task_id stringlengths 21 23 | challenge_id stringlengths 16 16 | proof_assistant stringclasses 1
value | session stringclasses 1
value | repo stringclasses 57
values | revision stringclasses 57
values | file_path stringlengths 13 92 | theory stringlengths 1 48 | variant int64 0 132 | challenge_type stringclasses 1
value | difficulty null | count null | by_centrality bool 1
class | ablation_prob float64 0.5 0.5 | min_depth int64 1 1 | max_depth int64 1 1 | leaves_only bool 1
class | min_size int64 0 0 | max_size stringclasses 1
value | min_centrality int64 0 0 | max_centrality stringclasses 1
value | seed int64 42 42 | n_proofs int64 1 173 | n_ablated int64 1 60 | holes_filled listlengths 1 60 | deleted_lemmas listlengths 1 1 | corollaries listlengths 1 1 | closure_size int64 1 172 | challenge_file_content stringlengths 133 350k | solution_file_content stringlengths 394 351k | solution_diff stringlengths 243 134k | manifest dict |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
ablate_79cf0ed3c77b_4 | 9319daa844f54f21 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 1 | [
{
"theorem_name": "take_map_sum_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 15,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [finsum_eq_finRange_sum]\n conv_rhs => rw [show (List.finRange n)\n = (List.finRange n).take m ++ (List.finRange n)... | [
{
"name": "mem_take_finRange",
"text": "/-- Every element of a `finRange` prefix has index below the cut. -/\ntheorem mem_take_finRange {m : Nat} {x : Fin n} (hx : x ∈ (List.finRange n).take m) :\n x.val < m := by\n obtain ⟨p, hp, hpx⟩ := List.getElem_of_mem hx\n rw [List.length_take, List.length_finRa... | [
{
"name": "sumsq_eq",
"fan_in": 2,
"n_deps_direct": 3,
"n_deps_transitive": 8,
"n_lines": 12,
"n_chars": 767,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 1,
"automation_only": false,
"max_nesting": 6
... | 8 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -141,6 +141,15 @@
/-! ### List/Finset partial-sum bridges -/
+/-- Every element of a `finRange` prefix has index below the cut. -/
+theorem mem_take_finRange {m : Nat} {x : Fin n} (hx : x ∈ (List.finRange n).take m) :
+ x.val < m := by
+ obtain ⟨p, hp, hpx⟩ := List.getElem_of_mem hx
+ rw [List.length_take,... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_79cf0ed3c77b_5 | f9fdf5d667575808 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 3 | [
{
"theorem_name": "cross_sum_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [prefix_eq_map, List.map_map, foldl_add_eq_sum, zero_add,\n show ((fun ck : Fin n → ℝ => ck i * ck j) ∘ fun k => fun r =... | [
{
"name": "take_map_sum_eq",
"text": "/-- Mapping `f` over a `finRange` prefix and summing equals the masked full sum. -/\ntheorem take_map_sum_eq (m : Nat) (f : Fin n → ℝ) :\n (((List.finRange n).take m).map f).sum = ∑ k : Fin n, if k.val < m then f k else 0 := by\n rw [finsum_eq_finRange_sum]\n conv_... | [
{
"name": "choleskyFn_diag_eq",
"fan_in": 2,
"n_deps_direct": 4,
"n_deps_transitive": 11,
"n_lines": 8,
"n_chars": 381,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nes... | 11 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -165,10 +165,32 @@
subst hpx
exact Nat.le_add_right m p
+/-- Mapping `f` over a `finRange` prefix and summing equals the masked full sum. -/
+theorem take_map_sum_eq (m : Nat) (f : Fin n → ℝ) :
+ (((List.finRange n).take m).map f).sum = ∑ k : Fin n, if k.val < m then f k else 0 := by
+ rw [finsum_eq_finR... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_79cf0ed3c77b_6 | ec3f88456db2f7d1 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 3 | [
{
"theorem_name": "cross_sum_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [prefix_eq_map, List.map_map, foldl_add_eq_sum, zero_add,\n show ((fun ck : Fin n → ℝ => ck i * ck j) ∘ fun k => fun r =... | [
{
"name": "take_map_sum_eq",
"text": "/-- Mapping `f` over a `finRange` prefix and summing equals the masked full sum. -/\ntheorem take_map_sum_eq (m : Nat) (f : Fin n → ℝ) :\n (((List.finRange n).take m).map f).sum = ∑ k : Fin n, if k.val < m then f k else 0 := by\n rw [finsum_eq_finRange_sum]\n conv_... | [
{
"name": "choleskyFn_offdiag_eq",
"fan_in": 1,
"n_deps_direct": 6,
"n_deps_transitive": 15,
"n_lines": 16,
"n_chars": 783,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max... | 15 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -181,15 +181,41 @@
subst hpx
exact Nat.le_add_right m p
+/-- Mapping `f` over a `finRange` prefix and summing equals the masked full sum. -/
+theorem take_map_sum_eq (m : Nat) (f : Fin n → ℝ) :
+ (((List.finRange n).take m).map f).sum = ∑ k : Fin n, if k.val < m then f k else 0 := by
+ rw [finsum_eq_finR... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_79cf0ed3c77b_7 | a5c15680e185071c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 1 | [
{
"theorem_name": "choleskyFn_offdiag_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [choleskyFn_eq_step A i j, cholStep_offdiag _ _ hij, cross_sum_eq, sumsq_eq, mfsqrt_eq,\n ← choleskyFn_diag_eq]... | [
{
"name": "cross_sum_eq",
"text": "/-- The Cholesky cross-sum equals the masked partial dot product of rows `i` and `j` of `L`. -/\ntheorem cross_sum_eq (A : Fin n → Fin n → ℝ) (i j : Fin n) :\n ((prefixCols A j).map (fun ck => ck i * ck j)).foldl (fun acc x => acc + x) 0\n = ∑ k : Fin n, if k.val <... | [
{
"name": "choleskyFn_dot_eq",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 16,
"n_lines": 39,
"n_chars": 2080,
"n_subproofs": 10,
"n_tactics": 38,
"cyclomatic": 3,
"n_automation": 6,
"n_rewrites": 14,
"n_structural": 7,
"automation_only": false,
"max... | 16 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -199,6 +199,15 @@
exact if_neg (by have := mem_drop_finRange hx; grind)
rw [htake, hdrop, add_zero]
+/-- The Cholesky cross-sum equals the masked partial dot product of rows `i` and `j` of `L`. -/
+theorem cross_sum_eq (A : Fin n → Fin n → ℝ) (i j : Fin n) :
+ ((prefixCols A j).map (fun ck => ck i * ck ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_79cf0ed3c77b_8 | a1d47fc5069884b8 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 2 | [
{
"theorem_name": "choleskyFn_diag_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [choleskyFn_eq_step, cholStep_diag, sumsq_eq, mfsqrt_eq]",
"n_chars": 65,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "sumsq_eq",
"text": "/-- The Cholesky diagonal sum-of-squares equals the masked partial squared norm of row `j` of `L`. -/\ntheorem sumsq_eq (A : Fin n → Fin n → ℝ) (j : Fin n) :\n ((prefixCols A j).map (fun ck => ck j)).foldl (fun s x => s + x * x) 0\n = ∑ k : Fin n, if k.val < j.val then... | [
{
"name": "choleskyFn_dot",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 17,
"n_lines": 12,
"n_chars": 620,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max_nestin... | 17 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -208,6 +208,17 @@
= (fun k => Spec.choleskyFn A i k * Spec.choleskyFn A j k) from rfl]
exact take_map_sum_eq j.val (fun k => Spec.choleskyFn A i k * Spec.choleskyFn A j k)
+/-- The Cholesky diagonal sum-of-squares equals the masked partial squared norm of row `j` of `L`. -/
+theorem sumsq_eq (A : 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_79cf0ed3c77b_9 | 92351ec25de81473 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 2 | [
{
"theorem_name": "choleskyFn_diag_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [choleskyFn_eq_step, cholStep_diag, sumsq_eq, mfsqrt_eq]",
"n_chars": 65,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "sumsq_eq",
"text": "/-- The Cholesky diagonal sum-of-squares equals the masked partial squared norm of row `j` of `L`. -/\ntheorem sumsq_eq (A : Fin n → Fin n → ℝ) (j : Fin n) :\n ((prefixCols A j).map (fun ck => ck j)).foldl (fun s x => s + x * x) 0\n = ∑ k : Fin n, if k.val < j.val then... | [
{
"name": "isCholesky_of_pos",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 18,
"n_lines": 16,
"n_chars": 792,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 5,
"automation_only": false,
"max_nes... | 18 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -208,6 +208,17 @@
= (fun k => Spec.choleskyFn A i k * Spec.choleskyFn A j k) from rfl]
exact take_map_sum_eq j.val (fun k => Spec.choleskyFn A i k * Spec.choleskyFn A j k)
+/-- The Cholesky diagonal sum-of-squares equals the masked partial squared norm of row `j` of `L`. -/
+theorem sumsq_eq (A : 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_79cf0ed3c77b_10 | 2c0344358360e37f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 2 | [
{
"theorem_name": "choleskyFn_diag_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [choleskyFn_eq_step, cholStep_diag, sumsq_eq, mfsqrt_eq]",
"n_chars": 65,
"n_subproofs": 0,
"n_tactics": ... | [
{
"name": "sumsq_eq",
"text": "/-- The Cholesky diagonal sum-of-squares equals the masked partial squared norm of row `j` of `L`. -/\ntheorem sumsq_eq (A : Fin n → Fin n → ℝ) (j : Fin n) :\n ((prefixCols A j).map (fun ck => ck j)).foldl (fun s x => s + x * x) 0\n = ∑ k : Fin n, if k.val < j.val then... | [
{
"name": "choleskySpec_reconstruction",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 18,
"n_lines": 25,
"n_chars": 1398,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 4,
"n_structural": 3,
"automation_only": false,
... | 18 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -208,6 +208,17 @@
= (fun k => Spec.choleskyFn A i k * Spec.choleskyFn A j k) from rfl]
exact take_map_sum_eq j.val (fun k => Spec.choleskyFn A i k * Spec.choleskyFn A j k)
+/-- The Cholesky diagonal sum-of-squares equals the masked partial squared norm of row `j` of `L`. -/
+theorem sumsq_eq (A : 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_79cf0ed3c77b_11 | c270dfddca0684bb | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 1 | [
{
"theorem_name": "Qmat_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 10,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hqs : (Spec.gramSchmidtFn A).qs\n = (List.finRange n).foldl (fun qs j => qs ++ [qStep A qs j]) [] := by\n rw [gramSch... | [
{
"name": "gs_proj_qs",
"text": "/-- The `Q`-list projection of the structure fold is the single-list `qStep` snoc-fold. -/\ntheorem gs_proj_qs (A : Fin m → Fin n → ℝ) (l : List (Fin n)) (q0 : List (Fin m → ℝ))\n (r0 : List (Fin n → ℝ)) :\n (l.foldl (fun st j => (⟨st.qs ++ [qStep A st.qs j], st.rcols ... | [
{
"name": "Qmat_eq",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 14,
"n_chars": 680,
"n_subproofs": 2,
"n_tactics": 14,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 6,
"n_structural": 3,
"automation_only": false,
"max_nesting": 6
... | 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.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -119,6 +119,16 @@
(fun st j => (⟨st.qs ++ [qStep A st.qs j], st.rcols ++ [rStep A st.qs j]⟩ : GSState m n ℝ))
⟨[], []⟩ := rfl
+/-- The `Q`-list projection of the structure fold is the single-list `qStep` snoc-fold. -/
+theorem gs_proj_qs (A : Fin m → Fin n → ℝ) (l : List (Fin n)) (q0 : List (... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_79cf0ed3c77b_12 | 0a245e7709f6541d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 1 | [
{
"theorem_name": "Rmat_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hrc : (Spec.gramSchmidtFn A).rcols = rTail A [] (List.finRange n) := by\n rw [gramSchmidtFn_eq, gs_fold_split]; simp\n unf... | [
{
"name": "gs_fold_split",
"text": "/-- The structure fold splits into the `qStep` snoc-fold (`Q`-list) and the `rTail` (`R`-list). -/\ntheorem gs_fold_split (A : Fin m → Fin n → ℝ) (l : List (Fin n)) (q0 : List (Fin m → ℝ))\n (r0 : List (Fin n → ℝ)) :\n (l.foldl (fun st j => (⟨st.qs ++ [qStep A st.qs... | [
{
"name": "Rmat_eq",
"fan_in": 3,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 12,
"n_chars": 563,
"n_subproofs": 2,
"n_tactics": 12,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 6,
"n_structural": 2,
"automation_only": false,
"max_nesting": 4
... | 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.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -129,6 +129,19 @@
| [] => []
| j :: rest => rStep A q0 j :: rTail A (q0 ++ [qStep A q0 j]) rest
+/-- The structure fold splits into the `qStep` snoc-fold (`Q`-list) and the `rTail` (`R`-list). -/
+theorem gs_fold_split (A : Fin m → Fin n → ℝ) (l : List (Fin n)) (q0 : List (Fin m → ℝ))
+ (r0 : List (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_79cf0ed3c77b_13 | 846bc9df948f5fa2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 13 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 1 | [
{
"theorem_name": "qStep_pos",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n simp only [qStep]; rw [if_pos (gtBool_true_iff.mpr h)]",
"n_chars": 60,
"n_subproofs": 0,
"n_tactics": 3,
"cyclom... | [
{
"name": "gtBool_true_iff",
"text": "/-- Semantics of the `Context` `>` test over `ℝ`. -/\ntheorem gtBool_true_iff {x y : ℝ} : Context.gtBool x y = true ↔ y < x := by\n unfold Context.gtBool; exact decide_eq_true_iff\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 186,
"n_subproofs": 0,
"n... | [
{
"name": "qStep_pos",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 370,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -122,6 +122,10 @@
| [] => []
| j :: rest => rStep A q0 j :: rTail A (q0 ++ [qStep A q0 j]) rest
+/-- Semantics of the `Context` `>` test over `ℝ`. -/
+theorem gtBool_true_iff {x y : ℝ} : Context.gtBool x y = true ↔ y < x := by
+ unfold Context.gtBool; exact decide_eq_true_iff
+
/-- Entry `(i, k)` of the `Q... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_79cf0ed3c77b_14 | 9783bfd5bb5b406a | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 14 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 1 | [
{
"theorem_name": "gsV_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold gsV gsRkjs\n rw [cross_fold_eq qs (fun qk => Spec.dotFn qk (gsA A j)) i 0, zero_add]",
"n_chars": 97,
"n_subproofs":... | [
{
"name": "cross_fold_eq",
"text": "/-- The zip-fold defining `v` collapses to a single map-fold over the `Q` columns. -/\ntheorem cross_fold_eq (qs : List (Fin m → ℝ)) (g : (Fin m → ℝ) → ℝ) (i : Fin m) (a : ℝ) :\n (List.zip qs (qs.map g)).foldl (fun acc (qk, r) => acc + r * qk i) a\n = a + (qs.map ... | [
{
"name": "gsV_eq",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 358,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nesting": 2
}
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -133,9 +133,21 @@
/-- Column `k` of `Q` as a function of the row. -/
noncomputable def Qcol (A : Fin m → Fin n → ℝ) (k : Fin n) : Fin m → ℝ := fun r => Qmat A r k
+/-- The zip-fold defining `v` collapses to a single map-fold over the `Q` columns. -/
+theorem cross_fold_eq (qs : List (Fin m → ℝ)) (g : (Fin m → 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_79cf0ed3c77b_15 | 7ea562835166cb75 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 15 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 2 | [
{
"theorem_name": "qsPrefix_eq_map",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hjval : ((List.finRange n).take j.val).length = j.val := by\n rw [List.length_take, List.length_finRange, Nat.min_... | [
{
"name": "Qmat_eq",
"text": "/-- Closed form of a `Q` entry: `qStep` evaluated on the `Q`-prefix. -/\ntheorem Qmat_eq (A : Fin m → Fin n → ℝ) (i : Fin m) (k : Fin n) :\n Qmat A i k = qStep A (qsPrefix A k) k i := by\n have hqs : (Spec.gramSchmidtFn A).qs\n = (List.finRange n).foldl (fun qs j => qs... | [
{
"name": "qsPrefix_eq_map",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 26,
"n_chars": 1280,
"n_subproofs": 3,
"n_tactics": 25,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 15,
"n_structural": 6,
"automation_only": false,
"max_nes... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -150,6 +150,19 @@
/-- Column `k` of `Q` as a function of the row. -/
noncomputable def Qcol (A : Fin m → Fin n → ℝ) (k : Fin n) : Fin m → ℝ := fun r => Qmat A r k
+/-- Closed form of a `Q` entry: `qStep` evaluated on the `Q`-prefix. -/
+theorem Qmat_eq (A : Fin m → Fin n → ℝ) (i : Fin m) (k : Fin n) :
+ Qmat ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_79cf0ed3c77b_16 | 0c977deb03ac7580 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 16 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 2 | [
{
"theorem_name": "qsPrefix_eq_map",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hjval : ((List.finRange n).take j.val).length = j.val := by\n rw [List.length_take, List.length_finRange, Nat.min_... | [
{
"name": "Qmat_eq",
"text": "/-- Closed form of a `Q` entry: `qStep` evaluated on the `Q`-prefix. -/\ntheorem Qmat_eq (A : Fin m → Fin n → ℝ) (i : Fin m) (k : Fin n) :\n Qmat A i k = qStep A (qsPrefix A k) k i := by\n have hqs : (Spec.gramSchmidtFn A).qs\n = (List.finRange n).foldl (fun qs j => qs... | [
{
"name": "qsPrefix_getD",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 4,
"n_lines": 11,
"n_chars": 490,
"n_subproofs": 0,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 4,
"n_structural": 2,
"automation_only": false,
"max_nesting"... | 4 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -150,6 +150,19 @@
/-- Column `k` of `Q` as a function of the row. -/
noncomputable def Qcol (A : Fin m → Fin n → ℝ) (k : Fin n) : Fin m → ℝ := fun r => Qmat A r k
+/-- Closed form of a `Q` entry: `qStep` evaluated on the `Q`-prefix. -/
+theorem Qmat_eq (A : Fin m → Fin n → ℝ) (i : Fin m) (k : Fin n) :
+ Qmat ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_79cf0ed3c77b_17 | 3fe5a31aac69bf27 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 17 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 1 | [
{
"theorem_name": "Rmat_above_diag_dot",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Rmat_eq]; simp only [rStep]; rw [if_pos hkj]; unfold gsRkjs\n rw [getD_map_dotFn (qsPrefix A j) (gsA A j) k.val (b... | [
{
"name": "qsPrefix_length",
"text": "/-- Length of the `Q`-prefix list. -/\ntheorem qsPrefix_length (A : Fin m → Fin n → ℝ) (j : Fin n) : (qsPrefix A j).length = j.val := by\n unfold qsPrefix\n rw [length_foldl_snoc (fun qs k => qStep A qs k), List.length_nil, Nat.zero_add, List.length_take,\n List.le... | [
{
"name": "Rmat_above_diag_dot",
"fan_in": 1,
"n_deps_direct": 4,
"n_deps_transitive": 10,
"n_lines": 9,
"n_chars": 465,
"n_subproofs": 0,
"n_tactics": 8,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 5,
"n_structural": 1,
"automation_only": false,
"max_ne... | 10 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -202,6 +202,12 @@
simp [List.getElem_finRange]
rw [hk]; rfl
+/-- Length of the `Q`-prefix list. -/
+theorem qsPrefix_length (A : Fin m → Fin n → ℝ) (j : Fin n) : (qsPrefix A j).length = j.val := by
+ unfold qsPrefix
+ rw [length_foldl_snoc (fun qs k => qStep A qs k), List.length_nil, Nat.zero_add, List.l... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_79cf0ed3c77b_18 | 148e8561a5c9b67f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 18 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 3 | [
{
"theorem_name": "Rmat_above_diag_dot",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Rmat_eq]; simp only [rStep]; rw [if_pos hkj]; unfold gsRkjs\n rw [getD_map_dotFn (qsPrefix A j) (gsA A j) k.val (b... | [
{
"name": "Rmat_eq",
"text": "/-- Closed form of an `R` entry: `rStep` evaluated on the `Q`-prefix. -/\ntheorem Rmat_eq (A : Fin m → Fin n → ℝ) (k j : Fin n) :\n Rmat A k j = rStep A (qsPrefix A j) j k := by\n have hrc : (Spec.gramSchmidtFn A).rcols = rTail A [] (List.finRange n) := by\n rw [gramSchm... | [
{
"name": "cross_sum_qr",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 15,
"n_lines": 18,
"n_chars": 672,
"n_subproofs": 0,
"n_tactics": 11,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 7,
"n_structural": 2,
"automation_only": false,
"max_nesting... | 15 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -237,6 +237,17 @@
simp [List.getElem_finRange]
rw [hk]; rfl
+/-- Closed form of an `R` entry: `rStep` evaluated on the `Q`-prefix. -/
+theorem Rmat_eq (A : Fin m → Fin n → ℝ) (k j : Fin n) :
+ Rmat A k j = rStep A (qsPrefix A j) j k := by
+ have hrc : (Spec.gramSchmidtFn A).rcols = rTail A [] (List.fin... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_79cf0ed3c77b_19 | faa1caf004528317 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 19 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 3 | [
{
"theorem_name": "Rmat_above_diag_dot",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [Rmat_eq]; simp only [rStep]; rw [if_pos hkj]; unfold gsRkjs\n rw [getD_map_dotFn (qsPrefix A j) (gsA A j) k.val (b... | [
{
"name": "Rmat_eq",
"text": "/-- Closed form of an `R` entry: `rStep` evaluated on the `Q`-prefix. -/\ntheorem Rmat_eq (A : Fin m → Fin n → ℝ) (k j : Fin n) :\n Rmat A k j = rStep A (qsPrefix A j) j k := by\n have hrc : (Spec.gramSchmidtFn A).rcols = rTail A [] (List.finRange n) := by\n rw [gramSchm... | [
{
"name": "Rmat_upper_triangular",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 5,
"n_lines": 7,
"n_chars": 300,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"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.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -168,6 +168,17 @@
/-- Column `k` of `Q` as a function of the row. -/
noncomputable def Qcol (A : Fin m → Fin n → ℝ) (k : Fin n) : Fin m → ℝ := fun r => Qmat A r k
+/-- Closed form of an `R` entry: `rStep` evaluated on the `Q`-prefix. -/
+theorem Rmat_eq (A : Fin m → Fin n → ℝ) (k j : Fin n) :
+ Rmat A k j = 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_79cf0ed3c77b_20 | 7aa46a3ef949bbf6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 20 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 1 | [
{
"theorem_name": "gsV_eq",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold gsV gsRkjs\n rw [cross_fold_eq qs (fun qk => Spec.dotFn qk (gsA A j)) i 0, zero_add]",
"n_chars": 97,
"n_subproofs":... | [
{
"name": "cross_fold_eq",
"text": "/-- The zip-fold defining `v` collapses to a single map-fold over the `Q` columns. -/\ntheorem cross_fold_eq (qs : List (Fin m → ℝ)) (g : (Fin m → ℝ) → ℝ) (i : Fin m) (a : ℝ) :\n (List.zip qs (qs.map g)).foldl (fun acc (qk, r) => acc + r * qk i) a\n = a + (qs.map ... | [
{
"name": "qr_reconstruction",
"fan_in": 2,
"n_deps_direct": 7,
"n_deps_transitive": 23,
"n_lines": 39,
"n_chars": 2113,
"n_subproofs": 7,
"n_tactics": 37,
"cyclomatic": 2,
"n_automation": 7,
"n_rewrites": 15,
"n_structural": 5,
"automation_only": false,
"max_... | 23 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -271,9 +271,21 @@
/-! ### The orthogonalization sum as a `Finset` sum -/
+/-- The zip-fold defining `v` collapses to a single map-fold over the `Q` columns. -/
+theorem cross_fold_eq (qs : List (Fin m → ℝ)) (g : (Fin m → ℝ) → ℝ) (i : Fin m) (a : ℝ) :
+ (List.zip qs (qs.map g)).foldl (fun acc (qk, r) => acc +... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_79cf0ed3c77b_21 | fd5fe75b578ffdf1 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 21 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 1 | [
{
"theorem_name": "qr_reconstruction",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have key : ∀ k : Fin n, Qmat A i k * Rmat A k j\n = (if k.val < j.val then Qmat A i k * Rmat A k j else 0)\n ... | [
{
"name": "gsV_eq",
"text": "/-- Closed form of `v i`: `A i j` minus the partial projection sum. -/\ntheorem gsV_eq (A : Fin m → Fin n → ℝ) (qs : List (Fin m → ℝ)) (j : Fin n) (i : Fin m) :\n gsV A qs j i = gsA A j i - (qs.map (fun qk => Spec.dotFn qk (gsA A j) * qk i)).sum := by\n unfold gsV gsRkjs\n ... | [
{
"name": "qr_mul_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 24,
"n_lines": 10,
"n_chars": 432,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 1,
"n_structural": 2,
"automation_only": false,
"max_nesting": 2... | 24 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -281,6 +281,12 @@
simp only [List.map_cons, List.zip_cons_cons, List.foldl_cons]
rw [ih]; simp only [List.sum_cons]; ring
+/-- Closed form of `v i`: `A i j` minus the partial projection sum. -/
+theorem gsV_eq (A : Fin m → Fin n → ℝ) (qs : List (Fin m → ℝ)) (j : Fin n) (i : Fin m) :
+ gsV A qs j i... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_79cf0ed3c77b_22 | c29f5a063768a512 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/FactorizationsReconstruction.lean | FactorizationsReconstruction | 22 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 38 | 1 | [
{
"theorem_name": "qr_reconstruction",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have key : ∀ k : Fin n, Qmat A i k * Rmat A k j\n = (if k.val < j.val then Qmat A i k * Rmat A k j else 0)\n ... | [
{
"name": "gsV_eq",
"text": "/-- Closed form of `v i`: `A i j` minus the partial projection sum. -/\ntheorem gsV_eq (A : Fin m → Fin n → ℝ) (qs : List (Fin m → ℝ)) (j : Fin n) (i : Fin m) :\n gsV A qs j i = gsA A j i - (qs.map (fun qk => Spec.dotFn qk (gsA A j) * qk i)).sum := by\n unfold gsV gsRkjs\n ... | [
{
"name": "qrSpec_reconstruction",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 24,
"n_lines": 14,
"n_chars": 852,
"n_subproofs": 2,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 2,
"n_structural": 2,
"automation_only": false,
"max... | 24 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Core.Tensor.Factorizations
public import NN.Proofs.Tensor.Basic.Factorizations
public import Mathlib.Data.List.GetD
public import Mathlib.Algebra.BigOperators.Fin
/-!
#... | @@ -281,6 +281,12 @@
simp only [List.map_cons, List.zip_cons_cons, List.foldl_cons]
rw [ih]; simp only [List.sum_cons]; ring
+/-- Closed form of `v i`: `A i j` minus the partial projection sum. -/
+theorem gsV_eq (A : Fin m → Fin n → ℝ) (qs : List (Fin m → ℝ)) (j : Fin n) (i : Fin m) :
+ gsV A qs j i... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_a823a11b4431_0 | 9c613194cb56ed97 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/DyadicRounding.lean | DyadicRounding | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "dyadicToReal_ofNatAbs",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n dsimp [dyadicToReal]\n rw [signFactor_natAbs_int (s := s)]",
"n_chars": 64,
"n_subproofs": 0,
"n_tactics... | [
{
"name": "signFactor_natAbs_int",
"text": "lemma signFactor_natAbs_int (s : Int) :\n (if decide (s < 0) then (-1 : ℝ) else (1 : ℝ)) * (Int.natAbs s : ℝ) = (s : ℝ) := by\n cases s with\n | ofNat n =>\n simp\n | negSucc n =>\n simp\n\n",
"fan_in": 1,
"n_lines": 9,
"n_chars": 206,
... | [
{
"name": "dyadicToReal_ofNatAbs",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 239,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Core
/-!
# IEEE32Exec and FP32: Dyadic Rounding Helpers
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
n... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Core
/-!
# IEEE32Exec and FP32: Dyadic Rounding Helpers
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
n... | @@ -36,9 +36,19 @@
noncomputable def signedMant (sign : Bool) (m : Nat) : Int :=
if sign then -(Int.ofNat m) else Int.ofNat m
+lemma signFactor_natAbs_int (s : Int) :
+ (if decide (s < 0) then (-1 : ℝ) else (1 : ℝ)) * (Int.natAbs s : ℝ) = (s : ℝ) := by
+ cases s with
+ | ofNat n =>
+ simp
+ | negSucc 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_a823a11b4431_1 | 4a80520372978bcf | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/DyadicRounding.lean | DyadicRounding | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "dyadicToReal_addDyadic_exact",
"depth": 1,
"n_commands": 0,
"n_lines": 135,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n by_cases hab : a.exp ≤ b.exp\n · -- align to `a.exp`\n let sh : Nat := Int.toNat (b.exp - a... | [
{
"name": "dyadicToReal_zero",
"text": "lemma dyadicToReal_zero (sign : Bool) :\n dyadicToReal { sign := sign, mant := 0, exp := 0 } = (0 : ℝ) := by\n by_cases hs : sign <;> simp [dyadicToReal, hs, TorchLean.Floats.neuralBpow, binaryRadix,\n NeuralRadix.toReal]\n\n",
"fan_in": 1,
"n_lines": 6... | [
{
"name": "dyadicToReal_addDyadic_exact",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 5,
"n_lines": 144,
"n_chars": 6570,
"n_subproofs": 33,
"n_tactics": 122,
"cyclomatic": 1,
"n_automation": 32,
"n_rewrites": 10,
"n_structural": 6,
"automation_only": fa... | 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.Core
/-!
# IEEE32Exec and FP32: Dyadic Rounding Helpers
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
n... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Core
/-!
# IEEE32Exec and FP32: Dyadic Rounding Helpers
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
n... | @@ -65,6 +65,11 @@
dsimp [dyadicToReal]
rw [signFactor_natAbs_int (s := s)]
+lemma dyadicToReal_zero (sign : Bool) :
+ dyadicToReal { sign := sign, mant := 0, exp := 0 } = (0 : ℝ) := by
+ by_cases hs : sign <;> simp [dyadicToReal, hs, TorchLean.Floats.neuralBpow, binaryRadix,
+ NeuralRadix.toReal]
+
/--... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_a823a11b4431_2 | 0362115a0e9aa237 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/DyadicRounding.lean | DyadicRounding | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 1 | [
{
"theorem_name": "neural_nearest_even_div_eq_roundQuotEven",
"depth": 1,
"n_commands": 0,
"n_lines": 32,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n set q : Nat := num / den\n set r : Nat := num % den\n have hfloor : (⌊((num : ℝ) /... | [
{
"name": "half_lt_div_iff",
"text": "lemma half_lt_div_iff (r den : Nat) (hden : den ≠ 0) :\n ((2⁻¹ : ℝ) < (r : ℝ) / (den : ℝ)) ↔ (den < 2 * r) := by\n have hdenpos : (0 : ℝ) < (den : ℝ) := by\n exact_mod_cast (Nat.pos_of_ne_zero hden)\n have h2pos : (0 : ℝ) < (2 : ℝ) := by norm_num\n have h1 :\n ... | [
{
"name": "neural_nearest_even_div_eq_roundQuotEven",
"fan_in": 0,
"n_deps_direct": 4,
"n_deps_transitive": 4,
"n_lines": 35,
"n_chars": 1661,
"n_subproofs": 8,
"n_tactics": 31,
"cyclomatic": 1,
"n_automation": 9,
"n_rewrites": 2,
"n_structural": 4,
"automation_on... | 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.Core
/-!
# IEEE32Exec and FP32: Dyadic Rounding Helpers
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
n... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Core
/-!
# IEEE32Exec and FP32: Dyadic Rounding Helpers
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
n... | @@ -102,6 +102,41 @@
have hr : (r : ℝ) < (2⁻¹ : ℝ) * (den : ℝ) := (mul_lt_mul_iff_right₀ h2pos).1 hmul'
exact h1.mpr hr
+lemma half_lt_div_iff (r den : Nat) (hden : den ≠ 0) :
+ ((2⁻¹ : ℝ) < (r : ℝ) / (den : ℝ)) ↔ (den < 2 * r) := by
+ have hdenpos : (0 : ℝ) < (den : ℝ) := by
+ exact_mod_cast (Nat.po... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_9ec4639d94ef_0 | 4eadc9bfb6f87fa2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Lipschitz.lean | Lipschitz | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "dot_quadratic_expand",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [dot_add_add]\n have h1 : dot x (scaleSpec y t) = t * dot x y := by\n -- Scale in the second argument via comm... | [
{
"name": "dot_add_add",
"text": "/--\nBilinearity of dot product over addition (distributive property).\n-/\ntheorem dot_add_add {s : Shape} (x y : Tensor ℝ s) :\n dot (addSpec x y) (addSpec x y) =\n dot x x + 2 * dot x y + dot y y := by\n -- This is the key bilinearity property: (x + y) · (x + y) = x·x... | [
{
"name": "dot_quadratic_expand",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 29,
"n_chars": 1323,
"n_subproofs": 3,
"n_tactics": 20,
"cyclomatic": 1,
"n_automation": 9,
"n_rewrites": 2,
"n_structural": 3,
"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.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | @@ -117,11 +117,76 @@
-/
/--
+Bilinearity of dot product over addition (distributive property).
+-/
+theorem dot_add_add {s : Shape} (x y : Tensor ℝ s) :
+ dot (addSpec x y) (addSpec x y) =
+ dot x x + 2 * dot x y + dot y y := by
+ -- This is the key bilinearity property: (x + y) · (x + y) = x·x + 2x·y + y·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_9ec4639d94ef_1 | 37877a928e83708d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Lipschitz.lean | Lipschitz | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "tensor_cauchy_schwarz",
"depth": 1,
"n_commands": 0,
"n_lines": 170,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold tensorL2Norm\n\n -- Handle the degenerate case where y = 0\n by_cases hy : tensorNormSquared y = 0\n · --... | [
{
"name": "dot_zero_right",
"text": "/--\nBasic lemma: dot product with zero tensor is zero.\n-/\ntheorem dot_zero_right {s : Shape} (x : Tensor ℝ s) :\n dot x (fill (0 : ℝ) s) = (0 : ℝ) := by\n -- By induction on the tensor `Shape`; the `dim` case reduces to “folding `(+ )` over zeros”.\n induction s wi... | [
{
"name": "tensor_cauchy_schwarz",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 178,
"n_chars": 8690,
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"cyclomatic": 2,
"n_automation": 21,
"n_rewrites": 12,
"n_structural": 22,
"automation_only": false,
... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | @@ -117,6 +117,77 @@
-/
/--
+Basic lemma: dot product with zero tensor is zero.
+-/
+theorem dot_zero_right {s : Shape} (x : Tensor ℝ s) :
+ dot x (fill (0 : ℝ) s) = (0 : ℝ) := by
+ -- By induction on the tensor `Shape`; the `dim` case reduces to “folding `(+ )` over zeros”.
+ induction s with
+ | scalar =>
+ ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_9ec4639d94ef_2 | 11bf098eb43a4500 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Lipschitz.lean | Lipschitz | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "tensor_l2_norm_triangle",
"depth": 1,
"n_commands": 0,
"n_lines": 53,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- We prove this by showing the squared version and taking square roots\n -- Since all norms are non-negative, ||... | [
{
"name": "tensor_l2_norm_nonneg",
"text": "/--\nL2 norm is non-negative.\n-/\ntheorem tensor_l2_norm_nonneg {s : Shape} (t : Tensor ℝ s) :\n tensorL2Norm t ≥ (0 : ℝ) := by\n simp [tensorL2Norm]\n\n",
"fan_in": 2,
"n_lines": 8,
"n_chars": 155,
"n_subproofs": 0,
"n_tactics": 2,
"cyc... | [
{
"name": "tensor_l2_norm_triangle",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 5,
"n_lines": 58,
"n_chars": 2582,
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"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 5,
"n_structural": 5,
"automation_only": false,
"... | 5 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | @@ -117,6 +117,13 @@
-/
/--
+L2 norm is non-negative.
+-/
+theorem tensor_l2_norm_nonneg {s : Shape} (t : Tensor ℝ s) :
+ tensorL2Norm t ≥ (0 : ℝ) := by
+ simp [tensorL2Norm]
+
+/--
Basic lemma: dot product with zero tensor is zero.
-/
theorem dot_zero_right {s : Shape} (x : Tensor ℝ s) :
@@ -480,7 +487,8 @@
... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_9ec4639d94ef_3 | 4353ee5c55f82460 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Lipschitz.lean | Lipschitz | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "relu_scalar_tensor_lipschitz",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases x with | scalar a =>\n cases y with | scalar b =>\n unfold reluSpec tensorL2Dist tensorL2Norm tensorN... | [
{
"name": "relu_scalar_lipschitz",
"text": "/--\nPointwise ReLU is 1-Lipschitz for scalars.\nFoundation for tensor-level Lipschitz bounds.\n-/\ntheorem relu_scalar_lipschitz (x y : ℝ) :\n |max (0 : ℝ) x - max (0 : ℝ) y| ≤ |x - y| := by\n -- ReLU is 1-Lipschitz: |max(0,x) - max(0,y)| ≤ |x - y|\n -- This f... | [
{
"name": "relu_scalar_tensor_lipschitz",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
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"cyclomatic": 3,
"n_automation": 3,
"n_rewrites": 4,
"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 Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | @@ -117,6 +117,43 @@
-/
/--
+Pointwise ReLU is 1-Lipschitz for scalars.
+Foundation for tensor-level Lipschitz bounds.
+-/
+theorem relu_scalar_lipschitz (x y : ℝ) :
+ |max (0 : ℝ) x - max (0 : ℝ) y| ≤ |x - y| := by
+ -- ReLU is 1-Lipschitz: |max(0,x) - max(0,y)| ≤ |x - y|
+ -- This follows from case analysis on... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_9ec4639d94ef_4 | 6bddbe1ffbec113f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Lipschitz.lean | Lipschitz | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "relu_scalar_tensor_lipschitz",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases x with | scalar a =>\n cases y with | scalar b =>\n unfold reluSpec tensorL2Dist tensorL2Norm tensorN... | [
{
"name": "relu_scalar_lipschitz",
"text": "/--\nPointwise ReLU is 1-Lipschitz for scalars.\nFoundation for tensor-level Lipschitz bounds.\n-/\ntheorem relu_scalar_lipschitz (x y : ℝ) :\n |max (0 : ℝ) x - max (0 : ℝ) y| ≤ |x - y| := by\n -- ReLU is 1-Lipschitz: |max(0,x) - max(0,y)| ≤ |x - y|\n -- This f... | [
{
"name": "relu_lipschitz_general",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 208,
"n_chars": 12346,
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"n_tactics": 163,
"cyclomatic": 5,
"n_automation": 15,
"n_rewrites": 12,
"n_structural": 15,
"automation_only": false,... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | @@ -117,6 +117,43 @@
-/
/--
+Pointwise ReLU is 1-Lipschitz for scalars.
+Foundation for tensor-level Lipschitz bounds.
+-/
+theorem relu_scalar_lipschitz (x y : ℝ) :
+ |max (0 : ℝ) x - max (0 : ℝ) y| ≤ |x - y| := by
+ -- ReLU is 1-Lipschitz: |max(0,x) - max(0,y)| ≤ |x - y|
+ -- This follows from case analysis on... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_9ec4639d94ef_5 | b74b10a19fe5d158 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Lipschitz.lean | Lipschitz | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "relu_scalar_tensor_lipschitz",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n cases x with | scalar a =>\n cases y with | scalar b =>\n unfold reluSpec tensorL2Dist tensorL2Norm tensorN... | [
{
"name": "relu_scalar_lipschitz",
"text": "/--\nPointwise ReLU is 1-Lipschitz for scalars.\nFoundation for tensor-level Lipschitz bounds.\n-/\ntheorem relu_scalar_lipschitz (x y : ℝ) :\n |max (0 : ℝ) x - max (0 : ℝ) y| ≤ |x - y| := by\n -- ReLU is 1-Lipschitz: |max(0,x) - max(0,y)| ≤ |x - y|\n -- This f... | [
{
"name": "relu_vector_lipschitz",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 3,
"n_lines": 13,
"n_chars": 493,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_n... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | @@ -117,6 +117,43 @@
-/
/--
+Pointwise ReLU is 1-Lipschitz for scalars.
+Foundation for tensor-level Lipschitz bounds.
+-/
+theorem relu_scalar_lipschitz (x y : ℝ) :
+ |max (0 : ℝ) x - max (0 : ℝ) y| ≤ |x - y| := by
+ -- ReLU is 1-Lipschitz: |max(0,x) - max(0,y)| ≤ |x - y|
+ -- This follows from case analysis on... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_9ec4639d94ef_6 | c8410665d2e984e6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Lipschitz.lean | Lipschitz | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "mat_vec_coord_eq_dot_row",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Expand both sides as `Finset.univ` sums and match terms.\n rw [toVec_mat_vec_mul_spec (A := W) (v... | [
{
"name": "toVec_get_eq_get2",
"text": "/--\nCompatibility between two row/column access views:\n\n`toVec (get W i) j` and `get2 W i j` name the same scalar entry of a matrix tensor.\n-/\nprivate lemma toVec_get_eq_get2 {m n : Nat}\n (W : Tensor ℝ (.dim m (.dim n .scalar))) (i : Fin m) (j : Fin n) :\n ... | [
{
"name": "mat_vec_coord_eq_dot_row",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 19,
"n_chars": 670,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 2,
"n_rewrites": 2,
"n_structural": 2,
"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 Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | @@ -200,6 +200,23 @@
Real.sqrt (∑ i : Fin m, tensorNormSquared (get W i))
/--
+Compatibility between two row/column access views:
+
+`toVec (get W i) j` and `get2 W i j` name the same scalar entry of a matrix tensor.
+-/
+private lemma toVec_get_eq_get2 {m n : Nat}
+ (W : Tensor ℝ (.dim m (.dim n .scalar))) (i... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_9ec4639d94ef_7 | 67f812d9652c764f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Lipschitz.lean | Lipschitz | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "tensor_cauchy_schwarz",
"depth": 1,
"n_commands": 0,
"n_lines": 170,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold tensorL2Norm\n\n -- Handle the degenerate case where y = 0\n by_cases hy : tensorNormSquared y = 0\n · --... | [
{
"name": "dot_zero_right",
"text": "/--\nBasic lemma: dot product with zero tensor is zero.\n-/\ntheorem dot_zero_right {s : Shape} (x : Tensor ℝ s) :\n dot x (fill (0 : ℝ) s) = (0 : ℝ) := by\n -- By induction on the tensor `Shape`; the `dim` case reduces to “folding `(+ )` over zeros”.\n induction s wi... | [
{
"name": "matrix_spectral_norm_bound",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 7,
"n_lines": 111,
"n_chars": 5020,
"n_subproofs": 19,
"n_tactics": 83,
"cyclomatic": 1,
"n_automation": 12,
"n_rewrites": 4,
"n_structural": 10,
"automation_only": false... | 7 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | @@ -124,6 +124,77 @@
simp [tensorL2Norm]
/--
+Basic lemma: dot product with zero tensor is zero.
+-/
+theorem dot_zero_right {s : Shape} (x : Tensor ℝ s) :
+ dot x (fill (0 : ℝ) s) = (0 : ℝ) := by
+ -- By induction on the tensor `Shape`; the `dim` case reduces to “folding `(+ )` over zeros”.
+ induction s with... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_9ec4639d94ef_8 | 328ee13088acc5a5 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Lipschitz.lean | Lipschitz | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 1 | [
{
"theorem_name": "tensor_cauchy_schwarz",
"depth": 1,
"n_commands": 0,
"n_lines": 170,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n unfold tensorL2Norm\n\n -- Handle the degenerate case where y = 0\n by_cases hy : tensorNormSquared y = 0\n · --... | [
{
"name": "dot_zero_right",
"text": "/--\nBasic lemma: dot product with zero tensor is zero.\n-/\ntheorem dot_zero_right {s : Shape} (x : Tensor ℝ s) :\n dot x (fill (0 : ℝ) s) = (0 : ℝ) := by\n -- By induction on the tensor `Shape`; the `dim` case reduces to “folding `(+ )` over zeros”.\n induction s wi... | [
{
"name": "linear_op_norm_bound",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 9,
"n_lines": 25,
"n_chars": 905,
"n_subproofs": 1,
"n_tactics": 10,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 5,
"n_structural": 1,
"automation_only": false,
"max_... | 9 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | @@ -124,6 +124,77 @@
simp [tensorL2Norm]
/--
+Basic lemma: dot product with zero tensor is zero.
+-/
+theorem dot_zero_right {s : Shape} (x : Tensor ℝ s) :
+ dot x (fill (0 : ℝ) s) = (0 : ℝ) := by
+ -- By induction on the tensor `Shape`; the `dim` case reduces to “folding `(+ )` over zeros”.
+ induction s with... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_9ec4639d94ef_9 | 0cb495f163fa24b6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Analysis/Lipschitz.lean | Lipschitz | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 13 | 2 | [
{
"theorem_name": "dot_quadratic_expand",
"depth": 1,
"n_commands": 0,
"n_lines": 22,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [dot_add_add]\n have h1 : dot x (scaleSpec y t) = t * dot x y := by\n -- Scale in the second argument via comm... | [
{
"name": "dot_add_add",
"text": "/--\nBilinearity of dot product over addition (distributive property).\n-/\ntheorem dot_add_add {s : Shape} (x y : Tensor ℝ s) :\n dot (addSpec x y) (addSpec x y) =\n dot x x + 2 * dot x y + dot y y := by\n -- This is the key bilinearity property: (x + y) · (x + y) = x·x... | [
{
"name": "relu_linear_lipschitz",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 13,
"n_lines": 20,
"n_chars": 869,
"n_subproofs": 0,
"n_tactics": 6,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max... | 13 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.BigOperators.Ring.Finset
public import Mathlib.Algebra.Order.BigOperators.Group.Finset
public import Mathlib.Analysis.Calculus.MeanValue
public import Mathlib.An... | @@ -195,11 +195,76 @@
exact ih (k + 1) k_plus_one_le h_next
/--
+Bilinearity of dot product over addition (distributive property).
+-/
+theorem dot_add_add {s : Shape} (x y : Tensor ℝ s) :
+ dot (addSpec x y) (addSpec x y) =
+ dot x x + 2 * dot x y + dot y y := by
+ -- This is the key bilinearity property:... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b44a8e373cff_0 | ec0b44bb5f0b0670 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/Float32Contract.lean | Float32Contract | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "native_add_eq_ieee32",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply ref_ext\n simp [fromNativeBits, toNativeBits, h.add_bits x y]",
"n_chars": 73,
"n_subproofs": 0,
"n... | [
{
"name": "ref_ext",
"text": "private 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": 5,
"n_lines": 7,
"n_chars": 131,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 4,
"n_automation": ... | [
{
"name": "native_add_eq_ieee32",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 323,
"n_subproofs": 0,
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | @@ -124,11 +124,19 @@
fma_bits : ∀ x y z, native.fmaBits x y z = toNativeBits (IEEE32Exec.fma x y z)
sqrt_bits : ∀ x, native.sqrtBits x = toNativeBits (IEEE32Exec.sqrt x)
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
var... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b44a8e373cff_1 | 085f53fb1261b9dd | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/Float32Contract.lean | Float32Contract | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "native_add_eq_ieee32",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply ref_ext\n simp [fromNativeBits, toNativeBits, h.add_bits x y]",
"n_chars": 73,
"n_subproofs": 0,
"n... | [
{
"name": "ref_ext",
"text": "private 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": 5,
"n_lines": 7,
"n_chars": 131,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 4,
"n_automation": ... | [
{
"name": "native_mul_eq_ieee32",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 329,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | @@ -124,11 +124,19 @@
fma_bits : ∀ x y z, native.fmaBits x y z = toNativeBits (IEEE32Exec.fma x y z)
sqrt_bits : ∀ x, native.sqrtBits x = toNativeBits (IEEE32Exec.sqrt x)
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
var... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b44a8e373cff_2 | 16436d3867c25573 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/Float32Contract.lean | Float32Contract | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "native_add_eq_ieee32",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply ref_ext\n simp [fromNativeBits, toNativeBits, h.add_bits x y]",
"n_chars": 73,
"n_subproofs": 0,
"n... | [
{
"name": "ref_ext",
"text": "private 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": 5,
"n_lines": 7,
"n_chars": 131,
"n_subproofs": 0,
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"cyclomatic": 4,
"n_automation": ... | [
{
"name": "native_div_eq_ieee32",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 323,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | @@ -124,11 +124,19 @@
fma_bits : ∀ x y z, native.fmaBits x y z = toNativeBits (IEEE32Exec.fma x y z)
sqrt_bits : ∀ x, native.sqrtBits x = toNativeBits (IEEE32Exec.sqrt x)
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
var... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b44a8e373cff_3 | 130453fe0ad399cc | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/Float32Contract.lean | Float32Contract | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "native_add_eq_ieee32",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply ref_ext\n simp [fromNativeBits, toNativeBits, h.add_bits x y]",
"n_chars": 73,
"n_subproofs": 0,
"n... | [
{
"name": "ref_ext",
"text": "private 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": 5,
"n_lines": 7,
"n_chars": 131,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 4,
"n_automation": ... | [
{
"name": "native_fma_eq_ieee32",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 341,
"n_subproofs": 0,
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_ne... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | @@ -124,11 +124,19 @@
fma_bits : ∀ x y z, native.fmaBits x y z = toNativeBits (IEEE32Exec.fma x y z)
sqrt_bits : ∀ x, native.sqrtBits x = toNativeBits (IEEE32Exec.sqrt x)
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
var... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b44a8e373cff_4 | 7c599fa226a321bf | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/Float32Contract.lean | Float32Contract | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "native_add_eq_ieee32",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply ref_ext\n simp [fromNativeBits, toNativeBits, h.add_bits x y]",
"n_chars": 73,
"n_subproofs": 0,
"n... | [
{
"name": "ref_ext",
"text": "private 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": 5,
"n_lines": 7,
"n_chars": 131,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 4,
"n_automation": ... | [
{
"name": "native_sqrt_eq_ieee32",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 384,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | @@ -124,11 +124,19 @@
fma_bits : ∀ x y z, native.fmaBits x y z = toNativeBits (IEEE32Exec.fma x y z)
sqrt_bits : ∀ x, native.sqrtBits x = toNativeBits (IEEE32Exec.sqrt x)
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
var... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b44a8e373cff_5 | b8a56c6fb527aeed | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/Float32Contract.lean | Float32Contract | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "native_add_eq_ieee32",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply ref_ext\n simp [fromNativeBits, toNativeBits, h.add_bits x y]",
"n_chars": 73,
"n_subproofs": 0,
"n... | [
{
"name": "ref_ext",
"text": "private 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": 5,
"n_lines": 7,
"n_chars": 131,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 4,
"n_automation": ... | [
{
"name": "native_add_abs_error_of_isFinite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 756,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | @@ -124,11 +124,19 @@
fma_bits : ∀ x y z, native.fmaBits x y z = toNativeBits (IEEE32Exec.fma x y z)
sqrt_bits : ∀ x, native.sqrtBits x = toNativeBits (IEEE32Exec.sqrt x)
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
var... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b44a8e373cff_6 | 95a1db5a56d45864 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/Float32Contract.lean | Float32Contract | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "native_add_eq_ieee32",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply ref_ext\n simp [fromNativeBits, toNativeBits, h.add_bits x y]",
"n_chars": 73,
"n_subproofs": 0,
"n... | [
{
"name": "ref_ext",
"text": "private 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": 5,
"n_lines": 7,
"n_chars": 131,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 4,
"n_automation": ... | [
{
"name": "native_mul_abs_error_of_isFinite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 768,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | @@ -124,11 +124,19 @@
fma_bits : ∀ x y z, native.fmaBits x y z = toNativeBits (IEEE32Exec.fma x y z)
sqrt_bits : ∀ x, native.sqrtBits x = toNativeBits (IEEE32Exec.sqrt x)
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
var... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b44a8e373cff_7 | edcd9b8ab1ccd30a | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/Float32Contract.lean | Float32Contract | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "native_add_eq_ieee32",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply ref_ext\n simp [fromNativeBits, toNativeBits, h.add_bits x y]",
"n_chars": 73,
"n_subproofs": 0,
"n... | [
{
"name": "ref_ext",
"text": "private 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": 5,
"n_lines": 7,
"n_chars": 131,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 4,
"n_automation": ... | [
{
"name": "native_div_abs_error_of_isFinite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 756,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | @@ -124,11 +124,19 @@
fma_bits : ∀ x y z, native.fmaBits x y z = toNativeBits (IEEE32Exec.fma x y z)
sqrt_bits : ∀ x, native.sqrtBits x = toNativeBits (IEEE32Exec.sqrt x)
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
var... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b44a8e373cff_8 | cf6d0176132e4461 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/Float32Contract.lean | Float32Contract | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "native_add_eq_ieee32",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply ref_ext\n simp [fromNativeBits, toNativeBits, h.add_bits x y]",
"n_chars": 73,
"n_subproofs": 0,
"n... | [
{
"name": "ref_ext",
"text": "private 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": 5,
"n_lines": 7,
"n_chars": 131,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 4,
"n_automation": ... | [
{
"name": "native_fma_abs_error_of_isFinite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 808,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": false... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | @@ -124,11 +124,19 @@
fma_bits : ∀ x y z, native.fmaBits x y z = toNativeBits (IEEE32Exec.fma x y z)
sqrt_bits : ∀ x, native.sqrtBits x = toNativeBits (IEEE32Exec.sqrt x)
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
var... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b44a8e373cff_9 | ae5abed9c50c1670 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Runtime/Autograd/Engine/Cuda/Float32Contract.lean | Float32Contract | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 6 | 5 | [
{
"theorem_name": "native_add_eq_ieee32",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n apply ref_ext\n simp [fromNativeBits, toNativeBits, h.add_bits x y]",
"n_chars": 73,
"n_subproofs": 0,
"n... | [
{
"name": "ref_ext",
"text": "private 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": 5,
"n_lines": 7,
"n_chars": 131,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 4,
"n_automation": ... | [
{
"name": "native_sqrt_abs_error_of_isFinite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 733,
"n_subproofs": 1,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 1,
"automation_only": fals... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.ErrorBounds
public import NN.Floats.IEEEExec.BridgeInitFloat32
/-!
# CUDA float32 contract
TorchLean's CUDA eager backend stores native `float` values in an... | @@ -124,11 +124,19 @@
fma_bits : ∀ x y z, native.fmaBits x y z = toNativeBits (IEEE32Exec.fma x y z)
sqrt_bits : ∀ x, native.sqrtBits x = toNativeBits (IEEE32Exec.sqrt x)
+private theorem ref_ext {x y : RefScalar} (h : toNativeBits x = toNativeBits y) : x = y := by
+ cases x
+ cases y
+ cases h
+ rfl
+
var... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c558663525ba_0 | 7be23ffd0b7d9b50 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Ops/Transformer/PostNorm.lean | PostNorm | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "twoSublayerPostNormBlock_hasFDerivAt",
"depth": 1,
"n_commands": 0,
"n_lines": 43,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n let norm1 :=\n fun z : E =>\n Graph.evalVec\n (Γ := ΓPostNorm seqLen dMod... | [
{
"name": "residualThenPostNorm_hasFDerivAt",
"text": "/--\nCalculus bridge for a residual block followed by post-norm LayerNorm.\n\nThis is the theorem we use to move from separately proved pieces to a whole Transformer sublayer.\nSuppose some residual-producing map\n\n`residualPack : E → [residual_stream,... | [
{
"name": "twoSublayerPostNormBlock_hasFDerivAt",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 161,
"n_chars": 6984,
"n_subproofs": 2,
"n_tactics": 43,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 1,
"automation_only"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Ops.Norm.LayerNorm
public import NN.Proofs.Autograd.Tape.Ops.Transformer.FeedForward
public import NN.Proofs.Autograd.Tape.Ops.Transformer.ResidualAttent... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Ops.Norm.LayerNorm
public import NN.Proofs.Autograd.Tape.Ops.Transformer.FeedForward
public import NN.Proofs.Autograd.Tape.Ops.Transformer.ResidualAttent... | @@ -427,6 +427,97 @@
(m := seqLen) (n := dModel) ε xV hVarEpsPos hStdNe0
/--
+Calculus bridge for a residual block followed by post-norm LayerNorm.
+
+This is the theorem we use to move from separately proved pieces to a whole Transformer sublayer.
+Suppose some residual-producing map
+
+`residualPack : E → [re... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c558663525ba_1 | 2ac0129499c5c0b7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Ops/Transformer/PostNorm.lean | PostNorm | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "residualAttentionPostNorm_backpropVec_eq_adjoint_fderiv_at",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n postNorm_backpropVec_eq_adjoint_fderiv_at\n (seqLen := seqLen) (dModel := dModel... | [
{
"name": "postNorm_backpropVec_eq_adjoint_fderiv_at",
"text": "/--\nVJP theorem for the post-norm Transformer boundary.\n\nThis is the model-level theorem used after either residual attention or a residual feed-forward\nblock has produced its sequence-shaped residual stream.\n-/\ntheorem postNorm_backpropV... | [
{
"name": "residualAttentionPostNorm_backpropVec_eq_adjoint_fderiv_at",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 45,
"n_chars": 1994,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,
... | 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.Ops.Norm.LayerNorm
public import NN.Proofs.Autograd.Tape.Ops.Transformer.FeedForward
public import NN.Proofs.Autograd.Tape.Ops.Transformer.ResidualAttent... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Ops.Norm.LayerNorm
public import NN.Proofs.Autograd.Tape.Ops.Transformer.FeedForward
public import NN.Proofs.Autograd.Tape.Ops.Transformer.ResidualAttent... | @@ -427,6 +427,49 @@
(m := seqLen) (n := dModel) ε xV hVarEpsPos hStdNe0
/--
+VJP theorem for the post-norm Transformer boundary.
+
+This is the model-level theorem used after either residual attention or a residual feed-forward
+block has produced its sequence-shaped residual stream.
+-/
+theorem postNorm_back... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_c558663525ba_2 | 5cf538a80b81bb8f | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Ops/Transformer/PostNorm.lean | PostNorm | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 2 | [
{
"theorem_name": "residualAttentionPostNorm_backpropVec_eq_adjoint_fderiv_at",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n postNorm_backpropVec_eq_adjoint_fderiv_at\n (seqLen := seqLen) (dModel := dModel... | [
{
"name": "postNorm_backpropVec_eq_adjoint_fderiv_at",
"text": "/--\nVJP theorem for the post-norm Transformer boundary.\n\nThis is the model-level theorem used after either residual attention or a residual feed-forward\nblock has produced its sequence-shaped residual stream.\n-/\ntheorem postNorm_backpropV... | [
{
"name": "residualFeedForwardPostNorm_backpropVec_eq_adjoint_fderiv_at",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 44,
"n_chars": 1962,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 0,
"n_structural": 0,... | 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.Ops.Norm.LayerNorm
public import NN.Proofs.Autograd.Tape.Ops.Transformer.FeedForward
public import NN.Proofs.Autograd.Tape.Ops.Transformer.ResidualAttent... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Ops.Norm.LayerNorm
public import NN.Proofs.Autograd.Tape.Ops.Transformer.FeedForward
public import NN.Proofs.Autograd.Tape.Ops.Transformer.ResidualAttent... | @@ -427,6 +427,49 @@
(m := seqLen) (n := dModel) ε xV hVarEpsPos hStdNe0
/--
+VJP theorem for the post-norm Transformer boundary.
+
+This is the model-level theorem used after either residual attention or a residual feed-forward
+block has produced its sequence-shaped residual stream.
+-/
+theorem postNorm_back... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8535d10ac8b6_0 | f20fa4f7e3d88007 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/Compare.lean | Compare | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 3 | [
{
"theorem_name": "cmpDyadic_lt_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 58,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n unfold cmpDyadic\n cases hzero : (a.mant == 0 && b.mant == 0) with\n | true =>\n -- Both are real zer... | [
{
"name": "dyadicToReal_eq_signedMant_shiftLeft_toExp",
"text": "lemma dyadicToReal_eq_signedMant_shiftLeft_toExp (d : Dyadic) (e : Int) (he : e ≤ d.exp) :\n dyadicToReal d =\n (signedMant d.sign (Nat.shiftLeft d.mant (Int.toNat (d.exp - e))) : ℝ) *\n neuralBpow binaryRadix e := by\n have hn... | [
{
"name": "cmpDyadic_lt_iff",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 67,
"n_chars": 3082,
"n_subproofs": 15,
"n_tactics": 54,
"cyclomatic": 3,
"n_automation": 13,
"n_rewrites": 3,
"n_structural": 5,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | @@ -28,6 +28,47 @@
real comparisons once NaNs/Infs are ruled out.
-/
+lemma dyadicToReal_eq_signedMant_shiftLeft_toExp (d : Dyadic) (e : Int) (he : e ≤ d.exp) :
+ dyadicToReal d =
+ (signedMant d.sign (Nat.shiftLeft d.mant (Int.toNat (d.exp - e))) : ℝ) *
+ neuralBpow binaryRadix e := by
+ have hnonn... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8535d10ac8b6_1 | 90753c812e519b99 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/Compare.lean | Compare | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 3 | [
{
"theorem_name": "cmpDyadic_lt_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 58,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n unfold cmpDyadic\n cases hzero : (a.mant == 0 && b.mant == 0) with\n | true =>\n -- Both are real zer... | [
{
"name": "dyadicToReal_eq_signedMant_shiftLeft_toExp",
"text": "lemma dyadicToReal_eq_signedMant_shiftLeft_toExp (d : Dyadic) (e : Int) (he : e ≤ d.exp) :\n dyadicToReal d =\n (signedMant d.sign (Nat.shiftLeft d.mant (Int.toNat (d.exp - e))) : ℝ) *\n neuralBpow binaryRadix e := by\n have hn... | [
{
"name": "cmpDyadic_eq_iff",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 60,
"n_chars": 2603,
"n_subproofs": 12,
"n_tactics": 51,
"cyclomatic": 3,
"n_automation": 14,
"n_rewrites": 3,
"n_structural": 6,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | @@ -28,6 +28,47 @@
real comparisons once NaNs/Infs are ruled out.
-/
+lemma dyadicToReal_eq_signedMant_shiftLeft_toExp (d : Dyadic) (e : Int) (he : e ≤ d.exp) :
+ dyadicToReal d =
+ (signedMant d.sign (Nat.shiftLeft d.mant (Int.toNat (d.exp - e))) : ℝ) *
+ neuralBpow binaryRadix e := by
+ have hnonn... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8535d10ac8b6_2 | 3b6ebe23811b4956 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/Compare.lean | Compare | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 3 | [
{
"theorem_name": "cmpDyadic_lt_iff",
"depth": 1,
"n_commands": 0,
"n_lines": 58,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n unfold cmpDyadic\n cases hzero : (a.mant == 0 && b.mant == 0) with\n | true =>\n -- Both are real zer... | [
{
"name": "dyadicToReal_eq_signedMant_shiftLeft_toExp",
"text": "lemma dyadicToReal_eq_signedMant_shiftLeft_toExp (d : Dyadic) (e : Int) (he : e ≤ d.exp) :\n dyadicToReal d =\n (signedMant d.sign (Nat.shiftLeft d.mant (Int.toNat (d.exp - e))) : ℝ) *\n neuralBpow binaryRadix e := by\n have hn... | [
{
"name": "cmpDyadic_gt_iff",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 63,
"n_chars": 2814,
"n_subproofs": 15,
"n_tactics": 54,
"cyclomatic": 3,
"n_automation": 13,
"n_rewrites": 3,
"n_structural": 5,
"automation_only": false,
"max_n... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | @@ -28,6 +28,47 @@
real comparisons once NaNs/Infs are ruled out.
-/
+lemma dyadicToReal_eq_signedMant_shiftLeft_toExp (d : Dyadic) (e : Int) (he : e ≤ d.exp) :
+ dyadicToReal d =
+ (signedMant d.sign (Nat.shiftLeft d.mant (Int.toNat (d.exp - e))) : ℝ) *
+ neuralBpow binaryRadix e := by
+ have hnonn... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_8535d10ac8b6_3 | aff1c9309e42b118 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/Compare.lean | Compare | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "compare_eq_some_lt_iff_toReal_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hcmp : compare x y = some (cmpDyadic dx dy) :=\n compare_eq_some_cmpDyadic_of_toDyadic? (x := x) (... | [
{
"name": "compare_eq_some_cmpDyadic_of_toDyadic?",
"text": "/--\nBridge for `IEEE32Exec.compare` on finite values.\n\nWhen both operands decode to dyadics (`toDyadic? = some`), `compare` returns a result and it is\nexactly `cmpDyadic` of those dyadics.\n-/\ntheorem compare_eq_some_cmpDyadic_of_toDyadic? (x... | [
{
"name": "compare_eq_some_lt_iff_toReal_lt",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 18,
"n_chars": 790,
"n_subproofs": 3,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 0,
"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.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | @@ -136,6 +136,22 @@
simpa [hcmp, compare_lt_iff_lt, hlt]
/--
+Bridge for `IEEE32Exec.compare` on finite values.
+
+When both operands decode to dyadics (`toDyadic? = some`), `compare` returns a result and it is
+exactly `cmpDyadic` of those dyadics.
+-/
+theorem compare_eq_some_cmpDyadic_of_toDyadic? (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_8535d10ac8b6_4 | 68228c85af52cfcf | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/Compare.lean | Compare | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "compare_eq_some_lt_iff_toReal_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hcmp : compare x y = some (cmpDyadic dx dy) :=\n compare_eq_some_cmpDyadic_of_toDyadic? (x := x) (... | [
{
"name": "compare_eq_some_cmpDyadic_of_toDyadic?",
"text": "/--\nBridge for `IEEE32Exec.compare` on finite values.\n\nWhen both operands decode to dyadics (`toDyadic? = some`), `compare` returns a result and it is\nexactly `cmpDyadic` of those dyadics.\n-/\ntheorem compare_eq_some_cmpDyadic_of_toDyadic? (x... | [
{
"name": "compare_eq_some_eq_iff_toReal_eq",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 17,
"n_chars": 772,
"n_subproofs": 3,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 0,
"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.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | @@ -129,6 +129,22 @@
simpa [hcmp, compare_eq_iff_eq, heq]
/--
+Bridge for `IEEE32Exec.compare` on finite values.
+
+When both operands decode to dyadics (`toDyadic? = some`), `compare` returns a result and it is
+exactly `cmpDyadic` of those dyadics.
+-/
+theorem compare_eq_some_cmpDyadic_of_toDyadic? (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_8535d10ac8b6_5 | f2d9bb467f6e7335 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/Compare.lean | Compare | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "compare_eq_some_lt_iff_toReal_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hcmp : compare x y = some (cmpDyadic dx dy) :=\n compare_eq_some_cmpDyadic_of_toDyadic? (x := x) (... | [
{
"name": "compare_eq_some_cmpDyadic_of_toDyadic?",
"text": "/--\nBridge for `IEEE32Exec.compare` on finite values.\n\nWhen both operands decode to dyadics (`toDyadic? = some`), `compare` returns a result and it is\nexactly `cmpDyadic` of those dyadics.\n-/\ntheorem compare_eq_some_cmpDyadic_of_toDyadic? (x... | [
{
"name": "compare_eq_some_gt_iff_toReal_gt",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 16,
"n_chars": 700,
"n_subproofs": 3,
"n_tactics": 7,
"cyclomatic": 1,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 0,
"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.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | @@ -132,6 +132,22 @@
simpa [hcmp, compare_gt_iff_gt, hgt]
/--
+Bridge for `IEEE32Exec.compare` on finite values.
+
+When both operands decode to dyadics (`toDyadic? = some`), `compare` returns a result and it is
+exactly `cmpDyadic` of those dyadics.
+-/
+theorem compare_eq_some_cmpDyadic_of_toDyadic? (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_8535d10ac8b6_6 | c768d1fecac0d480 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/Compare.lean | Compare | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "compare_eq_some_lt_iff_toReal_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hcmp : compare x y = some (cmpDyadic dx dy) :=\n compare_eq_some_cmpDyadic_of_toDyadic? (x := x) (... | [
{
"name": "compare_eq_some_cmpDyadic_of_toDyadic?",
"text": "/--\nBridge for `IEEE32Exec.compare` on finite values.\n\nWhen both operands decode to dyadics (`toDyadic? = some`), `compare` returns a result and it is\nexactly `cmpDyadic` of those dyadics.\n-/\ntheorem compare_eq_some_cmpDyadic_of_toDyadic? (x... | [
{
"name": "toReal_minimum_eq_min",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 9,
"n_lines": 75,
"n_chars": 3600,
"n_subproofs": 20,
"n_tactics": 62,
"cyclomatic": 4,
"n_automation": 15,
"n_rewrites": 2,
"n_structural": 9,
"automation_only": false,
"... | 9 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | @@ -257,6 +257,22 @@
simpa [hcmp, compare_gt_iff_gt, hgt]
/--
+Bridge for `IEEE32Exec.compare` on finite values.
+
+When both operands decode to dyadics (`toDyadic? = some`), `compare` returns a result and it is
+exactly `cmpDyadic` of those dyadics.
+-/
+theorem compare_eq_some_cmpDyadic_of_toDyadic? (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_8535d10ac8b6_7 | 1adf76d3ba7ad134 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/BridgeFP32/Compare.lean | Compare | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 9 | 5 | [
{
"theorem_name": "compare_eq_some_lt_iff_toReal_lt",
"depth": 1,
"n_commands": 0,
"n_lines": 8,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hcmp : compare x y = some (cmpDyadic dx dy) :=\n compare_eq_some_cmpDyadic_of_toDyadic? (x := x) (... | [
{
"name": "compare_eq_some_cmpDyadic_of_toDyadic?",
"text": "/--\nBridge for `IEEE32Exec.compare` on finite values.\n\nWhen both operands decode to dyadics (`toDyadic? = some`), `compare` returns a result and it is\nexactly `cmpDyadic` of those dyadics.\n-/\ntheorem compare_eq_some_cmpDyadic_of_toDyadic? (x... | [
{
"name": "toReal_maximum_eq_max",
"fan_in": 0,
"n_deps_direct": 5,
"n_deps_transitive": 9,
"n_lines": 72,
"n_chars": 3526,
"n_subproofs": 20,
"n_tactics": 62,
"cyclomatic": 4,
"n_automation": 15,
"n_rewrites": 2,
"n_structural": 9,
"automation_only": false,
"... | 9 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.BridgeFP32.Ops
/-!
# IEEE32Exec and FP32: Comparisons and Min/Max
-/
@[expose] public section
namespace TorchLean.Floats.IEEE754
open TorchLean.Floats
na... | @@ -257,6 +257,22 @@
simpa [hcmp, compare_gt_iff_gt, hgt]
/--
+Bridge for `IEEE32Exec.compare` on finite values.
+
+When both operands decode to dyadics (`toDyadic? = some`), `compare` returns a result and it is
+exactly `cmpDyadic` of those dyadics.
+-/
+theorem compare_eq_some_cmpDyadic_of_toDyadic? (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_5fd6cce19752_0 | b8dd78c9b58fe0c7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32DivSoundness.lean | IEEEExec32DivSoundness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "div_bounds_Icc",
"depth": 1,
"n_commands": 0,
"n_lines": 33,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hinv1 : (1 / y) ∈ Set.Icc (1 / d) (1 / c) := by\n cases h0 with\n | inl hd => exact inv_mem_Icc_of_mem_Icc_of_ne... | [
{
"name": "inv_mem_Icc_of_mem_Icc_of_neg",
"text": "/--\nReciprocal bounds for negative intervals.\n\nIf `d < 0` and `y ∈ [c,d]`, then `1/y ∈ [1/d, 1/c]`.\n-/\nprivate lemma inv_mem_Icc_of_mem_Icc_of_neg (c d y : ℝ)\n (hd : d < 0) (hy : y ∈ Set.Icc c d) :\n (1 / y) ∈ Set.Icc (1 / d) (1 / c) := by\n r... | [
{
"name": "div_bounds_Icc",
"fan_in": 1,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 46,
"n_chars": 2200,
"n_subproofs": 9,
"n_tactics": 30,
"cyclomatic": 3,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 6,
"automation_only": false,
"max_nesti... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Data.Bool.Basic
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEE... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Data.Bool.Basic
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEE... | @@ -78,6 +78,23 @@
exact ⟨hlo, hhi⟩
/--
+Reciprocal bounds for negative intervals.
+
+If `d < 0` and `y ∈ [c,d]`, then `1/y ∈ [1/d, 1/c]`.
+-/
+private lemma inv_mem_Icc_of_mem_Icc_of_neg (c d y : ℝ)
+ (hd : d < 0) (hy : y ∈ Set.Icc c d) :
+ (1 / y) ∈ Set.Icc (1 / d) (1 / c) := by
+ rcases hy with ⟨hcy, hy... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_5fd6cce19752_1 | 1debc8763a580d22 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32DivSoundness.lean | IEEEExec32DivSoundness | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "isNaN_divDown_eq_false_of_isFinite",
"depth": 1,
"n_commands": 0,
"n_lines": 26,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hxNaN : isNaN x = false := isNaN_eq_false_of_isFinite_eq_true (x := x) hx\n have hyNaN : isNaN y ... | [
{
"name": "isNaN_roundRatDown_eq_false",
"text": "/--\n`roundRatDown` never produces NaN.\n\nThis is used in the dyadic/rational implementation of `divDown` to show NaNs do not appear on the\nfinite, nonzero-denominator path.\n-/\nprivate lemma isNaN_roundRatDown_eq_false (sign : Bool) (num den : Nat) :\n ... | [
{
"name": "isNaN_divDown_eq_false_of_isFinite",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 35,
"n_chars": 1832,
"n_subproofs": 8,
"n_tactics": 26,
"cyclomatic": 7,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 4,
"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.Algebra.Order.Field.Basic
public import Mathlib.Data.Bool.Basic
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEE... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Data.Bool.Basic
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEE... | @@ -61,6 +61,22 @@
/-! ## `EReal` coercion helpers -/
/--
+`roundRatDown` never produces NaN.
+
+This is used in the dyadic/rational implementation of `divDown` to show NaNs do not appear on the
+finite, nonzero-denominator path.
+-/
+private lemma isNaN_roundRatDown_eq_false (sign : Bool) (num den : Nat) :
+ is... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_5fd6cce19752_2 | 370ef776fd4073ac | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32DivSoundness.lean | IEEEExec32DivSoundness | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "isNaN_divUp_eq_false_of_isFinite",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hxNaN : isNaN x = false := isNaN_eq_false_of_isFinite_eq_true (x := x) hx\n have hyNaN : isNaN y = ... | [
{
"name": "isNaN_roundRatUp_eq_false",
"text": "/--\n`roundRatUp` never produces NaN.\n\nThis is the “upper” analogue of `isNaN_roundRatDown_eq_false`.\n-/\nprivate lemma isNaN_roundRatUp_eq_false (sign : Bool) (num den : Nat) :\n isNaN (roundRatUp sign num den) = false := by\n by_cases hnum0 : num = 0\... | [
{
"name": "isNaN_divUp_eq_false_of_isFinite",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 35,
"n_chars": 1666,
"n_subproofs": 8,
"n_tactics": 26,
"cyclomatic": 7,
"n_automation": 5,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": fal... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Data.Bool.Basic
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEE... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Data.Bool.Basic
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEE... | @@ -61,6 +61,21 @@
/-! ## `EReal` coercion helpers -/
/--
+`roundRatUp` never produces NaN.
+
+This is the “upper” analogue of `isNaN_roundRatDown_eq_false`.
+-/
+private lemma isNaN_roundRatUp_eq_false (sign : Bool) (num den : Nat) :
+ isNaN (roundRatUp sign num den) = false := by
+ by_cases hnum0 : num = 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_5fd6cce19752_3 | f0e84d248c7fe7a4 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32DivSoundness.lean | IEEEExec32DivSoundness | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "div_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 213,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro x y hx hy\n have hAlo : isFinite A.lo = true := hA.1\n have hAhi : isFinite A.hi = true := hA.2.1\n have hBlo : isFini... | [
{
"name": "denom_sign_case",
"text": "/--\nIf the executable check says `0 ∉ B` (`containsZero B = false`), then the real interval\n`[toReal B.lo, toReal B.hi]` is sign-stable: either entirely negative or entirely positive.\n-/\nprivate lemma denom_sign_case (B : Interval32)\n (hBlo : isFinite B.lo = tru... | [
{
"name": "div_sound",
"fan_in": 1,
"n_deps_direct": 5,
"n_deps_transitive": 9,
"n_lines": 237,
"n_chars": 11563,
"n_subproofs": 57,
"n_tactics": 192,
"cyclomatic": 9,
"n_automation": 11,
"n_rewrites": 6,
"n_structural": 25,
"automation_only": false,
"max_nest... | 9 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Data.Bool.Basic
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEE... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Data.Bool.Basic
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEE... | @@ -277,6 +277,76 @@
simp [toReal_eq, hdy, dyadicToReal]
/--
+If the executable check says `0 ∉ B` (`containsZero B = false`), then the real interval
+`[toReal B.lo, toReal B.hi]` is sign-stable: either entirely negative or entirely positive.
+-/
+private lemma denom_sign_case (B : Interval32)
+ (hBlo : isFini... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_5fd6cce19752_4 | d4d7add07c2f5a65 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32DivSoundness.lean | IEEEExec32DivSoundness | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "toReal_posOne",
"depth": 1,
"n_commands": 0,
"n_lines": 41,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `posOne` is the binary32 constant `0x3F800000`, i.e. `mkBits false 127 0`.\n have hbits : (0x3F800000 : UInt32) = mkBits... | [
{
"name": "pow2_eq_two_pow",
"text": "/-- `pow2 k` is definitionaly `2^k`. (A small lemma for decoding float constants.) -/\nprivate lemma pow2_eq_two_pow (k : Nat) : (pow2 k) = 2 ^ k := by\n -- `pow2 k` is `1 <<< k`.\n simp [IEEE32Exec.pow2, Nat.shiftLeft_eq]\n\n",
"fan_in": 1,
"n_lines": 6,
... | [
{
"name": "toReal_posOne",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 44,
"n_chars": 2194,
"n_subproofs": 8,
"n_tactics": 35,
"cyclomatic": 1,
"n_automation": 13,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"max_nesti... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Data.Bool.Basic
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEE... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Data.Bool.Basic
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEE... | @@ -60,6 +60,11 @@
/-! ## `EReal` coercion helpers -/
+/-- `pow2 k` is definitionaly `2^k`. (A small lemma for decoding float constants.) -/
+private lemma pow2_eq_two_pow (k : Nat) : (pow2 k) = 2 ^ k := by
+ -- `pow2 k` is `1 <<< k`.
+ simp [IEEE32Exec.pow2, Nat.shiftLeft_eq]
+
/-- The IEEE32 constant `posOne`... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_5fd6cce19752_5 | 8dd8cec9f03d72a7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32DivSoundness.lean | IEEEExec32DivSoundness | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "toReal_posOne",
"depth": 1,
"n_commands": 0,
"n_lines": 41,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `posOne` is the binary32 constant `0x3F800000`, i.e. `mkBits false 127 0`.\n have hbits : (0x3F800000 : UInt32) = mkBits... | [
{
"name": "pow2_eq_two_pow",
"text": "/-- `pow2 k` is definitionaly `2^k`. (A small lemma for decoding float constants.) -/\nprivate lemma pow2_eq_two_pow (k : Nat) : (pow2 k) = 2 ^ k := by\n -- `pow2 k` is `1 <<< k`.\n simp [IEEE32Exec.pow2, Nat.shiftLeft_eq]\n\n",
"fan_in": 1,
"n_lines": 6,
... | [
{
"name": "inv_sound",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 12,
"n_lines": 34,
"n_chars": 1475,
"n_subproofs": 5,
"n_tactics": 18,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 1,
"n_structural": 2,
"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 Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Data.Bool.Basic
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEE... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Algebra.Order.Field.Basic
public import Mathlib.Data.Bool.Basic
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEE... | @@ -582,6 +582,11 @@
`posOne`.
-/
+/-- `pow2 k` is definitionaly `2^k`. (A small lemma for decoding float constants.) -/
+private lemma pow2_eq_two_pow (k : Nat) : (pow2 k) = 2 ^ k := by
+ -- `pow2 k` is `1 <<< k`.
+ simp [IEEE32Exec.pow2, Nat.shiftLeft_eq]
+
/-- The IEEE32 constant `posOne` decodes to the real ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_106459c553c9_0 | 63ec473c719e983c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/MinMaxERealSoundness.lean | MinMaxERealSoundness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "toEReal_minimum_eq_min",
"depth": 1,
"n_commands": 0,
"n_lines": 37,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hchoose : chooseNaN2 x y = none :=\n chooseNaN2_none_of_not_isNaN x y hxNaN hyNaN\n by_cases hxInf : isInf... | [
{
"name": "coe_min",
"text": "private lemma coe_min (a b : ℝ) : ((min a b : ℝ) : EReal) = min (a : EReal) (b : EReal) := by\n by_cases h : a ≤ b\n · have hE : (a : EReal) ≤ (b : EReal) := by simpa [EReal.coe_le_coe_iff] using h\n simp [min_eq_left h, min_eq_left hE]\n · have h' : b ≤ a := le_of_not_ge... | [
{
"name": "toEReal_minimum_eq_min",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 44,
"n_chars": 2288,
"n_subproofs": 9,
"n_tactics": 41,
"cyclomatic": 9,
"n_automation": 6,
"n_rewrites": 1,
"n_structural": 5,
"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 Mathlib.Data.EReal.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.ERealSemantics
/-!
# `minimum`/`maximum` in `EReal` semantics (IEEE32... | /-
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
public import NN.Floats.IEEEExec.ERealSemantics
/-!
# `minimum`/`maximum` in `EReal` semantics (IEEE32... | @@ -48,6 +48,14 @@
noncomputable section
+private lemma coe_min (a b : ℝ) : ((min a b : ℝ) : EReal) = min (a : EReal) (b : EReal) := by
+ by_cases h : a ≤ b
+ · have hE : (a : EReal) ≤ (b : EReal) := by simpa [EReal.coe_le_coe_iff] using h
+ simp [min_eq_left h, min_eq_left hE]
+ · have h' : b ≤ a := le_of_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_106459c553c9_1 | 89a2c8f4449edc9b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/MinMaxERealSoundness.lean | MinMaxERealSoundness | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "toEReal_maximum_eq_max",
"depth": 1,
"n_commands": 0,
"n_lines": 34,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hchoose : chooseNaN2 x y = none :=\n chooseNaN2_none_of_not_isNaN x y hxNaN hyNaN\n by_cases hxInf : isInf... | [
{
"name": "coe_max",
"text": "private lemma coe_max (a b : ℝ) : ((max a b : ℝ) : EReal) = max (a : EReal) (b : EReal) := by\n by_cases h : a ≤ b\n · have hE : (a : EReal) ≤ (b : EReal) := by simpa [EReal.coe_le_coe_iff] using h\n simp [max_eq_right h, max_eq_right hE]\n · have h' : b ≤ a := le_of_not_... | [
{
"name": "toEReal_maximum_eq_max",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 41,
"n_chars": 2001,
"n_subproofs": 9,
"n_tactics": 38,
"cyclomatic": 9,
"n_automation": 6,
"n_rewrites": 1,
"n_structural": 5,
"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 Mathlib.Data.EReal.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.ERealSemantics
/-!
# `minimum`/`maximum` in `EReal` semantics (IEEE32... | /-
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
public import NN.Floats.IEEEExec.ERealSemantics
/-!
# `minimum`/`maximum` in `EReal` semantics (IEEE32... | @@ -48,6 +48,16 @@
noncomputable section
+private lemma coe_max (a b : ℝ) : ((max a b : ℝ) : EReal) = max (a : EReal) (b : EReal) := by
+ by_cases h : a ≤ b
+ · have hE : (a : EReal) ≤ (b : EReal) := by simpa [EReal.coe_le_coe_iff] using h
+ simp [max_eq_right h, max_eq_right hE]
+ · have h' : b ≤ a := le_of... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d3707cdda33e_0 | ee8a8d5ea90fedb7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32AddSoundness.lean | IEEEExec32AddSoundness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "sub_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 44,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro x y hx hy\n have hAlo : isFinite A.lo = true := hA.1\n have hAhi : isFinite A.hi = true := hA.2.1\n have hBlo : isFinit... | [
{
"name": "isFinite_neg_of_isFinite",
"text": "/--\nNegation preserves finiteness.\n\nWe use this to justify that `subDown a b = addDown a (neg b)` is still in the finite regime when\n`b` is finite, so we can reuse directed-rounding soundness lemmas that assume finiteness.\n-/\nprivate lemma isFinite_neg_of... | [
{
"name": "sub_sound",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 57,
"n_chars": 2490,
"n_subproofs": 18,
"n_tactics": 35,
"cyclomatic": 2,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 4,
"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.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.ERealSemantics
public ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.ERealSemantics
public ... | @@ -61,6 +61,33 @@
/-! ## Small helpers -/
/--
+Negation preserves finiteness.
+
+We use this to justify that `subDown a b = addDown a (neg b)` is still in the finite regime when
+`b` is finite, so we can reuse directed-rounding soundness lemmas that assume finiteness.
+-/
+private lemma isFinite_neg_of_isFinite (x... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3f1e60c8afc1_0 | dd991b8d6ba30823 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/Error.lean | Error | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_abs_error",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- By definition, `a + b` rounds the exact real sum.\n simpa [HAdd.hAdd, Add.add, NF.ofReal, NF.roundR, round₃₂, round32, rn... | [
{
"name": "round_abs_error",
"text": "/--\nCore rounding lemma for the binary32 parameters fixed by `FP32`.\n\nThis is the “one thing we use everywhere”: once you know an operation is defined as “round the real\nresult”, the proof goal reduces to an instance of this lemma.\n\nInformal: if `fl32(x)` denotes ... | [
{
"name": "add_abs_error",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | @@ -58,6 +58,20 @@
/-! ## Per-op rounding error lemmas -/
/--
+Core rounding lemma for the binary32 parameters fixed by `FP32`.
+
+This is the “one thing we use everywhere”: once you know an operation is defined as “round the real
+result”, the proof goal reduces to an instance of this lemma.
+
+Informal: if `fl32(... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3f1e60c8afc1_1 | 47022a37539dfbf9 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/Error.lean | Error | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_abs_error",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- By definition, `a + b` rounds the exact real sum.\n simpa [HAdd.hAdd, Add.add, NF.ofReal, NF.roundR, round₃₂, round32, rn... | [
{
"name": "round_abs_error",
"text": "/--\nCore rounding lemma for the binary32 parameters fixed by `FP32`.\n\nThis is the “one thing we use everywhere”: once you know an operation is defined as “round the real\nresult”, the proof goal reduces to an instance of this lemma.\n\nInformal: if `fl32(x)` denotes ... | [
{
"name": "sub_abs_error",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 374,
"n_subproofs": 0,
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | @@ -58,13 +58,29 @@
/-! ## Per-op rounding error lemmas -/
/--
+Core rounding lemma for the binary32 parameters fixed by `FP32`.
+
+This is the “one thing we use everywhere”: once you know an operation is defined as “round the real
+result”, the proof goal reduces to an instance of this lemma.
+
+Informal: if `fl32... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3f1e60c8afc1_2 | a6511eab72993453 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/Error.lean | Error | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_abs_error",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- By definition, `a + b` rounds the exact real sum.\n simpa [HAdd.hAdd, Add.add, NF.ofReal, NF.roundR, round₃₂, round32, rn... | [
{
"name": "round_abs_error",
"text": "/--\nCore rounding lemma for the binary32 parameters fixed by `FP32`.\n\nThis is the “one thing we use everywhere”: once you know an operation is defined as “round the real\nresult”, the proof goal reduces to an instance of this lemma.\n\nInformal: if `fl32(x)` denotes ... | [
{
"name": "mul_abs_error",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 380,
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | @@ -58,13 +58,29 @@
/-! ## Per-op rounding error lemmas -/
/--
+Core rounding lemma for the binary32 parameters fixed by `FP32`.
+
+This is the “one thing we use everywhere”: once you know an operation is defined as “round the real
+result”, the proof goal reduces to an instance of this lemma.
+
+Informal: if `fl32... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3f1e60c8afc1_3 | 1e4007070bd9b2ba | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/Error.lean | Error | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_abs_error",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- By definition, `a + b` rounds the exact real sum.\n simpa [HAdd.hAdd, Add.add, NF.ofReal, NF.roundR, round₃₂, round32, rn... | [
{
"name": "round_abs_error",
"text": "/--\nCore rounding lemma for the binary32 parameters fixed by `FP32`.\n\nThis is the “one thing we use everywhere”: once you know an operation is defined as “round the real\nresult”, the proof goal reduces to an instance of this lemma.\n\nInformal: if `fl32(x)` denotes ... | [
{
"name": "div_abs_error",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 16,
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | @@ -58,6 +58,20 @@
/-! ## Per-op rounding error lemmas -/
/--
+Core rounding lemma for the binary32 parameters fixed by `FP32`.
+
+This is the “one thing we use everywhere”: once you know an operation is defined as “round the real
+result”, the proof goal reduces to an instance of this lemma.
+
+Informal: if `fl32(... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3f1e60c8afc1_4 | c9324004d777c0ab | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/Error.lean | Error | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_abs_error",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- By definition, `a + b` rounds the exact real sum.\n simpa [HAdd.hAdd, Add.add, NF.ofReal, NF.roundR, round₃₂, round32, rn... | [
{
"name": "round_abs_error",
"text": "/--\nCore rounding lemma for the binary32 parameters fixed by `FP32`.\n\nThis is the “one thing we use everywhere”: once you know an operation is defined as “round the real\nresult”, the proof goal reduces to an instance of this lemma.\n\nInformal: if `fl32(x)` denotes ... | [
{
"name": "exp_abs_error",
"fan_in": 0,
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"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 664,
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | @@ -58,6 +58,20 @@
/-! ## Per-op rounding error lemmas -/
/--
+Core rounding lemma for the binary32 parameters fixed by `FP32`.
+
+This is the “one thing we use everywhere”: once you know an operation is defined as “round the real
+result”, the proof goal reduces to an instance of this lemma.
+
+Informal: if `fl32(... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3f1e60c8afc1_5 | 153ce53117e1a995 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/Error.lean | Error | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_abs_error",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- By definition, `a + b` rounds the exact real sum.\n simpa [HAdd.hAdd, Add.add, NF.ofReal, NF.roundR, round₃₂, round32, rn... | [
{
"name": "round_abs_error",
"text": "/--\nCore rounding lemma for the binary32 parameters fixed by `FP32`.\n\nThis is the “one thing we use everywhere”: once you know an operation is defined as “round the real\nresult”, the proof goal reduces to an instance of this lemma.\n\nInformal: if `fl32(x)` denotes ... | [
{
"name": "tanh_abs_error",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | @@ -58,13 +58,29 @@
/-! ## Per-op rounding error lemmas -/
/--
+Core rounding lemma for the binary32 parameters fixed by `FP32`.
+
+This is the “one thing we use everywhere”: once you know an operation is defined as “round the real
+result”, the proof goal reduces to an instance of this lemma.
+
+Informal: if `fl32... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3f1e60c8afc1_6 | af9237f991d0885e | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/Error.lean | Error | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_abs_error",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- By definition, `a + b` rounds the exact real sum.\n simpa [HAdd.hAdd, Add.add, NF.ofReal, NF.roundR, round₃₂, round32, rn... | [
{
"name": "round_abs_error",
"text": "/--\nCore rounding lemma for the binary32 parameters fixed by `FP32`.\n\nThis is the “one thing we use everywhere”: once you know an operation is defined as “round the real\nresult”, the proof goal reduces to an instance of this lemma.\n\nInformal: if `fl32(x)` denotes ... | [
{
"name": "log_abs_error",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 534,
"n_subproofs": 0,
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | @@ -58,6 +58,20 @@
/-! ## Per-op rounding error lemmas -/
/--
+Core rounding lemma for the binary32 parameters fixed by `FP32`.
+
+This is the “one thing we use everywhere”: once you know an operation is defined as “round the real
+result”, the proof goal reduces to an instance of this lemma.
+
+Informal: if `fl32(... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3f1e60c8afc1_7 | 4089e77f14f4bef4 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/Error.lean | Error | 7 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_abs_error",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- By definition, `a + b` rounds the exact real sum.\n simpa [HAdd.hAdd, Add.add, NF.ofReal, NF.roundR, round₃₂, round32, rn... | [
{
"name": "round_abs_error",
"text": "/--\nCore rounding lemma for the binary32 parameters fixed by `FP32`.\n\nThis is the “one thing we use everywhere”: once you know an operation is defined as “round the real\nresult”, the proof goal reduces to an instance of this lemma.\n\nInformal: if `fl32(x)` denotes ... | [
{
"name": "cos_abs_error",
"fan_in": 0,
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"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 409,
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"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | @@ -58,13 +58,29 @@
/-! ## Per-op rounding error lemmas -/
/--
+Core rounding lemma for the binary32 parameters fixed by `FP32`.
+
+This is the “one thing we use everywhere”: once you know an operation is defined as “round the real
+result”, the proof goal reduces to an instance of this lemma.
+
+Informal: if `fl32... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3f1e60c8afc1_8 | 1c8c2d2c2099b145 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/Error.lean | Error | 8 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_abs_error",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- By definition, `a + b` rounds the exact real sum.\n simpa [HAdd.hAdd, Add.add, NF.ofReal, NF.roundR, round₃₂, round32, rn... | [
{
"name": "round_abs_error",
"text": "/--\nCore rounding lemma for the binary32 parameters fixed by `FP32`.\n\nThis is the “one thing we use everywhere”: once you know an operation is defined as “round the real\nresult”, the proof goal reduces to an instance of this lemma.\n\nInformal: if `fl32(x)` denotes ... | [
{
"name": "sin_abs_error",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 409,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | @@ -58,13 +58,29 @@
/-! ## Per-op rounding error lemmas -/
/--
+Core rounding lemma for the binary32 parameters fixed by `FP32`.
+
+This is the “one thing we use everywhere”: once you know an operation is defined as “round the real
+result”, the proof goal reduces to an instance of this lemma.
+
+Informal: if `fl32... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3f1e60c8afc1_9 | dc4b51db8666b0b8 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/Error.lean | Error | 9 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_abs_error",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- By definition, `a + b` rounds the exact real sum.\n simpa [HAdd.hAdd, Add.add, NF.ofReal, NF.roundR, round₃₂, round32, rn... | [
{
"name": "round_abs_error",
"text": "/--\nCore rounding lemma for the binary32 parameters fixed by `FP32`.\n\nThis is the “one thing we use everywhere”: once you know an operation is defined as “round the real\nresult”, the proof goal reduces to an instance of this lemma.\n\nInformal: if `fl32(x)` denotes ... | [
{
"name": "sinh_abs_error",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 420,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | @@ -58,13 +58,29 @@
/-! ## Per-op rounding error lemmas -/
/--
+Core rounding lemma for the binary32 parameters fixed by `FP32`.
+
+This is the “one thing we use everywhere”: once you know an operation is defined as “round the real
+result”, the proof goal reduces to an instance of this lemma.
+
+Informal: if `fl32... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3f1e60c8afc1_10 | e1bb83802e8aac62 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/Error.lean | Error | 10 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_abs_error",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- By definition, `a + b` rounds the exact real sum.\n simpa [HAdd.hAdd, Add.add, NF.ofReal, NF.roundR, round₃₂, round32, rn... | [
{
"name": "round_abs_error",
"text": "/--\nCore rounding lemma for the binary32 parameters fixed by `FP32`.\n\nThis is the “one thing we use everywhere”: once you know an operation is defined as “round the real\nresult”, the proof goal reduces to an instance of this lemma.\n\nInformal: if `fl32(x)` denotes ... | [
{
"name": "cosh_abs_error",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 420,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | @@ -58,13 +58,29 @@
/-! ## Per-op rounding error lemmas -/
/--
+Core rounding lemma for the binary32 parameters fixed by `FP32`.
+
+This is the “one thing we use everywhere”: once you know an operation is defined as “round the real
+result”, the proof goal reduces to an instance of this lemma.
+
+Informal: if `fl32... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3f1e60c8afc1_11 | ff57bbcd08f03baa | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/Error.lean | Error | 11 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_abs_error",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- By definition, `a + b` rounds the exact real sum.\n simpa [HAdd.hAdd, Add.add, NF.ofReal, NF.roundR, round₃₂, round32, rn... | [
{
"name": "round_abs_error",
"text": "/--\nCore rounding lemma for the binary32 parameters fixed by `FP32`.\n\nThis is the “one thing we use everywhere”: once you know an operation is defined as “round the real\nresult”, the proof goal reduces to an instance of this lemma.\n\nInformal: if `fl32(x)` denotes ... | [
{
"name": "sqrt_abs_error",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 12,
"n_chars": 420,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting"... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | @@ -58,13 +58,29 @@
/-! ## Per-op rounding error lemmas -/
/--
+Core rounding lemma for the binary32 parameters fixed by `FP32`.
+
+This is the “one thing we use everywhere”: once you know an operation is defined as “round the real
+result”, the proof goal reduces to an instance of this lemma.
+
+Informal: if `fl32... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_3f1e60c8afc1_12 | 0c3751ae2b919944 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/FP32/Error.lean | Error | 12 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 13 | [
{
"theorem_name": "add_abs_error",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- By definition, `a + b` rounds the exact real sum.\n simpa [HAdd.hAdd, Add.add, NF.ofReal, NF.roundR, round₃₂, round32, rn... | [
{
"name": "round_abs_error",
"text": "/--\nCore rounding lemma for the binary32 parameters fixed by `FP32`.\n\nThis is the “one thing we use everywhere”: once you know an operation is defined as “round the real\nresult”, the proof goal reduces to an instance of this lemma.\n\nInformal: if `fl32(x)` denotes ... | [
{
"name": "abs_abs_error",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 15,
"n_chars": 517,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nesting":... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.FP32.Notation
import Mathlib.Algebra.Order.Algebra
/-!
# `FP32` per-op error bounds
Proofs about numerical code should not have to expand the definition of “float32 ... | @@ -58,6 +58,20 @@
/-! ## Per-op rounding error lemmas -/
/--
+Core rounding lemma for the binary32 parameters fixed by `FP32`.
+
+This is the “one thing we use everywhere”: once you know an operation is defined as “round the real
+result”, the proof goal reduces to an instance of this lemma.
+
+Informal: if `fl32(... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_43e99f38bb67_0 | 9a6f171997f807cd | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/OpSandwich.lean | OpSandwich | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "toEReal_addDown_le_add_le_addUp_of_isFinite",
"depth": 1,
"n_commands": 0,
"n_lines": 29,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hxInf : isInf x = false := isInf_eq_false_of_isFinite_eq_true (x := x) hx\n ... | [
{
"name": "chooseNaN2_none_of_isFinite",
"text": "private lemma chooseNaN2_none_of_isFinite (x y : IEEE32Exec)\n (hx : isFinite x = true) (hy : isFinite y = true) :\n chooseNaN2 x y = none := by\n have hxNaN : isNaN x = false := isNaN_eq_false_of_isFinite_eq_true (x := x) hx\n have hyNaN : isNaN y =... | [
{
"name": "toEReal_addDown_le_add_le_addUp_of_isFinite",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 41,
"n_chars": 1778,
"n_subproofs": 10,
"n_tactics": 28,
"cyclomatic": 3,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 4,
"automatio... | 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.Exec32
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.ERealSemantics
public import N... | /-
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.Exec32
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.ERealSemantics
public import N... | @@ -40,6 +40,13 @@
/-! ## Small helpers -/
+private lemma chooseNaN2_none_of_isFinite (x y : IEEE32Exec)
+ (hx : isFinite x = true) (hy : isFinite y = true) :
+ chooseNaN2 x y = none := by
+ have hxNaN : isNaN x = false := isNaN_eq_false_of_isFinite_eq_true (x := x) hx
+ have hyNaN : isNaN y = false := isN... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_43e99f38bb67_1 | b6cb2fd0bb6053df | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/OpSandwich.lean | OpSandwich | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 2 | [
{
"theorem_name": "toEReal_addDown_le_add_le_addUp_of_isFinite",
"depth": 1,
"n_commands": 0,
"n_lines": 29,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n have hxInf : isInf x = false := isInf_eq_false_of_isFinite_eq_true (x := x) hx\n ... | [
{
"name": "chooseNaN2_none_of_isFinite",
"text": "private lemma chooseNaN2_none_of_isFinite (x y : IEEE32Exec)\n (hx : isFinite x = true) (hy : isFinite y = true) :\n chooseNaN2 x y = none := by\n have hxNaN : isNaN x = false := isNaN_eq_false_of_isFinite_eq_true (x := x) hx\n have hyNaN : isNaN y =... | [
{
"name": "toEReal_mulDown_le_mul_le_mulUp_of_isFinite",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 63,
"n_chars": 2933,
"n_subproofs": 13,
"n_tactics": 54,
"cyclomatic": 18,
"n_automation": 15,
"n_rewrites": 0,
"n_structural": 16,
"automa... | 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.Exec32
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.ERealSemantics
public import N... | /-
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.Exec32
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.ERealSemantics
public import N... | @@ -40,6 +40,13 @@
/-! ## Small helpers -/
+private lemma chooseNaN2_none_of_isFinite (x y : IEEE32Exec)
+ (hx : isFinite x = true) (hy : isFinite y = true) :
+ chooseNaN2 x y = none := by
+ have hxNaN : isNaN x = false := isNaN_eq_false_of_isFinite_eq_true (x := x) hx
+ have hyNaN : isNaN y = false := isN... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_43e99f38bb67_2 | 1530463b7b54f72b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/OpSandwich.lean | OpSandwich | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "toEReal_subDown_le_sub_le_subUp_of_isFinite",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hyNeg : isFinite (neg y) = true := isFinite_neg_of_isFinite (x := y) hy\n -- Reduce to th... | [
{
"name": "isFinite_neg_of_isFinite",
"text": "private lemma isFinite_neg_of_isFinite (x : IEEE32Exec) (hx : isFinite x = true) :\n isFinite (neg x) = true := by\n -- Use the dyadic decode witness to avoid bit-level facts about exponent fields.\n cases hdx : toDyadic? x with\n | none =>\n have : ... | [
{
"name": "toEReal_subDown_le_sub_le_subUp_of_isFinite",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 10,
"n_chars": 501,
"n_subproofs": 1,
"n_tactics": 4,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_o... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.EReal.Basic
public import NN.Floats.IEEEExec.Exec32
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.ERealSemantics
public import N... | /-
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.Exec32
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.ERealSemantics
public import N... | @@ -47,6 +47,29 @@
have hyNaN : isNaN y = false := isNaN_eq_false_of_isFinite_eq_true (x := y) hy
simpa using (chooseNaN2_none_of_not_isNaN (x := x) (y := y) hxNaN hyNaN)
+private lemma isFinite_neg_of_isFinite (x : IEEE32Exec) (hx : isFinite x = true) :
+ isFinite (neg x) = true := by
+ -- Use the dyadic 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_987109b55b8c_0 | fea818d0db6dbc28 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/StateSpace/Scan.lean | Scan | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "summarizeScalarAffine_append_apply",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [summarizeScalarAffine_apply_eq_run]\n rw [ScalarAffineTransition.compose_apply]\n rw [summarizeSca... | [
{
"name": "runScalarAffine_append",
"text": "/-- Running appended transition lists is the same as running the first list, then the second. -/\ntheorem runScalarAffine_append {α : Type} [Semiring α] (h0 : α)\n (xs ys : List (_root_.Spec.ScalarAffineTransition α)) :\n _root_.Spec.runScalarAffine h0 (xs ... | [
{
"name": "summarizeScalarAffine_append_apply",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 3,
"n_lines": 18,
"n_chars": 782,
"n_subproofs": 0,
"n_tactics": 5,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 3,
"n_structural": 1,
"automation_only": fal... | 3 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Layers.SelectiveScan
import Mathlib.Algebra.Ring.Basic
/-!
# Proofs for affine selective scan
The Mamba/S4 scan theorem is an algebra theorem about affine maps. A seq... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Layers.SelectiveScan
import Mathlib.Algebra.Ring.Basic
/-!
# Proofs for affine selective scan
The Mamba/S4 scan theorem is an algebra theorem about affine maps. A seq... | @@ -176,6 +176,17 @@
end DiagonalTransition
+/-- Running appended transition lists is the same as running the first list, then the second. -/
+theorem runScalarAffine_append {α : Type} [Semiring α] (h0 : α)
+ (xs ys : List (_root_.Spec.ScalarAffineTransition α)) :
+ _root_.Spec.runScalarAffine h0 (xs ++ ys) ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_987109b55b8c_1 | 650b6c9550e7d7ef | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/StateSpace/Scan.lean | Scan | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "summarizeScalarAffine_append",
"depth": 1,
"n_commands": 0,
"n_lines": 7,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n induction xs with\n | nil =>\n simp [_root_.Spec.summarizeScalarAffine]\n | cons tr rest ih =>\n s... | [
{
"name": "compose_assoc",
"text": "/-- Scalar affine transition composition is associative. -/\n@[simp] theorem compose_assoc [Semiring α]\n (t₃ t₂ t₁ : _root_.Spec.ScalarAffineTransition α) :\n _root_.Spec.ScalarAffineTransition.compose\n (_root_.Spec.ScalarAffineTransition.compose t₃ t₂) t₁ ... | [
{
"name": "summarizeScalarAffine_append",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 20,
"n_chars": 791,
"n_subproofs": 0,
"n_tactics": 7,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Layers.SelectiveScan
import Mathlib.Algebra.Ring.Basic
/-!
# Proofs for affine selective scan
The Mamba/S4 scan theorem is an algebra theorem about affine maps. A seq... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Layers.SelectiveScan
import Mathlib.Algebra.Ring.Basic
/-!
# Proofs for affine selective scan
The Mamba/S4 scan theorem is an algebra theorem about affine maps. A seq... | @@ -53,6 +53,18 @@
cases t
simp [_root_.Spec.ScalarAffineTransition.compose, _root_.Spec.ScalarAffineTransition.id]
+/-- Scalar affine transition composition is associative. -/
+@[simp] theorem compose_assoc [Semiring α]
+ (t₃ t₂ t₁ : _root_.Spec.ScalarAffineTransition α) :
+ _root_.Spec.ScalarAffineTrans... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_987109b55b8c_2 | 31af49738a3a58d7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/Proofs/StateSpace/Scan.lean | Scan | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 5 | 1 | [
{
"theorem_name": "abs_homogeneous_apply_le_self",
"depth": 1,
"n_commands": 0,
"n_lines": 5,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n calc\n |(_root_.Spec.ScalarAffineTransition.apply { a := a, b := 0 } h)| ≤ 1 * |h| :=\n abs_homogeneo... | [
{
"name": "abs_homogeneous_apply_le",
"text": "/--\nA homogeneous affine transition over `ℝ` is Lipschitz with factor `ρ` whenever `|a| ≤ ρ`.\n\nThis is the one-channel stability lemma used to lift diagonal SSMs into contraction proofs.\n-/\ntheorem abs_homogeneous_apply_le (a ρ h : ℝ) (ha : |a| ≤ ρ) :\n ... | [
{
"name": "abs_homogeneous_apply_le_self",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 9,
"n_chars": 383,
"n_subproofs": 0,
"n_tactics": 5,
"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.Spec.Layers.SelectiveScan
import Mathlib.Algebra.Ring.Basic
/-!
# Proofs for affine selective scan
The Mamba/S4 scan theorem is an algebra theorem about affine maps. A seq... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Spec.Layers.SelectiveScan
import Mathlib.Algebra.Ring.Basic
/-!
# Proofs for affine selective scan
The Mamba/S4 scan theorem is an algebra theorem about affine maps. A seq... | @@ -203,9 +203,26 @@
| cons tr rest ih =>
simp [_root_.Spec.diagonalSelectiveScan, ih]
+/--
+A homogeneous affine transition over `ℝ` is Lipschitz with factor `ρ` whenever `|a| ≤ ρ`.
+
+This is the one-channel stability lemma used to lift diagonal SSMs into contraction proofs.
+-/
+theorem abs_homogeneous_a... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_1fa61359aad5_0 | c69ad86816dc9017 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32NoNaN.lean | IEEEExec32NoNaN | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "isNaN_roundDyadicDown_eq_false",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hm0 : d.mant == 0\n · -- signed zero\n cases hs : d.sign <;> simp [roundDyadicDown, hm0, hs] <... | [
{
"name": "isNaN_roundDyadicPosDown_eq_false",
"text": "/-- `roundDyadicPosDown` never produces a NaN. -/\ntheorem isNaN_roundDyadicPosDown_eq_false (mant : Nat) (exp : Int) :\n isNaN (roundDyadicPosDown mant exp) = false := by\n obtain ⟨d, hd⟩ := IEEE32Exec.toDyadic?_roundDyadicPosDown_some (mant := ma... | [
{
"name": "isNaN_roundDyadicDown_eq_false",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 21,
"n_chars": 967,
"n_subproofs": 3,
"n_tactics": 20,
"cyclomatic": 6,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.MinMaxERealSoundness
public import NN.Floats.Interval.IEEEExec32
/-!
# Non-NaN helpers for `IEEE32... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.MinMaxERealSoundness
public import NN.Floats.Interval.IEEEExec32
/-!
# Non-NaN helpers for `IEEE32... | @@ -40,6 +40,12 @@
finite, nonzero-denominator path.
-/
+/-- `roundDyadicPosDown` never produces a NaN. -/
+theorem isNaN_roundDyadicPosDown_eq_false (mant : Nat) (exp : Int) :
+ isNaN (roundDyadicPosDown mant exp) = false := by
+ obtain ⟨d, hd⟩ := IEEE32Exec.toDyadic?_roundDyadicPosDown_some (mant := mant) (ex... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_1fa61359aad5_1 | 9e8b144a4da2de38 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32NoNaN.lean | IEEEExec32NoNaN | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "isNaN_roundDyadicDown_eq_false",
"depth": 1,
"n_commands": 0,
"n_lines": 17,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n by_cases hm0 : d.mant == 0\n · -- signed zero\n cases hs : d.sign <;> simp [roundDyadicDown, hm0, hs] <... | [
{
"name": "isNaN_roundDyadicPosDown_eq_false",
"text": "/-- `roundDyadicPosDown` never produces a NaN. -/\ntheorem isNaN_roundDyadicPosDown_eq_false (mant : Nat) (exp : Int) :\n isNaN (roundDyadicPosDown mant exp) = false := by\n obtain ⟨d, hd⟩ := IEEE32Exec.toDyadic?_roundDyadicPosDown_some (mant := ma... | [
{
"name": "isNaN_roundDyadicUp_eq_false",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 28,
"n_chars": 1205,
"n_subproofs": 3,
"n_tactics": 19,
"cyclomatic": 6,
"n_automation": 6,
"n_rewrites": 0,
"n_structural": 3,
"automation_only": false,
... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.MinMaxERealSoundness
public import NN.Floats.Interval.IEEEExec32
/-!
# Non-NaN helpers for `IEEE32... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.MinMaxERealSoundness
public import NN.Floats.Interval.IEEEExec32
/-!
# Non-NaN helpers for `IEEE32... | @@ -40,6 +40,12 @@
finite, nonzero-denominator path.
-/
+/-- `roundDyadicPosDown` never produces a NaN. -/
+theorem isNaN_roundDyadicPosDown_eq_false (mant : Nat) (exp : Int) :
+ isNaN (roundDyadicPosDown mant exp) = false := by
+ obtain ⟨d, hd⟩ := IEEE32Exec.toDyadic?_roundDyadicPosDown_some (mant := mant) (ex... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_1fa61359aad5_2 | 8e17823bd7af82c0 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32NoNaN.lean | IEEEExec32NoNaN | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "isNaN_minimum_eq_false_of_isNaN_eq_false",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hchoose : chooseNaN2 x y = none := chooseNaN2_none_of_not_isNaN x y hx hy\n have hcmp_ne : ... | [
{
"name": "compare_ne_none_of_isNaN_eq_false",
"text": "/--\nIf neither input is NaN, then IEEE `compare` is never unordered (`none`).\n\nThis is a small bridge lemma used to reason about `minimum`/`maximum`, which dispatch on the\n`compare` result and treat the unordered case as NaN-propagation.\n-/\ntheor... | [
{
"name": "isNaN_minimum_eq_false_of_isNaN_eq_false",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 34,
"n_chars": 1196,
"n_subproofs": 2,
"n_tactics": 23,
"cyclomatic": 3,
"n_automation": 8,
"n_rewrites": 1,
"n_structural": 3,
"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.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.MinMaxERealSoundness
public import NN.Floats.Interval.IEEEExec32
/-!
# Non-NaN helpers for `IEEE32... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.MinMaxERealSoundness
public import NN.Floats.Interval.IEEEExec32
/-!
# Non-NaN helpers for `IEEE32... | @@ -41,6 +41,62 @@
-/
/--
+If neither input is NaN, then IEEE `compare` is never unordered (`none`).
+
+This is a small bridge lemma used to reason about `minimum`/`maximum`, which dispatch on the
+`compare` result and treat the unordered case as NaN-propagation.
+-/
+theorem compare_ne_none_of_isNaN_eq_false (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_1fa61359aad5_3 | 03d0e123b40b5c1b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32NoNaN.lean | IEEEExec32NoNaN | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "isNaN_minimum_eq_false_of_isNaN_eq_false",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hchoose : chooseNaN2 x y = none := chooseNaN2_none_of_not_isNaN x y hx hy\n have hcmp_ne : ... | [
{
"name": "compare_ne_none_of_isNaN_eq_false",
"text": "/--\nIf neither input is NaN, then IEEE `compare` is never unordered (`none`).\n\nThis is a small bridge lemma used to reason about `minimum`/`maximum`, which dispatch on the\n`compare` result and treat the unordered case as NaN-propagation.\n-/\ntheor... | [
{
"name": "isNaN_maximum_eq_false_of_isNaN_eq_false",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 34,
"n_chars": 1200,
"n_subproofs": 2,
"n_tactics": 23,
"cyclomatic": 3,
"n_automation": 8,
"n_rewrites": 1,
"n_structural": 3,
"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.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.MinMaxERealSoundness
public import NN.Floats.Interval.IEEEExec32
/-!
# Non-NaN helpers for `IEEE32... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.MinMaxERealSoundness
public import NN.Floats.Interval.IEEEExec32
/-!
# Non-NaN helpers for `IEEE32... | @@ -41,6 +41,62 @@
-/
/--
+If neither input is NaN, then IEEE `compare` is never unordered (`none`).
+
+This is a small bridge lemma used to reason about `minimum`/`maximum`, which dispatch on the
+`compare` result and treat the unordered case as NaN-propagation.
+-/
+theorem compare_ne_none_of_isNaN_eq_false (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_1fa61359aad5_4 | 115b3a26f22f6cde | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32NoNaN.lean | IEEEExec32NoNaN | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "isNaN_minimum_eq_false_of_isNaN_eq_false",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hchoose : chooseNaN2 x y = none := chooseNaN2_none_of_not_isNaN x y hx hy\n have hcmp_ne : ... | [
{
"name": "compare_ne_none_of_isNaN_eq_false",
"text": "/--\nIf neither input is NaN, then IEEE `compare` is never unordered (`none`).\n\nThis is a small bridge lemma used to reason about `minimum`/`maximum`, which dispatch on the\n`compare` result and treat the unordered case as NaN-propagation.\n-/\ntheor... | [
{
"name": "toEReal_min4_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 17,
"n_chars": 854,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.MinMaxERealSoundness
public import NN.Floats.Interval.IEEEExec32
/-!
# Non-NaN helpers for `IEEE32... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.MinMaxERealSoundness
public import NN.Floats.Interval.IEEEExec32
/-!
# Non-NaN helpers for `IEEE32... | @@ -41,6 +41,62 @@
-/
/--
+If neither input is NaN, then IEEE `compare` is never unordered (`none`).
+
+This is a small bridge lemma used to reason about `minimum`/`maximum`, which dispatch on the
+`compare` result and treat the unordered case as NaN-propagation.
+-/
+theorem compare_ne_none_of_isNaN_eq_false (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_1fa61359aad5_5 | 6a515429359d6673 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/Interval/IEEEExec32NoNaN.lean | IEEEExec32NoNaN | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 4 | 2 | [
{
"theorem_name": "isNaN_minimum_eq_false_of_isNaN_eq_false",
"depth": 1,
"n_commands": 0,
"n_lines": 24,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hchoose : chooseNaN2 x y = none := chooseNaN2_none_of_not_isNaN x y hx hy\n have hcmp_ne : ... | [
{
"name": "compare_ne_none_of_isNaN_eq_false",
"text": "/--\nIf neither input is NaN, then IEEE `compare` is never unordered (`none`).\n\nThis is a small bridge lemma used to reason about `minimum`/`maximum`, which dispatch on the\n`compare` result and treat the unordered case as NaN-propagation.\n-/\ntheor... | [
{
"name": "toEReal_max4_eq",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 15,
"n_chars": 817,
"n_subproofs": 2,
"n_tactics": 9,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 2,
"n_structural": 0,
"automation_only": false,
"max_nestin... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.MinMaxERealSoundness
public import NN.Floats.Interval.IEEEExec32
/-!
# Non-NaN helpers for `IEEE32... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
public import NN.Floats.IEEEExec.MinMaxERealSoundness
public import NN.Floats.Interval.IEEEExec32
/-!
# Non-NaN helpers for `IEEE32... | @@ -41,6 +41,62 @@
-/
/--
+If neither input is NaN, then IEEE `compare` is never unordered (`none`).
+
+This is a small bridge lemma used to reason about `minimum`/`maximum`, which dispatch on the
+`compare` result and treat the unordered case as NaN-propagation.
+-/
+theorem compare_ne_none_of_isNaN_eq_false (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_109f9b157739_0 | 4d043c965f85e8a2 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/RuntimeApprox/Graph/LinkAutogradAlgebra.lean | LinkAutogradAlgebra | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "backpropRuntime_of_toGraphData",
"depth": 1,
"n_commands": 0,
"n_lines": 12,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n intro ss g xR seedR\n induction g with\n | nil =>\n simp [toGraphData, GraphData.backpropCtx,\n ... | [
{
"name": "evalRuntime_of_toGraphData",
"text": "/--\nErasing a `RevGraph` into executable `GraphData` preserves the runtime **forward** semantics.\n\nInformally: if you forget the spec and bound metadata and keep only the runtime closures, you still\nevaluate to the same runtime context.\n-/\ntheorem evalR... | [
{
"name": "backpropRuntime_of_toGraphData",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 29,
"n_chars": 1313,
"n_subproofs": 1,
"n_tactics": 12,
"cyclomatic": 2,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 2,
"automation_only": false... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Algebra.Soundness
public import NN.Proofs.RuntimeApprox.Graph.BackwardApprox
/-!
# Link `Proofs.RuntimeApprox.RevGraph` to the executable `Proofs.Autogr... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.Tape.Algebra.Soundness
public import NN.Proofs.RuntimeApprox.Graph.BackwardApprox
/-!
# Link `Proofs.RuntimeApprox.RevGraph` to the executable `Proofs.Autogr... | @@ -81,6 +81,31 @@
node)
/--
+Erasing a `RevGraph` into executable `GraphData` preserves the runtime **forward** semantics.
+
+Informally: if you forget the spec and bound metadata and keep only the runtime closures, you still
+evaluate to the same runtime context.
+-/
+theorem evalRuntime_of_toGraphData {Γ : L... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_9c01ef133add_0 | 23531f3947827e26 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Tensor/Basic/Algebra.lean | Algebra | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 2 | 1 | [
{
"theorem_name": "mat_vec_linear_combination",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- Combine mat_vec_add and mat_vec_scale\n rw [mat_vec_add, mat_vec_scale, mat_vec_scale]",
"n_chars": 95,
... | [
{
"name": "mat_vec_add",
"text": "/-- Linearity of matrix-vector multiplication in the vector argument (addition). -/\ntheorem mat_vec_add {m n : Nat}\n (W : Tensor ℝ (.dim m (.dim n .scalar)))\n (x y : Tensor ℝ (.dim n .scalar)) :\n matVecMulSpec W (addSpec x y) =\n addSpec (matVecMulSpec W x) (matVecM... | [
{
"name": "mat_vec_linear_combination",
"fan_in": 0,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 11,
"n_chars": 472,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.BoundsNorms
/-!
# Tensor Algebra Lemmas
This file collects foundational algebraic lemmas for `Spec.Tensor`: extensionality, map/fold
rewrites, and point... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Tensor.Basic.BoundsNorms
/-!
# Tensor Algebra Lemmas
This file collects foundational algebraic lemmas for `Spec.Tensor`: extensionality, map/fold
rewrites, and point... | @@ -23,6 +23,37 @@
open Tensor
open scoped BigOperators
+/-- Linearity of matrix-vector multiplication in the vector argument (addition). -/
+theorem mat_vec_add {m n : Nat}
+ (W : Tensor ℝ (.dim m (.dim n .scalar)))
+ (x y : Tensor ℝ (.dim n .scalar)) :
+ matVecMulSpec W (addSpec x y) =
+ addSpec (matVecMulSpe... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_88545f8e1bd3_0 | ce38f5384d4acc01 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Proofs/Autograd/Tape/Nodes/Context.lean | Context | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 1 | 1 | [
{
"theorem_name": "inner_get_single",
"depth": 1,
"n_commands": 0,
"n_lines": 23,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- unfold `get`/`single` and reduce to the raw statement + cast isometries\n let hsz : Shape.size (Γ.get id... | [
{
"name": "inner_getRaw_singleRaw",
"text": "/--\nAdjointness of raw projection/injection: `⟪x, singleRaw i v⟫ = ⟪getRaw i x, v⟫`.\n\nThis is the vectorized counterpart of the “one-hot cotangent” principle used in tape soundness.\n-/\ntheorem inner_getRaw_singleRaw :\n ∀ {Γ : List Shape} (i : Fin Γ.lengt... | [
{
"name": "inner_get_single",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 28,
"n_chars": 1398,
"n_subproofs": 3,
"n_tactics": 19,
"cyclomatic": 1,
"n_automation": 4,
"n_rewrites": 0,
"n_structural": 1,
"automation_only": false,
"max_nes... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Elementwise
public import NN.Proofs.Autograd.FDeriv.LogSoftmax
public import NN.Proofs.Autograd.FDeriv.Softmax
public import NN.Proofs.Autograd.Tape.Co... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.Proofs.Autograd.FDeriv.Elementwise
public import NN.Proofs.Autograd.FDeriv.LogSoftmax
public import NN.Proofs.Autograd.FDeriv.Softmax
public import NN.Proofs.Autograd.Tape.Co... | @@ -113,6 +113,101 @@
(vecOfFun (n := Shape.size s) fun _ => (0 : ℝ))
(singleRaw (Γ := ss) ⟨k, Nat.lt_of_succ_lt_succ hk⟩ v)
+/--
+Adjointness of raw projection/injection: `⟪x, singleRaw i v⟫ = ⟪getRaw i x, v⟫`.
+
+This is the vectorized counterpart of the “one-hot cotangent” principle used in tape ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b023d9281a22_0 | e6c9be015e2f661d | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Models/Mlp.lean | Mlp | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "relu_relax_vector_pointwise_upper_real",
"depth": 1,
"n_commands": 0,
"n_lines": 28,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": "\n by\n classical\n cases lo with\n | dim flo =>\n cases hi with\n | dim fhi =>\n cases x w... | [
{
"name": "relu_relax_scalar_upper_real",
"text": "/--\nScalar ReLU relaxation soundness over `ℝ` (upper bound).\n\nIf `x ∈ [l, u]` and `rp := ReLU.relax_scalar l u`, then:\n`relu(x) <= rp.slope * x + rp.bias`.\n\nThis is the standard CROWN/DeepPoly upper chord construction (arXiv:1811.00866).\n-/\ntheorem ... | [
{
"name": "relu_relax_vector_pointwise_upper_real",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 45,
"n_chars": 1795,
"n_subproofs": 4,
"n_tactics": 23,
"cyclomatic": 7,
"n_automation": 2,
"n_rewrites": 0,
"n_structural": 8,
"automation_only... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Core
public import NN.MLTheory.CROWN.Runtime.Ops
public import NN.Spec.Core.Context
public import NN.Spec.Core.Tensor
public import NN.Spec.Core.TensorOps
publ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Core
public import NN.MLTheory.CROWN.Runtime.Ops
public import NN.Spec.Core.Context
public import NN.Spec.Core.Tensor
public import NN.Spec.Core.TensorOps
publ... | @@ -421,6 +421,76 @@
open NN.MLTheory.CROWN
/--
+Scalar ReLU relaxation soundness over `ℝ` (upper bound).
+
+If `x ∈ [l, u]` and `rp := ReLU.relax_scalar l u`, then:
+`relu(x) <= rp.slope * x + rp.bias`.
+
+This is the standard CROWN/DeepPoly upper chord construction (arXiv:1811.00866).
+-/
+theorem relu_relax_scal... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_b023d9281a22_1 | 44390c2fac2e7843 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Models/Mlp.lean | Mlp | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "bound_ibp_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 50,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n classical\n -- Unfold bound_ibp and forward\n -- Step 1: z1 ∈ IBP.linear(hiddenWeight, xB, hiddenBias)\n -- Bias box is... | [
{
"name": "ibp_relu_sound_real",
"text": "private theorem ibp_relu_sound_real {n : Nat}\n (zB : Box ℝ (.dim n .scalar))\n (z : Tensor ℝ (.dim n .scalar))\n (hz : Box.contains (α:=ℝ) zB z) :\n Box.contains (α:=ℝ) (IBP.relu (α:=ℝ) zB) (Activation.reluSpec (α:=ℝ) z) := by\n classical\n -- Reduce big Box.... | [
{
"name": "bound_ibp_sound",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 58,
"n_chars": 2887,
"n_subproofs": 5,
"n_tactics": 40,
"cyclomatic": 5,
"n_automation": 3,
"n_rewrites": 0,
"n_structural": 9,
"automation_only": false,
"max_nest... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Core
public import NN.MLTheory.CROWN.Runtime.Ops
public import NN.Spec.Core.Context
public import NN.Spec.Core.Tensor
public import NN.Spec.Core.TensorOps
publ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Core
public import NN.MLTheory.CROWN.Runtime.Ops
public import NN.Spec.Core.Context
public import NN.Spec.Core.Tensor
public import NN.Spec.Core.TensorOps
publ... | @@ -936,6 +936,51 @@
simpa [Tensor.toScalar] using h2'
/- Helper: soundness of IBP.relu over ℝ -/
+private theorem ibp_relu_sound_real {n : Nat}
+ (zB : Box ℝ (.dim n .scalar))
+ (z : Tensor ℝ (.dim n .scalar))
+ (hz : Box.contains (α:=ℝ) zB z) :
+ Box.contains (α:=ℝ) (IBP.relu (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_b023d9281a22_2 | b957a54ddac857bd | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/MLTheory/CROWN/Models/Mlp.lean | Mlp | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 3 | 1 | [
{
"theorem_name": "bound_affine_sound",
"depth": 1,
"n_commands": 0,
"n_lines": 3,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `boundAffine` delegates to pure IBP bounds in this module.\n simpa [boundAffine] using bound_ibp_sound (net := net) ... | [
{
"name": "bound_ibp_sound",
"text": "/-- Soundness of pure IBP bounds for a 2-layer MLP over `ℝ`. -/\ntheorem bound_ibp_sound {inDim hidDim outDim : Nat}\n (net : TwoLayerMLP ℝ inDim hidDim outDim)\n (xB : Box ℝ (.dim inDim .scalar))\n (x : Tensor ℝ (.dim inDim .scalar))\n (hx : Box.contains (α:=ℝ) xB ... | [
{
"name": "bound_affine_sound",
"fan_in": 0,
"n_deps_direct": 1,
"n_deps_transitive": 2,
"n_lines": 16,
"n_chars": 654,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nest... | 2 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Core
public import NN.MLTheory.CROWN.Runtime.Ops
public import NN.Spec.Core.Context
public import NN.Spec.Core.Tensor
public import NN.Spec.Core.TensorOps
publ... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import NN.MLTheory.CROWN.Core
public import NN.MLTheory.CROWN.Runtime.Ops
public import NN.Spec.Core.Context
public import NN.Spec.Core.Tensor
public import NN.Spec.Core.TensorOps
publ... | @@ -981,6 +981,63 @@
have : max x 0 ≤ max u 0 := max_le_max hxhi (le_rfl)
simpa [ite_gt_zero_eq_max, Activation.Math.reluSpec] using this
+/-- Soundness of pure IBP bounds for a 2-layer MLP over `ℝ`. -/
+theorem bound_ibp_sound {inDim hidDim outDim : Nat}
+ (net : TwoLayerMLP 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_d86ab6b5f148_0 | 7f457ac0cecc1c48 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DivDirectedRoundingSoundness.lean | DivDirectedRoundingSoundness | 0 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "neural_bpow_neg_ofNat_div",
"depth": 1,
"n_commands": 0,
"n_lines": 2,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n rw [neuralBpow.neg_exp, neural_bpow_ofNat_div]",
"n_chars": 52,
"n_subproofs": 0,
"n_tactics": 2,
... | [
{
"name": "neural_bpow_ofNat_div",
"text": "private lemma neural_bpow_ofNat_div (k : Nat) :\n neuralBpow binaryRadix (Int.ofNat k) = (2 : ℝ) ^ k := by\n simp [TorchLean.Floats.neuralBpow, binaryRadix, NeuralRadix.toReal]\n\n",
"fan_in": 1,
"n_lines": 5,
"n_chars": 182,
"n_subproofs": 0,
... | [
{
"name": "neural_bpow_neg_ofNat_div",
"fan_in": 2,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 8,
"n_chars": 228,
"n_subproofs": 0,
"n_tactics": 2,
"cyclomatic": 1,
"n_automation": 0,
"n_rewrites": 1,
"n_structural": 0,
"automation_only": false,
"m... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | @@ -49,8 +49,13 @@
/-! ## Local helpers -/
+private lemma neural_bpow_ofNat_div (k : Nat) :
+ neuralBpow binaryRadix (Int.ofNat k) = (2 : ℝ) ^ k := by
+ simp [TorchLean.Floats.neuralBpow, binaryRadix, NeuralRadix.toReal]
+
private lemma neural_bpow_neg_ofNat_div (k : Nat) :
- neuralBpow binaryRadix (-(Int... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d86ab6b5f148_1 | 3a9fb5ada8b66dc7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DivDirectedRoundingSoundness.lean | DivDirectedRoundingSoundness | 1 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "ratUpperMant_mul_ge",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `ratUpperMant` is `ceil( (num*2^K) / den )`.\n simpa [ratUpperMant] using\n (quotCeil_mul_ge (num := Nat.shiftLe... | [
{
"name": "quotCeil_mul_ge",
"text": "private lemma quotCeil_mul_ge (num den : Nat) (hden : den ≠ 0) :\n num ≤ quotCeil num den * den := by\n classical\n have hden' : (den == 0) = false := (beq_eq_false_iff_ne).2 hden\n -- Work with the Euclidean decomposition `num = q*den + r`.\n set q : Nat := num ... | [
{
"name": "ratUpperMant_mul_ge",
"fan_in": 1,
"n_deps_direct": 1,
"n_deps_transitive": 1,
"n_lines": 7,
"n_chars": 307,
"n_subproofs": 0,
"n_tactics": 3,
"cyclomatic": 1,
"n_automation": 1,
"n_rewrites": 0,
"n_structural": 0,
"automation_only": true,
"max_nest... | 1 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | @@ -49,8 +49,50 @@
/-! ## Local helpers -/
+private lemma quotCeil_mul_ge (num den : Nat) (hden : den ≠ 0) :
+ num ≤ quotCeil num den * den := by
+ classical
+ have hden' : (den == 0) = false := (beq_eq_false_iff_ne).2 hden
+ -- Work with the Euclidean decomposition `num = q*den + r`.
+ set q : Nat := num ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d86ab6b5f148_2 | a0f8bda54cfe97f6 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DivDirectedRoundingSoundness.lean | DivDirectedRoundingSoundness | 2 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 2 | [
{
"theorem_name": "ratLower_le",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hdenpos : (0 : ℝ) < (den : ℝ) := by exact_mod_cast Nat.pos_of_ne_zero hden\n have hpowpos : (0 : ℝ) < (2 : ℝ) ^ ratAppro... | [
{
"name": "shiftLeft_cast",
"text": "private lemma shiftLeft_cast (n k : Nat) :\n ((Nat.shiftLeft n k : Nat) : ℝ) = (n : ℝ) * (2 : ℝ) ^ k := by\n simp [Nat.shiftLeft_eq, Nat.cast_mul, Nat.cast_pow]\n\n",
"fan_in": 2,
"n_lines": 5,
"n_chars": 170,
"n_subproofs": 0,
"n_tactics": 2,
... | [
{
"name": "ratLower_le",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 2,
"n_lines": 45,
"n_chars": 2649,
"n_subproofs": 10,
"n_tactics": 38,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 5,
"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.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | @@ -49,6 +49,10 @@
/-! ## Local helpers -/
+private lemma shiftLeft_cast (n k : Nat) :
+ ((Nat.shiftLeft n k : Nat) : ℝ) = (n : ℝ) * (2 : ℝ) ^ k := by
+ simp [Nat.shiftLeft_eq, Nat.cast_mul, Nat.cast_pow]
+
private lemma ratLowerMant_mul_le (num den : Nat) :
ratLowerMant num den * den ≤ Nat.shiftLeft nu... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d86ab6b5f148_3 | 4ec356557b954ea7 | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DivDirectedRoundingSoundness.lean | DivDirectedRoundingSoundness | 3 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "ratUpperMant_mul_ge",
"depth": 1,
"n_commands": 0,
"n_lines": 4,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n -- `ratUpperMant` is `ceil( (num*2^K) / den )`.\n simpa [ratUpperMant] using\n (quotCeil_mul_ge (num := Nat.shiftLe... | [
{
"name": "quotCeil_mul_ge",
"text": "private lemma quotCeil_mul_ge (num den : Nat) (hden : den ≠ 0) :\n num ≤ quotCeil num den * den := by\n classical\n have hden' : (den == 0) = false := (beq_eq_false_iff_ne).2 hden\n -- Work with the Euclidean decomposition `num = q*den + r`.\n set q : Nat := num ... | [
{
"name": "le_ratUpper",
"fan_in": 2,
"n_deps_direct": 2,
"n_deps_transitive": 3,
"n_lines": 47,
"n_chars": 2581,
"n_subproofs": 10,
"n_tactics": 40,
"cyclomatic": 1,
"n_automation": 7,
"n_rewrites": 0,
"n_structural": 6,
"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 Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | @@ -53,8 +53,50 @@
((Nat.shiftLeft n k : Nat) : ℝ) = (n : ℝ) * (2 : ℝ) ^ k := by
simp [Nat.shiftLeft_eq, Nat.cast_mul, Nat.cast_pow]
+private lemma quotCeil_mul_ge (num den : Nat) (hden : den ≠ 0) :
+ num ≤ quotCeil num den * den := by
+ classical
+ have hden' : (den == 0) = false := (beq_eq_false_iff_ne... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d86ab6b5f148_4 | 929043cf9b4c340b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DivDirectedRoundingSoundness.lean | DivDirectedRoundingSoundness | 4 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "ratLower_le",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hdenpos : (0 : ℝ) < (den : ℝ) := by exact_mod_cast Nat.pos_of_ne_zero hden\n have hpowpos : (0 : ℝ) < (2 : ℝ) ^ ratAppro... | [
{
"name": "ratLowerMant_mul_le",
"text": "private lemma ratLowerMant_mul_le (num den : Nat) :\n ratLowerMant num den * den ≤ Nat.shiftLeft num ratApproxShift := by\n -- `ratLowerMant = floor( (num*2^K) / den )` so `floor * den ≤ num*2^K`.\n simpa [ratLowerMant] using Nat.div_mul_le_self (Nat.shiftLeft ... | [
{
"name": "toEReal_roundRatDown_le",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 8,
"n_lines": 79,
"n_chars": 4247,
"n_subproofs": 17,
"n_tactics": 68,
"cyclomatic": 3,
"n_automation": 12,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
... | 8 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | @@ -102,6 +102,11 @@
/-! ## Dyadic enclosure of `num/den` at scale `2^ratApproxShift` -/
+private lemma ratLowerMant_mul_le (num den : Nat) :
+ ratLowerMant num den * den ≤ Nat.shiftLeft num ratApproxShift := by
+ -- `ratLowerMant = floor( (num*2^K) / den )` so `floor * den ≤ num*2^K`.
+ simpa [ratLowerMant] ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d86ab6b5f148_5 | 24b4ca949490704b | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DivDirectedRoundingSoundness.lean | DivDirectedRoundingSoundness | 5 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "ratLower_le",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hdenpos : (0 : ℝ) < (den : ℝ) := by exact_mod_cast Nat.pos_of_ne_zero hden\n have hpowpos : (0 : ℝ) < (2 : ℝ) ^ ratAppro... | [
{
"name": "ratLowerMant_mul_le",
"text": "private lemma ratLowerMant_mul_le (num den : Nat) :\n ratLowerMant num den * den ≤ Nat.shiftLeft num ratApproxShift := by\n -- `ratLowerMant = floor( (num*2^K) / den )` so `floor * den ≤ num*2^K`.\n simpa [ratLowerMant] using Nat.div_mul_le_self (Nat.shiftLeft ... | [
{
"name": "toEReal_roundRatUp_ge",
"fan_in": 1,
"n_deps_direct": 3,
"n_deps_transitive": 8,
"n_lines": 86,
"n_chars": 4340,
"n_subproofs": 17,
"n_tactics": 70,
"cyclomatic": 3,
"n_automation": 12,
"n_rewrites": 0,
"n_structural": 4,
"automation_only": false,
"... | 8 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | @@ -102,6 +102,11 @@
/-! ## Dyadic enclosure of `num/den` at scale `2^ratApproxShift` -/
+private lemma ratLowerMant_mul_le (num den : Nat) :
+ ratLowerMant num den * den ≤ Nat.shiftLeft num ratApproxShift := by
+ -- `ratLowerMant = floor( (num*2^K) / den )` so `floor * den ≤ num*2^K`.
+ simpa [ratLowerMant] ... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
ablate_d86ab6b5f148_6 | 14cb5b56f488221c | lean | lean | github.com/lean-dojo/TorchLean | a0c5bdf2bb02c25b270a2c89a12ad2335c86c530 | NN/Floats/IEEEExec/DivDirectedRoundingSoundness.lean | DivDirectedRoundingSoundness | 6 | lemma_delete | null | null | false | 0.5 | 1 | 1 | false | 0 | inf | 0 | inf | 42 | 12 | 1 | [
{
"theorem_name": "le_ratUpper",
"depth": 1,
"n_commands": 0,
"n_lines": 42,
"is_leaf": true,
"centrality": 0,
"method": "deleted-dep",
"proof_text": " by\n have hdenpos : (0 : ℝ) < (den : ℝ) := by exact_mod_cast Nat.pos_of_ne_zero hden\n have hpowpos : (0 : ℝ) < (2 : ℝ) ^ ratAppro... | [
{
"name": "ratUpperMant_mul_ge",
"text": "private lemma ratUpperMant_mul_ge (num den : Nat) (hden : den ≠ 0) :\n Nat.shiftLeft num ratApproxShift ≤ ratUpperMant num den * den := by\n -- `ratUpperMant` is `ceil( (num*2^K) / den )`.\n simpa [ratUpperMant] using\n (quotCeil_mul_ge (num := Nat.shiftLeft... | [
{
"name": "toEReal_divDown_le",
"fan_in": 0,
"n_deps_direct": 3,
"n_deps_transitive": 11,
"n_lines": 134,
"n_chars": 7620,
"n_subproofs": 32,
"n_tactics": 115,
"cyclomatic": 15,
"n_automation": 15,
"n_rewrites": 6,
"n_structural": 13,
"automation_only": false,
... | 11 | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | /-
Copyright (c) 2026 TorchLean
Released under MIT license as described in the file LICENSE.
Authors: TorchLean Team
-/
module
public import Mathlib.Data.Real.Basic
public import NN.Floats.IEEEExec.BridgeFP32Total
public import NN.Floats.IEEEExec.RatScaling
public import NN.Floats.IEEEExec.DirectedRoundingSoundness
p... | @@ -118,6 +118,12 @@
-- `ratLowerMant = floor( (num*2^K) / den )` so `floor * den ≤ num*2^K`.
simpa [ratLowerMant] using Nat.div_mul_le_self (Nat.shiftLeft num ratApproxShift) den
+private lemma ratUpperMant_mul_ge (num den : Nat) (hden : den ≠ 0) :
+ Nat.shiftLeft num ratApproxShift ≤ ratUpperMant num den *... | {
"repo": "TorchLean",
"git_repo": "github.com/lean-dojo/TorchLean",
"revision": "a0c5bdf2bb02c25b270a2c89a12ad2335c86c530",
"lean_toolchain": "leanprover/lean4:v4.31.0",
"proof_assistant": "lean",
"ablator": "ablators/lean (corollary-delete-lemmas-leaves-all)",
"ablator_flags": [
"--corollary-delete-... |
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