IEEEExec.ERealSemantics
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Fl... | @@ -60,8 +60,13 @@
abbrev bpow (e : Int) : ℝ :=
neuralBpow binaryRadix e
+lemma pow2_add (a b : Nat) : pow2 (a + b) = pow2 a * pow2 b := by
+ -- `pow2 k = 2^k`, so this is `2^(a+b) = 2^a * 2^b`.
+ simp [pow2_eq_two_pow, Nat.pow_add]
+
/-- Commuted form of `pow2_add`: `pow2 a * pow2 b = pow2 (a + b)`. -/
-lemma... | {
"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_e2d7664366f8_1 | cbdb10086089ecc8 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/Positive.lean | Positive | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 1 | [
{
"theorem_name": "toEReal_posMinSubnormal",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hfin : isFinite (posMinSubnormal : IEEE32Exec) = true := by decide\n have hcoe :\n toEReal (posMinSubnor... | [
{
"name": "toReal_posMinSubnormal",
"text": "private lemma toReal_posMinSubnormal :\n toReal (posMinSubnormal : IEEE32Exec) = bpow (-149) := by\n have hexp : (0 : Nat) < 255 := by decide\n have hfrac : (1 : Nat) < 2 ^ 23 := by decide\n have hbits : mkBits false 0 1 = 0x00000001 := by decide\n have hd... | [
{
"name": "toEReal_posMinSubnormal",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 503,
"n_subproofs": 2,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"ma... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Nat.Bitwise.Lemmas
public import Mathlib.Data.Nat.Log
public import NN.Floats.IEEEExec.ERealSemantics
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Fl... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Nat.Bitwise.Lemmas
public import Mathlib.Data.Nat.Log
public import NN.Floats.IEEEExec.ERealSemantics
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Fl... | @@ -77,9 +77,26 @@
@[simp] lemma directed_toEReal_negZero : toEReal (negZero : IEEE32Exec) = (0 : EReal) := by
simpa using (toEReal_signedZero (s := true))
+private lemma toReal_posMinSubnormal :
+ toReal (posMinSubnormal : IEEE32Exec) = bpow (-149) := by
+ have hexp : (0 : Nat) < 255 := by decide
+ have hfr... | {
"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_e2d7664366f8_2 | 95053e0cf919cfcf | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/Positive.lean | Positive | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 2 | [
{
"theorem_name": "toReal_posMaxFinite_lt_bpow128",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `posMaxFinite = mkBits false 254 (2^23-1)` so its real value is `(2^24-1)*2^104 < 2^128`.\n have hexp :... | [
{
"name": "bpow_pos",
"text": "/-- `bpow e = 2^e` is strictly positive. -/\nlemma bpow_pos (e : Int) : 0 < bpow e :=\n neuralBpow.pos binaryRadix e\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 117,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewri... | [
{
"name": "toReal_posMaxFinite_lt_bpow128",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 38,
"n_chars": 1959,
"n_subproofs": 10,
"n_tactics": 31,
"cyclomatic": 1,
"n_automation": 8,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": fals... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Nat.Bitwise.Lemmas
public import Mathlib.Data.Nat.Log
public import NN.Floats.IEEEExec.ERealSemantics
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Fl... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Nat.Bitwise.Lemmas
public import Mathlib.Data.Nat.Log
public import NN.Floats.IEEEExec.ERealSemantics
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Fl... | @@ -60,6 +60,10 @@
abbrev bpow (e : Int) : ℝ :=
neuralBpow binaryRadix e
+/-- `bpow e = 2^e` is strictly positive. -/
+lemma bpow_pos (e : Int) : 0 < bpow e :=
+ neuralBpow.pos binaryRadix e
+
/-- Exponent law for `bpow`: `bpow (e₁+e₂) = bpow e₁ * bpow e₂`. -/
lemma bpow_add (e1 e2 : Int) : bpow (e1 + e2) = bp... | {
"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_e2d7664366f8_3 | c0118c019589ad88 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/Positive.lean | Positive | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 2 | [
{
"theorem_name": "toReal_posMaxFinite_lt_bpow128",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `posMaxFinite = mkBits false 254 (2^23-1)` so its real value is `(2^24-1)*2^104 < 2^128`.\n have hexp :... | [
{
"name": "bpow_pos",
"text": "/-- `bpow e = 2^e` is strictly positive. -/\nlemma bpow_pos (e : Int) : 0 < bpow e :=\n neuralBpow.pos binaryRadix e\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 117,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewri... | [
{
"name": "toReal_roundDyadicPosDown_le",
"fan_in": 0,
"n_deps_direct": 10,
"n_deps_transitive": 11,
"n_lines": 513,
"n_chars": 27923,
"n_subproofs": 143,
"n_tactics": 434,
"cyclomatic": 8,
"n_automation": 98,
"n_rewrites": 28,
"n_structural": 41,
"automation_only... | 10 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Nat.Bitwise.Lemmas
public import Mathlib.Data.Nat.Log
public import NN.Floats.IEEEExec.ERealSemantics
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Fl... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Nat.Bitwise.Lemmas
public import Mathlib.Data.Nat.Log
public import NN.Floats.IEEEExec.ERealSemantics
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Fl... | @@ -60,6 +60,10 @@
abbrev bpow (e : Int) : ℝ :=
neuralBpow binaryRadix e
+/-- `bpow e = 2^e` is strictly positive. -/
+lemma bpow_pos (e : Int) : 0 < bpow e :=
+ neuralBpow.pos binaryRadix e
+
/-- `bpow e = 2^e` is nonnegative. -/
lemma bpow_nonneg (e : Int) : 0 ≤ bpow e :=
neuralBpow.nonneg binaryRadix e
@... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e2d7664366f8_4 | deaf6bc00f29754e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DirectedRoundingSoundness/Positive.lean | Positive | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 16 | 2 | [
{
"theorem_name": "toReal_posMaxFinite_lt_bpow128",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `posMaxFinite = mkBits false 254 (2^23-1)` so its real value is `(2^24-1)*2^104 < 2^128`.\n have hexp :... | [
{
"name": "bpow_pos",
"text": "/-- `bpow e = 2^e` is strictly positive. -/\nlemma bpow_pos (e : Int) : 0 < bpow e :=\n neuralBpow.pos binaryRadix e\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 117,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewri... | [
{
"name": "toEReal_roundDyadicPosUp_ge",
"fan_in": 0,
"n_deps_direct": 13,
"n_deps_transitive": 14,
"n_lines": 890,
"n_chars": 49704,
"n_subproofs": 250,
"n_tactics": 718,
"cyclomatic": 13,
"n_automation": 184,
"n_rewrites": 25,
"n_structural": 48,
"automation_onl... | 14 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Nat.Bitwise.Lemmas
public import Mathlib.Data.Nat.Log
public import NN.Floats.IEEEExec.ERealSemantics
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Fl... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Nat.Bitwise.Lemmas
public import Mathlib.Data.Nat.Log
public import NN.Floats.IEEEExec.ERealSemantics
public import NN.Floats.IEEEExec.MkBitsToReal
public import NN.Fl... | @@ -60,6 +60,10 @@
abbrev bpow (e : Int) : ℝ :=
neuralBpow binaryRadix e
+/-- `bpow e = 2^e` is strictly positive. -/
+lemma bpow_pos (e : Int) : 0 < bpow e :=
+ neuralBpow.pos binaryRadix e
+
/-- `bpow e = 2^e` is nonnegative. -/
lemma bpow_nonneg (e : Int) : 0 ≤ bpow e :=
neuralBpow.nonneg binaryRadix e
@... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_167dcb41d69a_0 | 5d72a484bf9cb2a2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/LogSoftmax.lean | LogSoftmax | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "sumExp_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ne_of_gt (sumExp_pos (n := n) x)",
"n_chars": 35,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_aut... | [
{
"name": "sumExp_pos",
"text": "/-- `sumExp x` is strictly positive when the index type is nonempty. -/\nlemma sumExp_pos {n : Nat} (x : Vec (Nat.succ n)) : 0 < sumExp (n := Nat.succ n) x := by\n have hterm : ∀ i : Fin (Nat.succ n), 0 < Real.exp (x i) := fun i => Real.exp_pos (x i)\n simpa [sumExp] using... | [
{
"name": "sumExp_ne_zero",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 195,
"n_subproofs": 0,
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"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nesting"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Softmax
public import Mathlib.Analysis.Calculus.FDeriv.Add
public import Mathlib.Analysis.Calculus.FDeriv.Comp
public import Mathlib.Analysis.Calculus... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Softmax
public import Mathlib.Analysis.Calculus.FDeriv.Add
public import Mathlib.Analysis.Calculus.FDeriv.Comp
public import Mathlib.Analysis.Calculus... | @@ -36,8 +36,14 @@
noncomputable section
+/-- `sumExp x` is strictly positive when the index type is nonempty. -/
+lemma sumExp_pos {n : Nat} (x : Vec (Nat.succ n)) : 0 < sumExp (n := Nat.succ n) x := by
+ have hterm : ∀ i : Fin (Nat.succ n), 0 < Real.exp (x i) := fun i => Real.exp_pos (x i)
+ simpa [sumExp] usi... | {
"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_167dcb41d69a_1 | 92ac587cbfb33153 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/LogSoftmax.lean | LogSoftmax | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "hasFDerivAt_logSoftmaxVec",
"depth": 1,
"n_commands": 0,
"n_lines": 135,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases n with\n | zero =>\n have hD : logSoftmaxDerivCLM (n := 0) x = (1 : (Vec 0) →L[ℝ] (Vec... | [
{
"name": "sumExp_ne_zero",
"text": "/-- Convenience corollary: `sumExp x ≠ 0` (for `n = succ _`). -/\nlemma sumExp_ne_zero {n : Nat} (x : Vec (Nat.succ n)) : sumExp (n := Nat.succ n) x ≠ 0 :=\n ne_of_gt (sumExp_pos (n := n) x)\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 195,
"n_subproofs":... | [
{
"name": "hasFDerivAt_logSoftmaxVec",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 139,
"n_chars": 6998,
"n_subproofs": 24,
"n_tactics": 126,
"cyclomatic": 2,
"n_automation": 10,
"n_rewrites": 4,
"n_structural": 15,
"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.Autograd.FDeriv.Softmax
public import Mathlib.Analysis.Calculus.FDeriv.Add
public import Mathlib.Analysis.Calculus.FDeriv.Comp
public import Mathlib.Analysis.Calculus... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Softmax
public import Mathlib.Analysis.Calculus.FDeriv.Add
public import Mathlib.Analysis.Calculus.FDeriv.Comp
public import Mathlib.Analysis.Calculus... | @@ -41,6 +41,10 @@
have hterm : ∀ i : Fin (Nat.succ n), 0 < Real.exp (x i) := fun i => Real.exp_pos (x i)
simpa [sumExp] using Finset.sum_pos (fun i _ => hterm i) (Finset.univ_nonempty)
+/-- Convenience corollary: `sumExp x ≠ 0` (for `n = succ _`). -/
+lemma sumExp_ne_zero {n : Nat} (x : Vec (Nat.succ n)) : sum... | {
"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_097210a12035_0 | 9b2d4ba8e2aad797 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/NeuralFloat/Core.lean | Core | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "forward_of_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [TrainingPhase.requiresHighPrecision] using\n (eq_base_of_ne_zero_of_not_high_precision (β := β) (fexp := fexp)... | [
{
"name": "eq_base_of_ne_zero_of_not_high_precision",
"text": "/--\nWhen `x ≠ 0` and the phase does **not** request high precision, `neural_ulp` is just the base grid\nstep `β^{cexp(x)}`.\n-/\nlemma eq_base_of_ne_zero_of_not_high_precision (x : ℝ) (hx : x ≠ 0)\n (phase : TrainingPhase) (hphase : phase.re... | [
{
"name": "forward_of_ne_zero",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 516,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nest... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.Basic
public import NN.Floats.NeuralFloat.Metadata
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# NeuralFloat core (Flocq-style r... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.Basic
public import NN.Floats.NeuralFloat.Metadata
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# NeuralFloat core (Flocq-style r... | @@ -250,6 +250,15 @@
simp [neuralUlp]
/--
+When `x ≠ 0` and the phase does **not** request high precision, `neural_ulp` is just the base grid
+step `β^{cexp(x)}`.
+-/
+lemma eq_base_of_ne_zero_of_not_high_precision (x : ℝ) (hx : x ≠ 0)
+ (phase : TrainingPhase) (hphase : phase.requiresHighPrecision = false) :
... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_097210a12035_1 | f12db938dd0ed96b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/NeuralFloat/Core.lean | Core | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "backward_of_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [TrainingPhase.requiresHighPrecision] using\n (eq_base_div_two_of_ne_zero_of_high_precision (β := β) (fexp := ... | [
{
"name": "eq_base_div_two_of_ne_zero_of_high_precision",
"text": "/--\nWhen `x ≠ 0` and the phase requests high precision, we use the same exponent scale but treat the\nULP as “one extra bit tighter” by dividing by 2.\n-/\nlemma eq_base_div_two_of_ne_zero_of_high_precision (x : ℝ) (hx : x ≠ 0)\n (phase ... | [
{
"name": "backward_of_ne_zero",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 428,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nest... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.Basic
public import NN.Floats.NeuralFloat.Metadata
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# NeuralFloat core (Flocq-style r... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Log.Basic
public import NN.Floats.NeuralFloat.Metadata
import Mathlib.Analysis.SpecialFunctions.Pow.Real
/-!
# NeuralFloat core (Flocq-style r... | @@ -259,6 +259,15 @@
simp [neuralUlp, hx, hphase]
/--
+When `x ≠ 0` and the phase requests high precision, we use the same exponent scale but treat the
+ULP as “one extra bit tighter” by dividing by 2.
+-/
+lemma eq_base_div_two_of_ne_zero_of_high_precision (x : ℝ) (hx : x ≠ 0)
+ (phase : TrainingPhase) (hphas... | {
"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_5fb021b057a8_0 | fc6f02617d1fe1d2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Convergence.lean | Convergence | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 2 | [
{
"theorem_name": "energy_iterate_antitone",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n obtain ⟨d, rfl⟩ := Nat.exists_eq_add_of_le hij\n -- Apply the `d`-step bound from the state `f^[i] s... | [
{
"name": "energy_iterate_le",
"text": "private lemma energy_iterate_le\n (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)\n (k : Nat) (s : State n) :\n energy (α := ℝ) p ((f (n := n) p)^[k] s) ≤ energy (α := ℝ) p s := by\n classical\n induction k with\n | zero =>\n simp\n ... | [
{
"name": "energy_iterate_antitone",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 27,
"n_chars": 1243,
"n_subproofs": 5,
"n_tactics": 17,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"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 Mathlib.Data.Fintype.Card
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Monotone.Basic
public import NN.... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Monotone.Basic
public import NN.... | @@ -44,6 +44,22 @@
/-- The full-sweep update map whose iterates define Hopfield cyclic dynamics. -/
noncomputable def f : State n → State n := cycleUpdate (n := n) p
+private lemma energy_iterate_le
+ (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)
+ (k : Nat) (s : State n) :
+ energy (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_5fb021b057a8_1 | 31702762068c213d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Convergence.lean | Convergence | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "energy_iterate_eq_of_iterate_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hle : energy (α := ℝ) p ((f (n := n) p)^[i] s) ≤ energy (α := ℝ) p s :=\n energy_iterate_le (n := n... | [
{
"name": "energy_iterate_antitone",
"text": "private lemma energy_iterate_antitone\n (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)\n {i j : Nat} (hij : i ≤ j) (s : State n) :\n energy (α := ℝ) p ((f (n := n) p)^[j] s) ≤ energy (α := ℝ) p ((f (n := n) p)^[i] s) := by\n classical... | [
{
"name": "energy_iterate_eq_of_iterate_eq",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 15,
"n_chars": 755,
"n_subproofs": 3,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Monotone.Basic
public import NN.... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Monotone.Basic
public import NN.... | @@ -60,6 +60,32 @@
energy_cycleUpdate_le (n := n) (p := p) hsym hdiag ((f (n := n) p)^[k] s)
simpa [Function.iterate_succ_apply'] using le_trans hstep IH
+private lemma energy_iterate_antitone
+ (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)
+ {i j : Nat} (hij : i ≤ j) (s : Sta... | {
"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_5fb021b057a8_2 | 073d455db7892437 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Convergence.lean | Convergence | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "pluses_iterate_step_mono_of_iterate_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 20,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hEi :\n energy (α := ℝ) p ((f (n := n) p)^[i] s) = energy (α := ℝ) p s :=\n energy_ite... | [
{
"name": "pluses_cycleUpdate_ge_of_energy_eq",
"text": "private lemma pluses_cycleUpdate_ge_of_energy_eq\n (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)\n (s : State n)\n (hE : energy (α := ℝ) p ((f (n := n) p) s) = energy (α := ℝ) p s) :\n pluses (n := n) ((f (n := n) p) s) ... | [
{
"name": "pluses_iterate_step_mono_of_iterate_eq",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 26,
"n_chars": 1329,
"n_subproofs": 4,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Monotone.Basic
public import NN.... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Monotone.Basic
public import NN.... | @@ -100,11 +100,43 @@
simpa [hcyc] using hk_le
exact le_antisymm hle hle'
+private lemma pluses_cycleUpdate_ge_of_energy_eq
+ (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)
+ (s : State n)
+ (hE : energy (α := ℝ) p ((f (n := n) p) s) = energy (α := ℝ) p s) :
+ pluses (n := n) ((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_5fb021b057a8_3 | fe538983b8f97a1b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Convergence.lean | Convergence | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "cycleUpdate_no_nontrivial_cycles",
"depth": 1,
"n_commands": 0,
"n_lines": 54,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n by_contra hne\n -- Energy is constant along the cycle.\n have hE1 :\n energy (α := ℝ)... | [
{
"name": "pluses_iterate_step_mono_of_iterate_eq",
"text": "private lemma pluses_iterate_step_mono_of_iterate_eq\n (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)\n {k i : Nat} (hi : i < k) {s : State n}\n (hcyc : (f (n := n) p)^[k] s = s) :\n pluses (n := n) ((f (n := n) p)^[i... | [
{
"name": "cycleUpdate_no_nontrivial_cycles",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 60,
"n_chars": 2910,
"n_subproofs": 19,
"n_tactics": 46,
"cyclomatic": 2,
"n_automation": 5,
"n_rewrites": 1,
"n_structural": 10,
"automation_only": f... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Monotone.Basic
public import NN.... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Monotone.Basic
public import NN.... | @@ -113,6 +113,31 @@
· exact False.elim (hlt.ne hE)
· exact le_of_lt hpl
+private lemma pluses_iterate_step_mono_of_iterate_eq
+ (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)
+ {k i : Nat} (hi : i < k) {s : State n}
+ (hcyc : (f (n := n) p)^[k] s = s) :
+ pluses (n := n) ((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_5fb021b057a8_4 | 8dea657faf73b305 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Convergence.lean | Convergence | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "cycleUpdate_exists_fixedpoint_le_card",
"depth": 1,
"n_commands": 0,
"n_lines": 71,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n let N : Nat := Fintype.card (State n)\n let g : Fin (N + 1) → State n := fun t => (f (... | [
{
"name": "cycleUpdate_no_nontrivial_cycles",
"text": "theorem cycleUpdate_no_nontrivial_cycles\n (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)\n {k : Nat} (hk : 0 < k) (s : State n)\n (hcyc : (f (n := n) p)^[k] s = s) :\n (f (n := n) p) s = s := by\n classical\n by_contra h... | [
{
"name": "cycleUpdate_exists_fixedpoint_le_card",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 76,
"n_chars": 3591,
"n_subproofs": 19,
"n_tactics": 64,
"cyclomatic": 2,
"n_automation": 14,
"n_rewrites": 0,
"n_structural": 10,
"automation_on... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Monotone.Basic
public import NN.... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Monotone.Basic
public import NN.... | @@ -138,6 +138,65 @@
pluses_cycleUpdate_ge_of_energy_eq (n := n) (p := p) hsym hdiag ((f (n := n) p)^[i] s) hE_step
simpa [Function.iterate_succ_apply'] using hpl
+theorem cycleUpdate_no_nontrivial_cycles
+ (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)
+ {k : Nat} (hk : 0 < k) (s : St... | {
"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_5fb021b057a8_5 | 84498d7f7a784957 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Convergence.lean | Convergence | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "cycleUpdate_exists_fixedpoint_le_pow",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hcard : Fintype.card (State n) = (2 : Nat) ^ n := by\n -- `State n = Fin n → Bool... | [
{
"name": "cycleUpdate_exists_fixedpoint_le_card",
"text": "theorem cycleUpdate_exists_fixedpoint_le_card\n (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)\n (s0 : State n) :\n ∃ m ≤ Fintype.card (State n), (f (n := n) p)^[m + 1] s0 = (f (n := n) p)^[m] s0 := by\n classical\n let... | [
{
"name": "cycleUpdate_exists_fixedpoint_le_pow",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 13,
"n_chars": 534,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": f... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Monotone.Basic
public import NN.... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Fintype.Card
public import Mathlib.Data.Fintype.Pigeonhole
public import Mathlib.Logic.Function.Iterate
public import Mathlib.Order.Monotone.Basic
public import NN.... | @@ -197,10 +197,92 @@
exact hlt
exact (lt_irrefl _ this)
+theorem cycleUpdate_exists_fixedpoint_le_card
+ (hsym : SymmetricW (n := n) p) (hdiag : DiagonalZero (n := n) p)
+ (s0 : State n) :
+ ∃ m ≤ Fintype.card (State n), (f (n := n) p)^[m + 1] s0 = (f (n := n) p)^[m] s0 := by
+ classical
+ let 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_5ea70b546dd9_0 | dc28e96d59327f3a | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/MkBitsToDyadic.lean | MkBitsToDyadic | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "mkBits_toNat",
"depth": 1,
"n_commands": 0,
"n_lines": 51,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hFracMask : fracMask.toNat = 2 ^ 23 - 1 := by decide\n have hMod32 : (2 ^ 32 : Nat) = 4294967296 := by decide\n have h... | [
{
"name": "nat_and_two_pow_sub_one_eq_self",
"text": "private lemma nat_and_two_pow_sub_one_eq_self {n k : Nat} (hn : n < 2 ^ k) :\n n &&& (2 ^ k - 1) = n := by\n apply Nat.eq_of_testBit_eq\n intro i\n by_cases hi : i < k\n · simp [hi]\n · have hi' : k ≤ i := Nat.le_of_not_gt hi\n have hn' : n < ... | [
{
"name": "mkBits_toNat",
"fan_in": 3,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 55,
"n_chars": 2539,
"n_subproofs": 20,
"n_tactics": 48,
"cyclomatic": 1,
"n_automation": 23,
"n_rewrites": 2,
"n_structural": 3,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# MkBitsToDyadic
`Exec32.lean` defines the bit-level encoding/decoding functions for IEEE-754 binary32, in... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# MkBitsToDyadic
`Exec32.lean` defines the bit-level encoding/decoding functions for IEEE-754 binary32, in... | @@ -27,6 +27,18 @@
/-! ## `toDyadic? (ofBits (mkBits …))` on the finite path -/
+private lemma nat_and_two_pow_sub_one_eq_self {n k : Nat} (hn : n < 2 ^ k) :
+ n &&& (2 ^ k - 1) = n := by
+ apply Nat.eq_of_testBit_eq
+ intro i
+ by_cases hi : i < k
+ · simp [hi]
+ · have hi' : k ≤ i := Nat.le_of_not_gt hi
... | {
"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_5ea70b546dd9_1 | b1538537c1c7821d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/MkBitsToDyadic.lean | MkBitsToDyadic | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 3 | [
{
"theorem_name": "fracField_ofBits_mkBits",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply UInt32.toNat_inj.1\n have hBits := mkBits_toNat (sign := sign) (exp := exp) (frac := frac) hexp hfrac\n ha... | [
{
"name": "mkBits_toNat",
"text": "private lemma mkBits_toNat (sign : Bool) (exp frac : Nat) (hexp : exp < 256) (hfrac : frac < 2 ^ 23)\n :\n (mkBits sign exp frac).toNat = (if sign then 2 ^ 31 else 0) ||| (exp <<< 23) ||| frac := by\n have hFracMask : fracMask.toNat = 2 ^ 23 - 1 := by decide\n have h... | [
{
"name": "fracField_ofBits_mkBits",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 23,
"n_chars": 1145,
"n_subproofs": 5,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 8,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# MkBitsToDyadic
`Exec32.lean` defines the bit-level encoding/decoding functions for IEEE-754 binary32, in... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# MkBitsToDyadic
`Exec32.lean` defines the bit-level encoding/decoding functions for IEEE-754 binary32, in... | @@ -39,6 +39,60 @@
have hnbit : n.testBit i = false := Nat.testBit_eq_false_of_lt hn'
simp [hi, hnbit]
+private lemma mkBits_toNat (sign : Bool) (exp frac : Nat) (hexp : exp < 256) (hfrac : frac < 2 ^ 23)
+ :
+ (mkBits sign exp frac).toNat = (if sign then 2 ^ 31 else 0) ||| (exp <<< 23) ||| frac := by
+... | {
"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_5ea70b546dd9_2 | 4333230ca5f748fd | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/MkBitsToDyadic.lean | MkBitsToDyadic | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 3 | [
{
"theorem_name": "fracField_ofBits_mkBits",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply UInt32.toNat_inj.1\n have hBits := mkBits_toNat (sign := sign) (exp := exp) (frac := frac) hexp hfrac\n ha... | [
{
"name": "mkBits_toNat",
"text": "private lemma mkBits_toNat (sign : Bool) (exp frac : Nat) (hexp : exp < 256) (hfrac : frac < 2 ^ 23)\n :\n (mkBits sign exp frac).toNat = (if sign then 2 ^ 31 else 0) ||| (exp <<< 23) ||| frac := by\n have hFracMask : fracMask.toNat = 2 ^ 23 - 1 := by decide\n have h... | [
{
"name": "expField_ofBits_mkBits",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 24,
"n_chars": 1207,
"n_subproofs": 6,
"n_tactics": 20,
"cyclomatic": 1,
"n_automation": 8,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"m... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# MkBitsToDyadic
`Exec32.lean` defines the bit-level encoding/decoding functions for IEEE-754 binary32, in... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# MkBitsToDyadic
`Exec32.lean` defines the bit-level encoding/decoding functions for IEEE-754 binary32, in... | @@ -39,6 +39,60 @@
have hnbit : n.testBit i = false := Nat.testBit_eq_false_of_lt hn'
simp [hi, hnbit]
+private lemma mkBits_toNat (sign : Bool) (exp frac : Nat) (hexp : exp < 256) (hfrac : frac < 2 ^ 23)
+ :
+ (mkBits sign exp frac).toNat = (if sign then 2 ^ 31 else 0) ||| (exp <<< 23) ||| frac := by
+... | {
"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_5ea70b546dd9_3 | 34ba286690e96a01 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/MkBitsToDyadic.lean | MkBitsToDyadic | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 3 | [
{
"theorem_name": "fracField_ofBits_mkBits",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply UInt32.toNat_inj.1\n have hBits := mkBits_toNat (sign := sign) (exp := exp) (frac := frac) hexp hfrac\n ha... | [
{
"name": "mkBits_toNat",
"text": "private lemma mkBits_toNat (sign : Bool) (exp frac : Nat) (hexp : exp < 256) (hfrac : frac < 2 ^ 23)\n :\n (mkBits sign exp frac).toNat = (if sign then 2 ^ 31 else 0) ||| (exp <<< 23) ||| frac := by\n have hFracMask : fracMask.toNat = 2 ^ 23 - 1 := by decide\n have h... | [
{
"name": "signBit_ofBits_mkBits",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 25,
"n_chars": 1219,
"n_subproofs": 8,
"n_tactics": 22,
"cyclomatic": 4,
"n_automation": 9,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"ma... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# MkBitsToDyadic
`Exec32.lean` defines the bit-level encoding/decoding functions for IEEE-754 binary32, in... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# MkBitsToDyadic
`Exec32.lean` defines the bit-level encoding/decoding functions for IEEE-754 binary32, in... | @@ -39,6 +39,60 @@
have hnbit : n.testBit i = false := Nat.testBit_eq_false_of_lt hn'
simp [hi, hnbit]
+private lemma mkBits_toNat (sign : Bool) (exp frac : Nat) (hexp : exp < 256) (hfrac : frac < 2 ^ 23)
+ :
+ (mkBits sign exp frac).toNat = (if sign then 2 ^ 31 else 0) ||| (exp <<< 23) ||| frac := by
+... | {
"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_5ea70b546dd9_4 | cb6d07a70dcdb9ec | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/MkBitsToDyadic.lean | MkBitsToDyadic | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "fracField_ofBits_mkBits",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply UInt32.toNat_inj.1\n have hBits := mkBits_toNat (sign := sign) (exp := exp) (frac := frac) hexp hfrac\n ha... | [
{
"name": "nat_extract_fracField",
"text": "private lemma nat_extract_fracField (sign : Bool) (exp frac : Nat)\n (_hexp : exp < 256) (hfrac : frac < 2 ^ 23) :\n (((if sign then 2 ^ 31 else 0) ||| (exp <<< 23) ||| frac) &&& (2 ^ 23 - 1)) = frac := by\n apply Nat.eq_of_testBit_eq\n intro i\n by_cases... | [
{
"name": "toDyadic?_ofBits_mkBits_fin",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 8,
"n_lines": 72,
"n_chars": 3174,
"n_subproofs": 20,
"n_tactics": 51,
"cyclomatic": 1,
"n_automation": 16,
"n_rewrites": 2,
"n_structural": 8,
"automation_only": false,... | 8 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# MkBitsToDyadic
`Exec32.lean` defines the bit-level encoding/decoding functions for IEEE-754 binary32, in... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# MkBitsToDyadic
`Exec32.lean` defines the bit-level encoding/decoding functions for IEEE-754 binary32, in... | @@ -93,6 +93,53 @@
simp [mkBits, hs', UInt32.toNat_or, hFracField, UInt32.toNat_shiftLeft, UInt32.toNat_ofNat,
hMod32, hExp_mod, hShift_mod]
+private lemma nat_extract_fracField (sign : Bool) (exp frac : Nat)
+ (_hexp : exp < 256) (hfrac : frac < 2 ^ 23) :
+ (((if sign then 2 ^ 31 else 0) ||| (exp <... | {
"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_2262d3ad3e99_0 | bdddc0c1bdb81fb3 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Generative/Latent/GAN.lean | GAN | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "generatorLoss_zero_of_fake_score_real",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [generatorLoss, ← hfake]\n exact mse_scalar_self_zero (fakeScore model z)",
"n_chars": 84,
... | [
{
"name": "mse_scalar_self_zero",
"text": "/-- Score-regression MSE is zero when the scalar prediction equals the scalar target. -/\nprivate theorem mse_scalar_self_zero (x : Tensor ℝ .scalar) :\n Spec.mseSpec (s := .scalar) x x = 0 := by\n cases x with\n | scalar a =>\n simp [Spec.mseSpec, Spec.t... | [
{
"name": "generatorLoss_zero_of_fake_score_real",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 429,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": ... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Models.Gan
public import NN.MLTheory.Generative.Latent.Objective
/-!
# GAN theory
TorchLean's baseline GAN spec uses least-squares GAN losses. This avoids partial log... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Models.Gan
public import NN.MLTheory.Generative.Latent.Objective
/-!
# GAN theory
TorchLean's baseline GAN spec uses least-squares GAN losses. This avoids partial log... | @@ -86,6 +86,15 @@
/-! ## Connection to shared objective algebra and equilibrium checks -/
+/-- Score-regression MSE is zero when the scalar prediction equals the scalar target. -/
+private theorem mse_scalar_self_zero (x : Tensor ℝ .scalar) :
+ Spec.mseSpec (s := .scalar) x x = 0 := by
+ cases x with
+ | sca... | {
"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_2262d3ad3e99_1 | b4d949971d2ad9cf | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Generative/Latent/GAN.lean | GAN | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "generatorLoss_zero_of_fake_score_real",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [generatorLoss, ← hfake]\n exact mse_scalar_self_zero (fakeScore model z)",
"n_chars": 84,
... | [
{
"name": "mse_scalar_self_zero",
"text": "/-- Score-regression MSE is zero when the scalar prediction equals the scalar target. -/\nprivate theorem mse_scalar_self_zero (x : Tensor ℝ .scalar) :\n Spec.mseSpec (s := .scalar) x x = 0 := by\n cases x with\n | scalar a =>\n simp [Spec.mseSpec, Spec.t... | [
{
"name": "discriminatorLoss_zero_of_perfect_scores",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 549,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Models.Gan
public import NN.MLTheory.Generative.Latent.Objective
/-!
# GAN theory
TorchLean's baseline GAN spec uses least-squares GAN losses. This avoids partial log... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Models.Gan
public import NN.MLTheory.Generative.Latent.Objective
/-!
# GAN theory
TorchLean's baseline GAN spec uses least-squares GAN losses. This avoids partial log... | @@ -86,6 +86,15 @@
/-! ## Connection to shared objective algebra and equilibrium checks -/
+/-- Score-regression MSE is zero when the scalar prediction equals the scalar target. -/
+private theorem mse_scalar_self_zero (x : Tensor ℝ .scalar) :
+ Spec.mseSpec (s := .scalar) x x = 0 := by
+ cases x with
+ | sca... | {
"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_644708ddeb4b_0 | fd64db74f78cd76b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Verification/ODE/Enclosure.lean | Enclosure | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "localEnclosure_fromClampedDynamics",
"depth": 1,
"n_commands": 0,
"n_lines": 170,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hLU0 : uL 0 ≤ uU 0 := hLU 0 ⟨le_rfl, hT⟩\n\n -- Upper enclosure: `u ≤ uU + ε(1+t)` for all ε>0.\... | [
{
"name": "clampToCorridor_eq_upper",
"text": "/-- If `u` lies strictly above the corridor, clamping snaps to the upper wall. -/\nlemma clampToCorridor_eq_upper {uL uU : ℝ → ℝ} {t u : ℝ}\n (hLU : uL t ≤ uU t) (hU : uU t < u) :\n clampToCorridor uL uU t u = uU t := by\n have hm : min (uU t) u = uU t :... | [
{
"name": "localEnclosure_fromClampedDynamics",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 197,
"n_chars": 9189,
"n_subproofs": 66,
"n_tactics": 154,
"cyclomatic": 3,
"n_automation": 41,
"n_rewrites": 5,
"n_structural": 17,
"automation_onl... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.Topology.Order.OrderClosed
/-!
# ODE Corridor Enclosures
This file formalizes the real-analysis endpoint used by Tana... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.Topology.Order.OrderClosed
/-!
# ODE Corridor Enclosures
This file formalizes the real-analysis endpoint used by Tana... | @@ -52,6 +52,14 @@
def clampToCorridor (uL uU : ℝ → ℝ) (t : ℝ) (u : ℝ) : ℝ :=
max (uL t) (min (uU t) u)
+/-- If `u` lies strictly above the corridor, clamping snaps to the upper wall. -/
+lemma clampToCorridor_eq_upper {uL uU : ℝ → ℝ} {t u : ℝ}
+ (hLU : uL t ≤ uU t) (hU : uU t < u) :
+ clampToCorridor uL uU... | {
"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_644708ddeb4b_1 | 2ecf1b68b660af9e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Verification/ODE/Enclosure.lean | Enclosure | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "localSolutionEnclosed_fromClampedDynamics",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hEnc :=\n localEnclosure_fromClampedDynamics (T := T) hT\n (f := f) (u := u) (uL :=... | [
{
"name": "clampToCorridor_eq_self",
"text": "/-- If `u` is already within the corridor, clamping is a no-op. -/\nlemma clampToCorridor_eq_self {uL uU : ℝ → ℝ} {t u : ℝ}\n (hL : uL t ≤ u) (hU : u ≤ uU t) :\n clampToCorridor uL uU t u = u := by\n simp [clampToCorridor, min_eq_right hU, max_eq_right hL... | [
{
"name": "localSolutionEnclosed_fromClampedDynamics",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 44,
"n_chars": 1933,
"n_subproofs": 5,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_o... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.Topology.Order.OrderClosed
/-!
# ODE Corridor Enclosures
This file formalizes the real-analysis endpoint used by Tana... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.Topology.Order.OrderClosed
/-!
# ODE Corridor Enclosures
This file formalizes the real-analysis endpoint used by Tana... | @@ -52,6 +52,12 @@
def clampToCorridor (uL uU : ℝ → ℝ) (t : ℝ) (u : ℝ) : ℝ :=
max (uL t) (min (uU t) u)
+/-- If `u` is already within the corridor, clamping is a no-op. -/
+lemma clampToCorridor_eq_self {uL uU : ℝ → ℝ} {t u : ℝ}
+ (hL : uL t ≤ u) (hU : u ≤ uU t) :
+ clampToCorridor uL uU t u = u := by
+ si... | {
"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_644708ddeb4b_2 | ab1a976a8ea41b0e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Verification/ODE/Enclosure.lean | Enclosure | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "localSolutionEnclosed_fromClampedDynamics",
"depth": 1,
"n_commands": 0,
"n_lines": 14,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hEnc :=\n localEnclosure_fromClampedDynamics (T := T) hT\n (f := f) (u := u) (uL :=... | [
{
"name": "clampToCorridor_eq_self",
"text": "/-- If `u` is already within the corridor, clamping is a no-op. -/\nlemma clampToCorridor_eq_self {uL uU : ℝ → ℝ} {t u : ℝ}\n (hL : uL t ≤ u) (hU : u ≤ uU t) :\n clampToCorridor uL uU t u = u := by\n simp [clampToCorridor, min_eq_right hU, max_eq_right hL... | [
{
"name": "extendedSolutionEnclosed_fromClampedDynamics",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 9,
"n_lines": 180,
"n_chars": 8842,
"n_subproofs": 54,
"n_tactics": 129,
"cyclomatic": 3,
"n_automation": 33,
"n_rewrites": 2,
"n_structural": 20,
"auto... | 9 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.Topology.Order.OrderClosed
/-!
# ODE Corridor Enclosures
This file formalizes the real-analysis endpoint used by Tana... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.Topology.Order.OrderClosed
/-!
# ODE Corridor Enclosures
This file formalizes the real-analysis endpoint used by Tana... | @@ -52,6 +52,12 @@
def clampToCorridor (uL uU : ℝ → ℝ) (t : ℝ) (u : ℝ) : ℝ :=
max (uL t) (min (uU t) u)
+/-- If `u` is already within the corridor, clamping is a no-op. -/
+lemma clampToCorridor_eq_self {uL uU : ℝ → ℝ} {t u : ℝ}
+ (hL : uL t ≤ u) (hU : u ≤ uU t) :
+ clampToCorridor uL uU t u = u := by
+ si... | {
"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_5deb75a236f7_0 | 55a14478d5042d21 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Generative/Latent/VQVAE.lean | VQVAE | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "exactCodeMatch_isNearestCode",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro j\n subst hmatch\n simpa using squaredL2_nonneg (embedding idx) (embedding j)",
"n_chars": 89,
... | [
{
"name": "squaredL2_nonneg",
"text": "/-- Squared Euclidean distance is nonnegative. -/\ntheorem squaredL2_nonneg {d : Nat} (x y : Fin d → ℝ) :\n 0 ≤ squaredL2 x y := by\n unfold squaredL2\n exact Finset.sum_nonneg (fun k _ => sq_nonneg (x k - y k))\n\n",
"fan_in": 1,
"n_lines": 7,
"n_char... | [
{
"name": "exactCodeMatch_isNearestCode",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 391,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"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.Spec.Models.VqVae
public import NN.MLTheory.Generative.Latent.Objective
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
/-!
# VQ-VAE theory
VQ-VAE has one mat... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Models.VqVae
public import NN.MLTheory.Generative.Latent.Objective
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
/-!
# VQ-VAE theory
VQ-VAE has one mat... | @@ -89,6 +89,12 @@
(embedding : Fin numCodes → Fin d → ℝ) (z : Fin d → ℝ) (idx : Fin numCodes) : Prop :=
∀ j, squaredL2 z (embedding idx) ≤ squaredL2 z (embedding j)
+/-- Squared Euclidean distance is nonnegative. -/
+theorem squaredL2_nonneg {d : Nat} (x y : Fin d → ℝ) :
+ 0 ≤ squaredL2 x y := by
+ unfol... | {
"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_1865bac07394_0 | bb506cf047659a6e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/OptimizerLaws.lean | OptimizerLaws | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "runSteps_eq_optimizer_runSteps",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction grads generalizing current with\n | nil =>\n rfl\n | cons grads rest ih =>\n simp [run... | [
{
"name": "step_eq_optimizer_step",
"text": "/-- A registered step spec agrees with the executable optimizer for one step. -/\ntheorem step_eq_optimizer_step (law : StepSpec opt) {s : Shape}\n (current : TensorOptimizer.Step opt s) (grads : Tensor α s) :\n law.step current grads = opt.step current gra... | [
{
"name": "runSteps_eq_optimizer_runSteps",
"fan_in": 8,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 14,
"n_chars": 567,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 2,
"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.Runtime.Optim.Optimizers
/-!
# Optimizer Law Interface
This module gives TorchLean optimizers a small proof layer interface.
Runtime optimizers live in `NN.Runtime.Optim.O... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Optim.Optimizers
/-!
# Optimizer Law Interface
This module gives TorchLean optimizers a small proof layer interface.
Runtime optimizers live in `NN.Runtime.Optim.O... | @@ -166,6 +166,14 @@
| current, [] => current
| current, grads :: rest => runSteps law (law.step current grads) rest
+/-- A registered step spec agrees with the executable optimizer for one step. -/
+theorem step_eq_optimizer_step (law : StepSpec opt) {s : Shape}
+ (current : TensorOptimizer.Step opt s) (gra... | {
"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_1865bac07394_1 | 855a03a2456b7606 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/OptimizerLaws.lean | OptimizerLaws | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "runSteps_eq_optimizer_runSteps",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction grads generalizing current with\n | nil =>\n rfl\n | cons grads rest ih =>\n simp [run... | [
{
"name": "step_eq_optimizer_step",
"text": "/-- A registered step spec agrees with the executable optimizer for one step. -/\ntheorem step_eq_optimizer_step (law : StepSpec opt) {s : Shape}\n (current : TensorOptimizer.Step opt s) (grads : Tensor α s) :\n law.step current grads = opt.step current gra... | [
{
"name": "runSteps_eq_stepSpec",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 9,
"n_chars": 459,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_ne... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Optim.Optimizers
/-!
# Optimizer Law Interface
This module gives TorchLean optimizers a small proof layer interface.
Runtime optimizers live in `NN.Runtime.Optim.O... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Optim.Optimizers
/-!
# Optimizer Law Interface
This module gives TorchLean optimizers a small proof layer interface.
Runtime optimizers live in `NN.Runtime.Optim.O... | @@ -166,6 +166,14 @@
| current, [] => current
| current, grads :: rest => runSteps law (law.step current grads) rest
+/-- A registered step spec agrees with the executable optimizer for one step. -/
+theorem step_eq_optimizer_step (law : StepSpec opt) {s : Shape}
+ (current : TensorOptimizer.Step opt s) (gra... | {
"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_1865bac07394_2 | 87cff3996e44ca2c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/OptimizerLaws.lean | OptimizerLaws | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "init_update_params_eq_momentumSGD_of_apply_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n exact update_params_eq_momentumSGD_of_apply_eq\n (state := init lr momentum orthogonalizer... | [
{
"name": "update_params_eq_momentumSGD_of_apply_eq",
"text": "/--\nIf a Muon backend returns the fresh momentum buffer unchanged on this step, then the parameter\nupdate agrees with momentum SGD for this step.\n-/\ntheorem update_params_eq_momentumSGD_of_apply_eq {s : Shape}\n (state : State α s) (param... | [
{
"name": "init_update_params_eq_momentumSGD_of_apply_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 717,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Optim.Optimizers
/-!
# Optimizer Law Interface
This module gives TorchLean optimizers a small proof layer interface.
Runtime optimizers live in `NN.Runtime.Optim.O... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Optim.Optimizers
/-!
# Optimizer Law Interface
This module gives TorchLean optimizers a small proof layer interface.
Runtime optimizers live in `NN.Runtime.Optim.O... | @@ -425,6 +425,23 @@
rfl
/--
+If a Muon backend returns the fresh momentum buffer unchanged on this step, then the parameter
+update agrees with momentum SGD for this step.
+-/
+theorem update_params_eq_momentumSGD_of_apply_eq {s : Shape}
+ (state : State α s) (params grads : Tensor α s)
+ (happly :
+ ... | {
"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_1865bac07394_3 | 83dbf8af56377798 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Optimization/OptimizerLaws.lean | OptimizerLaws | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 1 | [
{
"theorem_name": "init_identity_update_buffer_eq_momentumSGD",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n exact init_update_buffer_eq_momentumSGD\n (lr := lr) (momentum := momentum)\n (orthogonali... | [
{
"name": "init_update_buffer_eq_momentumSGD",
"text": "/--\nStarting from initialized states, Muon's first stored momentum buffer agrees with momentum SGD for\nany orthogonalizer backend.\n-/\ntheorem init_update_buffer_eq_momentumSGD {s : Shape}\n (lr momentum : α) (orthogonalizer : Orthogonalizer α s)... | [
{
"name": "init_identity_update_buffer_eq_momentumSGD",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 639,
"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.Runtime.Optim.Optimizers
/-!
# Optimizer Law Interface
This module gives TorchLean optimizers a small proof layer interface.
Runtime optimizers live in `NN.Runtime.Optim.O... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Optim.Optimizers
/-!
# Optimizer Law Interface
This module gives TorchLean optimizers a small proof layer interface.
Runtime optimizers live in `NN.Runtime.Optim.O... | @@ -425,6 +425,17 @@
rfl
/--
+Starting from initialized states, Muon's first stored momentum buffer agrees with momentum SGD for
+any orthogonalizer backend.
+-/
+theorem init_update_buffer_eq_momentumSGD {s : Shape}
+ (lr momentum : α) (orthogonalizer : Orthogonalizer α s)
+ (params grads : Tensor α 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_29920349f0c6_0 | 95c653383963fc71 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Normalization.lean | Normalization | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "batchNorm_inference_affine_tensor",
"depth": 1,
"n_commands": 0,
"n_lines": 25,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction s with\n | scalar =>\n cases x\n cases mean\n cases gamma\n cases beta\n ... | [
{
"name": "batchNorm_inference_affine_scalar",
"text": "/--\nScalar algebra behind inference-time BatchNorm folding.\n\nFor fixed mean `μ`, scale `γ`, shift `β`, and standard deviation `std`, the expression\n\n`((x - μ) / std) * γ + β`\n\nis affine in `x`, with multiplicative coefficient `γ / std` and bias\... | [
{
"name": "batchNorm_inference_affine_tensor",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 38,
"n_chars": 1363,
"n_subproofs": 0,
"n_tactics": 25,
"cyclomatic": 12,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 14,
"automation_only": ... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Layers.Normalization
import NN.Proofs.Tensor.Basic
import Mathlib.Tactic.Ring
/-!
# Normalization analysis properties
This file records theorem-level properties of Tor... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Layers.Normalization
import NN.Proofs.Tensor.Basic
import Mathlib.Tactic.Ring
/-!
# Normalization analysis properties
This file records theorem-level properties of Tor... | @@ -45,6 +45,31 @@
-/
/--
+Scalar algebra behind inference-time BatchNorm folding.
+
+For fixed mean `μ`, scale `γ`, shift `β`, and standard deviation `std`, the expression
+
+`((x - μ) / std) * γ + β`
+
+is affine in `x`, with multiplicative coefficient `γ / std` and bias
+`β - μ * (γ / std)`.
+-/
+private lemma b... | {
"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_29920349f0c6_1 | 75b967ced17abd8c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Normalization.lean | Normalization | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "batchNorm_inference_affine_tensor",
"depth": 1,
"n_commands": 0,
"n_lines": 25,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction s with\n | scalar =>\n cases x\n cases mean\n cases gamma\n cases beta\n ... | [
{
"name": "batchNorm_inference_affine_scalar",
"text": "/--\nScalar algebra behind inference-time BatchNorm folding.\n\nFor fixed mean `μ`, scale `γ`, shift `β`, and standard deviation `std`, the expression\n\n`((x - μ) / std) * γ + β`\n\nis affine in `x`, with multiplicative coefficient `γ / std` and bias\... | [
{
"name": "batchNorm_inference_eq_mul_add",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 41,
"n_chars": 1854,
"n_subproofs": 0,
"n_tactics": 2,
"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.Spec.Layers.Normalization
import NN.Proofs.Tensor.Basic
import Mathlib.Tactic.Ring
/-!
# Normalization analysis properties
This file records theorem-level properties of Tor... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Layers.Normalization
import NN.Proofs.Tensor.Basic
import Mathlib.Tactic.Ring
/-!
# Normalization analysis properties
This file records theorem-level properties of Tor... | @@ -45,6 +45,31 @@
-/
/--
+Scalar algebra behind inference-time BatchNorm folding.
+
+For fixed mean `μ`, scale `γ`, shift `β`, and standard deviation `std`, the expression
+
+`((x - μ) / std) * γ + β`
+
+is affine in `x`, with multiplicative coefficient `γ / std` and bias
+`β - μ * (γ / std)`.
+-/
+private lemma b... | {
"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_5f05d6f2513c_0 | 5dbe7a9004de2436 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/RuntimeApprox.lean | RuntimeApprox | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_approxR",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine approxR_absOnly_of_abs_sub_le (x := a.val + b.val) (y := (a + b).val) (eps := _)\n (eps32_nonneg (x := a.val + b.val)... | [
{
"name": "approxR_absOnly_of_abs_sub_le",
"text": "/--\nHelper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.\n\nInformal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.\n-/\nprivate lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps)... | [
{
"name": "add_approxR",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 19,
"n_chars": 709,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | @@ -57,6 +57,15 @@
-/
/--
+Helper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.
+
+Informal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.
+-/
+private lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps) (h : abs (y - x) ≤ eps) :
+ 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_5f05d6f2513c_1 | 02555290a3f686dd | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/RuntimeApprox.lean | RuntimeApprox | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_approxR",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine approxR_absOnly_of_abs_sub_le (x := a.val + b.val) (y := (a + b).val) (eps := _)\n (eps32_nonneg (x := a.val + b.val)... | [
{
"name": "approxR_absOnly_of_abs_sub_le",
"text": "/--\nHelper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.\n\nInformal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.\n-/\nprivate lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps)... | [
{
"name": "sub_approxR",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 541,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | @@ -57,6 +57,15 @@
-/
/--
+Helper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.
+
+Informal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.
+-/
+private lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps) (h : abs (y - x) ≤ eps) :
+ 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_5f05d6f2513c_2 | a2940c7f9a57d06f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/RuntimeApprox.lean | RuntimeApprox | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_approxR",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine approxR_absOnly_of_abs_sub_le (x := a.val + b.val) (y := (a + b).val) (eps := _)\n (eps32_nonneg (x := a.val + b.val)... | [
{
"name": "approxR_absOnly_of_abs_sub_le",
"text": "/--\nHelper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.\n\nInformal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.\n-/\nprivate lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps)... | [
{
"name": "mul_approxR",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 491,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | @@ -57,6 +57,15 @@
-/
/--
+Helper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.
+
+Informal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.
+-/
+private lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps) (h : abs (y - x) ≤ eps) :
+ 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_5f05d6f2513c_3 | e2dc2b162df0e0c3 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/RuntimeApprox.lean | RuntimeApprox | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_approxR",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine approxR_absOnly_of_abs_sub_le (x := a.val + b.val) (y := (a + b).val) (eps := _)\n (eps32_nonneg (x := a.val + b.val)... | [
{
"name": "approxR_absOnly_of_abs_sub_le",
"text": "/--\nHelper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.\n\nInformal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.\n-/\nprivate lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps)... | [
{
"name": "div_approxR",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 15,
"n_chars": 539,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | @@ -57,6 +57,15 @@
-/
/--
+Helper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.
+
+Informal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.
+-/
+private lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps) (h : abs (y - x) ≤ eps) :
+ 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_5f05d6f2513c_4 | 87d98b278f970e58 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/RuntimeApprox.lean | RuntimeApprox | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_approxR",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine approxR_absOnly_of_abs_sub_le (x := a.val + b.val) (y := (a + b).val) (eps := _)\n (eps32_nonneg (x := a.val + b.val)... | [
{
"name": "approxR_absOnly_of_abs_sub_le",
"text": "/--\nHelper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.\n\nInformal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.\n-/\nprivate lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps)... | [
{
"name": "exp_approxR",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 515,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | @@ -57,6 +57,15 @@
-/
/--
+Helper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.
+
+Informal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.
+-/
+private lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps) (h : abs (y - x) ≤ eps) :
+ 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_5f05d6f2513c_5 | 2ea7ae51534cbea1 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/RuntimeApprox.lean | RuntimeApprox | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_approxR",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine approxR_absOnly_of_abs_sub_le (x := a.val + b.val) (y := (a + b).val) (eps := _)\n (eps32_nonneg (x := a.val + b.val)... | [
{
"name": "approxR_absOnly_of_abs_sub_le",
"text": "/--\nHelper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.\n\nInformal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.\n-/\nprivate lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps)... | [
{
"name": "tanh_approxR",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 472,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | @@ -57,6 +57,15 @@
-/
/--
+Helper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.
+
+Informal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.
+-/
+private lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps) (h : abs (y - x) ≤ eps) :
+ 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_5f05d6f2513c_6 | ca7dc374781194f2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/RuntimeApprox.lean | RuntimeApprox | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_approxR",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine approxR_absOnly_of_abs_sub_le (x := a.val + b.val) (y := (a + b).val) (eps := _)\n (eps32_nonneg (x := a.val + b.val)... | [
{
"name": "approxR_absOnly_of_abs_sub_le",
"text": "/--\nHelper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.\n\nInformal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.\n-/\nprivate lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps)... | [
{
"name": "log_approxR",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 502,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | @@ -57,6 +57,15 @@
-/
/--
+Helper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.
+
+Informal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.
+-/
+private lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps) (h : abs (y - x) ≤ eps) :
+ 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_5f05d6f2513c_7 | 7e1f8cff2cf2796b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/RuntimeApprox.lean | RuntimeApprox | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_approxR",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine approxR_absOnly_of_abs_sub_le (x := a.val + b.val) (y := (a + b).val) (eps := _)\n (eps32_nonneg (x := a.val + b.val)... | [
{
"name": "approxR_absOnly_of_abs_sub_le",
"text": "/--\nHelper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.\n\nInformal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.\n-/\nprivate lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps)... | [
{
"name": "cos_approxR",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 460,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | @@ -57,6 +57,15 @@
-/
/--
+Helper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.
+
+Informal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.
+-/
+private lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps) (h : abs (y - x) ≤ eps) :
+ 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_5f05d6f2513c_8 | 227284d3b6c1c3b5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/RuntimeApprox.lean | RuntimeApprox | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_approxR",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine approxR_absOnly_of_abs_sub_le (x := a.val + b.val) (y := (a + b).val) (eps := _)\n (eps32_nonneg (x := a.val + b.val)... | [
{
"name": "approxR_absOnly_of_abs_sub_le",
"text": "/--\nHelper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.\n\nInformal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.\n-/\nprivate lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps)... | [
{
"name": "sin_approxR",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 460,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | @@ -57,6 +57,15 @@
-/
/--
+Helper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.
+
+Informal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.
+-/
+private lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps) (h : abs (y - x) ≤ eps) :
+ 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_5f05d6f2513c_9 | b4f8440bfe9f5098 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/RuntimeApprox.lean | RuntimeApprox | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_approxR",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine approxR_absOnly_of_abs_sub_le (x := a.val + b.val) (y := (a + b).val) (eps := _)\n (eps32_nonneg (x := a.val + b.val)... | [
{
"name": "approxR_absOnly_of_abs_sub_le",
"text": "/--\nHelper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.\n\nInformal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.\n-/\nprivate lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps)... | [
{
"name": "sinh_approxR",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 472,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | @@ -57,6 +57,15 @@
-/
/--
+Helper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.
+
+Informal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.
+-/
+private lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps) (h : abs (y - x) ≤ eps) :
+ 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_5f05d6f2513c_10 | d3d16b7b0f958d5c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/RuntimeApprox.lean | RuntimeApprox | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_approxR",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine approxR_absOnly_of_abs_sub_le (x := a.val + b.val) (y := (a + b).val) (eps := _)\n (eps32_nonneg (x := a.val + b.val)... | [
{
"name": "approxR_absOnly_of_abs_sub_le",
"text": "/--\nHelper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.\n\nInformal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.\n-/\nprivate lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps)... | [
{
"name": "cosh_approxR",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 472,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | @@ -57,6 +57,15 @@
-/
/--
+Helper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.
+
+Informal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.
+-/
+private lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps) (h : abs (y - x) ≤ eps) :
+ 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_5f05d6f2513c_11 | 24f9f12e845757c4 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/RuntimeApprox.lean | RuntimeApprox | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_approxR",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine approxR_absOnly_of_abs_sub_le (x := a.val + b.val) (y := (a + b).val) (eps := _)\n (eps32_nonneg (x := a.val + b.val)... | [
{
"name": "approxR_absOnly_of_abs_sub_le",
"text": "/--\nHelper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.\n\nInformal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.\n-/\nprivate lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps)... | [
{
"name": "sqrt_approxR",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 472,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | @@ -57,6 +57,15 @@
-/
/--
+Helper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.
+
+Informal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.
+-/
+private lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps) (h : abs (y - x) ≤ eps) :
+ 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_5f05d6f2513c_12 | f186eec855a3e399 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/RuntimeApprox.lean | RuntimeApprox | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_approxR",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n refine approxR_absOnly_of_abs_sub_le (x := a.val + b.val) (y := (a + b).val) (eps := _)\n (eps32_nonneg (x := a.val + b.val)... | [
{
"name": "approxR_absOnly_of_abs_sub_le",
"text": "/--\nHelper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.\n\nInformal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.\n-/\nprivate lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps)... | [
{
"name": "abs_approxR",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 15,
"n_chars": 479,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting": ... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
public import NN.Proofs.RuntimeApprox.Core.Tolerance
import Mathlib.Algebra.Order.Algebra
import NN.Floats.FP32.Error
/-!
# Bridging `FP32` error bounds... | @@ -57,6 +57,15 @@
-/
/--
+Helper: turn a plain absolute-error inequality into an `approxR` with an absolute-only tolerance.
+
+Informal: if `|y - x| ≤ eps` and `eps ≥ 0`, then `x ≈[absOnly eps] y`.
+-/
+private lemma approxR_absOnly_of_abs_sub_le {x y eps : ℝ} (heps : 0 ≤ eps) (h : abs (y - x) ≤ eps) :
+ 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_0f93b1d7f263_0 | ae463b8068195fc8 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Spec/Layers/Utils.lean | Utils | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "get_at_or_zero_pad_multi_channel",
"depth": 1,
"n_commands": 0,
"n_lines": 58,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases img with\n | dim fC =>\n by_cases hp : p < inH + 2 * padding\n · by_cases h... | [
{
"name": "get_at_or_zero_getValueAtPosition",
"text": "/--\n`getValueAtPosition` agrees with the generic list-indexing helper `get_at_or_zero`.\n\nIn particular, reading a scalar via the specialized `(x, y)` accessor is the same as reading\nwith indices `[x, y]`, where both return `0` out of bounds.\n-/\nl... | [
{
"name": "get_at_or_zero_pad_multi_channel",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 76,
"n_chars": 3771,
"n_subproofs": 12,
"n_tactics": 53,
"cyclomatic": 6,
"n_automation": 10,
"n_rewrites": 0,
"n_structural": 9,
"automation_only": f... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.TensorOps
/-!
# Image/tensor utilities (spec layer)
Convenience aliases and helpers for 2‑D images (`H×W`) and multi‑channel images (`C×H×W`),
plus padding and wi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.TensorOps
/-!
# Image/tensor utilities (spec layer)
Convenience aliases and helpers for 2‑D images (`H×W`) and multi‑channel images (`C×H×W`),
plus padding and wi... | @@ -85,6 +85,35 @@
else Tensor.scalar 0
/--
+`getValueAtPosition` agrees with the generic list-indexing helper `get_at_or_zero`.
+
+In particular, reading a scalar via the specialized `(x, y)` accessor is the same as reading
+with indices `[x, y]`, where both return `0` out of bounds.
+-/
+lemma get_at_or_zero_ge... | {
"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_0f93b1d7f263_1 | d567d61b14a1f1aa | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Spec/Layers/Utils.lean | Utils | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "get_at_or_zero_pad_multi_channel_shift",
"depth": 1,
"n_commands": 0,
"n_lines": 21,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Use the general pad read lemma; this coordinate is never in the top/left padding.\n have hpad :... | [
{
"name": "get_at_or_zero_pad_multi_channel",
"text": "/--\nCharacterization lemma for `pad_multi_channel` under list-indexing (`get_at_or_zero`).\n\nReading the padded tensor at `[c, p, q]` yields `0` in the top/left padding region, and otherwise\nreads the original tensor at `[c, p - padding, q - padding]... | [
{
"name": "get_at_or_zero_pad_multi_channel_shift",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 36,
"n_chars": 1590,
"n_subproofs": 5,
"n_tactics": 19,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 4,
"automation_only... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.TensorOps
/-!
# Image/tensor utilities (spec layer)
Convenience aliases and helpers for 2‑D images (`H×W`) and multi‑channel images (`C×H×W`),
plus padding and wi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.TensorOps
/-!
# Image/tensor utilities (spec layer)
Convenience aliases and helpers for 2‑D images (`H×W`) and multi‑channel images (`C×H×W`),
plus padding and wi... | @@ -149,6 +149,81 @@
getValueAtPosition (getAtSpec img c) x y)))
/--
+Characterization lemma for `pad_multi_channel` under list-indexing (`get_at_or_zero`).
+
+Reading the padded tensor at `[c, p, q]` yields `0` in the top/left padding region, and otherwise
+reads the original tensor at `[c, p - padding, ... | {
"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_59b47000e5dd_0 | a2ed1e881b9e0792 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/Geometry3D/Box3D.lean | Box3D | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "pinholePixelInterval_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n addInterval_sound\n (mulNonnegInterval_sound hfNonneg hcoordNonneg hf hcoord)\n hc",
"n_chars": 89,
"... | [
{
"name": "addInterval_sound",
"text": "/--\nSoundness of interval addition.\n\nIf `x ∈ I` and `y ∈ J`, then `x + y ∈ I + J`.\n-/\ntheorem addInterval_sound\n {α : Type} [Field α] [LinearOrder α] [IsStrictOrderedRing α]\n {I J : ScalarInterval α} {x y : α}\n (hx : InInterval I x) (hy : InInterval J... | [
{
"name": "pinholePixelInterval_sound",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 21,
"n_chars": 850,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"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.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | @@ -98,6 +98,21 @@
hi := num.hi / den.lo
/--
+Soundness of interval addition.
+
+If `x ∈ I` and `y ∈ J`, then `x + y ∈ I + J`.
+-/
+theorem addInterval_sound
+ {α : Type} [Field α] [LinearOrder α] [IsStrictOrderedRing α]
+ {I J : ScalarInterval α} {x y : α}
+ (hx : InInterval I x) (hy : InInterval J y) :... | {
"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_59b47000e5dd_1 | 85c3c855de0aa48d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/Geometry3D/Box3D.lean | Box3D | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "pinholePixelInterval_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n addInterval_sound\n (mulNonnegInterval_sound hfNonneg hcoordNonneg hf hcoord)\n hc",
"n_chars": 89,
"... | [
{
"name": "addInterval_sound",
"text": "/--\nSoundness of interval addition.\n\nIf `x ∈ I` and `y ∈ J`, then `x + y ∈ I + J`.\n-/\ntheorem addInterval_sound\n {α : Type} [Field α] [LinearOrder α] [IsStrictOrderedRing α]\n {I J : ScalarInterval α} {x y : α}\n (hx : InInterval I x) (hy : InInterval J... | [
{
"name": "pinhole_intrinsics_interval_inside_bbox_sound",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 4,
"n_lines": 53,
"n_chars": 2200,
"n_subproofs": 2,
"n_tactics": 13,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automati... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | @@ -98,6 +98,21 @@
hi := num.hi / den.lo
/--
+Soundness of interval addition.
+
+If `x ∈ I` and `y ∈ J`, then `x + y ∈ I + J`.
+-/
+theorem addInterval_sound
+ {α : Type} [Field α] [LinearOrder α] [IsStrictOrderedRing α]
+ {I J : ScalarInterval α} {x y : α}
+ (hx : InInterval I x) (hy : InInterval J y) :... | {
"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_59b47000e5dd_2 | b232fc0f67299d48 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/Geometry3D/Box3D.lean | Box3D | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "homogeneous_projection_interval_inside_bbox_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hx :\n InInterval (divNonnegByPosInterval uNumI zI) (uNum / z) :=\n divNonn... | [
{
"name": "divNonnegByPosInterval_sound",
"text": "/--\nSoundness of perspective-style interval division.\n\nIf `x ∈ num`, `z ∈ den`, `num` is nonnegative, and the denominator interval is bounded away from\nzero, then `x / z` lies in `[num.lo / den.hi, num.hi / den.lo]`.\n\nThis theorem is the mathematical ... | [
{
"name": "homogeneous_projection_interval_inside_bbox_sound",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 48,
"n_chars": 2006,
"n_subproofs": 2,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"auto... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | @@ -98,6 +98,35 @@
hi := num.hi / den.lo
/--
+Soundness of perspective-style interval division.
+
+If `x ∈ num`, `z ∈ den`, `num` is nonnegative, and the denominator interval is bounded away from
+zero, then `x / z` lies in `[num.lo / den.hi, num.hi / den.lo]`.
+
+This theorem is the mathematical core behind the ... | {
"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_59b47000e5dd_3 | edcefee5823a5251 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/Geometry3D/Box3D.lean | Box3D | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 3 | [
{
"theorem_name": "checkPositiveDepths_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro i\n have hi : decide (0 < certProjectZ cert i) = true :=\n list_all_true_of_mem h (by simp)\n exact of... | [
{
"name": "list_all_true_of_mem",
"text": "/-- If `List.all p xs` succeeds, then `p` succeeds on every member of `xs`. -/\ntheorem list_all_true_of_mem {α : Type} {p : α → Bool} {xs : List α}\n (h : xs.all p = true) {x : α} (hx : x ∈ xs) : p x = true := by\n induction xs with\n | nil =>\n simp at ... | [
{
"name": "checkPositiveDepths_sound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 10,
"n_chars": 370,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 2,
"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.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | @@ -133,6 +133,19 @@
x := divNonnegByPosInterval uNumI zI
y := divNonnegByPosInterval vNumI zI
+/-- If `List.all p xs` succeeds, then `p` succeeds on every member of `xs`. -/
+theorem list_all_true_of_mem {α : Type} {p : α → Bool} {xs : List α}
+ (h : xs.all p = true) {x : α} (hx : x ∈ xs) : p x = true := by... | {
"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_59b47000e5dd_4 | 1ac2b2413839e1b7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/Geometry3D/Box3D.lean | Box3D | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 3 | [
{
"theorem_name": "checkPositiveDepths_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro i\n have hi : decide (0 < certProjectZ cert i) = true :=\n list_all_true_of_mem h (by simp)\n exact of... | [
{
"name": "list_all_true_of_mem",
"text": "/-- If `List.all p xs` succeeds, then `p` succeeds on every member of `xs`. -/\ntheorem list_all_true_of_mem {α : Type} {p : α → Bool} {xs : List α}\n (h : xs.all p = true) {x : α} (hx : x ∈ xs) : p x = true := by\n induction xs with\n | nil =>\n simp at ... | [
{
"name": "checkProjectedInImage_sound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 522,
"n_subproofs": 1,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 2,
"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.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | @@ -133,6 +133,19 @@
x := divNonnegByPosInterval uNumI zI
y := divNonnegByPosInterval vNumI zI
+/-- If `List.all p xs` succeeds, then `p` succeeds on every member of `xs`. -/
+theorem list_all_true_of_mem {α : Type} {p : α → Bool} {xs : List α}
+ (h : xs.all p = true) {x : α} (hx : x ∈ xs) : p x = true := by... | {
"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_59b47000e5dd_5 | 1fbef6ca60d89e3c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/Geometry3D/Box3D.lean | Box3D | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 3 | [
{
"theorem_name": "checkPositiveDepths_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro i\n have hi : decide (0 < certProjectZ cert i) = true :=\n list_all_true_of_mem h (by simp)\n exact of... | [
{
"name": "list_all_true_of_mem",
"text": "/-- If `List.all p xs` succeeds, then `p` succeeds on every member of `xs`. -/\ntheorem list_all_true_of_mem {α : Type} {p : α → Bool} {xs : List α}\n (h : xs.all p = true) {x : α} (hx : x ∈ xs) : p x = true := by\n induction xs with\n | nil =>\n simp at ... | [
{
"name": "checkBBoxEnclosesProjection_sound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 610,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": fal... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | @@ -133,6 +133,19 @@
x := divNonnegByPosInterval uNumI zI
y := divNonnegByPosInterval vNumI zI
+/-- If `List.all p xs` succeeds, then `p` succeeds on every member of `xs`. -/
+theorem list_all_true_of_mem {α : Type} {p : α → Bool} {xs : List α}
+ (h : xs.all p = true) {x : α} (hx : x ∈ xs) : p x = true := by... | {
"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_59b47000e5dd_6 | 33dd59cbc9b4e8d7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/Geometry3D/Box3D.lean | Box3D | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 3 | [
{
"theorem_name": "checkPositiveDepths_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro i\n have hi : decide (0 < certProjectZ cert i) = true :=\n list_all_true_of_mem h (by simp)\n exact of... | [
{
"name": "list_all_true_of_mem",
"text": "/-- If `List.all p xs` succeeds, then `p` succeeds on every member of `xs`. -/\ntheorem list_all_true_of_mem {α : Type} {p : α → Bool} {xs : List α}\n (h : xs.all p = true) {x : α} (hx : x ∈ xs) : p x = true := by\n induction xs with\n | nil =>\n simp at ... | [
{
"name": "checkCert_sound",
"fan_in": 0,
"n_deps_direct": 6,
"n_deps_transitive": 7,
"n_lines": 24,
"n_chars": 913,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nesti... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.API.Public
public import NN.Verification.Util.FloatApprox
public import NN.Verification.Util.Json
public import NN.Verification.Util.Tensor
/-!
# Tensor-native 3D box camera... | @@ -133,6 +133,19 @@
x := divNonnegByPosInterval uNumI zI
y := divNonnegByPosInterval vNumI zI
+/-- If `List.all p xs` succeeds, then `p` succeeds on every member of `xs`. -/
+theorem list_all_true_of_mem {α : Type} {p : α → Bool} {xs : List α}
+ (h : xs.all p = true) {x : α} (hx : x ∈ xs) : p x = true := by... | {
"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_d5a7e1bd8a5e_0 | 2dbdf209f1b5b9d9 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "toReal_hinge_term_eq_fp32_val",
"depth": 1,
"n_commands": 0,
"n_lines": 49,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Subtraction refinement.\n have hsubR :\n IEEE32Exec.toReal (IEEE32Exec.sub x (t i)) =\n Torc... | [
{
"name": "fp32_sub_val",
"text": "/-- FP32 subtraction in the rounded-`ℝ` model uses the same `fp32Round` operation as IEEE32Exec. -/\nprivate theorem fp32_sub_val (a b : FP32) :\n (a - b).val = TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val - b.val) := by\n change TorchLean.Floats.round32 (a.val... | [
{
"name": "toReal_hinge_term_eq_fp32_val",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 65,
"n_chars": 3579,
"n_subproofs": 6,
"n_tactics": 43,
"cyclomatic": 1,
"n_automation": 8,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import 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... | @@ -199,6 +199,13 @@
HingeSumFinite t c x (Numbers.zero : IEEE32Exec) (List.finRange n) ∧
IEEE32Exec.isFinite (hingeFunIeee (t := t) (c := c) (b := b) x) = true
+/-- FP32 subtraction in the rounded-`ℝ` model uses the same `fp32Round` operation as IEEE32Exec. -/
+private theorem fp32_sub_val (a b : FP32) :
+... | {
"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_d5a7e1bd8a5e_1 | 3fc10deeac352b77 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "toReal_hinge_term_eq_fp32_val",
"depth": 1,
"n_commands": 0,
"n_lines": 49,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Subtraction refinement.\n have hsubR :\n IEEE32Exec.toReal (IEEE32Exec.sub x (t i)) =\n Torc... | [
{
"name": "fp32_sub_val",
"text": "/-- FP32 subtraction in the rounded-`ℝ` model uses the same `fp32Round` operation as IEEE32Exec. -/\nprivate theorem fp32_sub_val (a b : FP32) :\n (a - b).val = TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val - b.val) := by\n change TorchLean.Floats.round32 (a.val... | [
{
"name": "toReal_hinge_sum_ieee_eq_fp32_val",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 6,
"n_lines": 50,
"n_chars": 2533,
"n_subproofs": 5,
"n_tactics": 27,
"cyclomatic": 2,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": fa... | 6 | /-
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... | @@ -206,6 +206,13 @@
TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val + b.val)
rfl
+/-- FP32 subtraction in the rounded-`ℝ` model uses the same `fp32Round` operation as IEEE32Exec. -/
+private theorem fp32_sub_val (a b : FP32) :
+ (a - b).val = TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val - b.v... | {
"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_d5a7e1bd8a5e_2 | 76289803818696b9 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "toReal_hinge_term_eq_fp32_val",
"depth": 1,
"n_commands": 0,
"n_lines": 49,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Subtraction refinement.\n have hsubR :\n IEEE32Exec.toReal (IEEE32Exec.sub x (t i)) =\n Torc... | [
{
"name": "fp32_mul_val",
"text": "/-- FP32 multiplication in the rounded-`ℝ` model uses the same `fp32Round` operation as IEEE32Exec. -/\nprivate theorem fp32_mul_val (a b : FP32) :\n (a * b).val = TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val * b.val) := by\n change TorchLean.Floats.round32 (a.... | [
{
"name": "toReal_hinge_fun_ieee_eq_fp32_val",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 8,
"n_lines": 66,
"n_chars": 3529,
"n_subproofs": 8,
"n_tactics": 38,
"cyclomatic": 1,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": fa... | 8 | /-
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... | @@ -213,6 +213,13 @@
TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val - b.val)
rfl
+/-- FP32 multiplication in the rounded-`ℝ` model uses the same `fp32Round` operation as IEEE32Exec. -/
+private theorem fp32_mul_val (a b : FP32) :
+ (a * b).val = TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.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_d5a7e1bd8a5e_3 | a2d9ad3832bd6bc3 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "toReal_hinge_term_eq_fp32_val",
"depth": 1,
"n_commands": 0,
"n_lines": 49,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Subtraction refinement.\n have hsubR :\n IEEE32Exec.toReal (IEEE32Exec.sub x (t i)) =\n Torc... | [
{
"name": "fp32_mul_val",
"text": "/-- FP32 multiplication in the rounded-`ℝ` model uses the same `fp32Round` operation as IEEE32Exec. -/\nprivate theorem fp32_mul_val (a b : FP32) :\n (a * b).val = TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val * b.val) := by\n change TorchLean.Floats.round32 (a.... | [
{
"name": "hinge_fun_ieee_abs_error_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 9,
"n_lines": 28,
"n_chars": 1404,
"n_subproofs": 1,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 9 | /-
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... | @@ -213,6 +213,13 @@
TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val - b.val)
rfl
+/-- FP32 multiplication in the rounded-`ℝ` model uses the same `fp32Round` operation as IEEE32Exec. -/
+private theorem fp32_mul_val (a b : FP32) :
+ (a * b).val = TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.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_d5a7e1bd8a5e_4 | 51b6a8b89c44fcbe | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "toReal_hinge_term_eq_fp32_val",
"depth": 1,
"n_commands": 0,
"n_lines": 49,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Subtraction refinement.\n have hsubR :\n IEEE32Exec.toReal (IEEE32Exec.sub x (t i)) =\n Torc... | [
{
"name": "fp32_mul_val",
"text": "/-- FP32 multiplication in the rounded-`ℝ` model uses the same `fp32Round` operation as IEEE32Exec. -/\nprivate theorem fp32_mul_val (a b : FP32) :\n (a * b).val = TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val * b.val) := by\n change TorchLean.Floats.round32 (a.... | [
{
"name": "hinge_fun_total_abs_error_ieee_le",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 10,
"n_lines": 37,
"n_chars": 2031,
"n_subproofs": 2,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": f... | 10 | /-
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... | @@ -213,6 +213,13 @@
TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val - b.val)
rfl
+/-- FP32 multiplication in the rounded-`ℝ` model uses the same `fp32Round` operation as IEEE32Exec. -/
+private theorem fp32_mul_val (a b : FP32) :
+ (a * b).val = TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.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_d5a7e1bd8a5e_5 | b8479f2c222bf144 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 2 | [
{
"theorem_name": "toReal_hinge_sum_ieee_eq_fp32_val",
"depth": 1,
"n_commands": 0,
"n_lines": 31,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction hfin with\n | nil hacc =>\n simp [List.foldl]\n | cons hsub hmax hmul hadd hrest ih =>\... | [
{
"name": "fp32_ext",
"text": "/-- Extensionality for the rounded-`ℝ` FP32 wrapper. -/\nprivate theorem fp32_ext {u v : FP32} (h : u.val = v.val) : u = v := by\n cases u with\n | mk uval =>\n cases v with\n | mk vval =>\n cases h\n rfl\n\n",
"fan_in": 2,
"n_lines": 10,
... | [
{
"name": "hinge_fun_total_abs_error_ieee_lt",
"fan_in": 5,
"n_deps_direct": 1,
"n_deps_transitive": 11,
"n_lines": 31,
"n_chars": 1496,
"n_subproofs": 2,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": f... | 11 | /-
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... | @@ -220,6 +220,15 @@
TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val * b.val)
rfl
+/-- Extensionality for the rounded-`ℝ` FP32 wrapper. -/
+private theorem fp32_ext {u v : FP32} (h : u.val = v.val) : u = v := by
+ cases u with
+ | mk uval =>
+ cases v with
+ | mk vval =>
+ cases h
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d5a7e1bd8a5e_6 | 0f0bf8aeef33837b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 2 | [
{
"theorem_name": "toReal_hinge_sum_ieee_eq_fp32_val",
"depth": 1,
"n_commands": 0,
"n_lines": 31,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction hfin with\n | nil hacc =>\n simp [List.foldl]\n | cons hsub hmax hmul hadd hrest ih =>\... | [
{
"name": "fp32_ext",
"text": "/-- Extensionality for the rounded-`ℝ` FP32 wrapper. -/\nprivate theorem fp32_ext {u v : FP32} (h : u.val = v.val) : u = v := by\n cases u with\n | mk uval =>\n cases v with\n | mk vval =>\n cases h\n rfl\n\n",
"fan_in": 2,
"n_lines": 10,
... | [
{
"name": "reluApproximationIccIEEE32Exec_fromHinge",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 12,
"n_lines": 55,
"n_chars": 2569,
"n_subproofs": 1,
"n_tactics": 11,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 5,
"automation_o... | 12 | /-
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... | @@ -220,6 +220,15 @@
TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val * b.val)
rfl
+/-- Extensionality for the rounded-`ℝ` FP32 wrapper. -/
+private theorem fp32_ext {u v : FP32} (h : u.val = v.val) : u = v := by
+ cases u with
+ | mk uval =>
+ cases v with
+ | mk vval =>
+ cases h
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d5a7e1bd8a5e_7 | c84f432a89f23eff | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 2 | [
{
"theorem_name": "toReal_hinge_sum_ieee_eq_fp32_val",
"depth": 1,
"n_commands": 0,
"n_lines": 31,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction hfin with\n | nil hacc =>\n simp [List.foldl]\n | cons hsub hmax hmul hadd hrest ih =>\... | [
{
"name": "fp32_ext",
"text": "/-- Extensionality for the rounded-`ℝ` FP32 wrapper. -/\nprivate theorem fp32_ext {u v : FP32} (h : u.val = v.val) : u = v := by\n cases u with\n | mk uval =>\n cases v with\n | mk vval =>\n cases h\n rfl\n\n",
"fan_in": 2,
"n_lines": 10,
... | [
{
"name": "reluApproximationIccIEEE32Exec_threeTerm",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 12,
"n_lines": 83,
"n_chars": 4287,
"n_subproofs": 6,
"n_tactics": 36,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 3,
"automation_o... | 12 | /-
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... | @@ -220,6 +220,15 @@
TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val * b.val)
rfl
+/-- Extensionality for the rounded-`ℝ` FP32 wrapper. -/
+private theorem fp32_ext {u v : FP32} (h : u.val = v.val) : u = v := by
+ cases u with
+ | mk uval =>
+ cases v with
+ | mk vval =>
+ cases h
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d5a7e1bd8a5e_8 | bc3af78b90f01935 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 2 | [
{
"theorem_name": "toReal_hinge_sum_ieee_eq_fp32_val",
"depth": 1,
"n_commands": 0,
"n_lines": 31,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction hfin with\n | nil hacc =>\n simp [List.foldl]\n | cons hsub hmax hmul hadd hrest ih =>\... | [
{
"name": "fp32_ext",
"text": "/-- Extensionality for the rounded-`ℝ` FP32 wrapper. -/\nprivate theorem fp32_ext {u v : FP32} (h : u.val = v.val) : u = v := by\n cases u with\n | mk uval =>\n cases v with\n | mk vval =>\n cases h\n rfl\n\n",
"fan_in": 2,
"n_lines": 10,
... | [
{
"name": "hinge_fun_total_abs_error_ieee_lt_of_finiteProp",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 13,
"n_lines": 25,
"n_chars": 1175,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automa... | 13 | /-
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... | @@ -238,6 +238,15 @@
TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val * b.val)
rfl
+/-- Extensionality for the rounded-`ℝ` FP32 wrapper. -/
+private theorem fp32_ext {u v : FP32} (h : u.val = v.val) : u = v := by
+ cases u with
+ | mk uval =>
+ cases v with
+ | mk vval =>
+ cases h
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d5a7e1bd8a5e_9 | 82ca5f4086af9906 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 2 | [
{
"theorem_name": "toReal_hinge_sum_ieee_eq_fp32_val",
"depth": 1,
"n_commands": 0,
"n_lines": 31,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction hfin with\n | nil hacc =>\n simp [List.foldl]\n | cons hsub hmax hmul hadd hrest ih =>\... | [
{
"name": "fp32_ext",
"text": "/-- Extensionality for the rounded-`ℝ` FP32 wrapper. -/\nprivate theorem fp32_ext {u v : FP32} (h : u.val = v.val) : u = v := by\n cases u with\n | mk uval =>\n cases v with\n | mk vval =>\n cases h\n rfl\n\n",
"fan_in": 2,
"n_lines": 10,
... | [
{
"name": "reluApproximationIccIEEE32Exec_threeTerm_bias",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 12,
"n_lines": 78,
"n_chars": 4008,
"n_subproofs": 6,
"n_tactics": 35,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 3,
"automat... | 12 | /-
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... | @@ -220,6 +220,15 @@
TorchLean.Floats.IEEE754.IEEE32Exec.fp32Round (a.val * b.val)
rfl
+/-- Extensionality for the rounded-`ℝ` FP32 wrapper. -/
+private theorem fp32_ext {u v : FP32} (h : u.val = v.val) : u = v := by
+ cases u with
+ | mk uval =>
+ cases v with
+ | mk vval =>
+ cases h
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d5a7e1bd8a5e_10 | e0528daccf9cd9b6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "toReal_roundDyadicToIEEE32_abs_error_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hbridge :=\n TorchLean.Floats.IEEE754.IEEE32Exec.toReal_roundDyadicToIEEE32_eq_fp32Round... | [
{
"name": "fp32Round_abs_error_bound",
"text": "/--\nGeneric half-ulp absolute-error bound for the rounded-`ℝ` binary32 model.\n\nThis is the standard floating-point local rounding statement specialized to TorchLean's FP32\nformat parameters. It is the bridge from abstract approximation coefficients to exp... | [
{
"name": "toReal_roundDyadicToIEEE32_abs_error_bound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 27,
"n_chars": 1340,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"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.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... | @@ -200,6 +200,20 @@
IEEE32Exec.isFinite (hingeFunIeee (t := t) (c := c) (b := b) x) = true
/--
+Generic half-ulp absolute-error bound for the rounded-`ℝ` binary32 model.
+
+This is the standard floating-point local rounding statement specialized to TorchLean's FP32
+format parameters. It is the bridge from ab... | {
"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_d5a7e1bd8a5e_11 | c435eb2de755c683 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "abs_relu",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [abs_of_nonneg (relu_nonneg u)]",
"n_chars": 42,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_au... | [
{
"name": "relu_nonneg",
"text": "/-- Nonnegativity of the real ReLU used in the compact-domain perturbation bound. -/\nprivate lemma relu_nonneg (u : ℝ) : 0 ≤ relu u := by\n -- `relu u = max u 0`.\n simp [relu, Activation.Math.reluSpec]\n\n",
"fan_in": 1,
"n_lines": 6,
"n_chars": 208,
"n_... | [
{
"name": "abs_relu",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 5,
"n_chars": 167,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2
}... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.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... | @@ -199,8 +199,14 @@
HingeSumFinite t c x (Numbers.zero : IEEE32Exec) (List.finRange n) ∧
IEEE32Exec.isFinite (hingeFunIeee (t := t) (c := c) (b := b) x) = true
+/-- Nonnegativity of the real ReLU used in the compact-domain perturbation bound. -/
+private lemma relu_nonneg (u : ℝ) : 0 ≤ relu u := by
+ -- `... | {
"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_d5a7e1bd8a5e_12 | 213dd8b89941e5ec | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "abs_relu_sub_le_abs_width_Icc",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n calc\n abs (relu (x - t)) = relu (x - t) := abs_relu (x - t)\n _ ≤ abs (x - t) := relu_le_abs (x - t)\n... | [
{
"name": "abs_relu",
"text": "/-- Since ReLU is nonnegative, its absolute value is itself. -/\nprivate lemma abs_relu (u : ℝ) : abs (relu u) = relu u := by\n simp [abs_of_nonneg (relu_nonneg u)]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 167,
"n_subproofs": 0,
"n_tactics": 2,
"cyc... | [
{
"name": "abs_relu_sub_le_abs_width_Icc",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 10,
"n_chars": 431,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"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.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... | @@ -204,6 +204,10 @@
-- `relu u = max u 0`.
simp [relu, Activation.Math.reluSpec]
+/-- Since ReLU is nonnegative, its absolute value is itself. -/
+private lemma abs_relu (u : ℝ) : abs (relu u) = relu u := by
+ simp [abs_of_nonneg (relu_nonneg u)]
+
/-- ReLU is pointwise bounded by absolute value. -/
private... | {
"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_d5a7e1bd8a5e_13 | c2397000c8eba8f1 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "abs_relu_sub_le_abs_width_Icc",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n calc\n abs (relu (x - t)) = relu (x - t) := abs_relu (x - t)\n _ ≤ abs (x - t) := relu_le_abs (x - t)\n... | [
{
"name": "abs_relu",
"text": "/-- Since ReLU is nonnegative, its absolute value is itself. -/\nprivate lemma abs_relu (u : ℝ) : abs (relu u) = relu u := by\n simp [abs_of_nonneg (relu_nonneg u)]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 167,
"n_subproofs": 0,
"n_tactics": 2,
"cyc... | [
{
"name": "hinge_fun_abs_error_le_of_params_Icc",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 5,
"n_lines": 109,
"n_chars": 5410,
"n_subproofs": 16,
"n_tactics": 80,
"cyclomatic": 1,
"n_automation": 11,
"n_rewrites": 1,
"n_structural": 10,
"automation_on... | 5 | /-
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... | @@ -204,6 +204,10 @@
-- `relu u = max u 0`.
simp [relu, Activation.Math.reluSpec]
+/-- Since ReLU is nonnegative, its absolute value is itself. -/
+private lemma abs_relu (u : ℝ) : abs (relu u) = relu u := by
+ simp [abs_of_nonneg (relu_nonneg u)]
+
/-- ReLU is pointwise bounded by absolute value. -/
private... | {
"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_d5a7e1bd8a5e_14 | 807eb6f008206b1d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "abs_relu_sub_le_abs_width_Icc",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n calc\n abs (relu (x - t)) = relu (x - t) := abs_relu (x - t)\n _ ≤ abs (x - t) := relu_le_abs (x - t)\n... | [
{
"name": "relu_le_abs",
"text": "/-- ReLU is pointwise bounded by absolute value. -/\nprivate lemma relu_le_abs (u : ℝ) : relu u ≤ abs u := by\n by_cases hu : 0 ≤ u\n · simp [relu, Activation.Math.reluSpec, max_eq_left hu, abs_of_nonneg hu]\n · have hu' : u ≤ 0 := le_of_not_ge hu\n -- `relu u = 0` fo... | [
{
"name": "hinge_fun_abs_error_le_of_params_Icc_uniform",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 6,
"n_lines": 60,
"n_chars": 2532,
"n_subproofs": 8,
"n_tactics": 36,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 8,
"automatio... | 6 | /-
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... | @@ -208,6 +208,14 @@
private lemma abs_relu (u : ℝ) : abs (relu u) = relu u := by
simp [abs_of_nonneg (relu_nonneg u)]
+/-- ReLU is pointwise bounded by absolute value. -/
+private lemma relu_le_abs (u : ℝ) : relu u ≤ abs u := by
+ by_cases hu : 0 ≤ u
+ · simp [relu, Activation.Math.reluSpec, max_eq_left hu, ab... | {
"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_d5a7e1bd8a5e_15 | 32332ad36c46b2f0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "abs_relu_sub_le_abs_width_Icc",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n calc\n abs (relu (x - t)) = relu (x - t) := abs_relu (x - t)\n _ ≤ abs (x - t) := relu_le_abs (x - t)\n... | [
{
"name": "relu_le_abs",
"text": "/-- ReLU is pointwise bounded by absolute value. -/\nprivate lemma relu_le_abs (u : ℝ) : relu u ≤ abs u := by\n by_cases hu : 0 ≤ u\n · simp [relu, Activation.Math.reluSpec, max_eq_left hu, abs_of_nonneg hu]\n · have hu' : u ≤ 0 := le_of_not_ge hu\n -- `relu u = 0` fo... | [
{
"name": "hinge_fun_real_embed_eq_hinge_fun_toReal",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 76,
"n_chars": 3319,
"n_subproofs": 3,
"n_tactics": 43,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 0,
"automation_on... | 7 | /-
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... | @@ -208,6 +208,14 @@
private lemma abs_relu (u : ℝ) : abs (relu u) = relu u := by
simp [abs_of_nonneg (relu_nonneg u)]
+/-- ReLU is pointwise bounded by absolute value. -/
+private lemma relu_le_abs (u : ℝ) : relu u ≤ abs u := by
+ by_cases hu : 0 ≤ u
+ · simp [relu, Activation.Math.reluSpec, max_eq_left hu, ab... | {
"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_d5a7e1bd8a5e_16 | d60a290c625c42f5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "abs_relu_sub_le_abs_width_Icc",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n calc\n abs (relu (x - t)) = relu (x - t) := abs_relu (x - t)\n _ ≤ abs (x - t) := relu_le_abs (x - t)\n... | [
{
"name": "abs_sub_le_abs_width_Icc",
"text": "/--\nIf both points lie in `[a,b]`, their distance is bounded by the interval width.\n\nThis is the compact-domain geometric fact used to control the size of each hinge activation under\nparameter perturbations.\n-/\nprivate lemma abs_sub_le_abs_width_Icc {a b ... | [
{
"name": "hinge_fun_dyadic_quantization_error_le_Icc",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 8,
"n_lines": 65,
"n_chars": 3026,
"n_subproofs": 2,
"n_tactics": 30,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_... | 8 | /-
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... | @@ -216,10 +216,32 @@
-- `relu u = 0` for `u ≤ 0`, so the goal is `0 ≤ |u|`.
simp [relu, Activation.Math.reluSpec, max_eq_right hu']
+/--
+If both points lie in `[a,b]`, their distance is bounded by the interval width.
+
+This is the compact-domain geometric fact used to control the size of each hinge activ... | {
"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_d5a7e1bd8a5e_17 | 26fd6fd30c29dfa4 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "abs_relu_sub_le_abs_width_Icc",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n calc\n abs (relu (x - t)) = relu (x - t) := abs_relu (x - t)\n _ ≤ abs (x - t) := relu_le_abs (x - t)\n... | [
{
"name": "relu_le_abs",
"text": "/-- ReLU is pointwise bounded by absolute value. -/\nprivate lemma relu_le_abs (u : ℝ) : relu u ≤ abs u := by\n by_cases hu : 0 ≤ u\n · simp [relu, Activation.Math.reluSpec, max_eq_left hu, abs_of_nonneg hu]\n · have hu' : u ≤ 0 := le_of_not_ge hu\n -- `relu u = 0` fo... | [
{
"name": "hinge_fun_dyadic_quantization_error_le_Icc_halfUlp",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 11,
"n_lines": 125,
"n_chars": 6233,
"n_subproofs": 9,
"n_tactics": 74,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 6,
"a... | 11 | /-
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... | @@ -248,6 +248,14 @@
private lemma abs_relu (u : ℝ) : abs (relu u) = relu u := by
simp [abs_of_nonneg (relu_nonneg u)]
+/-- ReLU is pointwise bounded by absolute value. -/
+private lemma relu_le_abs (u : ℝ) : relu u ≤ abs u := by
+ by_cases hu : 0 ≤ u
+ · simp [relu, Activation.Math.reluSpec, max_eq_left hu, ab... | {
"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_d5a7e1bd8a5e_18 | e02ba5cd8c096903 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationIEEE32Exec.lean | UniversalApproximationIEEE32Exec | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 26 | 1 | [
{
"theorem_name": "hinge_fun_ieee_abs_error_le",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have href :\n IEEE32Exec.toReal (hingeFunIeee (t := t) (c := c) (b := b) x) =\n (hingeFunFp32 (t :=... | [
{
"name": "toReal_hinge_fun_ieee_eq_fp32_val",
"text": "/--\nRefine the whole executable hinge network to the FP32 rounded-`ℝ` network.\n\nThe theorem composes the fold refinement with the final rounded bias addition. Its hypotheses are\nexactly the finiteness obligations needed by the IEEE-754 bridge lemm... | [
{
"name": "reluApproximationIccIEEE32Exec_dyadicHalfUlp",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 25,
"n_lines": 89,
"n_chars": 4491,
"n_subproofs": 3,
"n_tactics": 33,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automati... | 25 | /-
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... | @@ -384,6 +384,71 @@
simpa [List.foldl, hingeSumStepIeee, termI, termFP, hstart] using ih
/--
+Refine the whole executable hinge network to the FP32 rounded-`ℝ` network.
+
+The theorem composes the fold refinement with the final rounded bias addition. Its hypotheses are
+exactly the finiteness obligations ne... | {
"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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