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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_647b0ad429d5_1 | 584fd928aff7bb78 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 9 | [
{
"theorem_name": "toReal?_eq_some_toReal_of_isFinite_eq_true",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `toDyadic? x` cannot be `none`, otherwise `isFinite x = false`.\n cases hdy : toDyadic? x w... | [
{
"name": "isFinite_eq_false_of_toDyadic?_eq_none",
"text": "/-- `toDyadic? x = none` implies `x` is not finite. -/\ntheorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :\n isFinite x = false := by\n unfold toDyadic? at hx\n cases hcond : (isNaN x || isInf x) with\... | [
{
"name": "toReal?_eq_some_toReal_of_isFinite_eq_true",
"fan_in": 7,
"n_deps_direct": 1,
"n_deps_transitive": 1,
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"n_tactics": 9,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_on... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -49,13 +49,42 @@
/-! ## Basic facts: `isFinite` ↔ `toDyadic?`/`toReal?` -/
+/-- `toDyadic? x = none` implies `x` is not finite. -/
+theorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :
+ isFinite x = false := by
+ unfold toDyadic? at hx
+ cases hcond : (isNaN x || isI... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_2 | ce37046acbf30a5f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 9 | [
{
"theorem_name": "toReal?_eq_some_toReal_of_isFinite_eq_true",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `toDyadic? x` cannot be `none`, otherwise `isFinite x = false`.\n cases hdy : toDyadic? x w... | [
{
"name": "isFinite_eq_false_of_toDyadic?_eq_none",
"text": "/-- `toDyadic? x = none` implies `x` is not finite. -/\ntheorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :\n isFinite x = false := by\n unfold toDyadic? at hx\n cases hcond : (isNaN x || isInf x) with\... | [
{
"name": "toReal_sub_eq_fp32Round_of_isFinite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 36,
"n_chars": 1244,
"n_subproofs": 6,
"n_tactics": 25,
"cyclomatic": 5,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 7,
"automation_only": ... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -49,6 +49,35 @@
/-! ## Basic facts: `isFinite` ↔ `toDyadic?`/`toReal?` -/
+/-- `toDyadic? x = none` implies `x` is not finite. -/
+theorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :
+ isFinite x = false := by
+ unfold toDyadic? at hx
+ cases hcond : (isNaN x || isIn... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_3 | 2974227904bcf99a | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 9 | [
{
"theorem_name": "toReal?_eq_some_toReal_of_isFinite_eq_true",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `toDyadic? x` cannot be `none`, otherwise `isFinite x = false`.\n cases hdy : toDyadic? x w... | [
{
"name": "isFinite_eq_false_of_toDyadic?_eq_none",
"text": "/-- `toDyadic? x = none` implies `x` is not finite. -/\ntheorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :\n isFinite x = false := by\n unfold toDyadic? at hx\n cases hcond : (isNaN x || isInf x) with\... | [
{
"name": "toReal_minimum_eq_min_of_isFinite",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 809,
"n_subproofs": 4,
"n_tactics": 17,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 5,
"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.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -49,6 +49,35 @@
/-! ## Basic facts: `isFinite` ↔ `toDyadic?`/`toReal?` -/
+/-- `toDyadic? x = none` implies `x` is not finite. -/
+theorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :
+ isFinite x = false := by
+ unfold toDyadic? at hx
+ cases hcond : (isNaN x || isIn... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_4 | 97a2c88e81dba650 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 9 | [
{
"theorem_name": "toReal?_eq_some_toReal_of_isFinite_eq_true",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `toDyadic? x` cannot be `none`, otherwise `isFinite x = false`.\n cases hdy : toDyadic? x w... | [
{
"name": "isFinite_eq_false_of_toDyadic?_eq_none",
"text": "/-- `toDyadic? x = none` implies `x` is not finite. -/\ntheorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :\n isFinite x = false := by\n unfold toDyadic? at hx\n cases hcond : (isNaN x || isInf x) with\... | [
{
"name": "toReal_maximum_eq_max_of_isFinite",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 809,
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"n_tactics": 17,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 5,
"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.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -49,6 +49,35 @@
/-! ## Basic facts: `isFinite` ↔ `toDyadic?`/`toReal?` -/
+/-- `toDyadic? x = none` implies `x` is not finite. -/
+theorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :
+ isFinite x = false := by
+ unfold toDyadic? at hx
+ cases hcond : (isNaN x || isIn... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_5 | 758ab374c7a474ec | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 9 | [
{
"theorem_name": "toReal?_eq_some_toReal_of_isFinite_eq_true",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `toDyadic? x` cannot be `none`, otherwise `isFinite x = false`.\n cases hdy : toDyadic? x w... | [
{
"name": "isFinite_eq_false_of_toDyadic?_eq_none",
"text": "/-- `toDyadic? x = none` implies `x` is not finite. -/\ntheorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :\n isFinite x = false := by\n unfold toDyadic? at hx\n cases hcond : (isNaN x || isInf x) with\... | [
{
"name": "compare_eq_some_lt_iff_toReal_lt_of_isFinite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 838,
"n_subproofs": 4,
"n_tactics": 17,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 5,
"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
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -49,6 +49,35 @@
/-! ## Basic facts: `isFinite` ↔ `toDyadic?`/`toReal?` -/
+/-- `toDyadic? x = none` implies `x` is not finite. -/
+theorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :
+ isFinite x = false := by
+ unfold toDyadic? at hx
+ cases hcond : (isNaN x || isIn... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_6 | 7046df090abc6466 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 9 | [
{
"theorem_name": "toReal?_eq_some_toReal_of_isFinite_eq_true",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `toDyadic? x` cannot be `none`, otherwise `isFinite x = false`.\n cases hdy : toDyadic? x w... | [
{
"name": "isFinite_eq_false_of_toDyadic?_eq_none",
"text": "/-- `toDyadic? x = none` implies `x` is not finite. -/\ntheorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :\n isFinite x = false := by\n unfold toDyadic? at hx\n cases hcond : (isNaN x || isInf x) with\... | [
{
"name": "compare_eq_some_eq_iff_toReal_eq_of_isFinite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 22,
"n_chars": 838,
"n_subproofs": 4,
"n_tactics": 17,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 5,
"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
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -49,6 +49,35 @@
/-! ## Basic facts: `isFinite` ↔ `toDyadic?`/`toReal?` -/
+/-- `toDyadic? x = none` implies `x` is not finite. -/
+theorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :
+ isFinite x = false := by
+ unfold toDyadic? at hx
+ cases hcond : (isNaN x || isIn... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_7 | 4701d431b05347a0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 9 | [
{
"theorem_name": "toReal?_eq_some_toReal_of_isFinite_eq_true",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `toDyadic? x` cannot be `none`, otherwise `isFinite x = false`.\n cases hdy : toDyadic? x w... | [
{
"name": "isFinite_eq_false_of_toDyadic?_eq_none",
"text": "/-- `toDyadic? x = none` implies `x` is not finite. -/\ntheorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :\n isFinite x = false := by\n unfold toDyadic? at hx\n cases hcond : (isNaN x || isInf x) with\... | [
{
"name": "compare_eq_some_gt_iff_toReal_gt_of_isFinite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 24,
"n_chars": 898,
"n_subproofs": 4,
"n_tactics": 17,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 5,
"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
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -49,6 +49,35 @@
/-! ## Basic facts: `isFinite` ↔ `toDyadic?`/`toReal?` -/
+/-- `toDyadic? x = none` implies `x` is not finite. -/
+theorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :
+ isFinite x = false := by
+ unfold toDyadic? at hx
+ cases hcond : (isNaN x || isIn... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_8 | c9c367134c9bb8c6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 7 | [
{
"theorem_name": "toReal?_add_eq_ite",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases hfin : isFinite (add x y) with\n | true =>\n have hto : toReal (add x y) = fp32Round (toReal x + toReal y) ... | [
{
"name": "toReal?_eq_none_of_isFinite_eq_false",
"text": "/-- `toReal?` returns `none` on non-finite values. -/\ntheorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :\n toReal? x = none := by\n have hdy : toDyadic? x = none := toDyadic?_eq_none_of_isFinite_eq_false (... | [
{
"name": "toReal?_add_eq_ite",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 20,
"n_chars": 773,
"n_subproofs": 3,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
"max_ne... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -100,6 +100,12 @@
have hnan : isNaN x = true := by simp [isNaN, hexpB, hfracNeB]
simp [hnan]
+/-- `toReal?` returns `none` on non-finite values. -/
+theorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :
+ toReal? x = none := by
+ have hdy : toDyadic? x = none := to... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_9 | e2339cbb535a2d7e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 7 | [
{
"theorem_name": "toReal?_add_eq_ite",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases hfin : isFinite (add x y) with\n | true =>\n have hto : toReal (add x y) = fp32Round (toReal x + toReal y) ... | [
{
"name": "toReal?_eq_none_of_isFinite_eq_false",
"text": "/-- `toReal?` returns `none` on non-finite values. -/\ntheorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :\n toReal? x = none := by\n have hdy : toDyadic? x = none := toDyadic?_eq_none_of_isFinite_eq_false (... | [
{
"name": "toReal?_mul_eq_ite",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 20,
"n_chars": 773,
"n_subproofs": 3,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
"max_ne... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -100,6 +100,12 @@
have hnan : isNaN x = true := by simp [isNaN, hexpB, hfracNeB]
simp [hnan]
+/-- `toReal?` returns `none` on non-finite values. -/
+theorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :
+ toReal? x = none := by
+ have hdy : toDyadic? x = none := to... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_10 | b61a9e531439b91a | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 7 | [
{
"theorem_name": "toReal?_add_eq_ite",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases hfin : isFinite (add x y) with\n | true =>\n have hto : toReal (add x y) = fp32Round (toReal x + toReal y) ... | [
{
"name": "toReal?_eq_none_of_isFinite_eq_false",
"text": "/-- `toReal?` returns `none` on non-finite values. -/\ntheorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :\n toReal? x = none := by\n have hdy : toDyadic? x = none := toDyadic?_eq_none_of_isFinite_eq_false (... | [
{
"name": "toReal?_fma_eq_ite",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 20,
"n_chars": 826,
"n_subproofs": 3,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
"max_ne... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -100,6 +100,12 @@
have hnan : isNaN x = true := by simp [isNaN, hexpB, hfracNeB]
simp [hnan]
+/-- `toReal?` returns `none` on non-finite values. -/
+theorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :
+ toReal? x = none := by
+ have hdy : toDyadic? x = none := to... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_11 | 92e79dacf6770ec4 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 7 | [
{
"theorem_name": "toReal?_add_eq_ite",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases hfin : isFinite (add x y) with\n | true =>\n have hto : toReal (add x y) = fp32Round (toReal x + toReal y) ... | [
{
"name": "toReal?_eq_none_of_isFinite_eq_false",
"text": "/-- `toReal?` returns `none` on non-finite values. -/\ntheorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :\n toReal? x = none := by\n have hdy : toDyadic? x = none := toDyadic?_eq_none_of_isFinite_eq_false (... | [
{
"name": "toReal?_sqrt_eq_ite",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 20,
"n_chars": 756,
"n_subproofs": 3,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
"max_n... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -100,6 +100,12 @@
have hnan : isNaN x = true := by simp [isNaN, hexpB, hfracNeB]
simp [hnan]
+/-- `toReal?` returns `none` on non-finite values. -/
+theorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :
+ toReal? x = none := by
+ have hdy : toDyadic? x = none := to... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_12 | 64b590ce3bb9bebf | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 7 | [
{
"theorem_name": "toReal?_add_eq_ite",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases hfin : isFinite (add x y) with\n | true =>\n have hto : toReal (add x y) = fp32Round (toReal x + toReal y) ... | [
{
"name": "toReal?_eq_none_of_isFinite_eq_false",
"text": "/-- `toReal?` returns `none` on non-finite values. -/\ntheorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :\n toReal? x = none := by\n have hdy : toDyadic? x = none := toDyadic?_eq_none_of_isFinite_eq_false (... | [
{
"name": "toReal?_div_eq_ite",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 20,
"n_chars": 773,
"n_subproofs": 3,
"n_tactics": 15,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": false,
"max_ne... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -100,6 +100,12 @@
have hnan : isNaN x = true := by simp [isNaN, hexpB, hfracNeB]
simp [hnan]
+/-- `toReal?` returns `none` on non-finite values. -/
+theorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :
+ toReal? x = none := by
+ have hdy : toDyadic? x = none := to... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_13 | 6840b70e7b215bf5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 9 | [
{
"theorem_name": "toReal?_eq_some_toReal_of_isFinite_eq_true",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `toDyadic? x` cannot be `none`, otherwise `isFinite x = false`.\n cases hdy : toDyadic? x w... | [
{
"name": "isFinite_eq_false_of_toDyadic?_eq_none",
"text": "/-- `toDyadic? x = none` implies `x` is not finite. -/\ntheorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :\n isFinite x = false := by\n unfold toDyadic? at hx\n cases hcond : (isNaN x || isInf x) with\... | [
{
"name": "isFinite_minimum_of_isFinite",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 49,
"n_chars": 2187,
"n_subproofs": 15,
"n_tactics": 44,
"cyclomatic": 8,
"n_automation": 15,
"n_rewrites": 0,
"n_structural": 7,
"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.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -49,6 +49,35 @@
/-! ## Basic facts: `isFinite` ↔ `toDyadic?`/`toReal?` -/
+/-- `toDyadic? x = none` implies `x` is not finite. -/
+theorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :
+ isFinite x = false := by
+ unfold toDyadic? at hx
+ cases hcond : (isNaN x || isIn... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_14 | 7acdfec91f1b25e0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 9 | [
{
"theorem_name": "toReal?_eq_some_toReal_of_isFinite_eq_true",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `toDyadic? x` cannot be `none`, otherwise `isFinite x = false`.\n cases hdy : toDyadic? x w... | [
{
"name": "isFinite_eq_false_of_toDyadic?_eq_none",
"text": "/-- `toDyadic? x = none` implies `x` is not finite. -/\ntheorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :\n isFinite x = false := by\n unfold toDyadic? at hx\n cases hcond : (isNaN x || isInf x) with\... | [
{
"name": "toReal?_minimum_eq_min_of_isFinite",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 14,
"n_chars": 665,
"n_subproofs": 3,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": fal... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -49,13 +49,42 @@
/-! ## Basic facts: `isFinite` ↔ `toDyadic?`/`toReal?` -/
+/-- `toDyadic? x = none` implies `x` is not finite. -/
+theorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :
+ isFinite x = false := by
+ unfold toDyadic? at hx
+ cases hcond : (isNaN x || isI... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_15 | f88354b1c545bd87 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 9 | [
{
"theorem_name": "toReal?_eq_some_toReal_of_isFinite_eq_true",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `toDyadic? x` cannot be `none`, otherwise `isFinite x = false`.\n cases hdy : toDyadic? x w... | [
{
"name": "isFinite_eq_false_of_toDyadic?_eq_none",
"text": "/-- `toDyadic? x = none` implies `x` is not finite. -/\ntheorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :\n isFinite x = false := by\n unfold toDyadic? at hx\n cases hcond : (isNaN x || isInf x) with\... | [
{
"name": "isFinite_maximum_of_isFinite",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 49,
"n_chars": 2201,
"n_subproofs": 15,
"n_tactics": 44,
"cyclomatic": 8,
"n_automation": 15,
"n_rewrites": 0,
"n_structural": 7,
"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.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -49,6 +49,35 @@
/-! ## Basic facts: `isFinite` ↔ `toDyadic?`/`toReal?` -/
+/-- `toDyadic? x = none` implies `x` is not finite. -/
+theorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :
+ isFinite x = false := by
+ unfold toDyadic? at hx
+ cases hcond : (isNaN x || isIn... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_16 | 2dc6770a38e634de | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 9 | [
{
"theorem_name": "toReal?_eq_some_toReal_of_isFinite_eq_true",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `toDyadic? x` cannot be `none`, otherwise `isFinite x = false`.\n cases hdy : toDyadic? x w... | [
{
"name": "isFinite_eq_false_of_toDyadic?_eq_none",
"text": "/-- `toDyadic? x = none` implies `x` is not finite. -/\ntheorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :\n isFinite x = false := by\n unfold toDyadic? at hx\n cases hcond : (isNaN x || isInf x) with\... | [
{
"name": "toReal?_maximum_eq_max_of_isFinite",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 4,
"n_lines": 16,
"n_chars": 731,
"n_subproofs": 3,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": fal... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -49,13 +49,42 @@
/-! ## Basic facts: `isFinite` ↔ `toDyadic?`/`toReal?` -/
+/-- `toDyadic? x = none` implies `x` is not finite. -/
+theorem isFinite_eq_false_of_toDyadic?_eq_none (x : IEEE32Exec) (hx : toDyadic? x = none) :
+ isFinite x = false := by
+ unfold toDyadic? at hx
+ cases hcond : (isNaN x || isI... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_17 | aab8fad39ebd8491 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 7 | [
{
"theorem_name": "toReal?_add_eq_ite",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases hfin : isFinite (add x y) with\n | true =>\n have hto : toReal (add x y) = fp32Round (toReal x + toReal y) ... | [
{
"name": "toReal?_eq_none_of_isFinite_eq_false",
"text": "/-- `toReal?` returns `none` on non-finite values. -/\ntheorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :\n toReal? x = none := by\n have hdy : toDyadic? x = none := toDyadic?_eq_none_of_isFinite_eq_false (... | [
{
"name": "toReal?_minimum_eq_match_total",
"fan_in": 0,
"n_deps_direct": 6,
"n_deps_transitive": 10,
"n_lines": 206,
"n_chars": 11136,
"n_subproofs": 58,
"n_tactics": 178,
"cyclomatic": 31,
"n_automation": 41,
"n_rewrites": 0,
"n_structural": 30,
"automation_only... | 10 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -100,6 +100,12 @@
have hnan : isNaN x = true := by simp [isNaN, hexpB, hfracNeB]
simp [hnan]
+/-- `toReal?` returns `none` on non-finite values. -/
+theorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :
+ toReal? x = none := by
+ have hdy : toDyadic? x = none := to... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_647b0ad429d5_18 | b5382f19710a0ca1 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32Total.lean | BridgeFP32Total | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 18 | 7 | [
{
"theorem_name": "toReal?_add_eq_ite",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases hfin : isFinite (add x y) with\n | true =>\n have hto : toReal (add x y) = fp32Round (toReal x + toReal y) ... | [
{
"name": "toReal?_eq_none_of_isFinite_eq_false",
"text": "/-- `toReal?` returns `none` on non-finite values. -/\ntheorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :\n toReal? x = none := by\n have hdy : toDyadic? x = none := toDyadic?_eq_none_of_isFinite_eq_false (... | [
{
"name": "toReal?_maximum_eq_match_total",
"fan_in": 0,
"n_deps_direct": 6,
"n_deps_transitive": 10,
"n_lines": 207,
"n_chars": 11022,
"n_subproofs": 58,
"n_tactics": 185,
"cyclomatic": 34,
"n_automation": 40,
"n_rewrites": 2,
"n_structural": 33,
"automation_only... | 10 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32
public import NN.Floats.IEEEExec.SpecialRules
/-!
# BridgeFP32Total
“Total” bridge theorems combining:
- `IEEE32Exec`'s proved NaN/Inf propagati... | @@ -100,6 +100,12 @@
have hnan : isNaN x = true := by simp [isNaN, hexpB, hfracNeB]
simp [hnan]
+/-- `toReal?` returns `none` on non-finite values. -/
+theorem toReal?_eq_none_of_isFinite_eq_false (x : IEEE32Exec) (hx : isFinite x = false) :
+ toReal? x = none := by
+ have hdy : toDyadic? x = none := to... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_ed66d64e9069_0 | 910f4385a6b32163 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/RatBounds.lean | RatBounds | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "rat_bounds_k0",
"depth": 1,
"n_commands": 0,
"n_lines": 82,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n set ln : Nat := Nat.log2 num\n set ld : Nat := Nat.log2 den\n set k0 : Int := (Int.ofNat ln) - (Int.ofNat ld)... | [
{
"name": "bpow_k0_add_one_eq",
"text": "lemma bpow_k0_add_one_eq (ln ld : Nat) :\n neuralBpow binaryRadix (Int.ofNat ln - Int.ofNat ld + 1) =\n (2 : ℝ) ^ ln.succ / (2 : ℝ) ^ ld := by\n have hk : (Int.ofNat ln) - (Int.ofNat ld) + 1 = (Int.ofNat ln.succ) - (Int.ofNat ld) := by\n simp [sub_eq_add_... | [
{
"name": "rat_bounds_k0",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 89,
"n_chars": 4252,
"n_subproofs": 35,
"n_tactics": 74,
"cyclomatic": 1,
"n_automation": 17,
"n_rewrites": 4,
"n_structural": 9,
"automation_only": false,
"max_nest... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.NearestEven
/-!
# IEEE32Exec and FP32: Rational Magnitude Bounds
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.NearestEven
/-!
# IEEE32Exec and FP32: Rational Magnitude Bounds
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.... | @@ -34,6 +34,20 @@
simp [TorchLean.Floats.neuralBpow, binaryRadix, NeuralRadix.toReal, zpow_sub₀]
simp [pow_succ, div_eq_mul_inv, mul_left_comm, mul_comm]
+lemma bpow_k0_add_one_eq (ln ld : Nat) :
+ neuralBpow binaryRadix (Int.ofNat ln - Int.ofNat ld + 1) =
+ (2 : ℝ) ^ ln.succ / (2 : ℝ) ^ ld := by
+ ha... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_ed66d64e9069_1 | aa0848024040b139 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/RatBounds.lean | RatBounds | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "rat_bounds_k0",
"depth": 1,
"n_commands": 0,
"n_lines": 82,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n set ln : Nat := Nat.log2 num\n set ld : Nat := Nat.log2 den\n set k0 : Int := (Int.ofNat ln) - (Int.ofNat ld)... | [
{
"name": "bpow_k0_add_one_eq",
"text": "lemma bpow_k0_add_one_eq (ln ld : Nat) :\n neuralBpow binaryRadix (Int.ofNat ln - Int.ofNat ld + 1) =\n (2 : ℝ) ^ ln.succ / (2 : ℝ) ^ ld := by\n have hk : (Int.ofNat ln) - (Int.ofNat ld) + 1 = (Int.ofNat ln.succ) - (Int.ofNat ld) := by\n simp [sub_eq_add_... | [
{
"name": "floorLog2Rat_bounds",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 89,
"n_chars": 3824,
"n_subproofs": 19,
"n_tactics": 60,
"cyclomatic": 3,
"n_automation": 19,
"n_rewrites": 0,
"n_structural": 5,
"automation_only": false,
"ma... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.NearestEven
/-!
# IEEE32Exec and FP32: Rational Magnitude Bounds
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.NearestEven
/-!
# IEEE32Exec and FP32: Rational Magnitude Bounds
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.... | @@ -209,6 +209,20 @@
simp [TorchLean.Floats.neuralBpow, binaryRadix, NeuralRadix.toReal, zpow_sub₀]
simp [pow_succ, div_eq_mul_inv, mul_left_comm, mul_comm]
+lemma bpow_k0_add_one_eq (ln ld : Nat) :
+ neuralBpow binaryRadix (Int.ofNat ln - Int.ofNat ld + 1) =
+ (2 : ℝ) ^ ln.succ / (2 : ℝ) ^ ld := 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_6426508b0b13_0 | ebbdb57750697fa6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/Ops.lean | Ops | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "toReal_sub_eq_fp32Round",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- `sub x y` is defined as `add x (neg y)`.\n let dyNeg : Dyadic := { sign := (!dy.sign), mant := dy... | [
{
"name": "toReal_add_eq_fp32Round",
"text": "/-- Finite refinement for addition: `IEEE32Exec.add` = exact real add + float32 rounding. -/\ntheorem toReal_add_eq_fp32Round (x y : IEEE32Exec) {dx dy : Dyadic}\n (hx : toDyadic? x = some dx) (hy : toDyadic? y = some dy)\n (hfin : isFinite (add x y) = tru... | [
{
"name": "toReal_sub_eq_fp32Round",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 23,
"n_chars": 1134,
"n_subproofs": 4,
"n_tactics": 16,
"cyclomatic": 1,
"n_automation": 5,
"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.BridgeFP32.RoundRat
/-!
# IEEE32Exec and FP32: Arithmetic Operation Refinement
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLe... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.RoundRat
/-!
# IEEE32Exec and FP32: Arithmetic Operation Refinement
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLe... | @@ -31,6 +31,25 @@
but made explicit and proved for our executable kernel.
-/
+/-- Finite refinement for addition: `IEEE32Exec.add` = exact real add + float32 rounding. -/
+theorem toReal_add_eq_fp32Round (x y : IEEE32Exec) {dx dy : Dyadic}
+ (hx : toDyadic? x = some dx) (hy : toDyadic? y = some dy)
+ (hfin :... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c3c999d9be27_0 | ab3eb763b670b1ad | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Gradients/Linear.lean | Linear | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "linear_gradients_mathematical_correctness",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · rfl\n constructor\n · simpa using (linear_weight_gradient_correct (x := x) (δ ... | [
{
"name": "linear_weight_gradient_correct",
"text": "/--\nSpec identity: weight gradient for a linear layer.\n\nFor `y = W x + b`, if `δ = ∂L/∂y` then the weight gradient is\n\n`∂L/∂W = δ ⊗ x`.\n\nPyTorch mental model: this is the per-sample formula whose batched version becomes a matmul\nagainst the input ... | [
{
"name": "linear_gradients_mathematical_correctness",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 25,
"n_chars": 995,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 3,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 2,
"automation_onl... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Layers.Linear
/-!
# Spec-level gradient identities for the linear layer
This file states (and in several cases, proves by definitional unfolding) the “obvious” gradien... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Layers.Linear
/-!
# Spec-level gradient identities for the linear layer
This file states (and in several cases, proves by definitional unfolding) the “obvious” gradien... | @@ -57,6 +57,28 @@
open Tensor
/--
+Spec identity: weight gradient for a linear layer.
+
+For `y = W x + b`, if `δ = ∂L/∂y` then the weight gradient is
+
+`∂L/∂W = δ ⊗ x`.
+
+PyTorch mental model: this is the per-sample formula whose batched version becomes a matmul
+against the input batch.
+-/
+theorem linear_wei... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_de9b684519a7_0 | b25c3b4b18df0a45 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/KernelSpec.lean | KernelSpec | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 10 | [
{
"theorem_name": "fromNativeBitsBuffer_eq_addSpec_of_bits",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i\n apply ref_ext\n simp [fromNativeBitsBuffer, addSpec, map2Spec, hbits i]",
"n_chars... | [
{
"name": "ref_ext",
"text": "/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/\nprivate theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n",
"fan_in": 10,
"n_lines": 8,
"n_chars": ... | [
{
"name": "fromNativeBitsBuffer_eq_addSpec_of_bits",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 464,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | @@ -65,6 +65,13 @@
/-- A native-result buffer represented only by raw binary32 bits. -/
abbrev NativeBitsBuffer (n : Nat) := Fin n → UInt32
+/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = 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_de9b684519a7_1 | b03adb0302e310e4 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/KernelSpec.lean | KernelSpec | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 10 | [
{
"theorem_name": "fromNativeBitsBuffer_eq_addSpec_of_bits",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i\n apply ref_ext\n simp [fromNativeBitsBuffer, addSpec, map2Spec, hbits i]",
"n_chars... | [
{
"name": "ref_ext",
"text": "/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/\nprivate theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n",
"fan_in": 10,
"n_lines": 8,
"n_chars": ... | [
{
"name": "fromNativeBitsBuffer_eq_mulSpec_of_bits",
"fan_in": 0,
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | @@ -65,6 +65,13 @@
/-- A native-result buffer represented only by raw binary32 bits. -/
abbrev NativeBitsBuffer (n : Nat) := Fin n → UInt32
+/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = 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_de9b684519a7_2 | 0bf7551d87c91ba5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/KernelSpec.lean | KernelSpec | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 10 | [
{
"theorem_name": "fromNativeBitsBuffer_eq_addSpec_of_bits",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i\n apply ref_ext\n simp [fromNativeBitsBuffer, addSpec, map2Spec, hbits i]",
"n_chars... | [
{
"name": "ref_ext",
"text": "/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/\nprivate theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n",
"fan_in": 10,
"n_lines": 8,
"n_chars": ... | [
{
"name": "fromNativeBitsBuffer_eq_divSpec_of_bits",
"fan_in": 0,
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"n_rewrites": 0,
"n_structural": 2,
"automation_only"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | @@ -65,6 +65,13 @@
/-- A native-result buffer represented only by raw binary32 bits. -/
abbrev NativeBitsBuffer (n : Nat) := Fin n → UInt32
+/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = 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_de9b684519a7_3 | fef77a1b27c46a49 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/KernelSpec.lean | KernelSpec | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 10 | [
{
"theorem_name": "fromNativeBitsBuffer_eq_addSpec_of_bits",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i\n apply ref_ext\n simp [fromNativeBitsBuffer, addSpec, map2Spec, hbits i]",
"n_chars... | [
{
"name": "ref_ext",
"text": "/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/\nprivate theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n",
"fan_in": 10,
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"n_chars": ... | [
{
"name": "fromNativeBitsBuffer_eq_sqrtSpec_of_bits",
"fan_in": 0,
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | @@ -65,6 +65,13 @@
/-- A native-result buffer represented only by raw binary32 bits. -/
abbrev NativeBitsBuffer (n : Nat) := Fin n → UInt32
+/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = 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_de9b684519a7_4 | c0a3700fc6d54069 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/KernelSpec.lean | KernelSpec | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 10 | [
{
"theorem_name": "fromNativeBitsBuffer_eq_addSpec_of_bits",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i\n apply ref_ext\n simp [fromNativeBitsBuffer, addSpec, map2Spec, hbits i]",
"n_chars... | [
{
"name": "ref_ext",
"text": "/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/\nprivate theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n",
"fan_in": 10,
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"n_chars": ... | [
{
"name": "native_add_pointwise_abs_error_of_bits",
"fan_in": 0,
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | @@ -65,6 +65,13 @@
/-- A native-result buffer represented only by raw binary32 bits. -/
abbrev NativeBitsBuffer (n : Nat) := Fin n → UInt32
+/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = 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_de9b684519a7_5 | e499393774d455e2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/KernelSpec.lean | KernelSpec | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 10 | [
{
"theorem_name": "fromNativeBitsBuffer_eq_addSpec_of_bits",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i\n apply ref_ext\n simp [fromNativeBitsBuffer, addSpec, map2Spec, hbits i]",
"n_chars... | [
{
"name": "ref_ext",
"text": "/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/\nprivate theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n",
"fan_in": 10,
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"n_chars": ... | [
{
"name": "native_mul_pointwise_abs_error_of_bits",
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"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | @@ -65,6 +65,13 @@
/-- A native-result buffer represented only by raw binary32 bits. -/
abbrev NativeBitsBuffer (n : Nat) := Fin n → UInt32
+/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = 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_de9b684519a7_6 | 4e15d412b2ba0725 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/KernelSpec.lean | KernelSpec | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 10 | [
{
"theorem_name": "fromNativeBitsBuffer_eq_addSpec_of_bits",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i\n apply ref_ext\n simp [fromNativeBitsBuffer, addSpec, map2Spec, hbits i]",
"n_chars... | [
{
"name": "ref_ext",
"text": "/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/\nprivate theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n",
"fan_in": 10,
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{
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"n_structural": 2,
"automation_only":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | @@ -65,6 +65,13 @@
/-- A native-result buffer represented only by raw binary32 bits. -/
abbrev NativeBitsBuffer (n : Nat) := Fin n → UInt32
+/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = 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_de9b684519a7_7 | b757d97a2e2a136b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/KernelSpec.lean | KernelSpec | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 10 | [
{
"theorem_name": "fromNativeBitsBuffer_eq_addSpec_of_bits",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i\n apply ref_ext\n simp [fromNativeBitsBuffer, addSpec, map2Spec, hbits i]",
"n_chars... | [
{
"name": "ref_ext",
"text": "/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/\nprivate theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n",
"fan_in": 10,
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{
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | @@ -65,6 +65,13 @@
/-- A native-result buffer represented only by raw binary32 bits. -/
abbrev NativeBitsBuffer (n : Nat) := Fin n → UInt32
+/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = 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_de9b684519a7_8 | e96368d13f7d575f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/KernelSpec.lean | KernelSpec | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 10 | [
{
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"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i\n apply ref_ext\n simp [fromNativeBitsBuffer, addSpec, map2Spec, hbits i]",
"n_chars... | [
{
"name": "ref_ext",
"text": "/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/\nprivate theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n",
"fan_in": 10,
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{
"name": "native_reduce_eq_leftSpec",
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"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.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | @@ -65,6 +65,13 @@
/-- A native-result buffer represented only by raw binary32 bits. -/
abbrev NativeBitsBuffer (n : Nat) := Fin n → UInt32
+/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = 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_de9b684519a7_9 | ad362ed798a59c17 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/KernelSpec.lean | KernelSpec | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 10 | [
{
"theorem_name": "fromNativeBitsBuffer_eq_addSpec_of_bits",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n funext i\n apply ref_ext\n simp [fromNativeBitsBuffer, addSpec, map2Spec, hbits i]",
"n_chars... | [
{
"name": "ref_ext",
"text": "/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/\nprivate theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n",
"fan_in": 10,
"n_lines": 8,
"n_chars": ... | [
{
"name": "native_bmm_eq_spec",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 465,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Runtime.Autograd.Engine.Cuda.Float32Contract
/-!
# Pure specifications for CUDA float32 kernels
This file is the proof layer companion to `NN.Runtime.Autograd.Engine.Cuda.*... | @@ -65,6 +65,13 @@
/-- A native-result buffer represented only by raw binary32 bits. -/
abbrev NativeBitsBuffer (n : Nat) := Fin n → UInt32
+/-- Extensionality for the thin `IEEE32Exec` wrapper, phrased through native bits. -/
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = 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_8bee98cf7a6f_0 | 51be1cafa4b4b983 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/Core/Tolerance.lean | Tolerance | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "approxBound_nonneg",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hinner : 0 ≤ (t.abs : ℝ) + (t.rel : ℝ) * max (abs x) (abs y) :=\n approxBound_inner_nonneg t x y\n have : 0 ≤ (... | [
{
"name": "approxBound_inner_nonneg",
"text": "lemma approxBound_inner_nonneg (t : ApproxTol) (x y : ℝ) :\n 0 ≤ (t.abs : ℝ) + (t.rel : ℝ) * max (abs x) (abs y) := by\n nlinarith [t.abs.coe_nonneg, t.rel.coe_nonneg, le_max_left (abs x) (abs y),\n le_max_right (abs x) (abs y), abs_nonneg x, abs_nonneg ... | [
{
"name": "approxBound_nonneg",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 362,
"n_subproofs": 2,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
/-!
# Tolerance
Approximation tolerances (absolute + relative).
This file defines a small, reusable tolerance object for "close enough" reasoning:
-... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
/-!
# Tolerance
Approximation tolerances (absolute + relative).
This file defines a small, reusable tolerance object for "close enough" reasoning:
-... | @@ -71,8 +71,14 @@
def approxR (x y : ℝ) (t : ApproxTol) : Prop :=
abs (y - x) ≤ approxBound t x y
+lemma approxBound_inner_nonneg (t : ApproxTol) (x y : ℝ) :
+ 0 ≤ (t.abs : ℝ) + (t.rel : ℝ) * max (abs x) (abs y) := by
+ nlinarith [t.abs.coe_nonneg, t.rel.coe_nonneg, le_max_left (abs x) (abs y),
+ le_max_r... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8bee98cf7a6f_1 | 536aef2470d1c973 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/Core/Tolerance.lean | Tolerance | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "approxBound_nonneg",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hinner : 0 ≤ (t.abs : ℝ) + (t.rel : ℝ) * max (abs x) (abs y) :=\n approxBound_inner_nonneg t x y\n have : 0 ≤ (... | [
{
"name": "approxBound_inner_nonneg",
"text": "lemma approxBound_inner_nonneg (t : ApproxTol) (x y : ℝ) :\n 0 ≤ (t.abs : ℝ) + (t.rel : ℝ) * max (abs x) (abs y) := by\n nlinarith [t.abs.coe_nonneg, t.rel.coe_nonneg, le_max_left (abs x) (abs y),\n le_max_right (abs x) (abs y), abs_nonneg x, abs_nonneg ... | [
{
"name": "approxBound_mono",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 26,
"n_chars": 1604,
"n_subproofs": 9,
"n_tactics": 22,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
/-!
# Tolerance
Approximation tolerances (absolute + relative).
This file defines a small, reusable tolerance object for "close enough" reasoning:
-... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
/-!
# Tolerance
Approximation tolerances (absolute + relative).
This file defines a small, reusable tolerance object for "close enough" reasoning:
-... | @@ -71,6 +71,11 @@
def approxR (x y : ℝ) (t : ApproxTol) : Prop :=
abs (y - x) ≤ approxBound t x y
+lemma approxBound_inner_nonneg (t : ApproxTol) (x y : ℝ) :
+ 0 ≤ (t.abs : ℝ) + (t.rel : ℝ) * max (abs x) (abs y) := by
+ nlinarith [t.abs.coe_nonneg, t.rel.coe_nonneg, le_max_left (abs x) (abs y),
+ le_max_r... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8bee98cf7a6f_2 | f82756ba0daef6be | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/Core/Tolerance.lean | Tolerance | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "approxBound_nonneg",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hinner : 0 ≤ (t.abs : ℝ) + (t.rel : ℝ) * max (abs x) (abs y) :=\n approxBound_inner_nonneg t x y\n have : 0 ≤ (... | [
{
"name": "approxBound_inner_nonneg",
"text": "lemma approxBound_inner_nonneg (t : ApproxTol) (x y : ℝ) :\n 0 ≤ (t.abs : ℝ) + (t.rel : ℝ) * max (abs x) (abs y) := by\n nlinarith [t.abs.coe_nonneg, t.rel.coe_nonneg, le_max_left (abs x) (abs y),\n le_max_right (abs x) (abs y), abs_nonneg x, abs_nonneg ... | [
{
"name": "approxR_mono",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 5,
"n_chars": 287,
"n_subproofs": 0,
"n_tactics": 1,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"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 Mathlib.Data.NNReal.Defs
/-!
# Tolerance
Approximation tolerances (absolute + relative).
This file defines a small, reusable tolerance object for "close enough" reasoning:
-... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
/-!
# Tolerance
Approximation tolerances (absolute + relative).
This file defines a small, reusable tolerance object for "close enough" reasoning:
-... | @@ -71,6 +71,11 @@
def approxR (x y : ℝ) (t : ApproxTol) : Prop :=
abs (y - x) ≤ approxBound t x y
+lemma approxBound_inner_nonneg (t : ApproxTol) (x y : ℝ) :
+ 0 ≤ (t.abs : ℝ) + (t.rel : ℝ) * max (abs x) (abs y) := by
+ nlinarith [t.abs.coe_nonneg, t.rel.coe_nonneg, le_max_left (abs x) (abs y),
+ le_max_r... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8bee98cf7a6f_3 | 217fdecd373d2871 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/Core/Tolerance.lean | Tolerance | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "approxR_absOnly_trans",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hxy' : abs (y - x) ≤ eps₁ := (approxR_absOnly_iff (x := x) (y := y) (eps := eps₁) h₁).1 hxy\n have hyz' : abs ... | [
{
"name": "approxR_absOnly_iff",
"text": "lemma approxR_absOnly_iff {x y eps : ℝ} (heps : 0 ≤ eps) :\n approxR x y (ApproxTol.absOnly eps) ↔ abs (y - x) ≤ eps := by\n have hcoe : (Real.toNNReal eps : ℝ) = eps := by\n simp [Real.toNNReal_of_nonneg heps]\n simp [approxR, approxBound_absOnly, hcoe]\n\n... | [
{
"name": "approxR_absOnly_trans",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 811,
"n_subproofs": 5,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
/-!
# Tolerance
Approximation tolerances (absolute + relative).
This file defines a small, reusable tolerance object for "close enough" reasoning:
-... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.NNReal.Defs
/-!
# Tolerance
Approximation tolerances (absolute + relative).
This file defines a small, reusable tolerance object for "close enough" reasoning:
-... | @@ -75,9 +75,24 @@
approxBound (ApproxTol.absOnly eps) x y = (Real.toNNReal eps : ℝ) := by
simp [approxBound, ApproxTol.absOnly, ApproxTol.ofReal]
+lemma approxR_absOnly_iff {x y eps : ℝ} (heps : 0 ≤ eps) :
+ approxR x y (ApproxTol.absOnly eps) ↔ abs (y - x) ≤ eps := by
+ have hcoe : (Real.toNNReal eps : ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e3443e189e07_0 | 4eee159c52d84848 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Energy.lean | Energy | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "quad_delta_update",
"depth": 1,
"n_commands": 0,
"n_lines": 171,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hu : u ∈ (U (n := n)) := by simp [U]\n let x1 : Fin n → ℝ := Function.update x0 u xu'\n have hx1u :... | [
{
"name": "quad_inner_delta_ne",
"text": "lemma quad_inner_delta_ne (p : Params ℝ n) {u i : Fin n} (hi : i ≠ u)\n (x0 : Fin n → ℝ) (xu' : ℝ) :\n (∑ j ∈ (U (n := n)), p.W i j * x0 i * (Function.update x0 u xu' j))\n -\n (∑ j ∈ (U (n := n)), p.W i j * x0 i * x0 j)\n =\n p.W i u * x0 i * (x... | [
{
"name": "quad_delta_update",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 178,
"n_chars": 8315,
"n_subproofs": 29,
"n_tactics": 147,
"cyclomatic": 1,
"n_automation": 32,
"n_rewrites": 3,
"n_structural": 12,
"automation_only": false,
"m... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
public import NN.MLTheory.Proofs.Hopfield.Basic
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
/-!
# Hopfield ene... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
public import NN.MLTheory.Proofs.Hopfield.Basic
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
/-!
# Hopfield ene... | @@ -95,6 +95,49 @@
_ = netx (n := n) p x0 u + p.W u u * (xu' - x0 u) := by
simp [netx, hs0]
+lemma quad_inner_delta_ne (p : Params ℝ n) {u i : Fin n} (hi : i ≠ u)
+ (x0 : Fin n → ℝ) (xu' : ℝ) :
+ (∑ j ∈ (U (n := n)), p.W i j * x0 i * (Function.update x0 u xu' j))
+ -
+ (∑ j ∈ (U (n := n)),... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e3443e189e07_1 | 35e507ce2060af92 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Energy.lean | Energy | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 2 | [
{
"theorem_name": "energy_updateAt_le",
"depth": 1,
"n_commands": 0,
"n_lines": 97,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Let `x0` be the activation vector, and `xu'` the updated activation at `u`.\n let x0 : Fin n → ℝ := x ... | [
{
"name": "x_updateAt_eq_update",
"text": "lemma x_updateAt_eq_update (p : Params ℝ n) (s : State n) (u : Fin n) :\n x (n := n) (updateAt (α := ℝ) p s u) =\n Function.update (x (n := n) s) u (act (α := ℝ) (decide (p.θ u ≤ net (α := ℝ) p s u))) := by\n classical\n funext i\n by_cases h : i = u\n ... | [
{
"name": "energy_updateAt_le",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 102,
"n_chars": 4882,
"n_subproofs": 20,
"n_tactics": 84,
"cyclomatic": 7,
"n_automation": 24,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,
"ma... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
public import NN.MLTheory.Proofs.Hopfield.Basic
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
/-!
# Hopfield ene... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
public import NN.MLTheory.Proofs.Hopfield.Basic
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
/-!
# Hopfield ene... | @@ -65,6 +65,16 @@
net (α := ℝ) p s u = netx (n := n) p (x (n := n) s) u := by
simp [Spec.Hopfield.net, Spec.Hopfield.mulVec, netx, x, U, Spec.Hopfield.actVec]
+lemma x_updateAt_eq_update (p : Params ℝ n) (s : State n) (u : Fin n) :
+ x (n := n) (updateAt (α := ℝ) p s u) =
+ Function.update (x (n := n... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e3443e189e07_2 | f91a28c1a91a718f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Energy.lean | Energy | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 2 | [
{
"theorem_name": "energy_updateAt_le",
"depth": 1,
"n_commands": 0,
"n_lines": 97,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Let `x0` be the activation vector, and `xu'` the updated activation at `u`.\n let x0 : Fin n → ℝ := x ... | [
{
"name": "x_updateAt_eq_update",
"text": "lemma x_updateAt_eq_update (p : Params ℝ n) (s : State n) (u : Fin n) :\n x (n := n) (updateAt (α := ℝ) p s u) =\n Function.update (x (n := n) s) u (act (α := ℝ) (decide (p.θ u ≤ net (α := ℝ) p s u))) := by\n classical\n funext i\n by_cases h : i = u\n ... | [
{
"name": "energy_updateAt_delta",
"fan_in": 2,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 73,
"n_chars": 3423,
"n_subproofs": 13,
"n_tactics": 64,
"cyclomatic": 1,
"n_automation": 14,
"n_rewrites": 2,
"n_structural": 4,
"automation_only": false,
"... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
public import NN.MLTheory.Proofs.Hopfield.Basic
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
/-!
# Hopfield ene... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
public import NN.MLTheory.Proofs.Hopfield.Basic
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
/-!
# Hopfield ene... | @@ -65,6 +65,16 @@
net (α := ℝ) p s u = netx (n := n) p (x (n := n) s) u := by
simp [Spec.Hopfield.net, Spec.Hopfield.mulVec, netx, x, U, Spec.Hopfield.actVec]
+lemma x_updateAt_eq_update (p : Params ℝ n) (s : State n) (u : Fin n) :
+ x (n := n) (updateAt (α := ℝ) p s u) =
+ Function.update (x (n := n... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e3443e189e07_3 | a8a68d546d128791 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Energy.lean | Energy | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "quad_delta_update",
"depth": 1,
"n_commands": 0,
"n_lines": 171,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hu : u ∈ (U (n := n)) := by simp [U]\n let x1 : Fin n → ℝ := Function.update x0 u xu'\n have hx1u :... | [
{
"name": "netx_update_eq",
"text": "lemma netx_update_eq (p : Params ℝ n) (x0 : Fin n → ℝ) (u : Fin n) (xu' : ℝ) :\n netx (n := n) p (Function.update x0 u xu') u\n =\n netx (n := n) p x0 u + p.W u u * (xu' - x0 u) := by\n classical\n -- Only the `j=u` term changes.\n have hu : u ∈ (U (n := n)... | [
{
"name": "energy_updateAt_eq_of_net_eq_theta",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 14,
"n_chars": 619,
"n_subproofs": 2,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": fal... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
public import NN.MLTheory.Proofs.Hopfield.Basic
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
/-!
# Hopfield ene... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
public import NN.MLTheory.Proofs.Hopfield.Basic
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
/-!
# Hopfield ene... | @@ -75,6 +75,47 @@
simp [x, updateAt, Spec.Hopfield.actVec, Function.update, Spec.Hopfield.act]
· simp [x, updateAt, Spec.Hopfield.actVec, Function.update, h, Spec.Hopfield.act]
+lemma netx_update_eq (p : Params ℝ n) (x0 : Fin n → ℝ) (u : Fin n) (xu' : ℝ) :
+ netx (n := n) p (Function.update x0 u xu') u
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e3443e189e07_4 | db98e9c4eb15dfa8 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Hopfield/Energy.lean | Energy | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 7 | 1 | [
{
"theorem_name": "quad_delta_update",
"depth": 1,
"n_commands": 0,
"n_lines": 171,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hu : u ∈ (U (n := n)) := by simp [U]\n let x1 : Fin n → ℝ := Function.update x0 u xu'\n have hx1u :... | [
{
"name": "netx_update_eq",
"text": "lemma netx_update_eq (p : Params ℝ n) (x0 : Fin n → ℝ) (u : Fin n) (xu' : ℝ) :\n netx (n := n) p (Function.update x0 u xu') u\n =\n netx (n := n) p x0 u + p.W u u * (xu' - x0 u) := by\n classical\n -- Only the `j=u` term changes.\n have hu : u ∈ (U (n := n)... | [
{
"name": "energy_updateAt_lt_of_change_of_ne",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 7,
"n_lines": 74,
"n_chars": 3383,
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"n_tactics": 62,
"cyclomatic": 7,
"n_automation": 23,
"n_rewrites": 4,
"n_structural": 10,
"automation_only"... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
public import NN.MLTheory.Proofs.Hopfield.Basic
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
/-!
# Hopfield ene... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Group.Finset.Piecewise
public import NN.MLTheory.Proofs.Hopfield.Basic
import Mathlib.Tactic.Linarith
import Mathlib.Tactic.Ring
/-!
# Hopfield ene... | @@ -75,6 +75,47 @@
simp [x, updateAt, Spec.Hopfield.actVec, Function.update, Spec.Hopfield.act]
· simp [x, updateAt, Spec.Hopfield.actVec, Function.update, h, Spec.Hopfield.act]
+lemma netx_update_eq (p : Params ℝ n) (x0 : Fin n → ℝ) (u : Fin n) (xu' : ℝ) :
+ netx (n := n) p (Function.update x0 u xu') u
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3a755c968bec_0 | 98b4f1d5b3ff2c59 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/Envs/GridWorld.lean | GridWorld | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "step_reward_bounds",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ⟨step_reward_ge_neg_one (gw := gw) (state := state) (action := action),\n step_reward_le_zero (gw := gw) (state := state... | [
{
"name": "step_reward_ge_neg_one",
"text": "/-- GridWorld rewards are bounded below by `-1`. -/\ntheorem step_reward_ge_neg_one\n (gw : Spec.RL.Envs.GridWorld width height)\n (state : Spec.RL.Envs.GridWorld.State width height)\n (action : Spec.RL.Envs.GridWorld.Action) :\n (-1 : ℝ) ≤ (gw.step s... | [
{
"name": "step_reward_bounds",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 18,
"n_chars": 765,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
"max_nes... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Spec.RL.Envs.GridWorld
/-!
# GridWorld proof layer
This module proves a small set of “environment well-formedness” facts for the Lean-... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Spec.RL.Envs.GridWorld
/-!
# GridWorld proof layer
This module proves a small set of “environment well-formedness” facts for the Lean-... | @@ -42,6 +42,20 @@
variable {width height : Nat}
+/-- GridWorld rewards are bounded below by `-1`. -/
+theorem step_reward_ge_neg_one
+ (gw : Spec.RL.Envs.GridWorld width height)
+ (state : Spec.RL.Envs.GridWorld.State width height)
+ (action : Spec.RL.Envs.GridWorld.Action) :
+ (-1 : ℝ) ≤ (gw.step 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_3a755c968bec_1 | 753637c33bd0bc87 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/Envs/GridWorld.lean | GridWorld | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "toFiniteStochasticMDP_actionValue_eq_toFiniteMDP_stateActionValue",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [Spec.RL.FiniteStochastic.actionValue, stateActionValue]\n rw ... | [
{
"name": "toFiniteStochasticMDP_expectedNextValue_eq_toFiniteMDP_successor",
"text": "/--\nExpected next-state value in the one-hot finite-stochastic GridWorld view equals the value of the\nsuccessor produced by the deterministic finite-MDP view.\n-/\ntheorem toFiniteStochasticMDP_expectedNextValue_eq_toFi... | [
{
"name": "toFiniteStochasticMDP_actionValue_eq_toFiniteMDP_stateActionValue",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 907,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 1,
"n_structural"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Spec.RL.Envs.GridWorld
/-!
# GridWorld proof layer
This module proves a small set of “environment well-formedness” facts for the Lean-... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Spec.RL.Envs.GridWorld
/-!
# GridWorld proof layer
This module proves a small set of “environment well-formedness” facts for the Lean-... | @@ -43,6 +43,28 @@
variable {width height : Nat}
/--
+Expected next-state value in the one-hot finite-stochastic GridWorld view equals the value of the
+successor produced by the deterministic finite-MDP view.
+-/
+theorem toFiniteStochasticMDP_expectedNextValue_eq_toFiniteMDP_successor
+ (gw : Spec.RL.Envs.Grid... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3df8600f0eb6_0 | 26268b53f86270b2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Examples/BugZoo/AttentionMask.lean | AttentionMask | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "exactCausalMaskedScore_future_exp_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [exactCausalMaskedScore_future_eq_bot scores i j hij]",
"n_chars": 64,
"n_subproofs": 0... | [
{
"name": "exactCausalMaskedScore_future_eq_bot",
"text": "/--\nFor a strict-future position, exact causal masking assigns literal `-∞`.\n\nThis is the formal version of the PyTorch operation\n`scores.masked_fill(future, -torch.inf)` at one matrix coordinate.\n-/\ntheorem exactCausalMaskedScore_future_eq_bo... | [
{
"name": "exactCausalMaskedScore_future_exp_zero",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 13,
"n_chars": 422,
"n_subproofs": 0,
"n_tactics": 2,
"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.Proofs.Models.Attention.CausalMask
public import Mathlib.Analysis.SpecialFunctions.Log.ERealExp
/-!
# BugZoo: attention-mask semantics
Attention code has its own failure mo... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Models.Attention.CausalMask
public import Mathlib.Analysis.SpecialFunctions.Log.ERealExp
/-!
# BugZoo: attention-mask semantics
Attention code has its own failure mo... | @@ -79,6 +79,20 @@
exactMaskedLogit (Spec.get2 scores i j) (Spec.get2 (Spec.causalMask n) i j)
/--
+For a strict-future position, exact causal masking assigns literal `-∞`.
+
+This is the formal version of the PyTorch operation
+`scores.masked_fill(future, -torch.inf)` at one matrix coordinate.
+-/
+theorem 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_6b30a74a49ae_0 | 0e72d1c900978432 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/InductiveProperties.lean | InductiveProperties | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "componentwise_bound_extension",
"depth": 1,
"n_commands": 0,
"n_lines": 119,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n by_cases hC : 0 ≤ C\n · -- Compare squares and use `le_of_sq_le_sq` (RHS nonnegative).\n h... | [
{
"name": "l2_norm_concatenation",
"text": "/--\nSquared L2 norm of a concatenation is the sum of squared L2 norms.\n\nInformally: `Tensor.dim f` is a “stack/concat along the outer dimension”. The Euclidean norm\nsatisfies `‖concat_i f i‖₂² = ∑ i, ‖f i‖₂²`.\n-/\ntheorem l2_norm_concatenation {n : Nat} {s : ... | [
{
"name": "componentwise_bound_extension",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 132,
"n_chars": 5851,
"n_subproofs": 33,
"n_tactics": 108,
"cyclomatic": 2,
"n_automation": 18,
"n_rewrites": 2,
"n_structural": 23,
"automation_only": f... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Exp
public import Mathlib.Data.Fin.Basic
public import Mathlib.Data.Nat.Basic
public import NN.Proofs.Analysis.Lipschitz
public import NN.Proof... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Exp
public import Mathlib.Data.Fin.Basic
public import Mathlib.Data.Nat.Basic
public import NN.Proofs.Analysis.Lipschitz
public import NN.Proof... | @@ -57,6 +57,45 @@
-- ====================================================================
/--
+Squared L2 norm of a concatenation is the sum of squared L2 norms.
+
+Informally: `Tensor.dim f` is a “stack/concat along the outer dimension”. The Euclidean norm
+satisfies `‖concat_i f i‖₂² = ∑ i, ‖f i‖₂²`.
+-/
+theore... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6b30a74a49ae_1 | d88df52f4f6c0a8e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/InductiveProperties.lean | InductiveProperties | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "relu_nonneg_inductive",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply tensor_induction_principle\n (P := fun {s} t =>\n ∀ indices : List Nat,\n match getSpec (Activa... | [
{
"name": "tensor_induction_principle",
"text": "/--\nStructural induction on tensors by their `Shape`.\n\nInformally: to prove `P t` for all tensors `t`, it suffices to prove it for scalars, and to prove\nthat it is preserved when we build a higher-dimensional tensor `Tensor.dim f` from its components.\n-/... | [
{
"name": "relu_nonneg_inductive",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 38,
"n_chars": 1228,
"n_subproofs": 0,
"n_tactics": 25,
"cyclomatic": 4,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 5,
"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 Mathlib.Analysis.SpecialFunctions.Exp
public import Mathlib.Data.Fin.Basic
public import Mathlib.Data.Nat.Basic
public import NN.Proofs.Analysis.Lipschitz
public import NN.Proof... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Exp
public import Mathlib.Data.Fin.Basic
public import Mathlib.Data.Nat.Basic
public import NN.Proofs.Analysis.Lipschitz
public import NN.Proof... | @@ -57,6 +57,28 @@
-- ====================================================================
/--
+Structural induction on tensors by their `Shape`.
+
+Informally: to prove `P t` for all tensors `t`, it suffices to prove it for scalars, and to prove
+that it is preserved when we build a higher-dimensional tensor `Tens... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6b30a74a49ae_2 | a746799c27297ec1 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/InductiveProperties.lean | InductiveProperties | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "relu_nonneg_inductive",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply tensor_induction_principle\n (P := fun {s} t =>\n ∀ indices : List Nat,\n match getSpec (Activa... | [
{
"name": "tensor_induction_principle",
"text": "/--\nStructural induction on tensors by their `Shape`.\n\nInformally: to prove `P t` for all tensors `t`, it suffices to prove it for scalars, and to prove\nthat it is preserved when we build a higher-dimensional tensor `Tensor.dim f` from its components.\n-/... | [
{
"name": "sigmoid_bounds_inductive",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 53,
"n_chars": 1747,
"n_subproofs": 5,
"n_tactics": 36,
"cyclomatic": 5,
"n_automation": 11,
"n_rewrites": 0,
"n_structural": 7,
"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.Analysis.SpecialFunctions.Exp
public import Mathlib.Data.Fin.Basic
public import Mathlib.Data.Nat.Basic
public import NN.Proofs.Analysis.Lipschitz
public import NN.Proof... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Exp
public import Mathlib.Data.Fin.Basic
public import Mathlib.Data.Nat.Basic
public import NN.Proofs.Analysis.Lipschitz
public import NN.Proof... | @@ -57,6 +57,28 @@
-- ====================================================================
/--
+Structural induction on tensors by their `Shape`.
+
+Informally: to prove `P t` for all tensors `t`, it suffices to prove it for scalars, and to prove
+that it is preserved when we build a higher-dimensional tensor `Tens... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_1bbd7dacf471_0 | d11676efa8e951c0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/Distillation.lean | Distillation | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "checkEquivalence_twoLayerMlp_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 66,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro x hx i\n -- Extract the checked predicate.\n have hwithin :\n boxWithinAbs (n := outDim)\n... | [
{
"name": "checkBoxWithinAbs_spec",
"text": "/-- Correctness of `checkBoxWithinAbs`. -/\ntheorem checkBoxWithinAbs_spec {n : Nat} {B : Box ℝ (.dim n .scalar)} {eps : ℝ} :\n checkBoxWithinAbs (n := n) B eps = true ↔ boxWithinAbs (n := n) B eps := by\n classical\n simp [checkBoxWithinAbs, decide_eq_true_... | [
{
"name": "checkEquivalence_twoLayerMlp_sound",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 83,
"n_chars": 3492,
"n_subproofs": 8,
"n_tactics": 56,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": f... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Models.Mlp
/-!
# Distillation / Equivalence certificates (TwoLayerMLP)
This module adds a distillation-style certificate:
> prove that a Student network mat... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Models.Mlp
/-!
# Distillation / Equivalence certificates (TwoLayerMLP)
This module adds a distillation-style certificate:
> prove that a Student network mat... | @@ -61,6 +61,12 @@
classical
exact decide (boxWithinAbs (n := n) B eps)
+/-- Correctness of `checkBoxWithinAbs`. -/
+theorem checkBoxWithinAbs_spec {n : Nat} {B : Box ℝ (.dim n .scalar)} {eps : ℝ} :
+ checkBoxWithinAbs (n := n) B eps = true ↔ boxWithinAbs (n := n) B eps := by
+ classical
+ simp [checkBoxWi... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_4a90014d5a1a_0 | 0fb13f38d1b781a9 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/RoundRat.lean | RoundRat | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "toReal_roundRatToIEEE32_eq_fp32Round",
"depth": 1,
"n_commands": 0,
"n_lines": 769,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n by_cases hnum : num = 0\n · -- Both sides are real `0`.\n have hto : toReal (roundR... | [
{
"name": "neural_magnitude_signedRat",
"text": "lemma neural_magnitude_signedRat (sign : Bool) (num den : Nat) (hnum : num ≠ 0) (hden : den\n ≠ 0) :\n TorchLean.Floats.neuralMagnitude binaryRadix ((if sign then (-1 : ℝ) else 1) * ((num : ℝ) /\n (den : ℝ))) =\n floorLog2Rat num den + 1 := by\n... | [
{
"name": "toReal_roundRatToIEEE32_eq_fp32Round",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 781,
"n_chars": 42938,
"n_subproofs": 209,
"n_tactics": 714,
"cyclomatic": 27,
"n_automation": 178,
"n_rewrites": 16,
"n_structural": 48,
"automat... | 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.RoundDyadic
/-!
# IEEE32Exec and FP32: Rational Rounder Correctness
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLe... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.RoundDyadic
/-!
# IEEE32Exec and FP32: Rational Rounder Correctness
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLe... | @@ -34,6 +34,75 @@
The lemmas below connect that algorithm to the `FP32` real rounding model.
-/
+lemma neural_magnitude_signedRat (sign : Bool) (num den : Nat) (hnum : num ≠ 0) (hden : den
+ ≠ 0) :
+ TorchLean.Floats.neuralMagnitude binaryRadix ((if sign then (-1 : ℝ) else 1) * ((num : ℝ) /
+ (den : ℝ))) ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_5785e18c17f3_0 | e07a8134781194fd | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphIBPBasicTheorems.lean | GraphIBPBasicTheorems | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "ibp_linear_valid_real",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- pick witnesses `x = xB.lo` and `b = bB.lo`\n have hx : Box.contains (α := ℝ) xB xB.lo := Box.contains_lo_of_valid... | [
{
"name": "valid_of_contains",
"text": "/-- If a box contains any point, then it is componentwise valid (`lo ≤ hi`). -/\ntheorem valid_of_contains {n : Nat} (B : Box ℝ (.dim n .scalar)) (x : Tensor ℝ (.dim n .scalar))\n (hx : Box.contains (α := ℝ) B x) : Valid B := by\n intro i\n cases B with\n | mk lo ... | [
{
"name": "ibp_linear_valid_real",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 840,
"n_subproofs": 3,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.MLTheory.CROWN.Graph
public import NN.MLTheory.CROWN.Models.Mlp
/-!
# GraphIBPBasicTheorems
Basic theorems about the graph-level IBP e... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.MLTheory.CROWN.Graph
public import NN.MLTheory.CROWN.Models.Mlp
/-!
# GraphIBPBasicTheorems
Basic theorems about the graph-level IBP e... | @@ -40,6 +40,29 @@
def Valid {n : Nat} (B : Box ℝ (.dim n .scalar)) : Prop :=
∀ i : Fin n, getScalar B.lo i ≤ getScalar B.hi i
+/-- If a box contains any point, then it is componentwise valid (`lo ≤ hi`). -/
+theorem valid_of_contains {n : Nat} (B : Box ℝ (.dim n .scalar)) (x : Tensor ℝ (.dim n .scalar))
+ (hx :... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
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"--corollary-delete-... |
ablate_5785e18c17f3_1 | a08194ab6504b40f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphIBPBasicTheorems.lean | GraphIBPBasicTheorems | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "graph_ibp_linear_valid_real",
"depth": 1,
"n_commands": 0,
"n_lines": 30,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n unfold ibp_linear\n cases hlin : ps.linearWB[id]? with\n | none => simp\n | some p =>\n b... | [
{
"name": "valid_castBoxDim",
"text": "/-- Validity is preserved by (definitional) casts of the vector dimension. -/\ntheorem valid_castBoxDim {n n' : Nat} (h : n = n')\n (B : Box ℝ (.dim n .scalar)) (hB : Valid B) :\n Valid (NN.MLTheory.CROWN.Graph.castBoxDim (α := ℝ) h B) := by\n cases h\n simpa [... | [
{
"name": "graph_ibp_linear_valid_real",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 37,
"n_chars": 1863,
"n_subproofs": 4,
"n_tactics": 27,
"cyclomatic": 3,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.MLTheory.CROWN.Graph
public import NN.MLTheory.CROWN.Models.Mlp
/-!
# GraphIBPBasicTheorems
Basic theorems about the graph-level IBP e... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.MLTheory.CROWN.Graph
public import NN.MLTheory.CROWN.Models.Mlp
/-!
# GraphIBPBasicTheorems
Basic theorems about the graph-level IBP e... | @@ -82,6 +82,13 @@
-- scalar containment: l ≤ l and l ≤ u
simp [Box.contains, hlu]
+/-- Validity is preserved by (definitional) casts of the vector dimension. -/
+theorem valid_castBoxDim {n n' : Nat} (h : n = n')
+ (B : Box ℝ (.dim n .scalar)) (hB : Valid B) :
+ Valid (NN.MLTheory.CRO... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_5785e18c17f3_2 | 488a2991fb0f47fa | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Proofs/GraphIBPBasicTheorems.lean | GraphIBPBasicTheorems | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 2 | [
{
"theorem_name": "graph_ibp_linear_valid_real",
"depth": 1,
"n_commands": 0,
"n_lines": 30,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n unfold ibp_linear\n cases hlin : ps.linearWB[id]? with\n | none => simp\n | some p =>\n b... | [
{
"name": "valid_castBoxDim",
"text": "/-- Validity is preserved by (definitional) casts of the vector dimension. -/\ntheorem valid_castBoxDim {n n' : Nat} (h : n = n')\n (B : Box ℝ (.dim n .scalar)) (hB : Valid B) :\n Valid (NN.MLTheory.CROWN.Graph.castBoxDim (α := ℝ) h B) := by\n cases h\n simpa [... | [
{
"name": "graph_ibp_matmul_valid_real",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 6,
"n_lines": 35,
"n_chars": 1716,
"n_subproofs": 4,
"n_tactics": 27,
"cyclomatic": 3,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 4,
"automation_only": false,
... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.MLTheory.CROWN.Graph
public import NN.MLTheory.CROWN.Models.Mlp
/-!
# GraphIBPBasicTheorems
Basic theorems about the graph-level IBP e... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.MLTheory.CROWN.Graph
public import NN.MLTheory.CROWN.Models.Mlp
/-!
# GraphIBPBasicTheorems
Basic theorems about the graph-level IBP e... | @@ -82,6 +82,13 @@
-- scalar containment: l ≤ l and l ≤ u
simp [Box.contains, hlu]
+/-- Validity is preserved by (definitional) casts of the vector dimension. -/
+theorem valid_castBoxDim {n n' : Nat} (h : n = n')
+ (B : Box ℝ (.dim n .scalar)) (hB : Valid B) :
+ Valid (NN.MLTheory.CRO... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_7782a1e84dbc_0 | a2cfac3c3b00057e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/ExactImageTheorem.lean | ExactImageTheorem | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "exists_minmax_for_idealSharp",
"depth": 1,
"n_commands": 0,
"n_lines": 74,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Work with the concrete image finset.\n let s : Finset F := (OpsExact.γFinsetBox B).image h\n... | [
{
"name": "not_exists_isNaN_true_of_forall_isNaN_false",
"text": "private theorem not_exists_isNaN_true_of_forall_isNaN_false (s : Finset F)\n (hn : ∀ z ∈ s, IEEE32Exec.isNaN z = false) :\n ¬∃ z ∈ s, IEEE32Exec.isNaN z = true := by\n intro hex\n rcases hex with ⟨z, hz, hzNaN⟩\n have hzFalse : IEEE3... | [
{
"name": "exists_minmax_for_idealSharp",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 87,
"n_chars": 3488,
"n_subproofs": 15,
"n_tactics": 65,
"cyclomatic": 7,
"n_automation": 10,
"n_rewrites": 4,
"n_structural": 23,
"automation_only": fals... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
public import NN.Floats.NeuralFloat.Core
public import NN.MLTheory.Proofs.Approximation.FloatInterval.Semantics
/-!
# Exact Interval ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
public import NN.Floats.NeuralFloat.Core
public import NN.MLTheory.Proofs.Approximation.FloatInterval.Semantics
/-!
# Exact Interval ... | @@ -368,7 +368,17 @@
open OpsExact
-/-- `chooseMin` is below every element of the finset (under the no-NaN side condition). -/
+private theorem not_exists_isNaN_true_of_forall_isNaN_false (s : Finset F)
+ (hn : ∀ z ∈ s, IEEE32Exec.isNaN z = false) :
+ ¬∃ z ∈ s, IEEE32Exec.isNaN z = true := by
+ intro hex
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_7782a1e84dbc_1 | 6b7ab70ebbcc4329 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/ExactImageTheorem.lean | ExactImageTheorem | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "exists_minmax_for_idealSharp",
"depth": 1,
"n_commands": 0,
"n_lines": 74,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Work with the concrete image finset.\n let s : Finset F := (OpsExact.γFinsetBox B).image h\n... | [
{
"name": "not_exists_isNaN_true_of_forall_isNaN_false",
"text": "private theorem not_exists_isNaN_true_of_forall_isNaN_false (s : Finset F)\n (hn : ∀ z ∈ s, IEEE32Exec.isNaN z = false) :\n ¬∃ z ∈ s, IEEE32Exec.isNaN z = true := by\n intro hex\n rcases hex with ⟨z, hz, hzNaN⟩\n have hzFalse : IEEE3... | [
{
"name": "roundedTargetExactIntervalImage_of_exactIntervalSemantics",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 17,
"n_chars": 770,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 6,
... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
public import NN.Floats.NeuralFloat.Core
public import NN.MLTheory.Proofs.Approximation.FloatInterval.Semantics
/-!
# Exact Interval ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
public import NN.Floats.NeuralFloat.Core
public import NN.MLTheory.Proofs.Approximation.FloatInterval.Semantics
/-!
# Exact Interval ... | @@ -368,7 +368,17 @@
open OpsExact
-/-- `chooseMin` is below every element of the finset (under the no-NaN side condition). -/
+private theorem not_exists_isNaN_true_of_forall_isNaN_false (s : Finset F)
+ (hn : ∀ z ∈ s, IEEE32Exec.isNaN z = false) :
+ ¬∃ z ∈ s, IEEE32Exec.isNaN z = true := by
+ intro hex
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_7782a1e84dbc_2 | 90867c5862d31b17 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/FloatInterval/ExactImageTheorem.lean | ExactImageTheorem | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 1 | [
{
"theorem_name": "exists_minmax_for_idealSharp",
"depth": 1,
"n_commands": 0,
"n_lines": 74,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Work with the concrete image finset.\n let s : Finset F := (OpsExact.γFinsetBox B).image h\n... | [
{
"name": "not_exists_isNaN_true_of_forall_isNaN_false",
"text": "private theorem not_exists_isNaN_true_of_forall_isNaN_false (s : Finset F)\n (hn : ∀ z ∈ s, IEEE32Exec.isNaN z = false) :\n ¬∃ z ∈ s, IEEE32Exec.isNaN z = true := by\n intro hex\n rcases hex with ⟨z, hz, hzNaN⟩\n have hzFalse : IEEE3... | [
{
"name": "roundedTargetExactIntervalImage_of_correctRounding",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 6,
"n_lines": 20,
"n_chars": 992,
"n_subproofs": 2,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"autom... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
public import NN.Floats.NeuralFloat.Core
public import NN.MLTheory.Proofs.Approximation.FloatInterval.Semantics
/-!
# Exact Interval ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Analysis.SpecialFunctions.Pow.Real
public import NN.Floats.NeuralFloat.Core
public import NN.MLTheory.Proofs.Approximation.FloatInterval.Semantics
/-!
# Exact Interval ... | @@ -368,7 +368,17 @@
open OpsExact
-/-- `chooseMin` is below every element of the finset (under the no-NaN side condition). -/
+private theorem not_exists_isNaN_true_of_forall_isNaN_false (s : Finset F)
+ (hn : ∀ z ∈ s, IEEE32Exec.isNaN z = false) :
+ ¬∃ z ∈ s, IEEE32Exec.isNaN z = true := by
+ intro hex
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c0f0aeaf8204_0 | 9b152f00ab231897 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationND.lean | UniversalApproximationND | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "coordSubalg_topologicalClosure_eq_top",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ContinuousMap.subalgebra_topologicalClosure_eq_top_of_separatesPoints\n (A := coordSubalg (K := K)) (... | [
{
"name": "coordSubalg_separatesPoints",
"text": "/--\nCoordinate functions separate points.\n\nIf two tensor points differ, the tensor/vector equivalence gives a coordinate where they differ,\nand that coordinate projection belongs to `coordSubalg`.\n-/\ntheorem coordSubalg_separatesPoints : (coordSubalg (... | [
{
"name": "coordSubalg_topologicalClosure_eq_top",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 533,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"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 Mathlib.Topology.ContinuousMap.StoneWeierstrass
public import NN.Spec.Core.Tensor
public import NN.Runtime.Context
/-!
# Universal approximation (nD, Stone–Weierstrass, Tensor ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Topology.ContinuousMap.StoneWeierstrass
public import NN.Spec.Core.Tensor
public import NN.Runtime.Context
/-!
# Universal approximation (nD, Stone–Weierstrass, Tensor ... | @@ -94,13 +94,51 @@
Algebra.adjoin ℝ (Set.range (coord (K := K)))
/--
+Coordinate functions separate points.
+
+If two tensor points differ, the tensor/vector equivalence gives a coordinate where they differ,
+and that coordinate projection belongs to `coordSubalg`.
+-/
+theorem coordSubalg_separatesPoints : (coo... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c0f0aeaf8204_1 | 5a2fca98fbeb8550 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/Approximation/Universal/UniversalApproximationND.lean | UniversalApproximationND | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "coordSubalg_topologicalClosure_eq_top",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n ContinuousMap.subalgebra_topologicalClosure_eq_top_of_separatesPoints\n (A := coordSubalg (K := K)) (... | [
{
"name": "coordSubalg_separatesPoints",
"text": "/--\nCoordinate functions separate points.\n\nIf two tensor points differ, the tensor/vector equivalence gives a coordinate where they differ,\nand that coordinate projection belongs to `coordSubalg`.\n-/\ntheorem coordSubalg_separatesPoints : (coordSubalg (... | [
{
"name": "exists_coordSubalg_near_continuousMap",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
"n_chars": 629,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 0,
"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 Mathlib.Topology.ContinuousMap.StoneWeierstrass
public import NN.Spec.Core.Tensor
public import NN.Runtime.Context
/-!
# Universal approximation (nD, Stone–Weierstrass, Tensor ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Topology.ContinuousMap.StoneWeierstrass
public import NN.Spec.Core.Tensor
public import NN.Runtime.Context
/-!
# Universal approximation (nD, Stone–Weierstrass, Tensor ... | @@ -94,6 +94,42 @@
Algebra.adjoin ℝ (Set.range (coord (K := K)))
/--
+Coordinate functions separate points.
+
+If two tensor points differ, the tensor/vector equivalence gives a coordinate where they differ,
+and that coordinate projection belongs to `coordSubalg`.
+-/
+theorem coordSubalg_separatesPoints : (coor... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_ef9e29ddb0c7_0 | 6d1b6fc89bf5746f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Ops/Recurrent/ElmanCell.lean | ElmanCell | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "elmanTwoStep_hasFDerivAt",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let cellEval :=\n Graph.evalVec\n (Γ := ΓElman inputSize hiddenSize)\n (ss := ssElmanCell inputSize ... | [
{
"name": "elmanCell_eval_hasFDerivAt",
"text": "/--\nForward evaluation of one Elman cell is differentiable at every input context.\n\nThis is the recurrent analogue of the Transformer sublayer calculus bridges: it exposes the cell as\na differentiable map that can be composed repeatedly when proving BPTT ... | [
{
"name": "elmanTwoStep_hasFDerivAt",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 84,
"n_chars": 3881,
"n_subproofs": 3,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 1,
"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.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Util.Idx
/-!
# Elman RNN Cell VJP
This file proves the core differentiable cell used by a ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Util.Idx
/-!
# Elman RNN Cell VJP
This file proves the core differentiable cell used by a ... | @@ -128,6 +128,37 @@
(idxPre (inputSize := inputSize) (hiddenSize := hiddenSize)))
/--
+Forward evaluation of one Elman cell is differentiable at every input context.
+
+This is the recurrent analogue of the Transformer sublayer calculus bridges: it exposes the cell as
+a differentiable map that can be comp... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_ef9e29ddb0c7_1 | 831262c4720e96db | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Ops/Recurrent/ElmanCell.lean | ElmanCell | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "elmanTwoStep_hasFDerivAt",
"depth": 1,
"n_commands": 0,
"n_lines": 19,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n let cellEval :=\n Graph.evalVec\n (Γ := ΓElman inputSize hiddenSize)\n (ss := ssElmanCell inputSize ... | [
{
"name": "elmanCell_eval_hasFDerivAt",
"text": "/--\nForward evaluation of one Elman cell is differentiable at every input context.\n\nThis is the recurrent analogue of the Transformer sublayer calculus bridges: it exposes the cell as\na differentiable map that can be composed repeatedly when proving BPTT ... | [
{
"name": "elmanUnroll_hasFDerivAt",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 42,
"n_chars": 2073,
"n_subproofs": 3,
"n_tactics": 21,
"cyclomatic": 4,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 6,
"automation_only": false,
"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Util.Idx
/-!
# Elman RNN Cell VJP
This file proves the core differentiable cell used by a ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Nodes.GraphComposition
public import NN.Proofs.Autograd.Tape.Util.Idx
/-!
# Elman RNN Cell VJP
This file proves the core differentiable cell used by a ... | @@ -127,6 +127,37 @@
(s := HShape hiddenSize)
(idxPre (inputSize := inputSize) (hiddenSize := hiddenSize)))
+/--
+Forward evaluation of one Elman cell is differentiable at every input context.
+
+This is the recurrent analogue of the Transformer sublayer calculus bridges: it exposes the cell as
+a 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_d622538874a0_0 | fd2fc2f880147513 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/ConvBackward/Common.lean | Common | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "mkInputIdx_match_eq_paddedInput",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Compare both sides via the explicit `paddedInput` read formula.\n rw [get_at_or_zero_padde... | [
{
"name": "get_at_or_zero_paddedInput",
"text": "lemma get_at_or_zero_paddedInput\n {α : Type} [Context α] {inC inH inW padding : Nat}\n (img : Spec.MultiChannelImage inC inH inW α) (c : Fin inC) (p q : Nat) :\n getAtOrZero (paddedInput (inC := inC) (inH := inH) (inW := inW) (padding := padding) im... | [
{
"name": "mkInputIdx_match_eq_paddedInput",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 938,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.BackwardOps
public import NN.Proofs.RuntimeApprox.NF.ConvForward
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Utils
/-... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.BackwardOps
public import NN.Proofs.RuntimeApprox.NF.ConvForward
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Utils
/-... | @@ -96,6 +96,24 @@
else
Spec.padMultiChannel img padding
+lemma get_at_or_zero_paddedInput
+ {α : Type} [Context α] {inC inH inW padding : Nat}
+ (img : Spec.MultiChannelImage inC inH inW α) (c : Fin inC) (p q : Nat) :
+ getAtOrZero (paddedInput (inC := inC) (inH := inH) (inW := inW) (padding := padd... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d622538874a0_1 | f0508469daf5620d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/ConvBackward/Common.lean | Common | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "mkInputIdx_match_eq_paddedInput",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Compare both sides via the explicit `paddedInput` read formula.\n rw [get_at_or_zero_padde... | [
{
"name": "get_at_or_zero_paddedInput",
"text": "lemma get_at_or_zero_paddedInput\n {α : Type} [Context α] {inC inH inW padding : Nat}\n (img : Spec.MultiChannelImage inC inH inW α) (c : Fin inC) (p q : Nat) :\n getAtOrZero (paddedInput (inC := inC) (inH := inH) (inW := inW) (padding := padding) im... | [
{
"name": "conv2dKernelFoldRead_eq_paddedFold",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 63,
"n_chars": 2809,
"n_subproofs": 1,
"n_tactics": 41,
"cyclomatic": 3,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": f... | 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.BackwardOps
public import NN.Proofs.RuntimeApprox.NF.ConvForward
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Utils
/-... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.RuntimeApprox.NF.BackwardOps
public import NN.Proofs.RuntimeApprox.NF.ConvForward
public import NN.Proofs.RuntimeApprox.NF.Utils
public import NN.Spec.Layers.Utils
/-... | @@ -96,6 +96,24 @@
else
Spec.padMultiChannel img padding
+lemma get_at_or_zero_paddedInput
+ {α : Type} [Context α] {inC inH inW padding : Nat}
+ (img : Spec.MultiChannelImage inC inH inW α) (c : Fin inC) (p q : Nat) :
+ getAtOrZero (paddedInput (inC := inC) (inH := inH) (inW := inW) (padding := padd... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_9f76ab792660_0 | 57e5d262c98714d2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/Ops/Plumbing.lean | Plumbing | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "approxT_map_spec_of_scalar_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 108,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro xS xR eps hx hscalar\n induction s with\n | scalar =>\n cases xS with\n | scalar x =>\... | [
{
"name": "approxT_dim_get",
"text": "/--\nProjection lemma for `approxT` on dimensioned tensors.\n\nIf `xS` approximates `xR` within `eps`, then each component `xS[i]` approximates `xR[i]` within\n `eps`.\n-/\nlemma approxT_dim_get {α : Type} {toSpec : α → SpecScalar} {n : Nat} {s : Shape}\n {xS : Spec... | [
{
"name": "approxT_map_spec_of_scalar_bound",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 131,
"n_chars": 6382,
"n_subproofs": 12,
"n_tactics": 108,
"cyclomatic": 6,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 12,
"automation_only":... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Group.MinMax
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.Analysis.Complex.Trigonometric
public import Mathlib.Analysis.SpecialF... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Group.MinMax
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.Analysis.Complex.Trigonometric
public import Mathlib.Analysis.SpecialF... | @@ -103,6 +103,57 @@
tensorLinfNorm, Spec.mapTensor, Spec.Tensor.subSpec, map2Spec, MathFunctions.abs] using h'
/--
+Projection lemma for `approxT` on dimensioned tensors.
+
+If `xS` approximates `xR` within `eps`, then each component `xS[i]` approximates `xR[i]` within
+ `eps`.
+-/
+lemma approxT_dim_get {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_9f76ab792660_1 | f1fccfae0aac8039 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/NF/Ops/Plumbing.lean | Plumbing | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "approxT_map_spec_of_scalar_bound",
"depth": 1,
"n_commands": 0,
"n_lines": 108,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro xS xR eps hx hscalar\n induction s with\n | scalar =>\n cases xS with\n | scalar x =>\... | [
{
"name": "approxT_dim_get",
"text": "/--\nProjection lemma for `approxT` on dimensioned tensors.\n\nIf `xS` approximates `xR` within `eps`, then each component `xS[i]` approximates `xR[i]` within\n `eps`.\n-/\nlemma approxT_dim_get {α : Type} {toSpec : α → SpecScalar} {n : Nat} {s : Shape}\n {xS : Spec... | [
{
"name": "approxT_map2_spec_of_scalar_bound",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 163,
"n_chars": 8881,
"n_subproofs": 14,
"n_tactics": 138,
"cyclomatic": 10,
"n_automation": 5,
"n_rewrites": 2,
"n_structural": 16,
"automation_only... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Group.MinMax
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.Analysis.Complex.Trigonometric
public import Mathlib.Analysis.SpecialF... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Group.MinMax
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.Analysis.Complex.Trigonometric
public import Mathlib.Analysis.SpecialF... | @@ -103,6 +103,57 @@
tensorLinfNorm, Spec.mapTensor, Spec.Tensor.subSpec, map2Spec, MathFunctions.abs] using h'
/--
+Projection lemma for `approxT` on dimensioned tensors.
+
+If `xS` approximates `xR` within `eps`, then each component `xS[i]` approximates `xR[i]` within
+ `eps`.
+-/
+lemma approxT_dim_get {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_6079c3128c6a_0 | 3677c4491db1ecc3 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeInitFloat32.lean | BridgeInitFloat32 | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 7 | [
{
"theorem_name": "toIEEE32Exec_add",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply bits_inj\n simpa [toIEEE32Exec, IEEE32Exec.ofBits] using\n (RuntimeFloat32MatchesIEEE32Exec.add_bits (a := a) (b... | [
{
"name": "bits_inj",
"text": "private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n-- We write these theorems using the usual notation (`a + b`, `a * b`) because that is how most\n-- downstream code is written; the assumptions are stated... | [
{
"name": "toIEEE32Exec_add",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 336,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"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 Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | @@ -117,9 +117,20 @@
-- `IEEE32Exec` stores a `UInt32` bit pattern; equality is extensional on `.bits`.
omit [RuntimeFloat32MatchesIEEE32Exec] in
+private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
+-- We write these theorems using the usual not... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6079c3128c6a_1 | 59286668b54fa08f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeInitFloat32.lean | BridgeInitFloat32 | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 7 | [
{
"theorem_name": "toIEEE32Exec_add",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply bits_inj\n simpa [toIEEE32Exec, IEEE32Exec.ofBits] using\n (RuntimeFloat32MatchesIEEE32Exec.add_bits (a := a) (b... | [
{
"name": "bits_inj",
"text": "private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n-- We write these theorems using the usual notation (`a + b`, `a * b`) because that is how most\n-- downstream code is written; the assumptions are stated... | [
{
"name": "toIEEE32Exec_sub",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 358,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"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 Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | @@ -117,9 +117,20 @@
-- `IEEE32Exec` stores a `UInt32` bit pattern; equality is extensional on `.bits`.
omit [RuntimeFloat32MatchesIEEE32Exec] in
+private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
+-- We write these theorems using the usual not... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6079c3128c6a_2 | 8163cc0c9a5902a4 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeInitFloat32.lean | BridgeInitFloat32 | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 7 | [
{
"theorem_name": "toIEEE32Exec_add",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply bits_inj\n simpa [toIEEE32Exec, IEEE32Exec.ofBits] using\n (RuntimeFloat32MatchesIEEE32Exec.add_bits (a := a) (b... | [
{
"name": "bits_inj",
"text": "private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n-- We write these theorems using the usual notation (`a + b`, `a * b`) because that is how most\n-- downstream code is written; the assumptions are stated... | [
{
"name": "toIEEE32Exec_mul",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 361,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"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 Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | @@ -117,9 +117,20 @@
-- `IEEE32Exec` stores a `UInt32` bit pattern; equality is extensional on `.bits`.
omit [RuntimeFloat32MatchesIEEE32Exec] in
+private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
+-- We write these theorems using the usual not... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6079c3128c6a_3 | b898017de264aedd | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeInitFloat32.lean | BridgeInitFloat32 | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 7 | [
{
"theorem_name": "toIEEE32Exec_add",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply bits_inj\n simpa [toIEEE32Exec, IEEE32Exec.ofBits] using\n (RuntimeFloat32MatchesIEEE32Exec.add_bits (a := a) (b... | [
{
"name": "bits_inj",
"text": "private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n-- We write these theorems using the usual notation (`a + b`, `a * b`) because that is how most\n-- downstream code is written; the assumptions are stated... | [
{
"name": "toIEEE32Exec_div",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 355,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"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 Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | @@ -117,9 +117,20 @@
-- `IEEE32Exec` stores a `UInt32` bit pattern; equality is extensional on `.bits`.
omit [RuntimeFloat32MatchesIEEE32Exec] in
+private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
+-- We write these theorems using the usual not... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6079c3128c6a_4 | 0d2f779d851d3f3e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeInitFloat32.lean | BridgeInitFloat32 | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 7 | [
{
"theorem_name": "toIEEE32Exec_add",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply bits_inj\n simpa [toIEEE32Exec, IEEE32Exec.ofBits] using\n (RuntimeFloat32MatchesIEEE32Exec.add_bits (a := a) (b... | [
{
"name": "bits_inj",
"text": "private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n-- We write these theorems using the usual notation (`a + b`, `a * b`) because that is how most\n-- downstream code is written; the assumptions are stated... | [
{
"name": "toIEEE32Exec_neg",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 325,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"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 Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | @@ -117,9 +117,20 @@
-- `IEEE32Exec` stores a `UInt32` bit pattern; equality is extensional on `.bits`.
omit [RuntimeFloat32MatchesIEEE32Exec] in
+private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
+-- We write these theorems using the usual not... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6079c3128c6a_5 | 843444c722b52f30 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeInitFloat32.lean | BridgeInitFloat32 | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 7 | [
{
"theorem_name": "toIEEE32Exec_add",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply bits_inj\n simpa [toIEEE32Exec, IEEE32Exec.ofBits] using\n (RuntimeFloat32MatchesIEEE32Exec.add_bits (a := a) (b... | [
{
"name": "bits_inj",
"text": "private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n-- We write these theorems using the usual notation (`a + b`, `a * b`) because that is how most\n-- downstream code is written; the assumptions are stated... | [
{
"name": "toIEEE32Exec_sqrt",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 333,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"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 Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | @@ -117,9 +117,20 @@
-- `IEEE32Exec` stores a `UInt32` bit pattern; equality is extensional on `.bits`.
omit [RuntimeFloat32MatchesIEEE32Exec] in
+private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
+-- We write these theorems using the usual not... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_6079c3128c6a_6 | 3eb1aefde2c80324 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeInitFloat32.lean | BridgeInitFloat32 | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 7 | [
{
"theorem_name": "toIEEE32Exec_add",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply bits_inj\n simpa [toIEEE32Exec, IEEE32Exec.ofBits] using\n (RuntimeFloat32MatchesIEEE32Exec.add_bits (a := a) (b... | [
{
"name": "bits_inj",
"text": "private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by\n cases x\n cases y\n cases h\n rfl\n\n-- We write these theorems using the usual notation (`a + b`, `a * b`) because that is how most\n-- downstream code is written; the assumptions are stated... | [
{
"name": "toIEEE32Exec_ofIEEE32Exec",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 340,
"n_subproofs": 0,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Init.Data.Float32
public import NN.Floats.IEEEExec.Exec32
/-!
# BridgeInitFloat32
External (assumption-based) bridge: Lean's `Init.Float32` ↔ `IEEE32Exec`.
Why assumptions ar... | @@ -117,9 +117,20 @@
-- `IEEE32Exec` stores a `UInt32` bit pattern; equality is extensional on `.bits`.
omit [RuntimeFloat32MatchesIEEE32Exec] in
+private theorem bits_inj {x y : IEEE32Exec} (h : x.bits = y.bits) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
+-- We write these theorems using the usual not... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_bf8751a4ca83_0 | 8fa94f86c9137dc5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/Soundness.lean | Soundness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "dotList_add_right",
"depth": 1,
"n_commands": 0,
"n_lines": 13,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction ss with\n | nil =>\n cases x; cases y; cases z; simp [dotList, Proofs.Autograd.Algebra.TList.add]\n | con... | [
{
"name": "dot_add_right",
"text": "private theorem dot_add_right {s : Shape} (a b c : Tensor ℝ s) :\n dot a (addSpec b c) = dot a b + dot a c := by\n calc\n dot a (addSpec b c) = dot (addSpec b c) a := by\n simpa using (dot_comm (a := a) (b := addSpec b c))\n _ = dot b a + dot c a := by\n ... | [
{
"name": "dotList_add_right",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 21,
"n_chars": 644,
"n_subproofs": 0,
"n_tactics": 16,
"cyclomatic": 8,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 7,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Tape.Algebra.Soundness
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness for the proved-corr... | /-
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.Tape.Algebra.Soundness
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness for the proved-corr... | @@ -111,6 +111,16 @@
export Proofs.Autograd.Algebra.TList (cast_rfl cast_cast cast_symm)
+private theorem dot_add_right {s : Shape} (a b c : Tensor ℝ s) :
+ dot a (addSpec b c) = dot a b + dot a c := by
+ calc
+ dot a (addSpec b c) = dot (addSpec b c) a := by
+ simpa using (dot_comm (a := a) (b := addS... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_bf8751a4ca83_1 | f46e7fc3a91d96e4 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/Soundness.lean | Soundness | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "dot_fill_zero_right",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hfill : fill (0 : ℝ) s = scaleSpec (α:=ℝ) (s:=s) (fill (1 : ℝ) s) 0 := by\n simpa using (fill_eq_scale_one (s ... | [
{
"name": "fill_eq_scale_one",
"text": "private theorem fill_eq_scale_one {s : Shape} (c : ℝ) :\n fill c s = scaleSpec (α:=ℝ) (s:=s) (fill (1 : ℝ) s) c := by\n induction s with\n | scalar =>\n simp [fill, scaleSpec, mapSpec]\n | dim n s ih =>\n simp [fill, scaleSpec, mapSpec, ih]\n\n",
"fan_... | [
{
"name": "dot_fill_zero_right",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 861,
"n_subproofs": 1,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 5,
"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.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Tape.Algebra.Soundness
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness for the proved-corr... | /-
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.Tape.Algebra.Soundness
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness for the proved-corr... | @@ -111,6 +111,14 @@
export Proofs.Autograd.Algebra.TList (cast_rfl cast_cast cast_symm)
+private theorem fill_eq_scale_one {s : Shape} (c : ℝ) :
+ fill c s = scaleSpec (α:=ℝ) (s:=s) (fill (1 : ℝ) s) c := by
+ induction s with
+ | scalar =>
+ simp [fill, scaleSpec, mapSpec]
+ | dim n s ih =>
+ simp [fi... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_bf8751a4ca83_2 | 37de5511916a404d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/Soundness.lean | Soundness | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "dotList_zero_right",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction ss with\n | nil =>\n cases x\n simp [dotList, Proofs.Autograd.Algebra.TList.zero]\n | cons s ss ih =>\... | [
{
"name": "dot_fill_zero_right",
"text": "/--\nDotting any tensor with a zero-filled tensor gives `0`.\n\nThis is the tensor-level fact used to show that “one-hot” cotangents behave as expected.\n-/\ntheorem dot_fill_zero_right {s : Shape} (a : Tensor ℝ s) :\n dot a (fill (0 : ℝ) s) = 0 := by\n have hfi... | [
{
"name": "dotList_zero_right",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 393,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 4,
"n_automation": 2,
"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.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Tape.Algebra.Soundness
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness for the proved-corr... | /-
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.Tape.Algebra.Soundness
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness for the proved-corr... | @@ -119,6 +119,25 @@
| dim n s ih =>
simp [fill, scaleSpec, mapSpec, ih]
+/--
+Dotting any tensor with a zero-filled tensor gives `0`.
+
+This is the tensor-level fact used to show that “one-hot” cotangents behave as expected.
+-/
+theorem dot_fill_zero_right {s : Shape} (a : Tensor ℝ s) :
+ dot a (fill (0... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_bf8751a4ca83_3 | 08c6402ccad05fe3 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/Soundness.lean | Soundness | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 2 | [
{
"theorem_name": "dotList_zero_right",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction ss with\n | nil =>\n cases x\n simp [dotList, Proofs.Autograd.Algebra.TList.zero]\n | cons s ss ih =>\... | [
{
"name": "dot_fill_zero_right",
"text": "/--\nDotting any tensor with a zero-filled tensor gives `0`.\n\nThis is the tensor-level fact used to show that “one-hot” cotangents behave as expected.\n-/\ntheorem dot_fill_zero_right {s : Shape} (a : Tensor ℝ s) :\n dot a (fill (0 : ℝ) s) = 0 := by\n have hfi... | [
{
"name": "dotList_single",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 75,
"n_chars": 3409,
"n_subproofs": 5,
"n_tactics": 55,
"cyclomatic": 10,
"n_automation": 10,
"n_rewrites": 0,
"n_structural": 15,
"automation_only": false,
"max_ne... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Tape.Algebra.Soundness
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness for the proved-corr... | /-
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.Tape.Algebra.Soundness
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness for the proved-corr... | @@ -119,6 +119,25 @@
| dim n s ih =>
simp [fill, scaleSpec, mapSpec, ih]
+/--
+Dotting any tensor with a zero-filled tensor gives `0`.
+
+This is the tensor-level fact used to show that “one-hot” cotangents behave as expected.
+-/
+theorem dot_fill_zero_right {s : Shape} (a : Tensor ℝ s) :
+ dot a (fill (0... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_bf8751a4ca83_4 | d58cef99eabaedfc | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Core/Soundness.lean | Soundness | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 8 | 1 | [
{
"theorem_name": "backprop_correct",
"depth": 1,
"n_commands": 0,
"n_lines": 50,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction g with\n | nil =>\n intro x dx seed\n -- `ss = []` so this is exactly the dotList/cast adjointness.\n ... | [
{
"name": "dotList_add_right",
"text": "/--\n`dotList` is linear in its right argument with respect to `TList.add`.\n\nInformally: `⟪x, y + z⟫ = ⟪x, y⟫ + ⟪x, z⟫` for contexts.\n-/\ntheorem dotList_add_right {ss : List Shape} (x y z : TList ss) :\n dotList x (add y z) = dotList x y + dotList x z := by\n ... | [
{
"name": "backprop_correct",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 5,
"n_lines": 66,
"n_chars": 3422,
"n_subproofs": 5,
"n_tactics": 47,
"cyclomatic": 2,
"n_automation": 10,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_ne... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Core.RealCorrectness
public import NN.Proofs.Autograd.Tape.Algebra.Soundness
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness for the proved-corr... | /-
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.Tape.Algebra.Soundness
/-!
# Soundness
Tape-style (SSA/DAG) reverse-mode soundness for the proved-corr... | @@ -127,6 +127,26 @@
simp [dot_comm]
/--
+`dotList` is linear in its right argument with respect to `TList.add`.
+
+Informally: `⟪x, y + z⟫ = ⟪x, y⟫ + ⟪x, z⟫` for contexts.
+-/
+theorem dotList_add_right {ss : List Shape} (x y z : TList ss) :
+ dotList x (add y z) = dotList x y + dotList x z := by
+ induc... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d3b4c9264b1d_0 | ee140a5b687a5bda | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/Core.lean | Core | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "discountedReturns_length",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simpa [Spec.RL.discountedReturns] using\n discountedReturnsFrom_length (α := α) gamma rewards 0",
"n_chars"... | [
{
"name": "discountedReturnsFrom_length",
"text": "/-- `discountedReturnsFrom` produces exactly one return per input reward. -/\ntheorem discountedReturnsFrom_length {α : Type} [Zero α] [Add α] [Mul α]\n (gamma : α) (rewards : List α) (bootstrap : α) :\n (Spec.RL.discountedReturnsFrom (α := α) gamma r... | [
{
"name": "discountedReturns_length",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 352,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.List.Basic
public import NN.Proofs.Utils.List
public import NN.Spec.RL.Core
/-!
# RL Core Proofs
Small structural theorems about TorchLean's pure RL helper functi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.List.Basic
public import NN.Proofs.Utils.List
public import NN.Spec.RL.Core
/-!
# RL Core Proofs
Small structural theorems about TorchLean's pure RL helper functi... | @@ -40,10 +40,22 @@
namespace RL
namespace Core
+/-- `discountedReturnsFrom` produces exactly one return per input reward. -/
+theorem discountedReturnsFrom_length {α : Type} [Zero α] [Add α] [Mul α]
+ (gamma : α) (rewards : List α) (bootstrap : α) :
+ (Spec.RL.discountedReturnsFrom (α := α) gamma rewards boo... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d3b4c9264b1d_1 | ce53451c739cddd6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RL/Core.lean | Core | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "discountedReturnsDone_length_of_eqLength",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [discountedReturnsDone_length_eq_min (α := α) (gamma := gamma) (rewards := rewards)\n (dones... | [
{
"name": "discountedReturnsDone_length_eq_min",
"text": "/-- `discountedReturnsDone` returns one value per paired reward/done entry. -/\ntheorem discountedReturnsDone_length_eq_min {α : Type} [Zero α] [One α] [Add α] [Mul α]\n (gamma : α) (rewards : List α) (dones : List Bool) (bootstrap : α) :\n (Sp... | [
{
"name": "discountedReturnsDone_length_of_eqLength",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 580,
"n_subproofs": 0,
"n_tactics": 4,
"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 Mathlib.Data.List.Basic
public import NN.Proofs.Utils.List
public import NN.Spec.RL.Core
/-!
# RL Core Proofs
Small structural theorems about TorchLean's pure RL helper functi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.List.Basic
public import NN.Proofs.Utils.List
public import NN.Spec.RL.Core
/-!
# RL Core Proofs
Small structural theorems about TorchLean's pure RL helper functi... | @@ -40,12 +40,26 @@
namespace RL
namespace Core
+/-- `discountedReturnsDone` returns one value per paired reward/done entry. -/
+theorem discountedReturnsDone_length_eq_min {α : Type} [Zero α] [One α] [Add α] [Mul α]
+ (gamma : α) (rewards : List α) (dones : List Bool) (bootstrap : α) :
+ (Spec.RL.discountedR... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_413ab10fd0a7_0 | f69afa8efe7a935c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/SelfSupervised/VICReg.lean | VICReg | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "varianceTerm_collapsed_positive",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [varianceTerm_replicate_zero]\n exact Nat.mul_pos (Nat.succ_pos d) hγ",
"n_chars": 79,
"n_subpr... | [
{
"name": "varianceTerm_replicate_zero",
"text": "/--\nCollapsed coordinates (`variance = 0`) pay exactly `d * gamma`.\n\nThis is the direct anti-collapse fact: if every coordinate has zero variance, the variance floor\ndoes not silently accept it.\n-/\ntheorem varianceTerm_replicate_zero (gamma d : Nat) :\... | [
{
"name": "varianceTerm_collapsed_positive",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 7,
"n_chars": 314,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"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
import Mathlib.Data.List.Basic
/-!
# VICReg and Barlow-Twins style collapse guards
This file formalizes the parts of recent redundancy-reduction SSL objectives that are cleanly
checkable wi... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
import Mathlib.Data.List.Basic
/-!
# VICReg and Barlow-Twins style collapse guards
This file formalizes the parts of recent redundancy-reduction SSL objectives that are cleanly
checkable wi... | @@ -72,9 +72,25 @@
varianceFloorPenalty gamma v + varianceTerm gamma vs := by
simp [varianceTerm]
+/--
+Collapsed coordinates (`variance = 0`) pay exactly `d * gamma`.
+
+This is the direct anti-collapse fact: if every coordinate has zero variance, the variance floor
+does not silently accept it.
+-/
+theor... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_2525814b0fe5_0 | 15dc2c6200c3a809 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Algebra.lean | Algebra | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "dot_scale_left",
"depth": 1,
"n_commands": 0,
"n_lines": 9,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Reduce to `dot_scale_right` by commutativity of the dot product.\n calc\n dot (α := α) (scaleSpec (α := α) (s := s) a... | [
{
"name": "dot_scale_right",
"text": "theorem dot_scale_right {s : Shape} (a b : Tensor α s) (k : α) :\n dot (α := α) a (scaleSpec (α := α) (s := s) b k) = dot (α := α) a b * k := by\n induction s with\n | scalar =>\n cases a; cases b\n simp [TensorAlgebra.dot, Tensor.scaleSpec, Tensor.mapSpec, m... | [
{
"name": "dot_scale_left",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 13,
"n_chars": 679,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 2,
"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.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | @@ -93,6 +93,54 @@
/-! ### Scaling -/
+theorem dot_scale_right {s : Shape} (a b : Tensor α s) (k : α) :
+ dot (α := α) a (scaleSpec (α := α) (s := s) b k) = dot (α := α) a b * k := by
+ induction s with
+ | scalar =>
+ cases a; cases b
+ simp [TensorAlgebra.dot, Tensor.scaleSpec, Tensor.mapSpec, mul_ass... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_2525814b0fe5_1 | ad0e7f7e55271bb0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Algebra.lean | Algebra | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "dot_add_left",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction s with\n | scalar =>\n cases a; cases b; cases c\n simp [dot, addSpec, map2Spec, add_mul]\n | dim n s ih =>... | [
{
"name": "foldl_add_distrib2",
"text": "/--\nDistribute a fold of `g1 x + g2 x` into the sum of two folds.\n\nThis is a general “sum splits over addition” lemma used to prove bilinearity-like properties of\n`dot`.\n-/\nlemma foldl_add_distrib2 {α β : Type} [AddCommMonoid α] (l : List β) (g1 g2 : β → α) :\n... | [
{
"name": "dot_add_left",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 46,
"n_chars": 2290,
"n_subproofs": 4,
"n_tactics": 41,
"cyclomatic": 8,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 8,
"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.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | @@ -83,6 +83,20 @@
/-! ## List-fold helpers -/
+/--
+Distribute a fold of `g1 x + g2 x` into the sum of two folds.
+
+This is a general “sum splits over addition” lemma used to prove bilinearity-like properties of
+`dot`.
+-/
+lemma foldl_add_distrib2 {α β : Type} [AddCommMonoid α] (l : List β) (g1 g2 : β → 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_2525814b0fe5_2 | 13e263efda53fd3f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Algebra.lean | Algebra | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 1 | [
{
"theorem_name": "dot_add_left",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction s with\n | scalar =>\n cases a; cases b; cases c\n simp [dot, addSpec, map2Spec, add_mul]\n | dim n s ih =>... | [
{
"name": "foldl_add_distrib2",
"text": "/--\nDistribute a fold of `g1 x + g2 x` into the sum of two folds.\n\nThis is a general “sum splits over addition” lemma used to prove bilinearity-like properties of\n`dot`.\n-/\nlemma foldl_add_distrib2 {α β : Type} [AddCommMonoid α] (l : List β) (g1 g2 : β → α) :\n... | [
{
"name": "dot_add_right",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 14,
"n_chars": 663,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nesting"... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | @@ -83,6 +83,20 @@
/-! ## List-fold helpers -/
+/--
+Distribute a fold of `g1 x + g2 x` into the sum of two folds.
+
+This is a general “sum splits over addition” lemma used to prove bilinearity-like properties of
+`dot`.
+-/
+lemma foldl_add_distrib2 {α β : Type} [AddCommMonoid α] (l : List β) (g1 g2 : β → 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_2525814b0fe5_3 | d8d18496ad6d2f5f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Algebra.lean | Algebra | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 3 | [
{
"theorem_name": "dot_vec_eq_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 30,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases a with\n | dim fa =>\n cases b with\n | dim fb =>\n have hfold :\n (List.finRange n... | [
{
"name": "finRange_foldl_add_eq_finset_sum",
"text": "/--\nRewrite the spec-style fold over `List.finRange n` into a proof-friendly `Finset.univ.sum`.\n\nMany spec definitions use `List.foldl` (it is definitional and convenient for computation), while\nproofs often prefer `Finset.sum` so they can use stand... | [
{
"name": "dot_vec_eq_sum",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 37,
"n_chars": 1499,
"n_subproofs": 2,
"n_tactics": 27,
"cyclomatic": 5,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 7,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | @@ -83,6 +83,16 @@
/-! ## List-fold helpers -/
+/--
+Rewrite the spec-style fold over `List.finRange n` into a proof-friendly `Finset.univ.sum`.
+
+Many spec definitions use `List.foldl` (it is definitional and convenient for computation), while
+proofs often prefer `Finset.sum` so they can use standard big-operat... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_2525814b0fe5_4 | ea09171cef1d7b20 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Algebra.lean | Algebra | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 3 | [
{
"theorem_name": "dot_vec_eq_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 30,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases a with\n | dim fa =>\n cases b with\n | dim fb =>\n have hfold :\n (List.finRange n... | [
{
"name": "finRange_foldl_add_eq_finset_sum",
"text": "/--\nRewrite the spec-style fold over `List.finRange n` into a proof-friendly `Finset.univ.sum`.\n\nMany spec definitions use `List.foldl` (it is definitional and convenient for computation), while\nproofs often prefer `Finset.sum` so they can use stand... | [
{
"name": "toVec_mat_vec_mul_spec",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 80,
"n_chars": 3505,
"n_subproofs": 6,
"n_tactics": 63,
"cyclomatic": 15,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 12,
"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.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | @@ -83,6 +83,16 @@
/-! ## List-fold helpers -/
+/--
+Rewrite the spec-style fold over `List.finRange n` into a proof-friendly `Finset.univ.sum`.
+
+Many spec definitions use `List.foldl` (it is definitional and convenient for computation), while
+proofs often prefer `Finset.sum` so they can use standard big-operat... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_2525814b0fe5_5 | bcd5bc5730103b9c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Algebra.lean | Algebra | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 3 | [
{
"theorem_name": "dot_vec_eq_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 30,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases a with\n | dim fa =>\n cases b with\n | dim fb =>\n have hfold :\n (List.finRange n... | [
{
"name": "finRange_foldl_add_eq_finset_sum",
"text": "/--\nRewrite the spec-style fold over `List.finRange n` into a proof-friendly `Finset.univ.sum`.\n\nMany spec definitions use `List.foldl` (it is definitional and convenient for computation), while\nproofs often prefer `Finset.sum` so they can use stand... | [
{
"name": "toVec_vec_mat_mul_spec",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 60,
"n_chars": 2088,
"n_subproofs": 3,
"n_tactics": 50,
"cyclomatic": 15,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 13,
"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.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | @@ -83,6 +83,16 @@
/-! ## List-fold helpers -/
+/--
+Rewrite the spec-style fold over `List.finRange n` into a proof-friendly `Finset.univ.sum`.
+
+Many spec definitions use `List.foldl` (it is definitional and convenient for computation), while
+proofs often prefer `Finset.sum` so they can use standard big-operat... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_2525814b0fe5_6 | 8e3c4a70f79e4837 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Algebra.lean | Algebra | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 11 | 3 | [
{
"theorem_name": "dot_vec_eq_sum",
"depth": 1,
"n_commands": 0,
"n_lines": 30,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n cases a with\n | dim fa =>\n cases b with\n | dim fb =>\n have hfold :\n (List.finRange n... | [
{
"name": "finRange_foldl_add_eq_finset_sum",
"text": "/--\nRewrite the spec-style fold over `List.finRange n` into a proof-friendly `Finset.univ.sum`.\n\nMany spec definitions use `List.foldl` (it is definitional and convenient for computation), while\nproofs often prefer `Finset.sum` so they can use stand... | [
{
"name": "dot_mat_linear_adjoint",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 7,
"n_lines": 65,
"n_chars": 3102,
"n_subproofs": 0,
"n_tactics": 48,
"cyclomatic": 1,
"n_automation": 13,
"n_rewrites": 0,
"n_structural": 12,
"automation_only": false,
... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Constructors
public import NN.Spec.Core.Tensor.Linalg
public import NN.Spec.Core.TensorOps
public import NN.Proofs.Utils.List
public import Mathlib.Data.List... | @@ -83,6 +83,16 @@
/-! ## List-fold helpers -/
+/--
+Rewrite the spec-style fold over `List.finRange n` into a proof-friendly `Finset.univ.sum`.
+
+Many spec definitions use `List.foldl` (it is definitional and convenient for computation), while
+proofs often prefer `Finset.sum` so they can use standard big-operat... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_84af89852730_0 | bf466dcda7cfb82e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeERealTotal.lean | BridgeERealTotal | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "toEReal?_add_eq_ite",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases hnan : isNaN (add x y) with\n | true =>\n simp [toEReal?, hnan]\n | false =>\n cases hinf : isInf (a... | [
{
"name": "isFinite_eq_true_of_isNaN_eq_false_of_isInf_eq_false",
"text": "/-- A non-NaN, non-infinite value is finite. -/\ntheorem isFinite_eq_true_of_isNaN_eq_false_of_isInf_eq_false (x : IEEE32Exec)\n (hnan : isNaN x = false) (hinf : isInf x = false) :\n isFinite x = true := by\n cases hexp : (exp... | [
{
"name": "toEReal?_add_eq_ite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 28,
"n_chars": 1109,
"n_subproofs": 3,
"n_tactics": 18,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
/-!
# BridgeERealTotal
Extended-real (`EReal`) semantics for `IEEE32Exec`.
We use `toReal?` as the m... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
/-!
# BridgeERealTotal
Extended-real (`EReal`) semantics for `IEEE32Exec`.
We use `toReal?` as the m... | @@ -51,6 +51,32 @@
else
some (toReal x : EReal)
+/-- A non-NaN, non-infinite value is finite. -/
+theorem isFinite_eq_true_of_isNaN_eq_false_of_isInf_eq_false (x : IEEE32Exec)
+ (hnan : isNaN x = false) (hinf : isInf x = false) :
+ isFinite x = true := by
+ cases hexp : (expField x == expAllOnes) with
... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_84af89852730_1 | bff250c8d4e01296 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeERealTotal.lean | BridgeERealTotal | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 2 | [
{
"theorem_name": "toEReal?_add_eq_ite",
"depth": 1,
"n_commands": 0,
"n_lines": 18,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases hnan : isNaN (add x y) with\n | true =>\n simp [toEReal?, hnan]\n | false =>\n cases hinf : isInf (a... | [
{
"name": "isFinite_eq_true_of_isNaN_eq_false_of_isInf_eq_false",
"text": "/-- A non-NaN, non-infinite value is finite. -/\ntheorem isFinite_eq_true_of_isNaN_eq_false_of_isInf_eq_false (x : IEEE32Exec)\n (hnan : isNaN x = false) (hinf : isInf x = false) :\n isFinite x = true := by\n cases hexp : (exp... | [
{
"name": "toEReal?_mul_eq_ite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 28,
"n_chars": 1121,
"n_subproofs": 3,
"n_tactics": 18,
"cyclomatic": 3,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
/-!
# BridgeERealTotal
Extended-real (`EReal`) semantics for `IEEE32Exec`.
We use `toReal?` as the m... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
/-!
# BridgeERealTotal
Extended-real (`EReal`) semantics for `IEEE32Exec`.
We use `toReal?` as the m... | @@ -51,6 +51,32 @@
else
some (toReal x : EReal)
+/-- A non-NaN, non-infinite value is finite. -/
+theorem isFinite_eq_true_of_isNaN_eq_false_of_isInf_eq_false (x : IEEE32Exec)
+ (hnan : isNaN x = false) (hinf : isInf x = false) :
+ isFinite x = true := by
+ cases hexp : (expField x == expAllOnes) with
... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_0847322cf8ad_0 | 2a1a4f7d0bf6558f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Proved/Correctness/Eval/Coverage.lean | Coverage | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "evalAtCoverageTags_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n constructor\n · intro h\n unfold evalAtCoverageTags at h\n rcases List.mem_map.mp h with ⟨kind, _hKind, hTag⟩... | [
{
"name": "evalAtCoverageTags_complete",
"text": "/--\nEvery current IR constructor family has an entry in the local evaluator bridge checklist.\n\nThe statement quantifies over `OpKind`, not only over the representative list above. If a new\nconstructor is added to the IR, this theorem stops compiling unti... | [
{
"name": "evalAtCoverageTags_iff",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 17,
"n_chars": 593,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 4,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 6,
"automation_only": false,
"max... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.Concat
public import NN.Verification.TorchLean.Proved... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved.Correctness.Eval.BatchNorm
public import NN.Verification.TorchLean.Proved.Correctness.Eval.Concat
public import NN.Verification.TorchLean.Proved... | @@ -85,6 +85,17 @@
evalAtCoverageWitnesses.map OpKind.tag
/--
+Every current IR constructor family has an entry in the local evaluator bridge checklist.
+
+The statement quantifies over `OpKind`, not only over the representative list above. If a new
+constructor is added to the IR, this theorem stops compiling un... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_54e7291f4fa0_0 | e5ef6855afcf2684 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/Params.lean | Params | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "inner_matApply_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 34,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hL :\n inner ℝ ((matApplyLin (m := m) (n := n) x) dW) δ\n = ∑ i : Fin m, ((toMatrix dW).mu... | [
{
"name": "inner_mat_eq_sum",
"text": "/-- Coordinate formula for the Frobenius/L2 inner product on `Mat m n`. -/\nlemma inner_mat_eq_sum {m n : Nat} (A B : Mat m n) :\n inner ℝ A B = ∑ i : Fin m, ∑ j : Fin n, A i j * B i j := by\n classical\n calc\n inner ℝ A B = ∑ i : Fin m, inner ℝ (A i) (B i) :=... | [
{
"name": "inner_matApply_eq",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 44,
"n_chars": 1685,
"n_subproofs": 2,
"n_tactics": 33,
"cyclomatic": 1,
"n_automation": 10,
"n_rewrites": 0,
"n_structural": 8,
"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.Proofs.Autograd.FDeriv.Core
public import Mathlib.Analysis.Normed.Module.FiniteDimension
/-!
# Params
Analytic (`HasFDerivAt`) building blocks for **parameter gradients**.... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Core
public import Mathlib.Analysis.Normed.Module.FiniteDimension
/-!
# Params
Analytic (`HasFDerivAt`) building blocks for **parameter gradients**.... | @@ -95,6 +95,18 @@
outer (m := m) (n := n) δ x i j = δ.ofLp i * x.ofLp j := by
simp [outer]
+/-- Coordinate formula for the Frobenius/L2 inner product on `Mat m n`. -/
+lemma inner_mat_eq_sum {m n : Nat} (A B : Mat m n) :
+ inner ℝ A B = ∑ i : Fin m, ∑ j : Fin n, A i j * B i j := by
+ classical
+ calc
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_54e7291f4fa0_1 | b47666e08eccdfd0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/FDeriv/Params.lean | Params | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "inner_matApply_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 34,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hL :\n inner ℝ ((matApplyLin (m := m) (n := n) x) dW) δ\n = ∑ i : Fin m, ((toMatrix dW).mu... | [
{
"name": "inner_mat_eq_sum",
"text": "/-- Coordinate formula for the Frobenius/L2 inner product on `Mat m n`. -/\nlemma inner_mat_eq_sum {m n : Nat} (A B : Mat m n) :\n inner ℝ A B = ∑ i : Fin m, ∑ j : Fin n, A i j * B i j := by\n classical\n calc\n inner ℝ A B = ∑ i : Fin m, inner ℝ (A i) (B i) :=... | [
{
"name": "matApplyLin_adjoint_apply",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 40,
"n_chars": 1526,
"n_subproofs": 7,
"n_tactics": 25,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Core
public import Mathlib.Analysis.Normed.Module.FiniteDimension
/-!
# Params
Analytic (`HasFDerivAt`) building blocks for **parameter gradients**.... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Core
public import Mathlib.Analysis.Normed.Module.FiniteDimension
/-!
# Params
Analytic (`HasFDerivAt`) building blocks for **parameter gradients**.... | @@ -95,6 +95,18 @@
outer (m := m) (n := n) δ x i j = δ.ofLp i * x.ofLp j := by
simp [outer]
+/-- Coordinate formula for the Frobenius/L2 inner product on `Mat m n`. -/
+lemma inner_mat_eq_sum {m n : Nat} (A B : Mat m n) :
+ inner ℝ A B = ∑ i : Fin m, ∑ j : Fin n, A i j * B i j := by
+ classical
+ calc
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_83d061754a44_0 | 1a7c2784b489873d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Verification/TorchLean/Verified.lean | Verified | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "forward_correct_eq_evalForward",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n compileForward_correct (α := α) (paramShapes := paramShapes) (inShape := inShape)\n (outShape := outShape) p... | [
{
"name": "compileForward_correct",
"text": "/-- Short, explicit alias for the main end-to-end compiler correctness theorem. -/\ntheorem compileForward_correct\n {α : Type} [Context α] [DecidableEq Shape]\n {paramShapes : List Shape} {inShape outShape : Shape}\n (p : Proved.Program α paramShapes in... | [
{
"name": "forward_correct_eq_evalForward",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 18,
"n_chars": 875,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved
/-!
# Verified forward compiler bridge
This module is the public naming layer for the verified forward compiler bridge.
The implementation pr... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Verification.TorchLean.Proved
/-!
# Verified forward compiler bridge
This module is the public naming layer for the verified forward compiler bridge.
The implementation pr... | @@ -38,6 +38,23 @@
NN.Verification.TorchLean.Proved.compileForward (α := α) (paramShapes := paramShapes)
(inShape := inShape) (outShape := outShape) p params
+/-- Short, explicit alias for the main end-to-end compiler correctness theorem. -/
+theorem compileForward_correct
+ {α : Type} [Context α] [Decidab... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_e09bed81cfc2_0 | e938887cb951c7e7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/NatLemmas.lean | NatLemmas | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "pow2_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp [pow2_eq_two_pow]",
"n_chars": 28,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
... | [
{
"name": "pow2_eq_two_pow",
"text": "/--\n`pow2 k` is just `2^k`.\n\nInformal: `pow2` is defined as `Nat.shiftLeft 1 k`, i.e. shifting the bit `1` left by `k` places,\nwhich equals the power of two `2^k`.\n-/\ntheorem pow2_eq_two_pow (k : Nat) : pow2 k = 2 ^ k := by\n simp [pow2, Nat.shiftLeft_eq]\n\n",
... | [
{
"name": "pow2_pos",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 179,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting": 2
}... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Nat.Bitwise
public import NN.Floats.IEEEExec.Exec32
/-!
# Small `Nat` lemmas for the IEEE32Exec float kernel
The executable IEEE-754 kernel (`NN/Floats/IEEEExec/E... | /-
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
/-!
# Small `Nat` lemmas for the IEEE32Exec float kernel
The executable IEEE-754 kernel (`NN/Floats/IEEEExec/E... | @@ -27,11 +27,21 @@
namespace IEEE32Exec
/--
+`pow2 k` is just `2^k`.
+
+Informal: `pow2` is defined as `Nat.shiftLeft 1 k`, i.e. shifting the bit `1` left by `k` places,
+which equals the power of two `2^k`.
+-/
+theorem pow2_eq_two_pow (k : Nat) : pow2 k = 2 ^ k := by
+ simp [pow2, Nat.shiftLeft_eq]
+
+/--
`pow... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_94e860d2a765_0 | 7fc0b84b3924b01e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsOrthonormal.lean | FactorizationsOrthonormal | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 4 | [
{
"theorem_name": "dotFn_eq_inner",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [dotFn_eq_sum, PiLp.inner_apply]\n apply Finset.sum_congr rfl\n intro i _\n rw [RCLike.inner_apply', PiLp.toLp_apply, ... | [
{
"name": "dotFn_eq_sum",
"text": "/-- `dotFn` as a `Finset` sum. -/\ntheorem dotFn_eq_sum {p : Nat} (u v : Fin p → ℝ) : Spec.dotFn u v = ∑ i, u i * v i := by\n unfold Spec.dotFn\n rw [foldl_addf_eq_sum (fun i => u i * v i) (List.finRange p) 0, zero_add,\n ← finsum_eq_finRange_sum (fun i => u i * v i)]... | [
{
"name": "dotFn_eq_inner",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 389,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 2,
"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.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | @@ -51,10 +51,21 @@
/-! ## Connectors between the executable scalar ops and the Euclidean inner product -/
+/-- `dotFn` as a `Finset` sum. -/
+theorem dotFn_eq_sum {p : Nat} (u v : Fin p → ℝ) : Spec.dotFn u v = ∑ i, u i * v i := by
+ unfold Spec.dotFn
+ rw [foldl_addf_eq_sum (fun i => u i * v i) (List.finRange p... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_94e860d2a765_1 | 9843d03e9804b936 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsOrthonormal.lean | FactorizationsOrthonormal | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 4 | [
{
"theorem_name": "dotFn_eq_inner",
"depth": 1,
"n_commands": 0,
"n_lines": 6,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [dotFn_eq_sum, PiLp.inner_apply]\n apply Finset.sum_congr rfl\n intro i _\n rw [RCLike.inner_apply', PiLp.toLp_apply, ... | [
{
"name": "dotFn_eq_sum",
"text": "/-- `dotFn` as a `Finset` sum. -/\ntheorem dotFn_eq_sum {p : Nat} (u v : Fin p → ℝ) : Spec.dotFn u v = ∑ i, u i * v i := by\n unfold Spec.dotFn\n rw [foldl_addf_eq_sum (fun i => u i * v i) (List.finRange p) 0, zero_add,\n ← finsum_eq_finRange_sum (fun i => u i * v i)]... | [
{
"name": "normFn_eq_norm",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 11,
"n_chars": 391,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 2,
"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.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | @@ -51,9 +51,21 @@
/-! ## Connectors between the executable scalar ops and the Euclidean inner product -/
+/-- `dotFn` as a `Finset` sum. -/
+theorem dotFn_eq_sum {p : Nat} (u v : Fin p → ℝ) : Spec.dotFn u v = ∑ i, u i * v i := by
+ unfold Spec.dotFn
+ rw [foldl_addf_eq_sum (fun i => u i * v i) (List.finRange p)... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_94e860d2a765_2 | 260a9c7b90040cd3 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsOrthonormal.lean | FactorizationsOrthonormal | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "gsV_bridge",
"depth": 1,
"n_commands": 0,
"n_lines": 37,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Rewrite Mathlib's vector via the explicit recurrence.\n rw [show gramSchmidt ℝ (gsCol A) k\n = gsCol A k - ∑ i ∈ Fin... | [
{
"name": "sum_Iio_eq_mask",
"text": "/-- A masked full sum equals the sum over `Iio`. -/\ntheorem sum_Iio_eq_mask {n : Nat} (k : Fin n) (h : Fin n → ℝ) :\n ∑ i ∈ Finset.Iio k, h i = ∑ i, if i.val < k.val then h i else 0 := by\n rw [← Finset.sum_filter]\n congr 1\n ext i\n simp only [Finset.mem_Iio, ... | [
{
"name": "gsV_bridge",
"fan_in": 2,
"n_deps_direct": 5,
"n_deps_transitive": 6,
"n_lines": 45,
"n_chars": 2558,
"n_subproofs": 2,
"n_tactics": 33,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 14,
"n_structural": 4,
"automation_only": false,
"max_nesting"... | 6 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | @@ -83,6 +83,16 @@
rw [gramSchmidtNormed]
norm_num
+/-- A masked full sum equals the sum over `Iio`. -/
+theorem sum_Iio_eq_mask {n : Nat} (k : Fin n) (h : Fin n → ℝ) :
+ ∑ i ∈ Finset.Iio k, h i = ∑ i, if i.val < k.val then h i else 0 := by
+ rw [← Finset.sum_filter]
+ congr 1
+ ext i
+ simp only [Finset... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_94e860d2a765_3 | e8280b2e0b75911a | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsOrthonormal.lean | FactorizationsOrthonormal | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "Qcol_bridge",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have main : ∀ N : Nat, ∀ k : Fin n, k.val = N →\n (WithLp.toLp 2 (Qcol A k) : EuclideanSpace ℝ (Fin m)) = gramSchmidtNorm... | [
{
"name": "gsV_bridge",
"text": "/-- **Orthogonalized-vector bridge.** Given that the earlier `Q` columns coincide with Mathlib's\nnormalized Gram–Schmidt vectors, the executable orthogonalized vector `v` at index `k` equals\nMathlib's (un-normalized) `gramSchmidt` vector. -/\ntheorem gsV_bridge (A : Fin m ... | [
{
"name": "Qcol_bridge",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 8,
"n_lines": 32,
"n_chars": 1616,
"n_subproofs": 5,
"n_tactics": 25,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 8,
"n_structural": 5,
"automation_only": false,
"max_nesting"... | 8 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | @@ -115,11 +115,78 @@
theorem gsCol_apply (A : Fin m → Fin n → ℝ) (k : Fin n) (r : Fin m) :
gsCol A k r = gsA A k r := rfl
+/-- **Orthogonalized-vector bridge.** Given that the earlier `Q` columns coincide with Mathlib's
+normalized Gram–Schmidt vectors, the executable orthogonalized vector `v` at index `k` equ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_94e860d2a765_4 | 7f184548ba281d05 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsOrthonormal.lean | FactorizationsOrthonormal | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "gn_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hpos : 0 < ‖gramSchmidt ℝ (gsCol A) j‖ := by\n have h := hrank j\n rw [Rmat_eq, rStep_diag] at h\n rwa [gsV_bridge... | [
{
"name": "Qcol_bridge",
"text": "/-- **Normalized-column bridge.** The executable `Q` column at index `k` equals Mathlib's\n`gramSchmidtNormed`. Proved by strong induction on `k`, under positive `R` pivots (full column rank). -/\ntheorem Qcol_bridge (A : Fin m → Fin n → ℝ) (hrank : ∀ j : Fin n, 0 < Rmat A ... | [
{
"name": "gn_ne_zero",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 9,
"n_lines": 11,
"n_chars": 517,
"n_subproofs": 2,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nesting": 4... | 9 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | @@ -159,10 +159,44 @@
rw [sum_Iio_eq_mask, qsPrefix_eq_map, List.map_map, take_map_sum_eq]
rfl
+/-- **Normalized-column bridge.** The executable `Q` column at index `k` equals Mathlib's
+`gramSchmidtNormed`. Proved by strong induction on `k`, under positive `R` pivots (full column rank). -/
+theorem Qcol_bridge... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_94e860d2a765_5 | 99e312741a8e7282 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsOrthonormal.lean | FactorizationsOrthonormal | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "gn_ne_zero",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hpos : 0 < ‖gramSchmidt ℝ (gsCol A) j‖ := by\n have h := hrank j\n rw [Rmat_eq, rStep_diag] at h\n rwa [gsV_bridge... | [
{
"name": "Qcol_bridge",
"text": "/-- **Normalized-column bridge.** The executable `Q` column at index `k` equals Mathlib's\n`gramSchmidtNormed`. Proved by strong induction on `k`, under positive `R` pivots (full column rank). -/\ntheorem Qcol_bridge (A : Fin m → Fin n → ℝ) (hrank : ∀ j : Fin n, 0 < Rmat A ... | [
{
"name": "Q_orthonormal",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 10,
"n_lines": 13,
"n_chars": 654,
"n_subproofs": 1,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 0,
"automation_only": false,
"max_nesting... | 10 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | @@ -159,17 +159,58 @@
rw [sum_Iio_eq_mask, qsPrefix_eq_map, List.map_map, take_map_sum_eq]
rfl
+/-- **Normalized-column bridge.** The executable `Q` column at index `k` equals Mathlib's
+`gramSchmidtNormed`. Proved by strong induction on `k`, under positive `R` pivots (full column rank). -/
+theorem Qcol_bridge... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_94e860d2a765_6 | bb7eaaa1c40cd105 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsOrthonormal.lean | FactorizationsOrthonormal | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "QT_mul_Q_eq_one",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext a b\n rw [Matrix.mul_apply]\n simp only [Matrix.transpose_apply, Matrix.of_apply, Matrix.one_apply]\n rw [show (∑ i,... | [
{
"name": "Q_orthonormal",
"text": "/-- **Orthonormality of the executable `Q` columns.** Under positive `R` pivots,\n`qₐ · q_b = δₐᵦ`. -/\ntheorem Q_orthonormal (A : Fin m → Fin n → ℝ) (hrank : ∀ j : Fin n, 0 < Rmat A j j) (a b : Fin n) :\n Spec.dotFn (Qcol A a) (Qcol A b) = if a = b then 1 else 0 := by... | [
{
"name": "QT_mul_Q_eq_one",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 11,
"n_lines": 11,
"n_chars": 541,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 1,
"automation_only": false,
"max_nesti... | 11 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | @@ -200,9 +200,27 @@
rw [gn_eq]
exact smul_ne_zero (inv_ne_zero (ne_of_gt hpos)) (norm_pos_iff.mp hpos)
+/-- **Orthonormality of the executable `Q` columns.** Under positive `R` pivots,
+`qₐ · q_b = δₐᵦ`. -/
+theorem Q_orthonormal (A : Fin m → Fin n → ℝ) (hrank : ∀ j : Fin n, 0 < Rmat A j j) (a b : Fin 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_94e860d2a765_7 | d6b9860cc51d05c0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsOrthonormal.lean | FactorizationsOrthonormal | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "QT_mul_Q_eq_one",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n ext a b\n rw [Matrix.mul_apply]\n simp only [Matrix.transpose_apply, Matrix.of_apply, Matrix.one_apply]\n rw [show (∑ i,... | [
{
"name": "Q_orthonormal",
"text": "/-- **Orthonormality of the executable `Q` columns.** Under positive `R` pivots,\n`qₐ · q_b = δₐᵦ`. -/\ntheorem Q_orthonormal (A : Fin m → Fin n → ℝ) (hrank : ∀ j : Fin n, 0 < Rmat A j j) (a b : Fin n) :\n Spec.dotFn (Qcol A a) (Qcol A b) = if a = b then 1 else 0 := by... | [
{
"name": "isQR_of_pos",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 12,
"n_lines": 12,
"n_chars": 596,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 3,
"automation_only": false,
"max_nesting":... | 12 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.FactorizationsReconstruction
public import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
public import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
... | @@ -200,9 +200,27 @@
rw [gn_eq]
exact smul_ne_zero (inv_ne_zero (ne_of_gt hpos)) (norm_pos_iff.mp hpos)
+/-- **Orthonormality of the executable `Q` columns.** Under positive `R` pivots,
+`qₐ · q_b = δₐᵦ`. -/
+theorem Q_orthonormal (A : Fin m → Fin n → ℝ) (hrank : ∀ j : Fin n, 0 < Rmat A j j) (a b : Fin 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-... |
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