zipfit/leandojo_benchmark_4_corpus · Datasets at Hugging Face

path stringlengths 12 84	imports sequencelengths 0 4.45k	premises listlengths 0 625
Mathlib/Data/Rbtree/Find.lean	[ "Mathlib/Mathport/Rename.lean", ".lake/packages/lean4/src/lean/Init.lean" ]	[]
Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean	[ "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean", "Mathlib/Combinatorics/SimpleGraph/Basic.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Data/Set/Finite.lean", "Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean" ]	[ { "full_name": "SimpleGraph.IsSRGWith", "code": "structure IsSRGWith (n k ℓ μ : ℕ) : Prop where\n card : Fintype.card V = n\n regular : G.IsRegularOfDegree k\n of_adj : ∀ v w : V, G.Adj v w → Fintype.card (G.commonNeighbors v w) = ℓ\n of_not_adj : Pairwise fun v w => ¬G.Adj v w → Fintype.card (G.commonNeighbors v w) = μ", "start": [ 43, 1 ], "end": [ 53, 89 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.bot_strongly_regular", "code": "theorem bot_strongly_regular : (⊥ : SimpleGraph V).IsSRGWith (Fintype.card V) 0 ℓ 0 where", "start": [ 59, 1 ], "end": [ 68, 31 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.top", "code": "theorem IsSRGWith.top :\n (⊤ : SimpleGraph V).IsSRGWith (Fintype.card V) (Fintype.card V - 1) (Fintype.card V - 2) μ where", "start": [ 71, 1 ], "end": [ 80, 68 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.card_neighborFinset_union_eq", "code": "theorem IsSRGWith.card_neighborFinset_union_eq {v w : V} (h : G.IsSRGWith n k ℓ μ) :\n (G.neighborFinset v ∪ G.neighborFinset w).card =\n 2 * k - Fintype.card (G.commonNeighbors v w)", "start": [ 84, 1 ], "end": [ 95, 40 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.card_neighborFinset_union_of_not_adj", "code": "theorem IsSRGWith.card_neighborFinset_union_of_not_adj {v w : V} (h : G.IsSRGWith n k ℓ μ)\n (hne : v ≠ w) (ha : ¬G.Adj v w) :\n (G.neighborFinset v ∪ G.neighborFinset w).card = 2 * k - μ", "start": [ 99, 1 ], "end": [ 106, 39 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.card_neighborFinset_union_of_adj", "code": "theorem IsSRGWith.card_neighborFinset_union_of_adj {v w : V} (h : G.IsSRGWith n k ℓ μ)\n (ha : G.Adj v w) : (G.neighborFinset v ∪ G.neighborFinset w).card = 2 * k - ℓ", "start": [ 110, 1 ], "end": [ 113, 39 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.compl_neighborFinset_sdiff_inter_eq", "code": "theorem compl_neighborFinset_sdiff_inter_eq {v w : V} :\n (G.neighborFinset v)ᶜ \\ {v} ∩ ((G.neighborFinset w)ᶜ \\ {w}) =\n ((G.neighborFinset v)ᶜ ∩ (G.neighborFinset w)ᶜ) \\ ({w} ∪ {v})", "start": [ 117, 1 ], "end": [ 122, 57 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.sdiff_compl_neighborFinset_inter_eq", "code": "theorem sdiff_compl_neighborFinset_inter_eq {v w : V} (h : G.Adj v w) :\n ((G.neighborFinset v)ᶜ ∩ (G.neighborFinset w)ᶜ) \\ ({w} ∪ {v}) =\n (G.neighborFinset v)ᶜ ∩ (G.neighborFinset w)ᶜ", "start": [ 125, 1 ], "end": [ 134, 19 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.compl_is_regular", "code": "theorem IsSRGWith.compl_is_regular (h : G.IsSRGWith n k ℓ μ) :\n Gᶜ.IsRegularOfDegree (n - k - 1)", "start": [ 137, 1 ], "end": [ 140, 24 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl", "code": "theorem IsSRGWith.card_commonNeighbors_eq_of_adj_compl (h : G.IsSRGWith n k ℓ μ) {v w : V}\n (ha : Gᶜ.Adj v w) : Fintype.card (Gᶜ.commonNeighbors v w) = n - (2 * k - μ) - 2", "start": [ 144, 1 ], "end": [ 156, 55 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl", "code": "theorem IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl (h : G.IsSRGWith n k ℓ μ) {v w : V}\n (hn : v ≠ w) (hna : ¬Gᶜ.Adj v w) :\n Fintype.card (Gᶜ.commonNeighbors v w) = n - (2 * k - ℓ)", "start": [ 160, 1 ], "end": [ 168, 87 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.compl", "code": "theorem IsSRGWith.compl (h : G.IsSRGWith n k ℓ μ) :\n Gᶜ.IsSRGWith n (n - k - 1) (n - (2 * k - μ) - 2) (n - (2 * k - ℓ)) where", "start": [ 172, 1 ], "end": [ 178, 86 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.param_eq", "code": "theorem IsSRGWith.param_eq (h : G.IsSRGWith n k ℓ μ) (hn : 0 < n) :\n k * (k - ℓ - 1) = (n - k - 1) * μ", "start": [ 182, 1 ], "end": [ 215, 11 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.matrix_eq", "code": "theorem IsSRGWith.matrix_eq {α : Type*} [Semiring α] (h : G.IsSRGWith n k ℓ μ) :\n G.adjMatrix α ^ 2 = k • (1 : Matrix V V α) + ℓ • G.adjMatrix α + μ • Gᶜ.adjMatrix α", "start": [ 217, 1 ], "end": [ 235, 30 ], "kind": "commanddeclaration" } ]
Mathlib/LinearAlgebra/TensorProduct/DirectLimit.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Algebra/DirectLimit.lean" ]	[ { "full_name": "TensorProduct.fromDirectLimit", "code": "noncomputable def fromDirectLimit :\n DirectLimit (G · ⊗[R] M) (f ▷ M) →ₗ[R] DirectLimit G f ⊗[R] M :=\n DirectLimit.lift _ _ _ _ (fun _ ↦ (of _ _ _ _ _).rTensor M)\n fun _ _ _ x ↦ by refine x.induction_on ?_ ?_ ?_ <;> aesop", "start": [ 39, 1 ], "end": [ 46, 62 ], "kind": "commanddeclaration" }, { "full_name": "TensorProduct.fromDirectLimit_of_tmul", "code": "@[simp] lemma fromDirectLimit_of_tmul {i : ι} (g : G i) (m : M) :\n fromDirectLimit f M (of _ _ _ _ i (g ⊗ₜ m)) = (of _ _ _ f i g) ⊗ₜ m :=\n lift_of (G := (G · ⊗[R] M)) _ _ (g ⊗ₜ m)", "start": [ 49, 1 ], "end": [ 51, 43 ], "kind": "lemma" }, { "full_name": "TensorProduct.toDirectLimit", "code": "noncomputable def toDirectLimit : DirectLimit G f ⊗[R] M →ₗ[R] DirectLimit (G · ⊗[R] M) (f ▷ M) :=\n TensorProduct.lift <\| DirectLimit.lift _ _ _ _\n (fun i ↦\n (TensorProduct.mk R _ _).compr₂ (of R ι _ (fun _i _j h ↦ (f _ _ h).rTensor M) i))\n fun _ _ _ g ↦ DFunLike.ext _ _ (of_f (G := (G · ⊗[R] M)) (x := g ⊗ₜ ·))", "start": [ 53, 1 ], "end": [ 62, 76 ], "kind": "commanddeclaration" }, { "full_name": "TensorProduct.toDirectLimit_tmul_of", "code": "@[simp] lemma toDirectLimit_tmul_of\n {i : ι} (g : G i) (m : M) :\n (toDirectLimit f M <\| (of _ _ G f i g) ⊗ₜ m) = (of _ _ _ _ i (g ⊗ₜ m)) := by\n rw [toDirectLimit, lift.tmul, lift_of]\n rfl", "start": [ 65, 1 ], "end": [ 69, 6 ], "kind": "lemma" }, { "full_name": "TensorProduct.directLimitLeft", "code": "noncomputable def directLimitLeft :\n DirectLimit G f ⊗[R] M ≃ₗ[R] DirectLimit (G · ⊗[R] M) (f ▷ M) := by\n refine LinearEquiv.ofLinear (toDirectLimit f M) (fromDirectLimit f M) ?_ ?_\n <;> cases isEmpty_or_nonempty ι\n · ext; apply Subsingleton.elim\n · refine DFunLike.ext _ _ fun x ↦ x.induction_on fun i g ↦ g.induction_on ?_ ?_ ?_ <;> aesop\n · ext; apply Subsingleton.elim\n · exact ext (DFunLike.ext _ _ fun g ↦ DFunLike.ext _ _ fun _ ↦ g.induction_on <\| by aesop)", "start": [ 73, 1 ], "end": [ 83, 93 ], "kind": "commanddeclaration" }, { "full_name": "TensorProduct.directLimitLeft_tmul_of", "code": "@[simp] lemma directLimitLeft_tmul_of {i : ι} (g : G i) (m : M) :\n directLimitLeft f M (of _ _ _ _ _ g ⊗ₜ m) = of _ _ _ (f ▷ M) _ (g ⊗ₜ m) :=\n toDirectLimit_tmul_of f g m", "start": [ 85, 1 ], "end": [ 87, 30 ], "kind": "lemma" }, { "full_name": "TensorProduct.directLimitLeft_symm_of_tmul", "code": "@[simp] lemma directLimitLeft_symm_of_tmul {i : ι} (g : G i) (m : M) :\n (directLimitLeft f M).symm (of _ _ _ _ _ (g ⊗ₜ m)) = of _ _ _ f _ g ⊗ₜ m :=\n fromDirectLimit_of_tmul f g m", "start": [ 89, 1 ], "end": [ 91, 32 ], "kind": "lemma" }, { "full_name": "TensorProduct.directLimitRight", "code": "noncomputable def directLimitRight :\n M ⊗[R] DirectLimit G f ≃ₗ[R] DirectLimit (M ⊗[R] G ·) (M ◁ f) :=\n TensorProduct.comm _ _ _ ≪≫ₗ directLimitLeft f M ≪≫ₗ\n Module.DirectLimit.congr (fun i ↦ TensorProduct.comm _ _ _)\n (fun i j h ↦ TensorProduct.ext <\| DFunLike.ext _ _ <\| by aesop)", "start": [ 93, 1 ], "end": [ 100, 70 ], "kind": "commanddeclaration" }, { "full_name": "TensorProduct.directLimitRight_tmul_of", "code": "@[simp] lemma directLimitRight_tmul_of {i : ι} (m : M) (g : G i):\n directLimitRight f M (m ⊗ₜ of _ _ _ _ _ g) = of _ _ _ _ i (m ⊗ₜ g) := by\n simp [directLimitRight, congr_apply_of]", "start": [ 102, 1 ], "end": [ 104, 42 ], "kind": "lemma" }, { "full_name": "TensorProduct.directLimitRight_symm_of_tmul", "code": "@[simp] lemma directLimitRight_symm_of_tmul {i : ι} (m : M) (g : G i) :\n (directLimitRight f M).symm (of _ _ _ _ _ (m ⊗ₜ g)) = m ⊗ₜ of _ _ _ f _ g := by\n simp [directLimitRight, congr_symm_apply_of]", "start": [ 106, 1 ], "end": [ 108, 47 ], "kind": "lemma" } ]
Mathlib/Analysis/Convex/Quasiconvex.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/Convex/Function.lean" ]	[ { "full_name": "QuasiconvexOn", "code": "def QuasiconvexOn : Prop :=\n ∀ r, Convex 𝕜 ({ x ∈ s \| f x ≤ r })", "start": [ 48, 1 ], "end": [ 51, 38 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconcaveOn", "code": "def QuasiconcaveOn : Prop :=\n ∀ r, Convex 𝕜 ({ x ∈ s \| r ≤ f x })", "start": [ 54, 1 ], "end": [ 57, 38 ], "kind": "commanddeclaration" }, { "full_name": "QuasilinearOn", "code": "def QuasilinearOn : Prop :=\n QuasiconvexOn 𝕜 s f ∧ QuasiconcaveOn 𝕜 s f", "start": [ 60, 1 ], "end": [ 64, 45 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconvexOn.dual", "code": "theorem QuasiconvexOn.dual : QuasiconvexOn 𝕜 s f → QuasiconcaveOn 𝕜 s (toDual ∘ f)", "start": [ 69, 1 ], "end": [ 70, 5 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconcaveOn.dual", "code": "theorem QuasiconcaveOn.dual : QuasiconcaveOn 𝕜 s f → QuasiconvexOn 𝕜 s (toDual ∘ f)", "start": [ 73, 1 ], "end": [ 74, 5 ], "kind": "commanddeclaration" }, { "full_name": "QuasilinearOn.dual", "code": "theorem QuasilinearOn.dual : QuasilinearOn 𝕜 s f → QuasilinearOn 𝕜 s (toDual ∘ f)", "start": [ 77, 1 ], "end": [ 78, 11 ], "kind": "commanddeclaration" }, { "full_name": "Convex.quasiconvexOn_of_convex_le", "code": "theorem Convex.quasiconvexOn_of_convex_le (hs : Convex 𝕜 s) (h : ∀ r, Convex 𝕜 { x \| f x ≤ r }) :\n QuasiconvexOn 𝕜 s f", "start": [ 81, 1 ], "end": [ 82, 51 ], "kind": "commanddeclaration" }, { "full_name": "Convex.quasiconcaveOn_of_convex_ge", "code": "theorem Convex.quasiconcaveOn_of_convex_ge (hs : Convex 𝕜 s) (h : ∀ r, Convex 𝕜 { x \| r ≤ f x }) :\n QuasiconcaveOn 𝕜 s f", "start": [ 85, 1 ], "end": [ 87, 62 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconvexOn.convex", "code": "theorem QuasiconvexOn.convex [IsDirected β (· ≤ ·)] (hf : QuasiconvexOn 𝕜 s f) : Convex 𝕜 s", "start": [ 90, 1 ], "end": [ 93, 41 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconcaveOn.convex", "code": "theorem QuasiconcaveOn.convex [IsDirected β (· ≥ ·)] (hf : QuasiconcaveOn 𝕜 s f) : Convex 𝕜 s", "start": [ 96, 1 ], "end": [ 97, 17 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconvexOn.sup", "code": "theorem QuasiconvexOn.sup [SemilatticeSup β] (hf : QuasiconvexOn 𝕜 s f)\n (hg : QuasiconvexOn 𝕜 s g) : QuasiconvexOn 𝕜 s (f ⊔ g)", "start": [ 106, 1 ], "end": [ 110, 28 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconcaveOn.inf", "code": "theorem QuasiconcaveOn.inf [SemilatticeInf β] (hf : QuasiconcaveOn 𝕜 s f)\n (hg : QuasiconcaveOn 𝕜 s g) : QuasiconcaveOn 𝕜 s (f ⊓ g)", "start": [ 113, 1 ], "end": [ 115, 17 ], "kind": "commanddeclaration" }, { "full_name": "quasiconvexOn_iff_le_max", "code": "theorem quasiconvexOn_iff_le_max : QuasiconvexOn 𝕜 s f ↔ Convex 𝕜 s ∧ ∀ ⦃x⦄, x ∈ s → ∀ ⦃y⦄,\n y ∈ s → ∀ ⦃a b : 𝕜⦄, 0 ≤ a → 0 ≤ b → a + b = 1 → f (a • x + b • y) ≤ max (f x) (f y)", "start": [ 124, 1 ], "end": [ 130, 86 ], "kind": "commanddeclaration" }, { "full_name": "quasiconcaveOn_iff_min_le", "code": "theorem quasiconcaveOn_iff_min_le : QuasiconcaveOn 𝕜 s f ↔ Convex 𝕜 s ∧ ∀ ⦃x⦄, x ∈ s → ∀ ⦃y⦄,\n y ∈ s → ∀ ⦃a b : 𝕜⦄, 0 ≤ a → 0 ≤ b → a + b = 1 → min (f x) (f y) ≤ f (a • x + b • y)", "start": [ 133, 1 ], "end": [ 135, 48 ], "kind": "commanddeclaration" }, { "full_name": "quasilinearOn_iff_mem_uIcc", "code": "theorem quasilinearOn_iff_mem_uIcc : QuasilinearOn 𝕜 s f ↔ Convex 𝕜 s ∧ ∀ ⦃x⦄, x ∈ s → ∀ ⦃y⦄,\n y ∈ s → ∀ ⦃a b : 𝕜⦄, 0 ≤ a → 0 ≤ b → a + b = 1 → f (a • x + b • y) ∈ uIcc (f x) (f y)", "start": [ 138, 1 ], "end": [ 143, 59 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconvexOn.convex_lt", "code": "theorem QuasiconvexOn.convex_lt (hf : QuasiconvexOn 𝕜 s f) (r : β) :\n Convex 𝕜 ({ x ∈ s \| f x < r })", "start": [ 146, 1 ], "end": [ 150, 48 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconcaveOn.convex_gt", "code": "theorem QuasiconcaveOn.convex_gt (hf : QuasiconcaveOn 𝕜 s f) (r : β) :\n Convex 𝕜 ({ x ∈ s \| r < f x })", "start": [ 153, 1 ], "end": [ 155, 22 ], "kind": "commanddeclaration" }, { "full_name": "ConvexOn.quasiconvexOn", "code": "theorem ConvexOn.quasiconvexOn (hf : ConvexOn 𝕜 s f) : QuasiconvexOn 𝕜 s f", "start": [ 165, 1 ], "end": [ 166, 15 ], "kind": "commanddeclaration" }, { "full_name": "ConcaveOn.quasiconcaveOn", "code": "theorem ConcaveOn.quasiconcaveOn (hf : ConcaveOn 𝕜 s f) : QuasiconcaveOn 𝕜 s f", "start": [ 169, 1 ], "end": [ 170, 15 ], "kind": "commanddeclaration" }, { "full_name": "MonotoneOn.quasiconvexOn", "code": "theorem MonotoneOn.quasiconvexOn (hf : MonotoneOn f s) (hs : Convex 𝕜 s) : QuasiconvexOn 𝕜 s f", "start": [ 182, 1 ], "end": [ 183, 18 ], "kind": "commanddeclaration" }, { "full_name": "MonotoneOn.quasiconcaveOn", "code": "theorem MonotoneOn.quasiconcaveOn (hf : MonotoneOn f s) (hs : Convex 𝕜 s) : QuasiconcaveOn 𝕜 s f", "start": [ 186, 1 ], "end": [ 187, 18 ], "kind": "commanddeclaration" }, { "full_name": "MonotoneOn.quasilinearOn", "code": "theorem MonotoneOn.quasilinearOn (hf : MonotoneOn f s) (hs : Convex 𝕜 s) : QuasilinearOn 𝕜 s f", "start": [ 190, 1 ], "end": [ 191, 46 ], "kind": "commanddeclaration" }, { "full_name": "AntitoneOn.quasiconvexOn", "code": "theorem AntitoneOn.quasiconvexOn (hf : AntitoneOn f s) (hs : Convex 𝕜 s) : QuasiconvexOn 𝕜 s f", "start": [ 194, 1 ], "end": [ 195, 18 ], "kind": "commanddeclaration" }, { "full_name": "AntitoneOn.quasiconcaveOn", "code": "theorem AntitoneOn.quasiconcaveOn (hf : AntitoneOn f s) (hs : Convex 𝕜 s) : QuasiconcaveOn 𝕜 s f", "start": [ 198, 1 ], "end": [ 199, 18 ], "kind": "commanddeclaration" }, { "full_name": "AntitoneOn.quasilinearOn", "code": "theorem AntitoneOn.quasilinearOn (hf : AntitoneOn f s) (hs : Convex 𝕜 s) : QuasilinearOn 𝕜 s f", "start": [ 202, 1 ], "end": [ 203, 46 ], "kind": "commanddeclaration" }, { "full_name": "Monotone.quasiconvexOn", "code": "theorem Monotone.quasiconvexOn (hf : Monotone f) : QuasiconvexOn 𝕜 univ f", "start": [ 206, 1 ], "end": [ 207, 46 ], "kind": "commanddeclaration" }, { "full_name": "Monotone.quasiconcaveOn", "code": "theorem Monotone.quasiconcaveOn (hf : Monotone f) : QuasiconcaveOn 𝕜 univ f", "start": [ 210, 1 ], "end": [ 211, 47 ], "kind": "commanddeclaration" }, { "full_name": "Monotone.quasilinearOn", "code": "theorem Monotone.quasilinearOn (hf : Monotone f) : QuasilinearOn 𝕜 univ f", "start": [ 214, 1 ], "end": [ 215, 40 ], "kind": "commanddeclaration" }, { "full_name": "Antitone.quasiconvexOn", "code": "theorem Antitone.quasiconvexOn (hf : Antitone f) : QuasiconvexOn 𝕜 univ f", "start": [ 218, 1 ], "end": [ 219, 46 ], "kind": "commanddeclaration" }, { "full_name": "Antitone.quasiconcaveOn", "code": "theorem Antitone.quasiconcaveOn (hf : Antitone f) : QuasiconcaveOn 𝕜 univ f", "start": [ 222, 1 ], "end": [ 223, 47 ], "kind": "commanddeclaration" }, { "full_name": "Antitone.quasilinearOn", "code": "theorem Antitone.quasilinearOn (hf : Antitone f) : QuasilinearOn 𝕜 univ f", "start": [ 226, 1 ], "end": [ 227, 40 ], "kind": "commanddeclaration" }, { "full_name": "QuasilinearOn.monotoneOn_or_antitoneOn", "code": "theorem QuasilinearOn.monotoneOn_or_antitoneOn [LinearOrder β] (hf : QuasilinearOn 𝕜 s f) :\n MonotoneOn f s ∨ AntitoneOn f s", "start": [ 238, 1 ], "end": [ 242, 97 ], "kind": "commanddeclaration" }, { "full_name": "quasilinearOn_iff_monotoneOn_or_antitoneOn", "code": "theorem quasilinearOn_iff_monotoneOn_or_antitoneOn [LinearOrderedAddCommMonoid β]\n (hs : Convex 𝕜 s) : QuasilinearOn 𝕜 s f ↔ MonotoneOn f s ∨ AntitoneOn f s", "start": [ 245, 1 ], "end": [ 248, 70 ], "kind": "commanddeclaration" } ]
Mathlib/Algebra/AddConstMap/Basic.lean	[ "Mathlib/Algebra/Module/Defs.lean", "Mathlib/Algebra/Order/Group/Instances.lean", "Mathlib/Logic/Function/Iterate.lean", "Mathlib/Algebra/GroupPower/IterateHom.lean", "Mathlib/GroupTheory/GroupAction/Pi.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Algebra/Order/Archimedean.lean" ]	[ { "full_name": "AddConstMap", "code": "structure AddConstMap (G H : Type) [Add G] [Add H] (a : G) (b : H) where\n \n protected toFun : G → H\n \n map_add_const' (x : G) : toFun (x + a) = toFun x + b", "start": [ 33, 1 ], "end": [ 41, 55 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass", "code": "class AddConstMapClass (F : Type) (G H : outParam Type) [Add G] [Add H]\n (a : outParam G) (b : outParam H) [FunLike F G H] : Prop where\n \n map_add_const (f : F) (x : G) : f (x + a) = f x + b", "start": [ 46, 1 ], "end": [ 55, 54 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.semiconj", "code": "protected theorem semiconj [Add G] [Add H] [AddConstMapClass F G H a b] (f : F) :\n Semiconj f (· + a) (· + b)", "start": [ 69, 1 ], "end": [ 71, 18 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_nsmul", "code": "@[scoped simp]\ntheorem map_add_nsmul [AddMonoid G] [AddMonoid H] [AddConstMapClass F G H a b]\n (f : F) (x : G) (n : ℕ) : f (x + n • a) = f x + n • b", "start": [ 73, 1 ], "end": [ 76, 62 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_nat'", "code": "@[scoped simp]\ntheorem map_add_nat' [AddMonoidWithOne G] [AddMonoid H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) (n : ℕ) : f (x + n) = f x + n • b", "start": [ 78, 1 ], "end": [ 80, 83 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_one", "code": "theorem map_add_one [AddMonoidWithOne G] [Add H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) : f (x + 1) = f x + b", "start": [ 82, 1 ], "end": [ 83, 63 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_ofNat'", "code": "@[scoped simp]\ntheorem map_add_ofNat' [AddMonoidWithOne G] [AddMonoid H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) (n : ℕ) [n.AtLeastTwo] :\n f (x + no_index (OfNat.ofNat n)) = f x + (OfNat.ofNat n : ℕ) • b", "start": [ 85, 1 ], "end": [ 89, 21 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_nat", "code": "theorem map_add_nat [AddMonoidWithOne G] [AddMonoidWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (x : G) (n : ℕ) : f (x + n) = f x + n", "start": [ 91, 1 ], "end": [ 92, 61 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_ofNat", "code": "theorem map_add_ofNat [AddMonoidWithOne G] [AddMonoidWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (x : G) (n : ℕ) [n.AtLeastTwo] :\n f (x + OfNat.ofNat n) = f x + OfNat.ofNat n", "start": [ 94, 1 ], "end": [ 96, 69 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_const", "code": "@[scoped simp]\ntheorem map_const [AddZeroClass G] [Add H] [AddConstMapClass F G H a b] (f : F) :\n f a = f 0 + b", "start": [ 98, 1 ], "end": [ 101, 32 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_one", "code": "theorem map_one [AddZeroClass G] [One G] [Add H] [AddConstMapClass F G H 1 b] (f : F) :\n f 1 = f 0 + b", "start": [ 103, 1 ], "end": [ 105, 14 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_nsmul_const", "code": "@[scoped simp]\ntheorem map_nsmul_const [AddMonoid G] [AddMonoid H] [AddConstMapClass F G H a b]\n (f : F) (n : ℕ) : f (n • a) = f 0 + n • b", "start": [ 107, 1 ], "end": [ 110, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_nat'", "code": "@[scoped simp]\ntheorem map_nat' [AddMonoidWithOne G] [AddMonoid H] [AddConstMapClass F G H 1 b]\n (f : F) (n : ℕ) : f n = f 0 + n • b", "start": [ 112, 1 ], "end": [ 115, 33 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_ofNat'", "code": "theorem map_ofNat' [AddMonoidWithOne G] [AddMonoid H] [AddConstMapClass F G H 1 b]\n (f : F) (n : ℕ) [n.AtLeastTwo] :\n f (OfNat.ofNat n) = f 0 + (OfNat.ofNat n : ℕ) • b", "start": [ 117, 1 ], "end": [ 120, 15 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_nat", "code": "theorem map_nat [AddMonoidWithOne G] [AddMonoidWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (n : ℕ) : f n = f 0 + n", "start": [ 122, 1 ], "end": [ 123, 47 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_ofNat", "code": "theorem map_ofNat [AddMonoidWithOne G] [AddMonoidWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (n : ℕ) [n.AtLeastTwo] :\n f (OfNat.ofNat n) = f 0 + OfNat.ofNat n", "start": [ 125, 1 ], "end": [ 127, 59 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_const_add", "code": "@[scoped simp]\ntheorem map_const_add [AddCommSemigroup G] [Add H] [AddConstMapClass F G H a b]\n (f : F) (x : G) : f (a + x) = f x + b", "start": [ 129, 1 ], "end": [ 132, 31 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_one_add", "code": "theorem map_one_add [AddCommMonoidWithOne G] [Add H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) : f (1 + x) = f x + b", "start": [ 134, 1 ], "end": [ 135, 63 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_nsmul_add", "code": "@[scoped simp]\ntheorem map_nsmul_add [AddCommMonoid G] [AddMonoid H] [AddConstMapClass F G H a b]\n (f : F) (n : ℕ) (x : G) : f (n • a + x) = f x + n • b", "start": [ 137, 1 ], "end": [ 140, 31 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_nat_add'", "code": "@[scoped simp]\ntheorem map_nat_add' [AddCommMonoidWithOne G] [AddMonoid H] [AddConstMapClass F G H 1 b]\n (f : F) (n : ℕ) (x : G) : f (↑n + x) = f x + n • b", "start": [ 142, 1 ], "end": [ 145, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_ofNat_add'", "code": "theorem map_ofNat_add' [AddCommMonoidWithOne G] [AddMonoid H] [AddConstMapClass F G H 1 b]\n (f : F) (n : ℕ) [n.AtLeastTwo] (x : G) :\n f (OfNat.ofNat n + x) = f x + OfNat.ofNat n • b", "start": [ 147, 1 ], "end": [ 150, 21 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_nat_add", "code": "theorem map_nat_add [AddCommMonoidWithOne G] [AddMonoidWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (n : ℕ) (x : G) : f (↑n + x) = f x + n", "start": [ 152, 1 ], "end": [ 153, 62 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_ofNat_add", "code": "theorem map_ofNat_add [AddCommMonoidWithOne G] [AddMonoidWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (n : ℕ) [n.AtLeastTwo] (x : G) :\n f (OfNat.ofNat n + x) = f x + OfNat.ofNat n", "start": [ 155, 1 ], "end": [ 158, 20 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_nsmul", "code": "@[scoped simp]\ntheorem map_sub_nsmul [AddGroup G] [AddGroup H] [AddConstMapClass F G H a b]\n (f : F) (x : G) (n : ℕ) : f (x - n • a) = f x - n • b", "start": [ 160, 1 ], "end": [ 163, 83 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_const", "code": "@[scoped simp]\ntheorem map_sub_const [AddGroup G] [AddGroup H] [AddConstMapClass F G H a b]\n (f : F) (x : G) : f (x - a) = f x - b", "start": [ 165, 1 ], "end": [ 168, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_one", "code": "theorem map_sub_one [AddGroup G] [One G] [AddGroup H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) : f (x - 1) = f x - b", "start": [ 170, 1 ], "end": [ 172, 20 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_nat'", "code": "@[scoped simp]\ntheorem map_sub_nat' [AddGroupWithOne G] [AddGroup H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) (n : ℕ) : f (x - n) = f x - n • b", "start": [ 174, 1 ], "end": [ 177, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_ofNat'", "code": "@[scoped simp]\ntheorem map_sub_ofNat' [AddGroupWithOne G] [AddGroup H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) (n : ℕ) [n.AtLeastTwo] :\n f (x - no_index (OfNat.ofNat n)) = f x - OfNat.ofNat n • b", "start": [ 179, 1 ], "end": [ 183, 21 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_zsmul", "code": "@[scoped simp]\ntheorem map_add_zsmul [AddGroup G] [AddGroup H] [AddConstMapClass F G H a b]\n (f : F) (x : G) : ∀ n : ℤ, f (x + n • a) = f x + n • b", "start": [ 185, 1 ], "end": [ 189, 45 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_zsmul_const", "code": "@[scoped simp]\ntheorem map_zsmul_const [AddGroup G] [AddGroup H] [AddConstMapClass F G H a b]\n (f : F) (n : ℤ) : f (n • a) = f 0 + n • b", "start": [ 191, 1 ], "end": [ 194, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_int'", "code": "@[scoped simp]\ntheorem map_add_int' [AddGroupWithOne G] [AddGroup H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) (n : ℤ) : f (x + n) = f x + n • b", "start": [ 196, 1 ], "end": [ 199, 40 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_int", "code": "theorem map_add_int [AddGroupWithOne G] [AddGroupWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (x : G) (n : ℤ) : f (x + n) = f x + n", "start": [ 201, 1 ], "end": [ 202, 61 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_zsmul", "code": "@[scoped simp]\ntheorem map_sub_zsmul [AddGroup G] [AddGroup H] [AddConstMapClass F G H a b]\n (f : F) (x : G) (n : ℤ) : f (x - n • a) = f x - n • b", "start": [ 204, 1 ], "end": [ 207, 54 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_int'", "code": "@[scoped simp]\ntheorem map_sub_int' [AddGroupWithOne G] [AddGroup H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) (n : ℤ) : f (x - n) = f x - n • b", "start": [ 209, 1 ], "end": [ 212, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_int", "code": "theorem map_sub_int [AddGroupWithOne G] [AddGroupWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (x : G) (n : ℤ) : f (x - n) = f x - n", "start": [ 214, 1 ], "end": [ 215, 61 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_zsmul_add", "code": "@[scoped simp]\ntheorem map_zsmul_add [AddCommGroup G] [AddGroup H] [AddConstMapClass F G H a b]\n (f : F) (n : ℤ) (x : G) : f (n • a + x) = f x + n • b", "start": [ 217, 1 ], "end": [ 220, 31 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_int_add'", "code": "@[scoped simp]\ntheorem map_int_add' [AddCommGroupWithOne G] [AddGroup H] [AddConstMapClass F G H 1 b]\n (f : F) (n : ℤ) (x : G) : f (↑n + x) = f x + n • b", "start": [ 222, 1 ], "end": [ 225, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_int_add", "code": "theorem map_int_add [AddCommGroupWithOne G] [AddGroupWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (n : ℤ) (x : G) : f (↑n + x) = f x + n", "start": [ 227, 1 ], "end": [ 228, 62 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_fract", "code": "theorem map_fract {R : Type} [LinearOrderedRing R] [FloorRing R] [AddGroup H]\n [FunLike F R H] [AddConstMapClass F R H 1 b] (f : F) (x : R) :\n f (Int.fract x) = f x - ⌊x⌋ • b", "start": [ 230, 1 ], "end": [ 233, 18 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.rel_map_of_Icc", "code": "protected theorem rel_map_of_Icc [LinearOrderedAddCommGroup G] [Archimedean G] [AddGroup H]\n [AddConstMapClass F G H a b] {f : F} {R : H → H → Prop} [IsTrans H R]\n [hR : CovariantClass H H (fun x y ↦ y + x) R] (ha : 0 < a) {l : G}\n (hf : ∀ x ∈ Icc l (l + a), ∀ y ∈ Icc l (l + a), x < y → R (f x) (f y)) :\n ((· < ·) ⇒ R) f f", "start": [ 235, 1 ], "end": [ 276, 19 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.monotone_iff_Icc", "code": "theorem monotone_iff_Icc [LinearOrderedAddCommGroup G] [Archimedean G] [OrderedAddCommGroup H]\n [AddConstMapClass F G H a b] {f : F} (ha : 0 < a) (l : G) :\n Monotone f ↔ MonotoneOn f (Icc l (l + a))", "start": [ 278, 1 ], "end": [ 282, 78 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.antitone_iff_Icc", "code": "theorem antitone_iff_Icc [LinearOrderedAddCommGroup G] [Archimedean G] [OrderedAddCommGroup H]\n [AddConstMapClass F G H a b] {f : F} (ha : 0 < a) (l : G) :\n Antitone f ↔ AntitoneOn f (Icc l (l + a))", "start": [ 284, 1 ], "end": [ 287, 35 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.strictMono_iff_Icc", "code": "theorem strictMono_iff_Icc [LinearOrderedAddCommGroup G] [Archimedean G] [OrderedAddCommGroup H]\n [AddConstMapClass F G H a b] {f : F} (ha : 0 < a) (l : G) :\n StrictMono f ↔ StrictMonoOn f (Icc l (l + a))", "start": [ 289, 1 ], "end": [ 292, 70 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.strictAnti_iff_Icc", "code": "theorem strictAnti_iff_Icc [LinearOrderedAddCommGroup G] [Archimedean G] [OrderedAddCommGroup H]\n [AddConstMapClass F G H a b] {f : F} (ha : 0 < a) (l : G) :\n StrictAnti f ↔ StrictAntiOn f (Icc l (l + a))", "start": [ 294, 1 ], "end": [ 297, 37 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.coe_mk", "code": "@[scoped simp] theorem coe_mk (f : G → H) (hf) : ⇑(mk f hf : G →+c[a, b] H) = f", "start": [ 317, 1 ], "end": [ 317, 87 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.mk_coe", "code": "@[scoped simp] theorem mk_coe (f : G →+c[a, b] H) : mk f f.2 = f", "start": [ 318, 1 ], "end": [ 318, 72 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.toFun_eq_coe", "code": "@[scoped simp] theorem toFun_eq_coe (f : G →+c[a, b] H) : f.toFun = f", "start": [ 319, 1 ], "end": [ 319, 77 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.ext", "code": "@[ext] protected theorem ext {f g : G →+c[a, b] H} (h : ∀ x, f x = g x) : f = g", "start": [ 324, 1 ], "end": [ 325, 21 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.id", "code": "@[simps (config := .asFn)]\nprotected def id : G →+c[a, a] G := ⟨id, fun _ ↦ rfl⟩", "start": [ 333, 1 ], "end": [ 335, 54 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.comp", "code": "@[simps (config := .asFn)]\ndef comp {K : Type} [Add K] {c : K} (g : H →+c[b, c] K) (f : G →+c[a, b] H) :\n G →+c[a, c] K :=\n ⟨g ∘ f, by simp⟩", "start": [ 339, 1 ], "end": [ 343, 19 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.comp_id", "code": "@[scoped simp] theorem comp_id (f : G →+c[a, b] H) : f.comp .id = f", "start": [ 345, 1 ], "end": [ 345, 75 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.id_comp", "code": "@[scoped simp] theorem id_comp (f : G →+c[a, b] H) : .comp .id f = f", "start": [ 346, 1 ], "end": [ 346, 76 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.replaceConsts", "code": "@[simps (config := .asFn)]\ndef replaceConsts (f : G →+c[a, b] H) (a' b') (ha : a = a') (hb : b = b') :\n G →+c[a', b'] H where\n toFun := f\n map_add_const' := ha ▸ hb ▸ f.map_add_const'", "start": [ 348, 1 ], "end": [ 353, 47 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.coe_vadd", "code": "@[scoped simp]\ntheorem coe_vadd {K : Type} [VAdd K H] [VAddAssocClass K H H] (c : K) (f : G →+c[a, b] H) :\n ⇑(c +ᵥ f) = c +ᵥ ⇑f", "start": [ 363, 1 ], "end": [ 366, 6 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.mul_def", "code": "theorem mul_def (f g : G →+c[a, a] G) : f * g = f.comp g", "start": [ 385, 1 ], "end": [ 385, 64 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.coe_mul", "code": "@[scoped simp] theorem coe_mul (f g : G →+c[a, a] G) : ⇑(f * g) = f ∘ g", "start": [ 386, 1 ], "end": [ 386, 79 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.one_def", "code": "theorem one_def : (1 : G →+c[a, a] G) = .id", "start": [ 388, 1 ], "end": [ 388, 51 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.coe_one", "code": "@[scoped simp] theorem coe_one : ⇑(1 : G →+c[a, a] G) = id", "start": [ 389, 1 ], "end": [ 389, 66 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.coe_pow", "code": "@[scoped simp] theorem coe_pow (f : G →+c[a, a] G) (n : ℕ) : ⇑(f ^ n) = f^[n]", "start": [ 391, 1 ], "end": [ 391, 85 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.pow_apply", "code": "theorem pow_apply (f : G →+c[a, a] G) (n : ℕ) (x : G) : (f ^ n) x = f^[n] x", "start": [ 393, 1 ], "end": [ 393, 83 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.smul", "code": "@[simps (config := .asFn)]\ndef smul [DistribSMul K H] (c : K) (f : G →+c[a, b] H) : G →+c[a, c • b] H where\n toFun := c • ⇑f\n map_add_const' x := by simp [smul_add]", "start": [ 411, 1 ], "end": [ 415, 41 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.addLeftHom", "code": "@[simps! (config := .asFn)]\ndef addLeftHom : Multiplicative G →* (G →+c[a, a] G) where\n toFun c := Multiplicative.toAdd c +ᵥ .id\n map_one' := by ext; apply zero_add\n map_mul' _ _ := by ext; apply add_assoc", "start": [ 423, 1 ], "end": [ 429, 42 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.conjNeg", "code": "@[simps! apply_coe]\ndef conjNeg : (G →+c[a, b] H) ≃ (G →+c[a, b] H) :=\n Involutive.toPerm (fun f ↦ ⟨fun x ↦ - f (-x), fun _ ↦ by simp [neg_add_eq_sub]⟩) fun _ ↦\n AddConstMap.ext fun _ ↦ by simp", "start": [ 437, 1 ], "end": [ 441, 36 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.conjNeg_symm", "code": "@[scoped simp] theorem conjNeg_symm : (conjNeg (a := a) (b := b)).symm = conjNeg", "start": [ 443, 1 ], "end": [ 443, 88 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.mkFract", "code": "def mkFract : (Ico (0 : R) 1 → G) ≃ (R →+c[1, a] G) where\n toFun f := ⟨fun x ↦ f ⟨Int.fract x, Int.fract_nonneg _, Int.fract_lt_one _⟩ + ⌊x⌋ • a, fun x ↦ by\n simp [add_one_zsmul, add_assoc]⟩\n invFun f x := f x\n left_inv _ := by ext x; simp [Int.fract_eq_self.2 x.2, Int.floor_eq_zero_iff.2 x.2]\n right_inv f := by ext x; simp [map_fract]", "start": [ 451, 1 ], "end": [ 457, 44 ], "kind": "commanddeclaration" } ]
Mathlib/Probability/BorelCantelli.lean	[ "Mathlib/Probability/ConditionalExpectation.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Probability/Martingale/BorelCantelli.lean", "Mathlib/Probability/Independence/Basic.lean" ]	[ { "full_name": "ProbabilityTheory.iIndepFun.indep_comap_natural_of_lt", "code": "theorem iIndepFun.indep_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f i))\n (hfi : iIndepFun (fun _ => mβ) f μ) (hij : i < j) :\n Indep (MeasurableSpace.comap (f j) mβ) (Filtration.natural f hf i) μ", "start": [ 43, 1 ], "end": [ 48, 84 ], "kind": "commanddeclaration" }, { "full_name": "ProbabilityTheory.iIndepFun.condexp_natural_ae_eq_of_lt", "code": "theorem iIndepFun.condexp_natural_ae_eq_of_lt [SecondCountableTopology β] [CompleteSpace β]\n [NormedSpace ℝ β] (hf : ∀ i, StronglyMeasurable (f i)) (hfi : iIndepFun (fun _ => mβ) f μ)\n (hij : i < j) : μ[f j\|Filtration.natural f hf i] =ᵐ[μ] fun _ => μ[f j]", "start": [ 52, 1 ], "end": [ 56, 88 ], "kind": "commanddeclaration" }, { "full_name": "ProbabilityTheory.iIndepSet.condexp_indicator_filtrationOfSet_ae_eq", "code": "theorem iIndepSet.condexp_indicator_filtrationOfSet_ae_eq (hsm : ∀ n, MeasurableSet (s n))\n (hs : iIndepSet s μ) (hij : i < j) :\n μ[(s j).indicator (fun _ => 1 : Ω → ℝ)\|filtrationOfSet hsm i] =ᵐ[μ]\n fun _ => (μ (s j)).toReal", "start": [ 60, 1 ], "end": [ 66, 87 ], "kind": "commanddeclaration" }, { "full_name": "ProbabilityTheory.measure_limsup_eq_one", "code": "theorem measure_limsup_eq_one {s : ℕ → Set Ω} (hsm : ∀ n, MeasurableSet (s n)) (hs : iIndepSet s μ)\n (hs' : (∑' n, μ (s n)) = ∞) : μ (limsup s atTop) = 1", "start": [ 72, 1 ], "end": [ 105, 44 ], "kind": "commanddeclaration" } ]
Mathlib/Combinatorics/SetFamily/Compression/UV.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Combinatorics/SetFamily/Shadow.lean" ]	[ { "full_name": "sup_sdiff_injOn", "code": "theorem sup_sdiff_injOn [GeneralizedBooleanAlgebra α] (u v : α) :\n { x \| Disjoint u x ∧ v ≤ x }.InjOn fun x => (x ⊔ u) \\ v", "start": [ 56, 1 ], "end": [ 64, 89 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress", "code": "def compress (u v a : α) : α :=\n if Disjoint u a ∧ v ≤ a then (a ⊔ u) \\ v else a", "start": [ 78, 1 ], "end": [ 82, 50 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_of_disjoint_of_le", "code": "theorem compress_of_disjoint_of_le (hua : Disjoint u a) (hva : v ≤ a) :\n compress u v a = (a ⊔ u) \\ v", "start": [ 85, 1 ], "end": [ 87, 20 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_of_disjoint_of_le'", "code": "theorem compress_of_disjoint_of_le' (hva : Disjoint v a) (hua : u ≤ a) :\n compress u v ((a ⊔ v) \\ u) = a", "start": [ 90, 1 ], "end": [ 94, 79 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_self", "code": "@[simp]\ntheorem compress_self (u a : α) : compress u u a = a", "start": [ 97, 1 ], "end": [ 102, 8 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_sdiff_sdiff", "code": "@[simp]\ntheorem compress_sdiff_sdiff (a b : α) : compress (a \\ b) (b \\ a) b = a", "start": [ 105, 1 ], "end": [ 110, 23 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_idem", "code": "@[simp]\ntheorem compress_idem (u v a : α) : compress u v (compress u v a) = compress u v a", "start": [ 113, 1 ], "end": [ 120, 8 ], "kind": "commanddeclaration" }, { "full_name": "UV.compression", "code": "def compression (u v : α) (s : Finset α) :=\n (s.filter (compress u v · ∈ s)) ∪ (s.image <\| compress u v).filter (· ∉ s)", "start": [ 125, 1 ], "end": [ 128, 77 ], "kind": "commanddeclaration" }, { "full_name": "UV.IsCompressed", "code": "def IsCompressed (u v : α) (s : Finset α) :=\n 𝓒 u v s = s", "start": [ 136, 1 ], "end": [ 138, 14 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_injOn", "code": "theorem compress_injOn : Set.InjOn (compress u v) ↑(s.filter (compress u v · ∉ s))", "start": [ 141, 1 ], "end": [ 151, 27 ], "kind": "commanddeclaration" }, { "full_name": "UV.mem_compression", "code": "theorem mem_compression :\n a ∈ 𝓒 u v s ↔ a ∈ s ∧ compress u v a ∈ s ∨ a ∉ s ∧ ∃ b ∈ s, compress u v b = a", "start": [ 154, 1 ], "end": [ 158, 68 ], "kind": "commanddeclaration" }, { "full_name": "UV.IsCompressed.eq", "code": "protected theorem IsCompressed.eq (h : IsCompressed u v s) : 𝓒 u v s = s", "start": [ 161, 1 ], "end": [ 161, 78 ], "kind": "commanddeclaration" }, { "full_name": "UV.compression_self", "code": "@[simp]\ntheorem compression_self (u : α) (s : Finset α) : 𝓒 u u s = s", "start": [ 164, 1 ], "end": [ 173, 17 ], "kind": "commanddeclaration" }, { "full_name": "UV.isCompressed_self", "code": "theorem isCompressed_self (u : α) (s : Finset α) : IsCompressed u u s", "start": [ 176, 1 ], "end": [ 177, 94 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_disjoint", "code": "theorem compress_disjoint :\n Disjoint (s.filter (compress u v · ∈ s)) ((s.image <\| compress u v).filter (· ∉ s))", "start": [ 180, 1 ], "end": [ 182, 77 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_mem_compression", "code": "theorem compress_mem_compression (ha : a ∈ s) : compress u v a ∈ 𝓒 u v s", "start": [ 185, 1 ], "end": [ 190, 33 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_mem_compression_of_mem_compression", "code": "theorem compress_mem_compression_of_mem_compression (ha : a ∈ 𝓒 u v s) :\n compress u v a ∈ 𝓒 u v s", "start": [ 194, 1 ], "end": [ 200, 77 ], "kind": "commanddeclaration" }, { "full_name": "UV.compression_idem", "code": "@[simp]\ntheorem compression_idem (u v : α) (s : Finset α) : 𝓒 u v (𝓒 u v s) = 𝓒 u v s", "start": [ 203, 1 ], "end": [ 209, 57 ], "kind": "commanddeclaration" }, { "full_name": "UV.card_compression", "code": "@[simp]\ntheorem card_compression (u v : α) (s : Finset α) : (𝓒 u v s).card = s.card", "start": [ 212, 1 ], "end": [ 217, 32 ], "kind": "commanddeclaration" }, { "full_name": "UV.le_of_mem_compression_of_not_mem", "code": "theorem le_of_mem_compression_of_not_mem (h : a ∈ 𝓒 u v s) (ha : a ∉ s) : u ≤ a", "start": [ 220, 1 ], "end": [ 228, 41 ], "kind": "commanddeclaration" }, { "full_name": "UV.disjoint_of_mem_compression_of_not_mem", "code": "theorem disjoint_of_mem_compression_of_not_mem (h : a ∈ 𝓒 u v s) (ha : a ∉ s) : Disjoint v a", "start": [ 231, 1 ], "end": [ 239, 41 ], "kind": "commanddeclaration" }, { "full_name": "UV.sup_sdiff_mem_of_mem_compression_of_not_mem", "code": "theorem sup_sdiff_mem_of_mem_compression_of_not_mem (h : a ∈ 𝓒 u v s) (ha : a ∉ s) :\n (a ⊔ v) \\ u ∈ s", "start": [ 242, 1 ], "end": [ 251, 41 ], "kind": "commanddeclaration" }, { "full_name": "UV.sup_sdiff_mem_of_mem_compression", "code": "theorem sup_sdiff_mem_of_mem_compression (ha : a ∈ 𝓒 u v s) (hva : v ≤ a) (hua : Disjoint u a) :\n (a ⊔ u) \\ v ∈ s", "start": [ 254, 1 ], "end": [ 271, 53 ], "kind": "commanddeclaration" }, { "full_name": "UV.mem_of_mem_compression", "code": "theorem mem_of_mem_compression (ha : a ∈ 𝓒 u v s) (hva : v ≤ a) (hvu : v = ⊥ → u = ⊥) :\n a ∈ s", "start": [ 274, 1 ], "end": [ 285, 14 ], "kind": "commanddeclaration" }, { "full_name": "UV.card_compress", "code": "theorem card_compress (huv : u.card = v.card) (a : Finset α) : (compress u v a).card = a.card", "start": [ 296, 1 ], "end": [ 302, 8 ], "kind": "commanddeclaration" }, { "full_name": "Set.Sized.uvCompression", "code": "lemma _root_.Set.Sized.uvCompression (huv : u.card = v.card) (h𝒜 : (𝒜 : Set (Finset α)).Sized r) :\n (𝓒 u v 𝒜 : Set (Finset α)).Sized r := by\n simp_rw [Set.Sized, mem_coe, mem_compression]\n rintro s (hs \| ⟨huvt, t, ht, rfl⟩)\n · exact h𝒜 hs.1\n · rw [card_compress huv, h𝒜 ht]", "start": [ 305, 1 ], "end": [ 310, 34 ], "kind": "lemma" }, { "full_name": "UV.aux", "code": "private theorem aux (huv : ∀ x ∈ u, ∃ y ∈ v, IsCompressed (u.erase x) (v.erase y) 𝒜) :\n v = ∅ → u = ∅", "start": [ 312, 1 ], "end": [ 314, 93 ], "kind": "commanddeclaration" }, { "full_name": "UV.shadow_compression_subset_compression_shadow", "code": "theorem shadow_compression_subset_compression_shadow (u v : Finset α)\n (huv : ∀ x ∈ u, ∃ y ∈ v, IsCompressed (u.erase x) (v.erase y) 𝒜) :\n ∂ (𝓒 u v 𝒜) ⊆ 𝓒 u v (∂ 𝒜)", "start": [ 316, 1 ], "end": [ 420, 93 ], "kind": "commanddeclaration" }, { "full_name": "UV.card_shadow_compression_le", "code": "theorem card_shadow_compression_le (u v : Finset α)\n (huv : ∀ x ∈ u, ∃ y ∈ v, IsCompressed (u.erase x) (v.erase y) 𝒜) :\n (∂ (𝓒 u v 𝒜)).card ≤ (∂ 𝒜).card", "start": [ 423, 1 ], "end": [ 430, 32 ], "kind": "commanddeclaration" } ]
Mathlib/LinearAlgebra/AffineSpace/Pointwise.lean	[ "Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean", ".lake/packages/lean4/src/lean/Init.lean" ]	[ { "full_name": "AffineSubspace.pointwiseAddAction", "code": "protected def pointwiseAddAction : AddAction V (AffineSubspace k P) where\n vadd x S := S.map (AffineEquiv.constVAdd k P x)\n zero_vadd p := ((congr_arg fun f => p.map f) <\| AffineMap.ext <\| zero_vadd _).trans p.map_id\n add_vadd _ _ p :=\n ((congr_arg fun f => p.map f) <\| AffineMap.ext <\| add_vadd _ _).trans (p.map_map _ _).symm", "start": [ 30, 1 ], "end": [ 37, 95 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.pointwise_vadd_eq_map", "code": "theorem pointwise_vadd_eq_map (v : V) (s : AffineSubspace k P) :\n v +ᵥ s = s.map (AffineEquiv.constVAdd k P v)", "start": [ 44, 1 ], "end": [ 46, 6 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.coe_pointwise_vadd", "code": "@[simp]\ntheorem coe_pointwise_vadd (v : V) (s : AffineSubspace k P) :\n ((v +ᵥ s : AffineSubspace k P) : Set P) = v +ᵥ (s : Set P)", "start": [ 48, 1 ], "end": [ 51, 6 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.vadd_mem_pointwise_vadd_iff", "code": "theorem vadd_mem_pointwise_vadd_iff {v : V} {s : AffineSubspace k P} {p : P} :\n v +ᵥ p ∈ v +ᵥ s ↔ p ∈ s", "start": [ 54, 1 ], "end": [ 56, 24 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.pointwise_vadd_bot", "code": "theorem pointwise_vadd_bot (v : V) : v +ᵥ (⊥ : AffineSubspace k P) = ⊥", "start": [ 59, 1 ], "end": [ 60, 45 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.pointwise_vadd_direction", "code": "theorem pointwise_vadd_direction (v : V) (s : AffineSubspace k P) :\n (v +ᵥ s).direction = s.direction", "start": [ 63, 1 ], "end": [ 66, 27 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.pointwise_vadd_span", "code": "theorem pointwise_vadd_span (v : V) (s : Set P) : v +ᵥ affineSpan k s = affineSpan k (v +ᵥ s)", "start": [ 69, 1 ], "end": [ 70, 15 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.map_pointwise_vadd", "code": "theorem map_pointwise_vadd (f : P₁ →ᵃ[k] P₂) (v : V₁) (s : AffineSubspace k P₁) :\n (v +ᵥ s).map f = f.linear v +ᵥ s.map f", "start": [ 73, 1 ], "end": [ 78, 23 ], "kind": "commanddeclaration" } ]
Mathlib/Lean/CoreM.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Tactic/ToExpr.lean" ]	[ { "full_name": "CoreM.withImportModules", "code": "def CoreM.withImportModules (modules : Array Name) (run : CoreM α)\n (searchPath : Option SearchPath := none) (options : Options := {})\n (trustLevel : UInt32 := 0) (fileName := \"\") :\n IO α := unsafe do\n if let some sp := searchPath then searchPathRef.set sp\n Lean.withImportModules (modules.map (Import.mk · false)) options trustLevel fun env =>\n let ctx := {fileName, options, fileMap := default}\n let state := {env}\n Prod.fst <$> (CoreM.toIO · ctx state) do\n run", "start": [ 16, 1 ], "end": [ 28, 10 ], "kind": "commanddeclaration" } ]
Mathlib/Algebra/Algebra/Subalgebra/Rank.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/LinearAlgebra/Dimension/Free.lean", "Mathlib/LinearAlgebra/FreeModule/StrongRankCondition.lean", "Mathlib/LinearAlgebra/Dimension/Finite.lean" ]	[ { "full_name": "Subalgebra.rank_sup_eq_rank_left_mul_rank_of_free", "code": "theorem rank_sup_eq_rank_left_mul_rank_of_free :\n Module.rank R ↥(A ⊔ B) = Module.rank R A * Module.rank A (Algebra.adjoin A (B : Set S))", "start": [ 30, 1 ], "end": [ 41, 43 ], "kind": "commanddeclaration" }, { "full_name": "Subalgebra.rank_sup_eq_rank_right_mul_rank_of_free", "code": "theorem rank_sup_eq_rank_right_mul_rank_of_free :\n Module.rank R ↥(A ⊔ B) = Module.rank R B * Module.rank B (Algebra.adjoin B (A : Set S))", "start": [ 43, 1 ], "end": [ 45, 56 ], "kind": "commanddeclaration" }, { "full_name": "Subalgebra.finrank_sup_eq_finrank_left_mul_finrank_of_free", "code": "theorem finrank_sup_eq_finrank_left_mul_finrank_of_free :\n finrank R ↥(A ⊔ B) = finrank R A * finrank A (Algebra.adjoin A (B : Set S))", "start": [ 47, 1 ], "end": [ 49, 97 ], "kind": "commanddeclaration" }, { "full_name": "Subalgebra.finrank_sup_eq_finrank_right_mul_finrank_of_free", "code": "theorem finrank_sup_eq_finrank_right_mul_finrank_of_free :\n finrank R ↥(A ⊔ B) = finrank R B * finrank B (Algebra.adjoin B (A : Set S))", "start": [ 51, 1 ], "end": [ 53, 65 ], "kind": "commanddeclaration" }, { "full_name": "Subalgebra.finrank_left_dvd_finrank_sup_of_free", "code": "theorem finrank_left_dvd_finrank_sup_of_free :\n finrank R A ∣ finrank R ↥(A ⊔ B)", "start": [ 55, 1 ], "end": [ 56, 97 ], "kind": "commanddeclaration" }, { "full_name": "Subalgebra.finrank_right_dvd_finrank_sup_of_free", "code": "theorem finrank_right_dvd_finrank_sup_of_free :\n finrank R B ∣ finrank R ↥(A ⊔ B)", "start": [ 58, 1 ], "end": [ 59, 98 ], "kind": "commanddeclaration" } ]
Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean	[ "Mathlib/Analysis/Convex/Hull.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/LinearAlgebra/AffineSpace/Independent.lean" ]	[ { "full_name": "Geometry.SimplicialComplex", "code": "@[ext]\nstructure SimplicialComplex where\n \n faces : Set (Finset E)\n \n not_empty_mem : ∅ ∉ faces\n \n indep : ∀ {s}, s ∈ faces → AffineIndependent 𝕜 ((↑) : s → E)\n \n down_closed : ∀ {s t}, s ∈ faces → t ⊆ s → t ≠ ∅ → t ∈ faces\n inter_subset_convexHull : ∀ {s t}, s ∈ faces → t ∈ faces →\n convexHull 𝕜 ↑s ∩ convexHull 𝕜 ↑t ⊆ convexHull 𝕜 (s ∩ t : Set E)", "start": [ 53, 1 ], "end": [ 68, 69 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.space", "code": "def space (K : SimplicialComplex 𝕜 E) : Set E :=\n ⋃ s ∈ K.faces, convexHull 𝕜 (s : Set E)", "start": [ 80, 1 ], "end": [ 82, 42 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.mem_space_iff", "code": "theorem mem_space_iff : x ∈ K.space ↔ ∃ s ∈ K.faces, x ∈ convexHull 𝕜 (s : Set E)", "start": [ 86, 1 ], "end": [ 87, 15 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.convexHull_subset_space", "code": "theorem convexHull_subset_space (hs : s ∈ K.faces) : convexHull 𝕜 ↑s ⊆ K.space", "start": [ 91, 1 ], "end": [ 93, 6 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.subset_space", "code": "protected theorem subset_space (hs : s ∈ K.faces) : (s : Set E) ⊆ K.space", "start": [ 96, 1 ], "end": [ 97, 62 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.convexHull_inter_convexHull", "code": "theorem convexHull_inter_convexHull (hs : s ∈ K.faces) (ht : t ∈ K.faces) :\n convexHull 𝕜 ↑s ∩ convexHull 𝕜 ↑t = convexHull 𝕜 (s ∩ t : Set E)", "start": [ 100, 1 ], "end": [ 104, 45 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHull", "code": "theorem disjoint_or_exists_inter_eq_convexHull (hs : s ∈ K.faces) (ht : t ∈ K.faces) :\n Disjoint (convexHull 𝕜 (s : Set E)) (convexHull 𝕜 ↑t) ∨\n ∃ u ∈ K.faces, convexHull 𝕜 (s : Set E) ∩ convexHull 𝕜 ↑t = convexHull 𝕜 ↑u", "start": [ 107, 1 ], "end": [ 119, 54 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.ofErase", "code": "@[simps]\ndef ofErase (faces : Set (Finset E)) (indep : ∀ s ∈ faces, AffineIndependent 𝕜 ((↑) : s → E))\n (down_closed : ∀ s ∈ faces, ∀ t ⊆ s, t ∈ faces)\n (inter_subset_convexHull : ∀ᵉ (s ∈ faces) (t ∈ faces),\n convexHull 𝕜 ↑s ∩ convexHull 𝕜 ↑t ⊆ convexHull 𝕜 (s ∩ t : Set E)) :\n SimplicialComplex 𝕜 E where\n faces := faces \\ {∅}\n not_empty_mem h := h.2 (mem_singleton _)\n indep hs := indep _ hs.1\n down_closed hs hts ht := ⟨down_closed _ hs.1 _ hts, ht⟩\n inter_subset_convexHull hs ht := inter_subset_convexHull _ hs.1 _ ht.1", "start": [ 122, 1 ], "end": [ 133, 73 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.ofSubcomplex", "code": "@[simps]\ndef ofSubcomplex (K : SimplicialComplex 𝕜 E) (faces : Set (Finset E)) (subset : faces ⊆ K.faces)\n (down_closed : ∀ {s t}, s ∈ faces → t ⊆ s → t ∈ faces) : SimplicialComplex 𝕜 E :=\n { faces\n not_empty_mem := fun h => K.not_empty_mem (subset h)\n indep := fun hs => K.indep (subset hs)\n down_closed := fun hs hts _ => down_closed hs hts\n inter_subset_convexHull := fun hs ht => K.inter_subset_convexHull (subset hs) (subset ht) }", "start": [ 136, 1 ], "end": [ 144, 96 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.vertices", "code": "def vertices (K : SimplicialComplex 𝕜 E) : Set E :=\n { x \| {x} ∈ K.faces }", "start": [ 150, 1 ], "end": [ 152, 24 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.mem_vertices", "code": "theorem mem_vertices : x ∈ K.vertices ↔ {x} ∈ K.faces", "start": [ 155, 1 ], "end": [ 155, 65 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.vertices_eq", "code": "theorem vertices_eq : K.vertices = ⋃ k ∈ K.faces, (k : Set E)", "start": [ 158, 1 ], "end": [ 162, 96 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.vertices_subset_space", "code": "theorem vertices_subset_space : K.vertices ⊆ K.space", "start": [ 165, 1 ], "end": [ 166, 86 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.vertex_mem_convexHull_iff", "code": "theorem vertex_mem_convexHull_iff (hx : x ∈ K.vertices) (hs : s ∈ K.faces) :\n x ∈ convexHull 𝕜 (s : Set E) ↔ x ∈ s", "start": [ 169, 1 ], "end": [ 176, 38 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.face_subset_face_iff", "code": "theorem face_subset_face_iff (hs : s ∈ K.faces) (ht : t ∈ K.faces) :\n convexHull 𝕜 (s : Set E) ⊆ convexHull 𝕜 ↑t ↔ s ⊆ t", "start": [ 179, 1 ], "end": [ 186, 21 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.facets", "code": "def facets (K : SimplicialComplex 𝕜 E) : Set (Finset E) :=\n { s ∈ K.faces \| ∀ ⦃t⦄, t ∈ K.faces → s ⊆ t → s = t }", "start": [ 192, 1 ], "end": [ 194, 55 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.mem_facets", "code": "theorem mem_facets : s ∈ K.facets ↔ s ∈ K.faces ∧ ∀ t ∈ K.faces, s ⊆ t → s = t", "start": [ 197, 1 ], "end": [ 198, 14 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.facets_subset", "code": "theorem facets_subset : K.facets ⊆ K.faces", "start": [ 201, 1 ], "end": [ 201, 63 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.not_facet_iff_subface", "code": "theorem not_facet_iff_subface (hs : s ∈ K.faces) : s ∉ K.facets ↔ ∃ t, t ∈ K.faces ∧ s ⊂ t", "start": [ 204, 1 ], "end": [ 212, 33 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.hasBot", "code": "instance hasBot : Bot (SimplicialComplex 𝕜 E) :=\n ⟨{ faces := ∅\n not_empty_mem := Set.not_mem_empty ∅\n indep := fun hs => (Set.not_mem_empty _ hs).elim\n down_closed := fun hs => (Set.not_mem_empty _ hs).elim\n inter_subset_convexHull := fun hs => (Set.not_mem_empty _ hs).elim }⟩", "start": [ 241, 1 ], "end": [ 246, 76 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.faces_bot", "code": "theorem faces_bot : (⊥ : SimplicialComplex 𝕜 E).faces = ∅", "start": [ 256, 1 ], "end": [ 256, 65 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.space_bot", "code": "theorem space_bot : (⊥ : SimplicialComplex 𝕜 E).space = ∅", "start": [ 259, 1 ], "end": [ 260, 22 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.facets_bot", "code": "theorem facets_bot : (⊥ : SimplicialComplex 𝕜 E).facets = ∅", "start": [ 263, 1 ], "end": [ 264, 41 ], "kind": "commanddeclaration" } ]
Mathlib/Analysis/Calculus/Gradient/Basic.lean	[ "Mathlib/Analysis/Calculus/FDeriv/Basic.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/InnerProductSpace/Dual.lean", "Mathlib/Analysis/Calculus/Deriv/Basic.lean" ]	[ { "full_name": "HasGradientAtFilter", "code": "def HasGradientAtFilter (f : F → 𝕜) (f' x : F) (L : Filter F) :=\n HasFDerivAtFilter f (toDual 𝕜 F f') x L", "start": [ 48, 1 ], "end": [ 51, 42 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt", "code": "def HasGradientWithinAt (f : F → 𝕜) (f' : F) (s : Set F) (x : F) :=\n HasGradientAtFilter f f' x (𝓝[s] x)", "start": [ 53, 1 ], "end": [ 56, 38 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt", "code": "def HasGradientAt (f : F → 𝕜) (f' x : F) :=\n HasGradientAtFilter f f' x (𝓝 x)", "start": [ 58, 1 ], "end": [ 61, 35 ], "kind": "commanddeclaration" }, { "full_name": "gradientWithin", "code": "def gradientWithin (f : F → 𝕜) (s : Set F) (x : F) : F :=\n (toDual 𝕜 F).symm (fderivWithin 𝕜 f s x)", "start": [ 63, 1 ], "end": [ 68, 43 ], "kind": "commanddeclaration" }, { "full_name": "gradient", "code": "def gradient (f : F → 𝕜) (x : F) : F :=\n (toDual 𝕜 F).symm (fderiv 𝕜 f x)", "start": [ 70, 1 ], "end": [ 75, 35 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_iff_hasFDerivWithinAt", "code": "theorem hasGradientWithinAt_iff_hasFDerivWithinAt {s : Set F} :\n HasGradientWithinAt f f' s x ↔ HasFDerivWithinAt f (toDual 𝕜 F f') s x", "start": [ 86, 1 ], "end": [ 88, 10 ], "kind": "commanddeclaration" }, { "full_name": "hasFDerivWithinAt_iff_hasGradientWithinAt", "code": "theorem hasFDerivWithinAt_iff_hasGradientWithinAt {frechet : F →L[𝕜] 𝕜} {s : Set F} :\n HasFDerivWithinAt f frechet s x ↔ HasGradientWithinAt f ((toDual 𝕜 F).symm frechet) s x", "start": [ 90, 1 ], "end": [ 92, 88 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAt_iff_hasFDerivAt", "code": "theorem hasGradientAt_iff_hasFDerivAt :\n HasGradientAt f f' x ↔ HasFDerivAt f (toDual 𝕜 F f') x", "start": [ 94, 1 ], "end": [ 96, 10 ], "kind": "commanddeclaration" }, { "full_name": "hasFDerivAt_iff_hasGradientAt", "code": "theorem hasFDerivAt_iff_hasGradientAt {frechet : F →L[𝕜] 𝕜} :\n HasFDerivAt f frechet x ↔ HasGradientAt f ((toDual 𝕜 F).symm frechet) x", "start": [ 98, 1 ], "end": [ 100, 76 ], "kind": "commanddeclaration" }, { "full_name": "gradient_eq_zero_of_not_differentiableAt", "code": "theorem gradient_eq_zero_of_not_differentiableAt (h : ¬DifferentiableAt 𝕜 f x) : ∇ f x = 0", "start": [ 110, 1 ], "end": [ 111, 65 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.unique", "code": "theorem HasGradientAt.unique {gradf gradg : F}\n (hf : HasGradientAt f gradf x) (hg : HasGradientAt f gradg x) :\n gradf = gradg", "start": [ 113, 1 ], "end": [ 116, 64 ], "kind": "commanddeclaration" }, { "full_name": "DifferentiableAt.hasGradientAt", "code": "theorem DifferentiableAt.hasGradientAt (h : DifferentiableAt 𝕜 f x) :\n HasGradientAt f (∇ f x) x", "start": [ 118, 1 ], "end": [ 121, 22 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.differentiableAt", "code": "theorem HasGradientAt.differentiableAt (h : HasGradientAt f f' x) :\n DifferentiableAt 𝕜 f x", "start": [ 123, 1 ], "end": [ 125, 33 ], "kind": "commanddeclaration" }, { "full_name": "DifferentiableWithinAt.hasGradientWithinAt", "code": "theorem DifferentiableWithinAt.hasGradientWithinAt (h : DifferentiableWithinAt 𝕜 f s x) :\n HasGradientWithinAt f (gradientWithin f s x) s x", "start": [ 127, 1 ], "end": [ 131, 28 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.differentiableWithinAt", "code": "theorem HasGradientWithinAt.differentiableWithinAt (h : HasGradientWithinAt f f' s x) :\n DifferentiableWithinAt 𝕜 f s x", "start": [ 133, 1 ], "end": [ 135, 45 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_univ", "code": "@[simp]\ntheorem hasGradientWithinAt_univ : HasGradientWithinAt f f' univ x ↔ HasGradientAt f f' x", "start": [ 137, 1 ], "end": [ 140, 31 ], "kind": "commanddeclaration" }, { "full_name": "DifferentiableOn.hasGradientAt", "code": "theorem DifferentiableOn.hasGradientAt (h : DifferentiableOn 𝕜 f s) (hs : s ∈ 𝓝 x) :\n HasGradientAt f (∇ f x) x", "start": [ 142, 1 ], "end": [ 144, 35 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.gradient", "code": "theorem HasGradientAt.gradient (h : HasGradientAt f f' x) : ∇ f x = f'", "start": [ 146, 1 ], "end": [ 147, 44 ], "kind": "commanddeclaration" }, { "full_name": "gradient_eq", "code": "theorem gradient_eq {f' : F → F} (h : ∀ x, HasGradientAt f (f' x) x) : ∇ f = f'", "start": [ 149, 1 ], "end": [ 150, 33 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAtFilter.hasDerivAtFilter", "code": "theorem HasGradientAtFilter.hasDerivAtFilter (h : HasGradientAtFilter g g' u L') :\n HasDerivAtFilter g (starRingEnd 𝕜 g') u L'", "start": [ 156, 1 ], "end": [ 160, 31 ], "kind": "commanddeclaration" }, { "full_name": "HasDerivAtFilter.hasGradientAtFilter", "code": "theorem HasDerivAtFilter.hasGradientAtFilter (h : HasDerivAtFilter g g' u L') :\n HasGradientAtFilter g (starRingEnd 𝕜 g') u L'", "start": [ 162, 1 ], "end": [ 166, 36 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.hasDerivAt", "code": "theorem HasGradientAt.hasDerivAt (h : HasGradientAt g g' u) :\n HasDerivAt g (starRingEnd 𝕜 g') u", "start": [ 168, 1 ], "end": [ 171, 16 ], "kind": "commanddeclaration" }, { "full_name": "HasDerivAt.hasGradientAt", "code": "theorem HasDerivAt.hasGradientAt (h : HasDerivAt g g' u) :\n HasGradientAt g (starRingEnd 𝕜 g') u", "start": [ 173, 1 ], "end": [ 176, 8 ], "kind": "commanddeclaration" }, { "full_name": "gradient_eq_deriv", "code": "theorem gradient_eq_deriv : ∇ g u = starRingEnd 𝕜 (deriv g u)", "start": [ 178, 1 ], "end": [ 181, 100 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAtFilter.hasDerivAtFilter'", "code": "theorem HasGradientAtFilter.hasDerivAtFilter' (h : HasGradientAtFilter g g' u L') :\n HasDerivAtFilter g g' u L'", "start": [ 189, 1 ], "end": [ 190, 53 ], "kind": "commanddeclaration" }, { "full_name": "HasDerivAtFilter.hasGradientAtFilter'", "code": "theorem HasDerivAtFilter.hasGradientAtFilter' (h : HasDerivAtFilter g g' u L') :\n HasGradientAtFilter g g' u L'", "start": [ 192, 1 ], "end": [ 193, 59 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.hasDerivAt'", "code": "theorem HasGradientAt.hasDerivAt' (h : HasGradientAt g g' u) :\n HasDerivAt g g' u", "start": [ 195, 1 ], "end": [ 196, 38 ], "kind": "commanddeclaration" }, { "full_name": "HasDerivAt.hasGradientAt'", "code": "theorem HasDerivAt.hasGradientAt' (h : HasDerivAt g g' u) :\n HasGradientAt g g' u", "start": [ 198, 1 ], "end": [ 199, 44 ], "kind": "commanddeclaration" }, { "full_name": "gradient_eq_deriv'", "code": "theorem gradient_eq_deriv' : ∇ g u = deriv g u", "start": [ 201, 1 ], "end": [ 201, 68 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAtFilter_iff_isLittleO", "code": "theorem hasGradientAtFilter_iff_isLittleO :\n HasGradientAtFilter f f' x L ↔\n (fun x' : F => f x' - f x - ⟪f', x' - x⟫) =o[L] fun x' => x' - x", "start": [ 209, 1 ], "end": [ 212, 37 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_iff_isLittleO", "code": "theorem hasGradientWithinAt_iff_isLittleO :\n HasGradientWithinAt f f' s x ↔\n (fun x' : F => f x' - f x - ⟪f', x' - x⟫) =o[𝓝[s] x] fun x' => x' - x", "start": [ 214, 1 ], "end": [ 217, 36 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_iff_tendsto", "code": "theorem hasGradientWithinAt_iff_tendsto :\n HasGradientWithinAt f f' s x ↔\n Tendsto (fun x' => ‖x' - x‖⁻¹ * ‖f x' - f x - ⟪f', x' - x⟫‖) (𝓝[s] x) (𝓝 0)", "start": [ 219, 1 ], "end": [ 222, 32 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAt_iff_isLittleO", "code": "theorem hasGradientAt_iff_isLittleO : HasGradientAt f f' x ↔\n (fun x' : F => f x' - f x - ⟪f', x' - x⟫) =o[𝓝 x] fun x' => x' - x", "start": [ 224, 1 ], "end": [ 226, 36 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAt_iff_tendsto", "code": "theorem hasGradientAt_iff_tendsto :\n HasGradientAt f f' x ↔\n Tendsto (fun x' => ‖x' - x‖⁻¹ * ‖f x' - f x - ⟪f', x' - x⟫‖) (𝓝 x) (𝓝 0)", "start": [ 228, 1 ], "end": [ 231, 32 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAtFilter.isBigO_sub", "code": "theorem HasGradientAtFilter.isBigO_sub (h : HasGradientAtFilter f f' x L) :\n (fun x' => f x' - f x) =O[L] fun x' => x' - x", "start": [ 233, 1 ], "end": [ 235, 33 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_congr_set'", "code": "theorem hasGradientWithinAt_congr_set' {s t : Set F} (y : F) (h : s =ᶠ[𝓝[{y}ᶜ] x] t) :\n HasGradientWithinAt f f' s x ↔ HasGradientWithinAt f f' t x", "start": [ 237, 1 ], "end": [ 239, 35 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_congr_set", "code": "theorem hasGradientWithinAt_congr_set {s t : Set F} (h : s =ᶠ[𝓝 x] t) :\n HasGradientWithinAt f f' s x ↔ HasGradientWithinAt f f' t x", "start": [ 241, 1 ], "end": [ 243, 32 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAt_iff_isLittleO_nhds_zero", "code": "theorem hasGradientAt_iff_isLittleO_nhds_zero : HasGradientAt f f' x ↔\n (fun h => f (x + h) - f x - ⟪f', h⟫) =o[𝓝 0] fun h => h", "start": [ 245, 1 ], "end": [ 247, 38 ], "kind": "commanddeclaration" }, { "full_name": "Filter.EventuallyEq.hasGradientAtFilter_iff", "code": "theorem Filter.EventuallyEq.hasGradientAtFilter_iff (h₀ : f₀ =ᶠ[L] f₁) (hx : f₀ x = f₁ x)\n (h₁ : f₀' = f₁') : HasGradientAtFilter f₀ f₀' x L ↔ HasGradientAtFilter f₁ f₁' x L", "start": [ 257, 1 ], "end": [ 259, 45 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAtFilter.congr_of_eventuallyEq", "code": "theorem HasGradientAtFilter.congr_of_eventuallyEq (h : HasGradientAtFilter f f' x L)\n (hL : f₁ =ᶠ[L] f) (hx : f₁ x = f x) : HasGradientAtFilter f₁ f' x L", "start": [ 261, 1 ], "end": [ 263, 42 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.congr_mono", "code": "theorem HasGradientWithinAt.congr_mono (h : HasGradientWithinAt f f' s x) (ht : ∀ x ∈ t, f₁ x = f x)\n (hx : f₁ x = f x) (h₁ : t ⊆ s) : HasGradientWithinAt f₁ f' t x", "start": [ 265, 1 ], "end": [ 267, 42 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.congr", "code": "theorem HasGradientWithinAt.congr (h : HasGradientWithinAt f f' s x) (hs : ∀ x ∈ s, f₁ x = f x)\n (hx : f₁ x = f x) : HasGradientWithinAt f₁ f' s x", "start": [ 269, 1 ], "end": [ 271, 32 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.congr_of_mem", "code": "theorem HasGradientWithinAt.congr_of_mem (h : HasGradientWithinAt f f' s x)\n (hs : ∀ x ∈ s, f₁ x = f x) (hx : x ∈ s) : HasGradientWithinAt f₁ f' s x", "start": [ 273, 1 ], "end": [ 275, 23 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.congr_of_eventuallyEq", "code": "theorem HasGradientWithinAt.congr_of_eventuallyEq (h : HasGradientWithinAt f f' s x)\n (h₁ : f₁ =ᶠ[𝓝[s] x] f) (hx : f₁ x = f x) : HasGradientWithinAt f₁ f' s x", "start": [ 277, 1 ], "end": [ 279, 52 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.congr_of_eventuallyEq_of_mem", "code": "theorem HasGradientWithinAt.congr_of_eventuallyEq_of_mem (h : HasGradientWithinAt f f' s x)\n (h₁ : f₁ =ᶠ[𝓝[s] x] f) (hx : x ∈ s) : HasGradientWithinAt f₁ f' s x", "start": [ 281, 1 ], "end": [ 283, 54 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.congr_of_eventuallyEq", "code": "theorem HasGradientAt.congr_of_eventuallyEq (h : HasGradientAt f f' x) (h₁ : f₁ =ᶠ[𝓝 x] f) :\n HasGradientAt f₁ f' x", "start": [ 285, 1 ], "end": [ 287, 74 ], "kind": "commanddeclaration" }, { "full_name": "Filter.EventuallyEq.gradient_eq", "code": "theorem Filter.EventuallyEq.gradient_eq (hL : f₁ =ᶠ[𝓝 x] f) : ∇ f₁ x = ∇ f x", "start": [ 289, 1 ], "end": [ 291, 38 ], "kind": "commanddeclaration" }, { "full_name": "Filter.EventuallyEq.gradient", "code": "protected theorem Filter.EventuallyEq.gradient (h : f₁ =ᶠ[𝓝 x] f) : ∇ f₁ =ᶠ[𝓝 x] ∇ f", "start": [ 293, 1 ], "end": [ 294, 52 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAtFilter_const", "code": "theorem hasGradientAtFilter_const : HasGradientAtFilter (fun _ => c) 0 x L", "start": [ 304, 1 ], "end": [ 305, 74 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_const", "code": "theorem hasGradientWithinAt_const : HasGradientWithinAt (fun _ => c) 0 s x", "start": [ 307, 1 ], "end": [ 308, 34 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAt_const", "code": "theorem hasGradientAt_const : HasGradientAt (fun _ => c) 0 x", "start": [ 310, 1 ], "end": [ 311, 34 ], "kind": "commanddeclaration" }, { "full_name": "gradient_const", "code": "theorem gradient_const : ∇ (fun _ => c) x = 0", "start": [ 313, 1 ], "end": [ 314, 55 ], "kind": "commanddeclaration" }, { "full_name": "gradient_const'", "code": "@[simp]\ntheorem gradient_const' : (∇ fun _ : 𝕜 => c) = fun _ => 0", "start": [ 316, 1 ], "end": [ 318, 37 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAtFilter.tendsto_nhds", "code": "nonrec theorem HasGradientAtFilter.tendsto_nhds (hL : L ≤ 𝓝 x) (h : HasGradientAtFilter f f' x L) :\n Tendsto f L (𝓝 (f x))", "start": [ 326, 1 ], "end": [ 328, 20 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.continuousWithinAt", "code": "theorem HasGradientWithinAt.continuousWithinAt (h : HasGradientWithinAt f f' s x) :\n ContinuousWithinAt f s x", "start": [ 330, 1 ], "end": [ 332, 49 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.continuousAt", "code": "theorem HasGradientAt.continuousAt (h : HasGradientAt f f' x) : ContinuousAt f x", "start": [ 334, 1 ], "end": [ 335, 44 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.continuousOn", "code": "protected theorem HasGradientAt.continuousOn {f' : F → F} (h : ∀ x ∈ s, HasGradientAt f (f' x) x) :\n ContinuousOn f s", "start": [ 337, 1 ], "end": [ 339, 55 ], "kind": "commanddeclaration" } ]
Mathlib/LinearAlgebra/TensorAlgebra/Grading.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/RingTheory/GradedAlgebra/Basic.lean", "Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean" ]	[ { "full_name": "TensorAlgebra.GradedAlgebra.ι", "code": "nonrec def GradedAlgebra.ι : M →ₗ[R] ⨁ i : ℕ, ↥(LinearMap.range (ι R : M →ₗ[_] _) ^ i) :=\n DirectSum.lof R ℕ (fun i => ↥(LinearMap.range (ι R : M →ₗ[_] _) ^ i)) 1 ∘ₗ\n (ι R).codRestrict _ fun m => by simpa only [pow_one] using LinearMap.mem_range_self _ m", "start": [ 28, 1 ], "end": [ 32, 92 ], "kind": "commanddeclaration" }, { "full_name": "TensorAlgebra.GradedAlgebra.ι_apply", "code": "theorem GradedAlgebra.ι_apply (m : M) :\n GradedAlgebra.ι R M m =\n DirectSum.of (fun (i : ℕ) => ↥(LinearMap.range (TensorAlgebra.ι R : M →ₗ[_] _) ^ i)) 1\n ⟨TensorAlgebra.ι R m, by simpa only [pow_one] using LinearMap.mem_range_self _ m⟩", "start": [ 35, 1 ], "end": [ 39, 6 ], "kind": "commanddeclaration" }, { "full_name": "TensorAlgebra.gradedAlgebra", "code": "instance gradedAlgebra :\n GradedAlgebra ((LinearMap.range (ι R : M →ₗ[R] TensorAlgebra R M) ^ ·) : ℕ → Submodule R _) :=\n GradedAlgebra.ofAlgHom _ (lift R <\| GradedAlgebra.ι R M)\n (by\n ext m\n dsimp only [LinearMap.comp_apply, AlgHom.toLinearMap_apply, AlgHom.comp_apply,\n AlgHom.id_apply]\n rw [lift_ι_apply, GradedAlgebra.ι_apply R M, DirectSum.coeAlgHom_of, Subtype.coe_mk])\n fun i x => by\n cases' x with x hx\n dsimp only [Subtype.coe_mk, DirectSum.lof_eq_of]\n induction hx using Submodule.pow_induction_on_left' with\n \| algebraMap r =>\n rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl\n \| add x y i hx hy ihx ihy =>\n rw [AlgHom.map_add, ihx, ihy, ← AddMonoidHom.map_add]\n rfl\n \| mem_mul m hm i x hx ih =>\n obtain ⟨_, rfl⟩ := hm\n rw [AlgHom.map_mul, ih, lift_ι_apply, GradedAlgebra.ι_apply R M, DirectSum.of_mul_of]\n exact DirectSum.of_eq_of_gradedMonoid_eq (Sigma.subtype_ext (add_comm _ _) rfl)", "start": [ 44, 1 ], "end": [ 68, 86 ], "kind": "commanddeclaration" } ]
Mathlib/Data/QPF/Multivariate/Constructions/Const.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Control/Functor/Multivariate.lean", "Mathlib/Data/QPF/Multivariate/Basic.lean" ]	[ { "full_name": "MvQPF.Const", "code": "@[nolint unusedArguments]\ndef Const (A : Type*) (_v : TypeVec.{u} n) : Type _ := A", "start": [ 30, 1 ], "end": [ 32, 57 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.inhabited", "code": "instance Const.inhabited {A α} [Inhabited A] : Inhabited (Const n A α) := ⟨(default : A)⟩", "start": [ 35, 1 ], "end": [ 35, 90 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.mk", "code": "protected def mk (x : A) : Const n A α := x", "start": [ 44, 1 ], "end": [ 45, 44 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.get", "code": "protected def get (x : Const n A α) : A := x", "start": [ 48, 1 ], "end": [ 49, 45 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.mk_get", "code": "@[simp]\nprotected theorem mk_get (x : Const n A α) : Const.mk (Const.get x) = x", "start": [ 52, 1 ], "end": [ 53, 79 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.get_mk", "code": "@[simp]\nprotected theorem get_mk (x : A) : Const.get (Const.mk x : Const n A α) = x", "start": [ 56, 1 ], "end": [ 57, 83 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.map", "code": "protected def map : Const n A α → Const n A β := fun x => x", "start": [ 60, 1 ], "end": [ 61, 60 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.MvFunctor", "code": "instance MvFunctor : MvFunctor (Const n A) where map _f := Const.map", "start": [ 64, 1 ], "end": [ 64, 69 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.map_mk", "code": "theorem map_mk (x : A) : f <$$> Const.mk x = Const.mk x", "start": [ 66, 1 ], "end": [ 66, 63 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.get_map", "code": "theorem get_map (x : (Const n A) α) : Const.get (f <$$> x) = Const.get x", "start": [ 69, 1 ], "end": [ 69, 80 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.mvqpf", "code": "instance mvqpf : @MvQPF _ (Const n A) where\n P := MvPFunctor.const n A\n abs x := MvPFunctor.const.get x\n repr x := MvPFunctor.const.mk n x\n abs_repr := fun _ => const.get_mk _\n abs_map := fun _ => const.get_map _", "start": [ 72, 1 ], "end": [ 77, 38 ], "kind": "commanddeclaration" } ]
Mathlib/Combinatorics/Configuration.lean	[ "Mathlib/Combinatorics/Hall/Basic.lean", "Mathlib/Data/Fintype/BigOperators.lean", "Mathlib/SetTheory/Cardinal/Finite.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Algebra/Order/BigOperators/Group/Finset.lean" ]	[ { "full_name": "Configuration.Dual", "code": "def Dual :=\n P", "start": [ 44, 1 ], "end": [ 46, 4 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.Nondegenerate", "code": "class Nondegenerate : Prop where\n exists_point : ∀ l : L, ∃ p, p ∉ l\n exists_line : ∀ p, ∃ l : L, p ∉ l\n eq_or_eq : ∀ {p₁ p₂ : P} {l₁ l₂ : L}, p₁ ∈ l₁ → p₂ ∈ l₁ → p₁ ∈ l₂ → p₂ ∈ l₂ → p₁ = p₂ ∨ l₁ = l₂", "start": [ 65, 1 ], "end": [ 74, 98 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasPoints", "code": "class HasPoints extends Nondegenerate P L where\n mkPoint : ∀ {l₁ l₂ : L}, l₁ ≠ l₂ → P\n mkPoint_ax : ∀ {l₁ l₂ : L} (h : l₁ ≠ l₂), mkPoint h ∈ l₁ ∧ mkPoint h ∈ l₂", "start": [ 77, 1 ], "end": [ 80, 76 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines", "code": "class HasLines extends Nondegenerate P L where\n mkLine : ∀ {p₁ p₂ : P}, p₁ ≠ p₂ → L\n mkLine_ax : ∀ {p₁ p₂ : P} (h : p₁ ≠ p₂), p₁ ∈ mkLine h ∧ p₂ ∈ mkLine h", "start": [ 83, 1 ], "end": [ 86, 73 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.Dual.Nondegenerate", "code": "instance Dual.Nondegenerate [Nondegenerate P L] : Nondegenerate (Dual L) (Dual P) where\n exists_point := @exists_line P L _ _\n exists_line := @exists_point P L _ _\n eq_or_eq := @fun l₁ l₂ p₁ p₂ h₁ h₂ h₃ h₄ => (@eq_or_eq P L _ _ p₁ p₂ l₁ l₂ h₁ h₃ h₂ h₄).symm", "start": [ 95, 1 ], "end": [ 98, 95 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.Dual.hasLines", "code": "instance Dual.hasLines [HasPoints P L] : HasLines (Dual L) (Dual P) :=\n { Dual.Nondegenerate _ _ with\n mkLine := @mkPoint P L _ _\n mkLine_ax := @mkPoint_ax P L _ _ }", "start": [ 100, 1 ], "end": [ 103, 39 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.Dual.hasPoints", "code": "instance Dual.hasPoints [HasLines P L] : HasPoints (Dual L) (Dual P) :=\n { Dual.Nondegenerate _ _ with\n mkPoint := @mkLine P L _ _\n mkPoint_ax := @mkLine_ax P L _ _ }", "start": [ 105, 1 ], "end": [ 108, 39 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasPoints.existsUnique_point", "code": "theorem HasPoints.existsUnique_point [HasPoints P L] (l₁ l₂ : L) (hl : l₁ ≠ l₂) :\n ∃! p, p ∈ l₁ ∧ p ∈ l₂", "start": [ 110, 1 ], "end": [ 113, 79 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines.existsUnique_line", "code": "theorem HasLines.existsUnique_line [HasLines P L] (p₁ p₂ : P) (hp : p₁ ≠ p₂) :\n ∃! l : L, p₁ ∈ l ∧ p₂ ∈ l", "start": [ 116, 1 ], "end": [ 118, 58 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.Nondegenerate.exists_injective_of_card_le", "code": "theorem Nondegenerate.exists_injective_of_card_le [Nondegenerate P L] [Fintype P] [Fintype L]\n (h : Fintype.card L ≤ Fintype.card P) : ∃ f : L → P, Function.Injective f ∧ ∀ l, f l ∉ l", "start": [ 123, 1 ], "end": [ 166, 55 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.lineCount", "code": "noncomputable def lineCount (p : P) : ℕ :=\n Nat.card { l : L // p ∈ l }", "start": [ 172, 1 ], "end": [ 174, 30 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.pointCount", "code": "noncomputable def pointCount (l : L) : ℕ :=\n Nat.card { p : P // p ∈ l }", "start": [ 179, 1 ], "end": [ 181, 30 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.sum_lineCount_eq_sum_pointCount", "code": "theorem sum_lineCount_eq_sum_pointCount [Fintype P] [Fintype L] :\n ∑ p : P, lineCount L p = ∑ l : L, pointCount P l", "start": [ 186, 1 ], "end": [ 195, 96 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines.pointCount_le_lineCount", "code": "theorem HasLines.pointCount_le_lineCount [HasLines P L] {p : P} {l : L} (h : p ∉ l)\n [Finite { l : L // p ∈ l }] : pointCount P l ≤ lineCount L p", "start": [ 200, 1 ], "end": [ 214, 74 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasPoints.lineCount_le_pointCount", "code": "theorem HasPoints.lineCount_le_pointCount [HasPoints P L] {p : P} {l : L} (h : p ∉ l)\n [hf : Finite { p : P // p ∈ l }] : lineCount L p ≤ pointCount P l", "start": [ 217, 1 ], "end": [ 219, 67 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines.card_le", "code": "theorem HasLines.card_le [HasLines P L] [Fintype P] [Fintype L] :\n Fintype.card P ≤ Fintype.card L", "start": [ 224, 1 ], "end": [ 245, 25 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasPoints.card_le", "code": "theorem HasPoints.card_le [HasPoints P L] [Fintype P] [Fintype L] :\n Fintype.card L ≤ Fintype.card P", "start": [ 248, 1 ], "end": [ 251, 46 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines.exists_bijective_of_card_eq", "code": "theorem HasLines.exists_bijective_of_card_eq [HasLines P L] [Fintype P] [Fintype L]\n (h : Fintype.card P = Fintype.card L) :\n ∃ f : L → P, Function.Bijective f ∧ ∀ l, pointCount P l = lineCount L (f l)", "start": [ 256, 1 ], "end": [ 263, 95 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines.lineCount_eq_pointCount", "code": "theorem HasLines.lineCount_eq_pointCount [HasLines P L] [Fintype P] [Fintype L]\n (hPL : Fintype.card P = Fintype.card L) {p : P} {l : L} (hpl : p ∉ l) :\n lineCount L p = pointCount P l", "start": [ 266, 1 ], "end": [ 290, 61 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasPoints.lineCount_eq_pointCount", "code": "theorem HasPoints.lineCount_eq_pointCount [HasPoints P L] [Fintype P] [Fintype L]\n (hPL : Fintype.card P = Fintype.card L) {p : P} {l : L} (hpl : p ∉ l) :\n lineCount L p = pointCount P l", "start": [ 293, 1 ], "end": [ 296, 86 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines.hasPoints", "code": "noncomputable def HasLines.hasPoints [HasLines P L] [Fintype P] [Fintype L]\n (h : Fintype.card P = Fintype.card L) : HasPoints P L :=\n let this : ∀ l₁ l₂ : L, l₁ ≠ l₂ → ∃ p : P, p ∈ l₁ ∧ p ∈ l₂ := fun l₁ l₂ hl => by\n classical\n obtain ⟨f, _, hf2⟩ := HasLines.exists_bijective_of_card_eq h\n haveI : Nontrivial L := ⟨⟨l₁, l₂, hl⟩⟩\n haveI := Fintype.one_lt_card_iff_nontrivial.mp ((congr_arg _ h).mpr Fintype.one_lt_card)\n have h₁ : ∀ p : P, 0 < lineCount L p := fun p =>\n Exists.elim (exists_ne p) fun q hq =>\n (congr_arg _ Nat.card_eq_fintype_card).mpr\n (Fintype.card_pos_iff.mpr ⟨⟨mkLine hq, (mkLine_ax hq).2⟩⟩)\n have h₂ : ∀ l : L, 0 < pointCount P l := fun l => (congr_arg _ (hf2 l)).mpr (h₁ (f l))\n obtain ⟨p, hl₁⟩ := Fintype.card_pos_iff.mp ((congr_arg _ Nat.card_eq_fintype_card).mp (h₂ l₁))\n by_cases hl₂ : p ∈ l₂\n · exact ⟨p, hl₁, hl₂⟩\n have key' : Fintype.card { q : P // q ∈ l₂ } = Fintype.card { l : L // p ∈ l } :=\n ((HasLines.lineCount_eq_pointCount h hl₂).trans Nat.card_eq_fintype_card).symm.trans\n Nat.card_eq_fintype_card\n have : ∀ q : { q // q ∈ l₂ }, p ≠ q := fun q hq => hl₂ ((congr_arg (· ∈ l₂) hq).mpr q.2)\n let f : { q : P // q ∈ l₂ } → { l : L // p ∈ l } := fun q =>\n ⟨mkLine (this q), (mkLine_ax (this q)).1⟩\n have hf : Function.Injective f := fun q₁ q₂ hq =>\n Subtype.ext\n ((eq_or_eq q₁.2 q₂.2 (mkLine_ax (this q₁)).2\n ((congr_arg _ (Subtype.ext_iff.mp hq)).mpr (mkLine_ax (this q₂)).2)).resolve_right\n fun h => (congr_arg (¬p ∈ ·) h).mp hl₂ (mkLine_ax (this q₁)).1)\n have key' := ((Fintype.bijective_iff_injective_and_card f).mpr ⟨hf, key'⟩).2\n obtain ⟨q, hq⟩ := key' ⟨l₁, hl₁⟩\n exact ⟨q, (congr_arg _ (Subtype.ext_iff.mp hq)).mp (mkLine_ax (this q)).2, q.2⟩\n { ‹HasLines P L› with\n mkPoint := fun {l₁ l₂} hl => Classical.choose (this l₁ l₂ hl)\n mkPoint_ax := fun {l₁ l₂} hl => Classical.choose_spec (this l₁ l₂ hl) }", "start": [ 299, 1 ], "end": [ 332, 76 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasPoints.hasLines", "code": "noncomputable def HasPoints.hasLines [HasPoints P L] [Fintype P] [Fintype L]\n (h : Fintype.card P = Fintype.card L) : HasLines P L :=\n let this := @HasLines.hasPoints (Dual L) (Dual P) _ _ _ _ h.symm\n { ‹HasPoints P L› with\n mkLine := @fun _ _ => this.mkPoint\n mkLine_ax := @fun _ _ => this.mkPoint_ax }", "start": [ 335, 1 ], "end": [ 342, 47 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane", "code": "class ProjectivePlane extends HasPoints P L, HasLines P L where\n exists_config :\n ∃ (p₁ p₂ p₃ : P) (l₁ l₂ l₃ : L),\n p₁ ∉ l₂ ∧ p₁ ∉ l₃ ∧ p₂ ∉ l₁ ∧ p₂ ∈ l₂ ∧ p₂ ∈ l₃ ∧ p₃ ∉ l₁ ∧ p₃ ∈ l₂ ∧ p₃ ∉ l₃", "start": [ 347, 1 ], "end": [ 353, 84 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.order", "code": "noncomputable def order : ℕ :=\n lineCount L (Classical.choose (@exists_config P L _ _)) - 1", "start": [ 366, 1 ], "end": [ 369, 62 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.card_points_eq_card_lines", "code": "theorem card_points_eq_card_lines [Fintype P] [Fintype L] : Fintype.card P = Fintype.card L", "start": [ 372, 1 ], "end": [ 373, 61 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.lineCount_eq_lineCount", "code": "theorem lineCount_eq_lineCount [Finite P] [Finite L] (p q : P) : lineCount L p = lineCount L q", "start": [ 378, 1 ], "end": [ 395, 54 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.pointCount_eq_pointCount", "code": "theorem pointCount_eq_pointCount [Finite P] [Finite L] (l m : L) :\n pointCount P l = pointCount P m", "start": [ 400, 1 ], "end": [ 402, 40 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.lineCount_eq_pointCount", "code": "theorem lineCount_eq_pointCount [Finite P] [Finite L] (p : P) (l : L) :\n lineCount L p = pointCount P l", "start": [ 407, 1 ], "end": [ 413, 80 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.Dual.order", "code": "theorem Dual.order [Finite P] [Finite L] : order (Dual L) (Dual P) = order P L", "start": [ 418, 1 ], "end": [ 419, 59 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.lineCount_eq", "code": "theorem lineCount_eq [Finite P] [Finite L] (p : P) : lineCount L p = order P L + 1", "start": [ 424, 1 ], "end": [ 430, 44 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.pointCount_eq", "code": "theorem pointCount_eq [Finite P] [Finite L] (l : L) : pointCount P l = order P L + 1", "start": [ 435, 1 ], "end": [ 436, 80 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.one_lt_order", "code": "theorem one_lt_order [Finite P] [Finite L] : 1 < order P L", "start": [ 441, 1 ], "end": [ 450, 66 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.two_lt_lineCount", "code": "theorem two_lt_lineCount [Finite P] [Finite L] (p : P) : 2 < lineCount L p", "start": [ 455, 1 ], "end": [ 456, 77 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.two_lt_pointCount", "code": "theorem two_lt_pointCount [Finite P] [Finite L] (l : L) : 2 < pointCount P l", "start": [ 461, 1 ], "end": [ 462, 78 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.card_points", "code": "theorem card_points [Fintype P] [Finite L] : Fintype.card P = order P L ^ 2 + order P L + 1", "start": [ 467, 1 ], "end": [ 493, 94 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.card_lines", "code": "theorem card_lines [Finite P] [Fintype L] : Fintype.card L = order P L ^ 2 + order P L + 1", "start": [ 496, 1 ], "end": [ 497, 94 ], "kind": "commanddeclaration" } ]
Mathlib/FieldTheory/Laurent.lean	[ "Mathlib/Algebra/Polynomial/Taylor.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/FieldTheory/RatFunc/AsPolynomial.lean" ]	[ { "full_name": "RatFunc.taylor_mem_nonZeroDivisors", "code": "theorem taylor_mem_nonZeroDivisors (hp : p ∈ R[X]⁰) : taylor r p ∈ R[X]⁰", "start": [ 39, 1 ], "end": [ 45, 60 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurentAux", "code": "def laurentAux : RatFunc R →+* RatFunc R :=\n RatFunc.mapRingHom\n ( { toFun := taylor r\n map_add' := map_add (taylor r)\n map_mul' := taylor_mul _\n map_zero' := map_zero (taylor r)\n map_one' := taylor_one r } : R[X] →+* R[X])\n (taylor_mem_nonZeroDivisors _)", "start": [ 48, 1 ], "end": [ 57, 35 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurentAux_ofFractionRing_mk", "code": "theorem laurentAux_ofFractionRing_mk (q : R[X]⁰) :\n laurentAux r (ofFractionRing (Localization.mk p q)) =\n ofFractionRing (.mk (taylor r p) ⟨taylor r q, taylor_mem_nonZeroDivisors r q q.prop⟩)", "start": [ 60, 1 ], "end": [ 63, 38 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurentAux_div", "code": "theorem laurentAux_div :\n laurentAux r (algebraMap _ _ p / algebraMap _ _ q) =\n algebraMap _ _ (taylor r p) / algebraMap _ _ (taylor r q)", "start": [ 66, 1 ], "end": [ 70, 62 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurentAux_algebraMap", "code": "@[simp]\ntheorem laurentAux_algebraMap : laurentAux r (algebraMap _ _ p) = algebraMap _ _ (taylor r p)", "start": [ 73, 1 ], "end": [ 75, 94 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent", "code": "def laurent : RatFunc R →ₐ[R] RatFunc R :=\n RatFunc.mapAlgHom (.ofLinearMap (taylor r) (taylor_one _) (taylor_mul _))\n (taylor_mem_nonZeroDivisors _)", "start": [ 78, 1 ], "end": [ 81, 35 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_div", "code": "theorem laurent_div :\n laurent r (algebraMap _ _ p / algebraMap _ _ q) =\n algebraMap _ _ (taylor r p) / algebraMap _ _ (taylor r q)", "start": [ 84, 1 ], "end": [ 87, 23 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_algebraMap", "code": "@[simp]\ntheorem laurent_algebraMap : laurent r (algebraMap _ _ p) = algebraMap _ _ (taylor r p)", "start": [ 90, 1 ], "end": [ 92, 28 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_X", "code": "@[simp]\ntheorem laurent_X : laurent r X = X + C r", "start": [ 95, 1 ], "end": [ 97, 82 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_C", "code": "@[simp]\ntheorem laurent_C (x : R) : laurent r (C x) = C x", "start": [ 101, 1 ], "end": [ 103, 52 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_at_zero", "code": "@[simp]\ntheorem laurent_at_zero : laurent 0 f = f", "start": [ 107, 1 ], "end": [ 108, 93 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_laurent", "code": "theorem laurent_laurent : laurent r (laurent s f) = laurent (r + s) f", "start": [ 111, 1 ], "end": [ 113, 39 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_injective", "code": "theorem laurent_injective : Function.Injective (laurent r)", "start": [ 116, 1 ], "end": [ 117, 59 ], "kind": "commanddeclaration" } ]
Mathlib/LinearAlgebra/Matrix/Dual.lean	[ "Mathlib/LinearAlgebra/Dual.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/LinearAlgebra/Matrix/ToLin.lean" ]	[ { "full_name": "LinearMap.toMatrix_transpose", "code": "@[simp]\ntheorem LinearMap.toMatrix_transpose (u : V₁ →ₗ[K] V₂) :\n LinearMap.toMatrix B₂.dualBasis B₁.dualBasis (Module.Dual.transpose (R := K) u) =\n (LinearMap.toMatrix B₁ B₂ u)ᵀ", "start": [ 31, 1 ], "end": [ 37, 70 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.toLin_transpose", "code": "@[simp]\ntheorem Matrix.toLin_transpose (M : Matrix ι₁ ι₂ K) : Matrix.toLin B₁.dualBasis B₂.dualBasis Mᵀ =\n Module.Dual.transpose (R := K) (Matrix.toLin B₂ B₁ M)", "start": [ 40, 1 ], "end": [ 44, 88 ], "kind": "commanddeclaration" } ]
Mathlib/Geometry/Euclidean/Sphere/Ptolemy.lean	[ "Mathlib/Geometry/Euclidean/Sphere/Power.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Geometry/Euclidean/Triangle.lean" ]	[ { "full_name": "EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical", "code": "theorem mul_dist_add_mul_dist_eq_mul_dist_of_cospherical {a b c d p : P}\n (h : Cospherical ({a, b, c, d} : Set P)) (hapc : ∠ a p c = π) (hbpd : ∠ b p d = π) :\n dist a b * dist c d + dist b c * dist d a = dist a c * dist b d", "start": [ 52, 1 ], "end": [ 70, 51 ], "kind": "commanddeclaration" } ]
Mathlib/Topology/Order/Hom/Esakia.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Order/Hom/Bounded.lean", "Mathlib/Topology/Order/Hom/Basic.lean" ]	[ { "full_name": "PseudoEpimorphism", "code": "structure PseudoEpimorphism (α β : Type) [Preorder α] [Preorder β] extends α →o β where\n exists_map_eq_of_map_le' ⦃a : α⦄ ⦃b : β⦄ : toFun a ≤ b → ∃ c, a ≤ c ∧ toFun c = b", "start": [ 40, 1 ], "end": [ 42, 84 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom", "code": "structure EsakiaHom (α β : Type) [TopologicalSpace α] [Preorder α] [TopologicalSpace β]\n [Preorder β] extends α →Co β where\n exists_map_eq_of_map_le' ⦃a : α⦄ ⦃b : β⦄ : toFun a ≤ b → ∃ c, a ≤ c ∧ toFun c = b", "start": [ 45, 1 ], "end": [ 48, 84 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphismClass", "code": "class PseudoEpimorphismClass (F : Type) (α β : outParam Type)\n [Preorder α] [Preorder β] [FunLike F α β]\n extends RelHomClass F ((· ≤ ·) : α → α → Prop) ((· ≤ ·) : β → β → Prop) : Prop where\n exists_map_eq_of_map_le (f : F) ⦃a : α⦄ ⦃b : β⦄ : f a ≤ b → ∃ c, a ≤ c ∧ f c = b", "start": [ 53, 1 ], "end": [ 59, 83 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHomClass", "code": "class EsakiaHomClass (F : Type) (α β : outParam Type) [TopologicalSpace α] [Preorder α]\n [TopologicalSpace β] [Preorder β] [FunLike F α β]\n extends ContinuousOrderHomClass F α β : Prop where\n exists_map_eq_of_map_le (f : F) ⦃a : α⦄ ⦃b : β⦄ : f a ≤ b → ∃ c, a ≤ c ∧ f c = b", "start": [ 62, 1 ], "end": [ 68, 83 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphismClass.toTopHomClass", "code": "instance (priority := 100) PseudoEpimorphismClass.toTopHomClass [PartialOrder α] [OrderTop α]\n [Preorder β] [OrderTop β] [PseudoEpimorphismClass F α β] : TopHomClass F α β where\n map_top f := by\n let ⟨b, h⟩ := exists_map_eq_of_map_le f (@le_top _ _ _ <\| f ⊤)\n rw [← top_le_iff.1 h.1, h.2]", "start": [ 80, 1 ], "end": [ 84, 33 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHomClass.toPseudoEpimorphismClass", "code": "instance (priority := 100) EsakiaHomClass.toPseudoEpimorphismClass [TopologicalSpace α] [Preorder α]\n [TopologicalSpace β] [Preorder β] [EsakiaHomClass F α β] : PseudoEpimorphismClass F α β :=\n { ‹EsakiaHomClass F α β› with\n map_rel := ContinuousOrderHomClass.map_monotone }", "start": [ 88, 1 ], "end": [ 91, 54 ], "kind": "commanddeclaration" }, { "full_name": "OrderIsoClass.toPseudoEpimorphismClass", "code": "instance (priority := 100) OrderIsoClass.toPseudoEpimorphismClass [Preorder α] [Preorder β]\n [EquivLike F α β] [OrderIsoClass F α β] : PseudoEpimorphismClass F α β where\n exists_map_eq_of_map_le f _a b h :=\n ⟨EquivLike.inv f b, (le_map_inv_iff f).2 h, EquivLike.right_inv _ _⟩", "start": [ 105, 1 ], "end": [ 108, 73 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.instFunLike", "code": "instance instFunLike : FunLike (PseudoEpimorphism α β) α β where\n coe f := f.toFun\n coe_injective' f g h := by\n obtain ⟨⟨_, _⟩, _⟩ := f\n obtain ⟨⟨_, _⟩, _⟩ := g\n congr", "start": [ 118, 1 ], "end": [ 123, 10 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.toOrderHom_eq_coe", "code": "@[simp]\ntheorem toOrderHom_eq_coe (f : PseudoEpimorphism α β) : ⇑f.toOrderHom = f", "start": [ 129, 1 ], "end": [ 130, 81 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.toFun_eq_coe", "code": "theorem toFun_eq_coe {f : PseudoEpimorphism α β} : f.toFun = (f : α → β)", "start": [ 132, 1 ], "end": [ 132, 80 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.ext", "code": "@[ext]\ntheorem ext {f g : PseudoEpimorphism α β} (h : ∀ a, f a = g a) : f = g", "start": [ 135, 1 ], "end": [ 137, 21 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.copy", "code": "protected def copy (f : PseudoEpimorphism α β) (f' : α → β) (h : f' = f) : PseudoEpimorphism α β :=\n ⟨f.toOrderHom.copy f' h, by simpa only [h.symm, toFun_eq_coe] using f.exists_map_eq_of_map_le'⟩", "start": [ 140, 1 ], "end": [ 143, 98 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.coe_copy", "code": "@[simp]\ntheorem coe_copy (f : PseudoEpimorphism α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f'", "start": [ 146, 1 ], "end": [ 147, 100 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.copy_eq", "code": "theorem copy_eq (f : PseudoEpimorphism α β) (f' : α → β) (h : f' = f) : f.copy f' h = f", "start": [ 150, 1 ], "end": [ 151, 18 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.id", "code": "protected def id : PseudoEpimorphism α α :=\n ⟨OrderHom.id, fun _ b h => ⟨b, h, rfl⟩⟩", "start": [ 156, 1 ], "end": [ 158, 42 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.coe_id", "code": "@[simp]\ntheorem coe_id : ⇑(PseudoEpimorphism.id α) = id", "start": [ 164, 1 ], "end": [ 165, 55 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.coe_id_orderHom", "code": "@[simp]\ntheorem coe_id_orderHom : (PseudoEpimorphism.id α : α →o α) = OrderHom.id", "start": [ 168, 1 ], "end": [ 169, 81 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.id_apply", "code": "@[simp]\ntheorem id_apply (a : α) : PseudoEpimorphism.id α a = a", "start": [ 174, 1 ], "end": [ 175, 63 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.comp", "code": "def comp (g : PseudoEpimorphism β γ) (f : PseudoEpimorphism α β) : PseudoEpimorphism α γ :=\n ⟨g.toOrderHom.comp f.toOrderHom, fun a b h₀ => by\n obtain ⟨b, h₁, rfl⟩ := g.exists_map_eq_of_map_le' h₀\n obtain ⟨b, h₂, rfl⟩ := f.exists_map_eq_of_map_le' h₁\n exact ⟨b, h₂, rfl⟩⟩", "start": [ 178, 1 ], "end": [ 183, 24 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.coe_comp", "code": "@[simp]\ntheorem coe_comp (g : PseudoEpimorphism β γ) (f : PseudoEpimorphism α β) :\n (g.comp f : α → γ) = g ∘ f", "start": [ 186, 1 ], "end": [ 188, 38 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.coe_comp_orderHom", "code": "@[simp]\ntheorem coe_comp_orderHom (g : PseudoEpimorphism β γ) (f : PseudoEpimorphism α β) :\n (g.comp f : α →o γ) = (g : β →o γ).comp f", "start": [ 191, 1 ], "end": [ 193, 53 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.comp_apply", "code": "@[simp]\ntheorem comp_apply (g : PseudoEpimorphism β γ) (f : PseudoEpimorphism α β) (a : α) :\n (g.comp f) a = g (f a)", "start": [ 196, 1 ], "end": [ 198, 34 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.comp_assoc", "code": "@[simp]\ntheorem comp_assoc (h : PseudoEpimorphism γ δ) (g : PseudoEpimorphism β γ)\n (f : PseudoEpimorphism α β) : (h.comp g).comp f = h.comp (g.comp f)", "start": [ 201, 1 ], "end": [ 203, 79 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.comp_id", "code": "@[simp]\ntheorem comp_id (f : PseudoEpimorphism α β) : f.comp (PseudoEpimorphism.id α) = f", "start": [ 206, 1 ], "end": [ 208, 19 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.id_comp", "code": "@[simp]\ntheorem id_comp (f : PseudoEpimorphism α β) : (PseudoEpimorphism.id β).comp f = f", "start": [ 211, 1 ], "end": [ 213, 19 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.cancel_right", "code": "@[simp]\ntheorem cancel_right {g₁ g₂ : PseudoEpimorphism β γ} {f : PseudoEpimorphism α β}\n (hf : Surjective f) : g₁.comp f = g₂.comp f ↔ g₁ = g₂", "start": [ 216, 1 ], "end": [ 219, 78 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.cancel_left", "code": "@[simp]\ntheorem cancel_left {g : PseudoEpimorphism β γ} {f₁ f₂ : PseudoEpimorphism α β} (hg : Injective g) :\n g.comp f₁ = g.comp f₂ ↔ f₁ = f₂", "start": [ 222, 1 ], "end": [ 225, 81 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.toPseudoEpimorphism", "code": "def toPseudoEpimorphism (f : EsakiaHom α β) : PseudoEpimorphism α β :=\n { f with }", "start": [ 238, 1 ], "end": [ 239, 13 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.instFunLike", "code": "instance instFunLike : FunLike (EsakiaHom α β) α β where\n coe f := f.toFun\n coe_injective' f g h := by\n obtain ⟨⟨⟨_, _⟩, _⟩, _⟩ := f\n obtain ⟨⟨⟨_, _⟩, _⟩, _⟩ := g\n congr", "start": [ 242, 1 ], "end": [ 247, 10 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.toContinuousOrderHom_coe", "code": "@[simp]\ntheorem toContinuousOrderHom_coe {f : EsakiaHom α β} :\n f.toContinuousOrderHom = (f : α → β)", "start": [ 255, 1 ], "end": [ 257, 48 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.toFun_eq_coe", "code": "theorem toFun_eq_coe {f : EsakiaHom α β} : f.toFun = (f : α → β)", "start": [ 260, 1 ], "end": [ 260, 72 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.ext", "code": "@[ext]\ntheorem ext {f g : EsakiaHom α β} (h : ∀ a, f a = g a) : f = g", "start": [ 263, 1 ], "end": [ 265, 21 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.copy", "code": "protected def copy (f : EsakiaHom α β) (f' : α → β) (h : f' = f) : EsakiaHom α β :=\n ⟨f.toContinuousOrderHom.copy f' h, by\n simpa only [h.symm, toFun_eq_coe] using f.exists_map_eq_of_map_le'⟩", "start": [ 268, 1 ], "end": [ 272, 72 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_copy", "code": "@[simp]\ntheorem coe_copy (f : EsakiaHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f'", "start": [ 275, 1 ], "end": [ 276, 92 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.copy_eq", "code": "theorem copy_eq (f : EsakiaHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f", "start": [ 279, 1 ], "end": [ 280, 18 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.id", "code": "protected def id : EsakiaHom α α :=\n ⟨ContinuousOrderHom.id α, fun _ b h => ⟨b, h, rfl⟩⟩", "start": [ 285, 1 ], "end": [ 287, 54 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_id", "code": "@[simp]\ntheorem coe_id : ⇑(EsakiaHom.id α) = id", "start": [ 293, 1 ], "end": [ 294, 47 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_id_pseudoEpimorphism", "code": "@[simp]\ntheorem coe_id_pseudoEpimorphism :\n (EsakiaHom.id α : PseudoEpimorphism α α) = PseudoEpimorphism.id α", "start": [ 297, 1 ], "end": [ 299, 77 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.id_apply", "code": "@[simp]\ntheorem id_apply (a : α) : EsakiaHom.id α a = a", "start": [ 304, 1 ], "end": [ 305, 55 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_id_continuousOrderHom", "code": "@[simp]\ntheorem coe_id_continuousOrderHom : (EsakiaHom.id α : α →Co α) = ContinuousOrderHom.id α", "start": [ 308, 1 ], "end": [ 309, 96 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.comp", "code": "def comp (g : EsakiaHom β γ) (f : EsakiaHom α β) : EsakiaHom α γ :=\n ⟨g.toContinuousOrderHom.comp f.toContinuousOrderHom, fun a b h₀ => by\n obtain ⟨b, h₁, rfl⟩ := g.exists_map_eq_of_map_le' h₀\n obtain ⟨b, h₂, rfl⟩ := f.exists_map_eq_of_map_le' h₁\n exact ⟨b, h₂, rfl⟩⟩", "start": [ 312, 1 ], "end": [ 317, 24 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_comp_continuousOrderHom", "code": "@[simp]\ntheorem coe_comp_continuousOrderHom (g : EsakiaHom β γ) (f : EsakiaHom α β) :\n (g.comp f : α →Co γ) = (g: β →Co γ).comp f", "start": [ 320, 1 ], "end": [ 322, 54 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_comp_pseudoEpimorphism", "code": "@[simp]\ntheorem coe_comp_pseudoEpimorphism (g : EsakiaHom β γ) (f : EsakiaHom α β) :\n (g.comp f : PseudoEpimorphism α γ) = (g : PseudoEpimorphism β γ).comp f", "start": [ 325, 1 ], "end": [ 327, 83 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_comp", "code": "@[simp]\ntheorem coe_comp (g : EsakiaHom β γ) (f : EsakiaHom α β) : (g.comp f : α → γ) = g ∘ f", "start": [ 330, 1 ], "end": [ 331, 93 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.comp_apply", "code": "@[simp]\ntheorem comp_apply (g : EsakiaHom β γ) (f : EsakiaHom α β) (a : α) : (g.comp f) a = g (f a)", "start": [ 334, 1 ], "end": [ 335, 99 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.comp_assoc", "code": "@[simp]\ntheorem comp_assoc (h : EsakiaHom γ δ) (g : EsakiaHom β γ) (f : EsakiaHom α β) :\n (h.comp g).comp f = h.comp (g.comp f)", "start": [ 338, 1 ], "end": [ 340, 49 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.comp_id", "code": "@[simp]\ntheorem comp_id (f : EsakiaHom α β) : f.comp (EsakiaHom.id α) = f", "start": [ 343, 1 ], "end": [ 345, 19 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.id_comp", "code": "@[simp]\ntheorem id_comp (f : EsakiaHom α β) : (EsakiaHom.id β).comp f = f", "start": [ 348, 1 ], "end": [ 350, 19 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.cancel_right", "code": "@[simp]\ntheorem cancel_right {g₁ g₂ : EsakiaHom β γ} {f : EsakiaHom α β} (hf : Surjective f) :\n g₁.comp f = g₂.comp f ↔ g₁ = g₂", "start": [ 353, 1 ], "end": [ 356, 78 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.cancel_left", "code": "@[simp]\ntheorem cancel_left {g : EsakiaHom β γ} {f₁ f₂ : EsakiaHom α β} (hg : Injective g) :\n g.comp f₁ = g.comp f₂ ↔ f₁ = f₂", "start": [ 359, 1 ], "end": [ 362, 81 ], "kind": "commanddeclaration" } ]
Mathlib/Analysis/Convex/EGauge.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/Seminorm.lean" ]	[ { "full_name": "egauge", "code": "noncomputable def egauge (𝕜 : Type) [NNNorm 𝕜] {E : Type} [SMul 𝕜 E] (s : Set E) (x : E) : ℝ≥0∞ :=\n ⨅ (c : 𝕜) (_ : x ∈ c • s), ‖c‖₊", "start": [ 32, 1 ], "end": [ 43, 34 ], "kind": "commanddeclaration" }, { "full_name": "egauge_anti", "code": "@[mono, gcongr]\nlemma egauge_anti (h : s ⊆ t) (x : E) : egauge 𝕜 t x ≤ egauge 𝕜 s x :=\n iInf_mono fun _c ↦ iInf_mono' fun hc ↦ ⟨smul_set_mono h hc, le_rfl⟩", "start": [ 47, 1 ], "end": [ 49, 70 ], "kind": "lemma" }, { "full_name": "egauge_empty", "code": "@[simp] lemma egauge_empty (x : E) : egauge 𝕜 ∅ x = ∞ := by simp [egauge]", "start": [ 51, 1 ], "end": [ 51, 74 ], "kind": "lemma" }, { "full_name": "egauge_le_of_mem_smul", "code": "lemma egauge_le_of_mem_smul (h : x ∈ c • s) : egauge 𝕜 s x ≤ ‖c‖₊ := iInf₂_le c h", "start": [ 55, 1 ], "end": [ 55, 82 ], "kind": "lemma" }, { "full_name": "le_egauge_iff", "code": "lemma le_egauge_iff : r ≤ egauge 𝕜 s x ↔ ∀ c : 𝕜, x ∈ c • s → r ≤ ‖c‖₊ := le_iInf₂_iff", "start": [ 57, 1 ], "end": [ 57, 87 ], "kind": "lemma" }, { "full_name": "egauge_eq_top", "code": "lemma egauge_eq_top : egauge 𝕜 s x = ∞ ↔ ∀ c : 𝕜, x ∉ c • s := by simp [egauge]", "start": [ 59, 1 ], "end": [ 59, 80 ], "kind": "lemma" }, { "full_name": "egauge_lt_iff", "code": "lemma egauge_lt_iff : egauge 𝕜 s x < r ↔ ∃ c : 𝕜, x ∈ c • s ∧ ‖c‖₊ < r := by\n simp [egauge, iInf_lt_iff]", "start": [ 61, 1 ], "end": [ 62, 29 ], "kind": "lemma" }, { "full_name": "egauge_zero_left_eq_top", "code": "@[simp] lemma egauge_zero_left_eq_top : egauge 𝕜 0 x = ∞ ↔ x ≠ 0 := by\n simp [egauge_eq_top]", "start": [ 71, 1 ], "end": [ 72, 23 ], "kind": "lemma" }, { "full_name": "egauge_le_of_smul_mem_of_ne", "code": "lemma egauge_le_of_smul_mem_of_ne (h : c • x ∈ s) (hc : c ≠ 0) :\n egauge 𝕜 s x ≤ ↑(‖c‖₊⁻¹ : ℝ≥0) := by\n rw [← nnnorm_inv]\n exact egauge_le_of_mem_smul <\| (mem_inv_smul_set_iff₀ hc _ _).2 h", "start": [ 83, 1 ], "end": [ 89, 68 ], "kind": "lemma" }, { "full_name": "egauge_le_of_smul_mem", "code": "lemma egauge_le_of_smul_mem (h : c • x ∈ s) : egauge 𝕜 s x ≤ (‖c‖₊ : ℝ≥0∞)⁻¹ := by\n rcases eq_or_ne c 0 with rfl \| hc\n · simp\n · exact (egauge_le_of_smul_mem_of_ne h hc).trans ENNReal.coe_inv_le", "start": [ 91, 1 ], "end": [ 97, 70 ], "kind": "lemma" }, { "full_name": "mem_of_egauge_lt_one", "code": "lemma mem_of_egauge_lt_one (hs : Balanced 𝕜 s) (hx : egauge 𝕜 s x < 1) : x ∈ s :=\n let ⟨c, hxc, hc⟩ := egauge_lt_iff.1 hx\n hs c (mod_cast hc.le) hxc", "start": [ 99, 1 ], "end": [ 101, 28 ], "kind": "lemma" }, { "full_name": "egauge_zero_right", "code": "@[simp]\nlemma egauge_zero_right (hs : s.Nonempty) : egauge 𝕜 s 0 = 0 := by\n have : 0 ∈ (0 : 𝕜) • s := by simp [zero_smul_set hs]\n simpa using egauge_le_of_mem_smul this", "start": [ 105, 1 ], "end": [ 108, 41 ], "kind": "lemma" }, { "full_name": "egauge_zero_zero", "code": "@[simp]\nlemma egauge_zero_zero : egauge 𝕜 (0 : Set E) 0 = 0 := egauge_zero_right _ ⟨0, rfl⟩", "start": [ 110, 1 ], "end": [ 111, 84 ], "kind": "lemma" }, { "full_name": "egauge_le_one", "code": "lemma egauge_le_one (h : x ∈ s) : egauge 𝕜 s x ≤ 1 := by\n rw [← one_smul 𝕜 s] at h\n simpa using egauge_le_of_mem_smul h", "start": [ 113, 1 ], "end": [ 115, 38 ], "kind": "lemma" }, { "full_name": "le_egauge_smul_left", "code": "lemma le_egauge_smul_left (c : 𝕜) (s : Set E) (x : E) :\n egauge 𝕜 s x / ‖c‖₊ ≤ egauge 𝕜 (c • s) x := by\n simp_rw [le_egauge_iff, smul_smul]\n rintro a ⟨x, hx, rfl⟩\n apply ENNReal.div_le_of_le_mul\n rw [← ENNReal.coe_mul, ← nnnorm_mul]\n exact egauge_le_of_mem_smul <\| smul_mem_smul_set hx", "start": [ 119, 1 ], "end": [ 125, 54 ], "kind": "lemma" }, { "full_name": "egauge_smul_left", "code": "lemma egauge_smul_left (hc : c ≠ 0) (s : Set E) (x : E) :\n egauge 𝕜 (c • s) x = egauge 𝕜 s x / ‖c‖₊ := by\n refine le_antisymm ?_ (le_egauge_smul_left _ _ _)\n rw [ENNReal.le_div_iff_mul_le (by simp []) (by simp)]\n calc\n egauge 𝕜 (c • s) x ‖c‖₊ = egauge 𝕜 (c • s) x / ‖c⁻¹‖₊ := by\n rw [nnnorm_inv, ENNReal.coe_inv (by simpa), div_eq_mul_inv, inv_inv]\n _ ≤ egauge 𝕜 (c⁻¹ • c • s) x := le_egauge_smul_left _ _ _\n _ = egauge 𝕜 s x := by rw [inv_smul_smul₀ hc]", "start": [ 127, 1 ], "end": [ 135, 50 ], "kind": "lemma" }, { "full_name": "le_egauge_smul_right", "code": "lemma le_egauge_smul_right (c : 𝕜) (s : Set E) (x : E) :\n ‖c‖₊ * egauge 𝕜 s x ≤ egauge 𝕜 s (c • x) := by\n rw [le_egauge_iff]\n rintro a ⟨y, hy, hxy⟩\n rcases eq_or_ne c 0 with rfl \| hc\n · simp\n · refine ENNReal.mul_le_of_le_div' <\| le_trans ?_ ENNReal.coe_div_le\n rw [div_eq_inv_mul, ← nnnorm_inv, ← nnnorm_mul]\n refine egauge_le_of_mem_smul ⟨y, hy, ?_⟩\n simp only [mul_smul, hxy, inv_smul_smul₀ hc]", "start": [ 137, 1 ], "end": [ 146, 49 ], "kind": "lemma" }, { "full_name": "egauge_smul_right", "code": "lemma egauge_smul_right (h : c = 0 → s.Nonempty) (x : E) :\n egauge 𝕜 s (c • x) = ‖c‖₊ * egauge 𝕜 s x := by\n refine le_antisymm ?_ (le_egauge_smul_right c s x)\n rcases eq_or_ne c 0 with rfl \| hc\n · simp [egauge_zero_right _ (h rfl)]\n · rw [mul_comm, ← ENNReal.div_le_iff_le_mul (.inl <\| by simpa) (.inl ENNReal.coe_ne_top),\n ENNReal.div_eq_inv_mul, ← ENNReal.coe_inv (by simpa), ← nnnorm_inv]\n refine (le_egauge_smul_right _ _ _).trans_eq ?_\n rw [inv_smul_smul₀ hc]", "start": [ 148, 1 ], "end": [ 156, 27 ], "kind": "lemma" }, { "full_name": "div_le_egauge_closedBall", "code": "lemma div_le_egauge_closedBall (r : ℝ≥0) (x : E) : ‖x‖₊ / r ≤ egauge 𝕜 (closedBall 0 r) x := by\n rw [le_egauge_iff]\n rintro c ⟨y, hy, rfl⟩\n rw [mem_closedBall_zero_iff, ← coe_nnnorm, NNReal.coe_le_coe] at hy\n simp only [nnnorm_smul, ENNReal.coe_mul]\n apply ENNReal.div_le_of_le_mul\n gcongr", "start": [ 165, 1 ], "end": [ 171, 9 ], "kind": "lemma" }, { "full_name": "le_egauge_closedBall_one", "code": "lemma le_egauge_closedBall_one (x : E) : ‖x‖₊ ≤ egauge 𝕜 (closedBall 0 1) x := by\n simpa using div_le_egauge_closedBall 𝕜 1 x", "start": [ 173, 1 ], "end": [ 174, 45 ], "kind": "lemma" }, { "full_name": "div_le_egauge_ball", "code": "lemma div_le_egauge_ball (r : ℝ≥0) (x : E) : ‖x‖₊ / r ≤ egauge 𝕜 (ball 0 r) x :=\n (div_le_egauge_closedBall 𝕜 r x).trans <\| egauge_anti _ ball_subset_closedBall _", "start": [ 176, 1 ], "end": [ 177, 83 ], "kind": "lemma" }, { "full_name": "le_egauge_ball_one", "code": "lemma le_egauge_ball_one (x : E) : ‖x‖₊ ≤ egauge 𝕜 (ball 0 1) x := by\n simpa using div_le_egauge_ball 𝕜 1 x", "start": [ 179, 1 ], "end": [ 180, 39 ], "kind": "lemma" }, { "full_name": "egauge_ball_le_of_one_lt_norm", "code": "lemma egauge_ball_le_of_one_lt_norm (hc : 1 < ‖c‖) (h₀ : r ≠ 0 ∨ x ≠ 0) :\n egauge 𝕜 (ball 0 r) x ≤ ‖c‖₊ * ‖x‖₊ / r := by\n rcases (zero_le r).eq_or_lt with rfl \| hr\n · rw [ENNReal.coe_zero, ENNReal.div_zero (mul_ne_zero _ _)]\n · apply le_top\n · simpa using one_pos.trans hc\n · simpa using h₀\n · rcases eq_or_ne x 0 with rfl \| hx\n · rw [egauge_zero_right] <;> simp []\n rcases rescale_to_shell hc hr hx with ⟨a, ha₀, har, -, hainv⟩\n calc\n egauge 𝕜 (ball 0 r) x ≤ ↑(‖a‖₊⁻¹) := egauge_le_of_smul_mem_of_ne (mem_ball_zero_iff.2 har) ha₀\n _ ≤ ↑(‖c‖₊ ‖x‖₊ / r) := by rwa [ENNReal.coe_le_coe, div_eq_inv_mul, ← mul_assoc]\n _ ≤ ‖c‖₊ * ‖x‖₊ / r := ENNReal.coe_div_le.trans <\| by rw [ENNReal.coe_mul]", "start": [ 189, 1 ], "end": [ 202, 81 ], "kind": "lemma" }, { "full_name": "egauge_ball_one_le_of_one_lt_norm", "code": "lemma egauge_ball_one_le_of_one_lt_norm (hc : 1 < ‖c‖) (x : E) :\n egauge 𝕜 (ball 0 1) x ≤ ‖c‖₊ * ‖x‖₊ := by\n simpa using egauge_ball_le_of_one_lt_norm hc (.inl one_ne_zero)", "start": [ 204, 1 ], "end": [ 206, 66 ], "kind": "lemma" } ]
Mathlib/CategoryTheory/Localization/FiniteProducts.lean	[ "Mathlib/CategoryTheory/Localization/HasLocalization.lean", "Mathlib/CategoryTheory/Localization/Adjunction.lean", "Mathlib/CategoryTheory/MorphismProperty/Limits.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/CategoryTheory/Limits/Preserves/Finite.lean", "Mathlib/CategoryTheory/Limits/ConeCategory.lean", "Mathlib/CategoryTheory/Localization/Pi.lean" ]	[ { "full_name": "CategoryTheory.Localization.HasProductsOfShapeAux.inverts", "code": "lemma inverts :\n (W.functorCategory (Discrete J)).IsInvertedBy (lim ⋙ L) :=\n fun _ _ f hf => Localization.inverts L W _ (hW.lim_map f hf)", "start": [ 38, 1 ], "end": [ 40, 63 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Localization.HasProductsOfShapeAux.limitFunctor", "code": "noncomputable abbrev limitFunctor :\n (Discrete J ⥤ D) ⥤ D :=\n Localization.lift _ (inverts L hW)\n ((whiskeringRight (Discrete J) C D).obj L)", "start": [ 42, 1 ], "end": [ 47, 47 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Localization.HasProductsOfShapeAux.compLimitFunctorIso", "code": "noncomputable def compLimitFunctorIso :\n ((whiskeringRight (Discrete J) C D).obj L) ⋙ limitFunctor L hW ≅\n lim ⋙ L := by\n apply Localization.fac", "start": [ 49, 1 ], "end": [ 53, 25 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Localization.HasProductsOfShapeAux.adj", "code": "noncomputable def adj :\n Functor.const _ ⊣ limitFunctor L hW :=\n constLimAdj.localization L W ((whiskeringRight (Discrete J) C D).obj L)\n (W.functorCategory (Discrete J)) (Functor.const _) (limitFunctor L hW)", "start": [ 64, 1 ], "end": [ 69, 75 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Localization.HasProductsOfShapeAux.adj_counit_app", "code": "lemma adj_counit_app (F : Discrete J ⥤ C) :\n (adj L hW).counit.app (F ⋙ L) =\n (Functor.const (Discrete J)).map ((compLimitFunctorIso L hW).hom.app F) ≫\n (Functor.compConstIso (Discrete J) L).hom.app (lim.obj F) ≫\n whiskerRight (constLimAdj.counit.app F) L := by\n apply constLimAdj.localization_counit_app", "start": [ 71, 1 ], "end": [ 76, 44 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Localization.HasProductsOfShapeAux.isLimitMapCone", "code": "noncomputable def isLimitMapCone (F : Discrete J ⥤ C) :\n IsLimit (L.mapCone (limit.cone F)) :=\n IsLimit.ofIsoLimit (isLimitConeOfAdj (adj L hW) (F ⋙ L))\n (Cones.ext ((compLimitFunctorIso L hW).app F) (by simp [adj_counit_app, constLimAdj]))", "start": [ 78, 1 ], "end": [ 82, 91 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Localization.hasProductsOfShape", "code": "lemma hasProductsOfShape (J : Type) [Finite J] [HasProductsOfShape J C]\n (hW : W.IsStableUnderProductsOfShape J) :\n HasProductsOfShape J D :=\n hasLimitsOfShape_iff_isLeftAdjoint_const.2\n (HasProductsOfShapeAux.adj L hW).isLeftAdjoint", "start": [ 88, 1 ], "end": [ 92, 51 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Localization.preservesProductsOfShape", "code": "noncomputable def preservesProductsOfShape (J : Type) [Finite J]\n [HasProductsOfShape J C] (hW : W.IsStableUnderProductsOfShape J) :\n PreservesLimitsOfShape (Discrete J) L where\n preservesLimit {F} := preservesLimitOfPreservesLimitCone (limit.isLimit F)\n (HasProductsOfShapeAux.isLimitMapCone L hW F)", "start": [ 94, 1 ], "end": [ 101, 50 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Localization.hasFiniteProducts", "code": "lemma hasFiniteProducts : HasFiniteProducts D :=\n ⟨fun _ => hasProductsOfShape L W _\n (W.isStableUnderProductsOfShape_of_isStableUnderFiniteProducts _)⟩", "start": [ 105, 1 ], "end": [ 107, 71 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Localization.preservesFiniteProducts", "code": "noncomputable def preservesFiniteProducts :\n PreservesFiniteProducts L where\n preserves J _ := preservesProductsOfShape L W J\n (W.isStableUnderProductsOfShape_of_isStableUnderFiniteProducts _)", "start": [ 109, 1 ], "end": [ 115, 72 ], "kind": "commanddeclaration" } ]
Mathlib/Analysis/Fourier/RiemannLebesgueLemma.lean	[ "Mathlib/MeasureTheory/Function/ContinuousMapDense.lean", "Mathlib/MeasureTheory/Integral/SetIntegral.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/Fourier/FourierTransform.lean", "Mathlib/Analysis/InnerProductSpace/Dual.lean", "Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean", "Mathlib/Topology/EMetricSpace/Paracompact.lean", "Mathlib/MeasureTheory/Group/Integral.lean", "Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean", "Mathlib/MeasureTheory/Measure/Haar/Unique.lean" ]	[ { "full_name": "fourierIntegral_half_period_translate", "code": "theorem fourierIntegral_half_period_translate {w : V} (hw : w ≠ 0) :\n (∫ v : V, 𝐞 (-⟪v, w⟫) • f (v + i w)) = -∫ v : V, 𝐞 (-⟪v, w⟫) • f v", "start": [ 67, 1 ], "end": [ 92, 37 ], "kind": "commanddeclaration" }, { "full_name": "fourierIntegral_eq_half_sub_half_period_translate", "code": "theorem fourierIntegral_eq_half_sub_half_period_translate {w : V} (hw : w ≠ 0)\n (hf : Integrable f) :\n ∫ v : V, 𝐞 (-⟪v, w⟫) • f v = (1 / (2 : ℂ)) • ∫ v : V, 𝐞 (-⟪v, w⟫) • (f v - f (v + i w))", "start": [ 95, 1 ], "end": [ 104, 69 ], "kind": "commanddeclaration" }, { "full_name": "tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support", "code": "theorem tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support (hf1 : Continuous f)\n (hf2 : HasCompactSupport f) :\n Tendsto (fun w : V => ∫ v : V, 𝐞 (-⟪v, w⟫) • f v) (cocompact V) (𝓝 0)", "start": [ 107, 1 ], "end": [ 194, 74 ], "kind": "commanddeclaration" }, { "full_name": "tendsto_integral_exp_inner_smul_cocompact", "code": "theorem tendsto_integral_exp_inner_smul_cocompact :\n Tendsto (fun w : V => ∫ v, 𝐞 (-⟪v, w⟫) • f v) (cocompact V) (𝓝 0)", "start": [ 199, 1 ], "end": [ 226, 39 ], "kind": "commanddeclaration" }, { "full_name": "Real.tendsto_integral_exp_smul_cocompact", "code": "theorem Real.tendsto_integral_exp_smul_cocompact (f : ℝ → E) :\n Tendsto (fun w : ℝ => ∫ v : ℝ, 𝐞 (-(v * w)) • f v) (cocompact ℝ) (𝓝 0)", "start": [ 229, 1 ], "end": [ 232, 46 ], "kind": "commanddeclaration" }, { "full_name": "Real.zero_at_infty_fourierIntegral", "code": "theorem Real.zero_at_infty_fourierIntegral (f : ℝ → E) : Tendsto (𝓕 f) (cocompact ℝ) (𝓝 0)", "start": [ 235, 1 ], "end": [ 237, 46 ], "kind": "commanddeclaration" }, { "full_name": "tendsto_integral_exp_smul_cocompact_of_inner_product", "code": "theorem tendsto_integral_exp_smul_cocompact_of_inner_product (μ : Measure V) [μ.IsAddHaarMeasure] :\n Tendsto (fun w : V →L[ℝ] ℝ => ∫ v, 𝐞 (-w v) • f v ∂μ) (cocompact (V →L[ℝ] ℝ)) (𝓝 0)", "start": [ 240, 1 ], "end": [ 256, 55 ], "kind": "commanddeclaration" }, { "full_name": "tendsto_integral_exp_smul_cocompact", "code": "theorem tendsto_integral_exp_smul_cocompact (μ : Measure V) [μ.IsAddHaarMeasure] :\n Tendsto (fun w : V →L[ℝ] ℝ => ∫ v, 𝐞 (-w v) • f v ∂μ) (cocompact (V →L[ℝ] ℝ)) (𝓝 0)", "start": [ 267, 1 ], "end": [ 320, 60 ], "kind": "commanddeclaration" }, { "full_name": "Real.zero_at_infty_vector_fourierIntegral", "code": "theorem Real.zero_at_infty_vector_fourierIntegral (μ : Measure V) [μ.IsAddHaarMeasure] :\n Tendsto (VectorFourier.fourierIntegral 𝐞 μ (topDualPairing ℝ V).flip f) (cocompact (V →L[ℝ] ℝ))\n (𝓝 0)", "start": [ 323, 1 ], "end": [ 329, 49 ], "kind": "commanddeclaration" } ]
Mathlib/Analysis/Calculus/InverseFunctionTheorem/FiniteDimensional.lean	[ "Mathlib/Analysis/Calculus/InverseFunctionTheorem/ApproximatesLinearOn.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/NormedSpace/FiniteDimension.lean" ]	[ { "full_name": "ApproximatesLinearOn.exists_homeomorph_extension", "code": "theorem exists_homeomorph_extension {E : Type} [NormedAddCommGroup E] [NormedSpace ℝ E]\n {F : Type} [NormedAddCommGroup F] [NormedSpace ℝ F] [FiniteDimensional ℝ F] {s : Set E}\n {f : E → F} {f' : E ≃L[ℝ] F} {c : ℝ≥0} (hf : ApproximatesLinearOn f (f' : E →L[ℝ] F) s c)\n (hc : Subsingleton E ∨ lipschitzExtensionConstant F * c < ‖(f'.symm : F →L[ℝ] E)‖₊⁻¹) :\n ∃ g : E ≃ₜ F, EqOn f g s", "start": [ 25, 1 ], "end": [ 47, 35 ], "kind": "commanddeclaration" } ]
Mathlib/Analysis/Convex/Radon.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/Convex/Combination.lean", "Mathlib/Tactic/Linarith.lean" ]	[ { "full_name": "radon_partition", "code": "theorem radon_partition (h : ¬ AffineIndependent 𝕜 f) :\n ∃ I, (convexHull 𝕜 (f '' I) ∩ convexHull 𝕜 (f '' Iᶜ)).Nonempty", "start": [ 24, 1 ], "end": [ 50, 60 ], "kind": "commanddeclaration" } ]
Mathlib/RepresentationTheory/Character.lean	[ "Mathlib/LinearAlgebra/Trace.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/RepresentationTheory/Invariants.lean", "Mathlib/RepresentationTheory/FdRep.lean" ]	[ { "full_name": "FdRep.character", "code": "def character (V : FdRep k G) (g : G) :=\n LinearMap.trace k V (V.ρ g)", "start": [ 48, 1 ], "end": [ 51, 30 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_mul_comm", "code": "theorem char_mul_comm (V : FdRep k G) (g : G) (h : G) :\n V.character (h * g) = V.character (g * h)", "start": [ 54, 1 ], "end": [ 55, 99 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_one", "code": "@[simp]\ntheorem char_one (V : FdRep k G) : V.character 1 = FiniteDimensional.finrank k V", "start": [ 58, 1 ], "end": [ 60, 44 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_tensor", "code": "theorem char_tensor (V W : FdRep k G) : (V ⊗ W).character = V.character * W.character", "start": [ 63, 1 ], "end": [ 65, 54 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_tensor'", "code": "@[simp]\ntheorem char_tensor' (V W : FdRep k G) :\n character (Action.FunctorCategoryEquivalence.inverse.obj\n (Action.FunctorCategoryEquivalence.functor.obj V ⊗\n Action.FunctorCategoryEquivalence.functor.obj W)) = V.character * W.character", "start": [ 69, 1 ], "end": [ 74, 23 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_iso", "code": "theorem char_iso {V W : FdRep k G} (i : V ≅ W) : V.character = W.character", "start": [ 76, 1 ], "end": [ 78, 87 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_conj", "code": "@[simp]\ntheorem char_conj (V : FdRep k G) (g : G) (h : G) : V.character (h * g * h⁻¹) = V.character g", "start": [ 87, 1 ], "end": [ 90, 42 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_dual", "code": "@[simp]\ntheorem char_dual (V : FdRep k G) (g : G) : (of (dual V.ρ)).character g = V.character g⁻¹", "start": [ 93, 1 ], "end": [ 95, 29 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_linHom", "code": "@[simp]\ntheorem char_linHom (V W : FdRep k G) (g : G) :\n (of (linHom V.ρ W.ρ)).character g = V.character g⁻¹ * W.character g", "start": [ 98, 1 ], "end": [ 101, 82 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.average_char_eq_finrank_invariants", "code": "theorem average_char_eq_finrank_invariants (V : FdRep k G) :\n ⅟ (Fintype.card G : k) • ∑ g : G, V.character g = finrank k (invariants V.ρ)", "start": [ 106, 1 ], "end": [ 109, 57 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_orthonormal", "code": "theorem char_orthonormal (V W : FdRep k G) [Simple V] [Simple W] :\n ⅟ (Fintype.card G : k) • ∑ g : G, V.character g * W.character g⁻¹ =\n if Nonempty (V ≅ W) then ↑1 else ↑0", "start": [ 122, 1 ], "end": [ 142, 69 ], "kind": "commanddeclaration" } ]
Mathlib/Algebra/Homology/HomotopyCategory/SingleFunctors.lean	[ "Mathlib/CategoryTheory/Shift/SingleFunctors.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Algebra/Homology/HomotopyCategory/Shift.lean" ]	[ { "full_name": "CochainComplex.singleFunctors", "code": "noncomputable def singleFunctors : SingleFunctors C (CochainComplex C ℤ) ℤ where\n functor n := single _ _ n\n shiftIso n a a' ha' := NatIso.ofComponents\n (fun X => Hom.isoOfComponents\n (fun i => eqToIso (by\n obtain rfl : a' = a + n := by omega\n dsimp [CategoryTheory.shiftFunctor, shiftMonoidalFunctor, single]\n by_cases h : i = a\n · subst h\n simp only [ite_true]\n · rw [if_neg h, if_neg (fun h' => h (by omega))])) (by simp))\n (fun {X Y} f => by\n obtain rfl : a' = a + n := by omega\n ext\n simp [single])\n shiftIso_zero a := by\n ext\n dsimp\n simp only [single, shiftFunctorZero_eq, shiftFunctorZero'_hom_app_f,\n XIsoOfEq, eqToIso.hom]\n shiftIso_add n m a a' a'' ha' ha'' := by\n ext\n dsimp\n simp only [shiftFunctorAdd_eq, shiftFunctorAdd'_hom_app_f, XIsoOfEq,\n eqToIso.hom, eqToHom_trans, id_comp]", "start": [ 31, 1 ], "end": [ 58, 43 ], "kind": "commanddeclaration" }, { "full_name": "CochainComplex.singleFunctor", "code": "noncomputable abbrev singleFunctor (n : ℤ) := (singleFunctors C).functor n", "start": [ 64, 1 ], "end": [ 68, 75 ], "kind": "commanddeclaration" }, { "full_name": "HomotopyCategory.singleFunctors", "code": "noncomputable def singleFunctors : SingleFunctors C (HomotopyCategory C (ComplexShape.up ℤ)) ℤ :=\n (CochainComplex.singleFunctors C).postcomp (HomotopyCategory.quotient _ _)", "start": [ 74, 1 ], "end": [ 77, 77 ], "kind": "commanddeclaration" }, { "full_name": "HomotopyCategory.singleFunctor", "code": "noncomputable abbrev singleFunctor (n : ℤ) :\n C ⥤ HomotopyCategory C (ComplexShape.up ℤ) :=\n (singleFunctors C).functor n", "start": [ 79, 1 ], "end": [ 83, 31 ], "kind": "commanddeclaration" }, { "full_name": "HomotopyCategory.singleFunctorsPostcompQuotientIso", "code": "noncomputable def singleFunctorsPostcompQuotientIso :\n singleFunctors C ≅\n (CochainComplex.singleFunctors C).postcomp (HomotopyCategory.quotient _ _) :=\n Iso.refl _", "start": [ 89, 1 ], "end": [ 93, 13 ], "kind": "commanddeclaration" }, { "full_name": "HomotopyCategory.singleFunctorPostcompQuotientIso", "code": "noncomputable def singleFunctorPostcompQuotientIso (n : ℤ) :\n singleFunctor C n ≅ CochainComplex.singleFunctor C n ⋙ quotient _ _ :=\n (SingleFunctors.evaluation _ _ n).mapIso (singleFunctorsPostcompQuotientIso C)", "start": [ 95, 1 ], "end": [ 98, 81 ], "kind": "commanddeclaration" } ]
Mathlib/Algebra/Lie/CartanMatrix.lean	[ "Mathlib/Data/Matrix/Notation.lean", "Mathlib/Algebra/Lie/Quotient.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Algebra/Lie/Free.lean" ]	[ { "full_name": "CartanMatrix.Generators", "code": "inductive Generators\n \| H : B → Generators\n \| E : B → Generators\n \| F : B → Generators", "start": [ 96, 1 ], "end": [ 101, 23 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.HH", "code": "def HH : B × B → FreeLieAlgebra R (Generators B) :=\n uncurry fun i j => ⁅H i, H j⁆", "start": [ 118, 1 ], "end": [ 120, 32 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.EF", "code": "def EF : B × B → FreeLieAlgebra R (Generators B) :=\n uncurry fun i j => if i = j then ⁅E i, F i⁆ - H i else ⁅E i, F j⁆", "start": [ 123, 1 ], "end": [ 125, 68 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.HE", "code": "def HE : B × B → FreeLieAlgebra R (Generators B) :=\n uncurry fun i j => ⁅H i, E j⁆ - A i j • E j", "start": [ 128, 1 ], "end": [ 130, 46 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.HF", "code": "def HF : B × B → FreeLieAlgebra R (Generators B) :=\n uncurry fun i j => ⁅H i, F j⁆ + A i j • F j", "start": [ 133, 1 ], "end": [ 135, 46 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.adE", "code": "def adE : B × B → FreeLieAlgebra R (Generators B) :=\n uncurry fun i j => ad (E i) ^ (-A i j).toNat <\| ⁅E i, E j⁆", "start": [ 138, 1 ], "end": [ 144, 61 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.adF", "code": "def adF : B × B → FreeLieAlgebra R (Generators B) :=\n uncurry fun i j => ad (F i) ^ (-A i j).toNat <\| ⁅F i, F j⁆", "start": [ 147, 1 ], "end": [ 151, 61 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.adE_of_eq_eq_zero", "code": "private theorem adE_of_eq_eq_zero (i : B) (h : A i i = 2) : adE R A ⟨i, i⟩ = 0", "start": [ 154, 1 ], "end": [ 156, 20 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.adF_of_eq_eq_zero", "code": "private theorem adF_of_eq_eq_zero (i : B) (h : A i i = 2) : adF R A ⟨i, i⟩ = 0", "start": [ 158, 1 ], "end": [ 160, 20 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.toSet", "code": "def toSet : Set (FreeLieAlgebra R (Generators B)) :=\n (Set.range <\| HH R) ∪ (Set.range <\| EF R) ∪ (Set.range <\| HE R A) ∪ (Set.range <\| HF R A) ∪\n (Set.range <\| adE R A) ∪\n (Set.range <\| adF R A)", "start": [ 162, 1 ], "end": [ 166, 27 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.toIdeal", "code": "def toIdeal : LieIdeal R (FreeLieAlgebra R (Generators B)) :=\n LieSubmodule.lieSpan R _ <\| toSet R A", "start": [ 169, 1 ], "end": [ 171, 40 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.ToLieAlgebra", "code": "def Matrix.ToLieAlgebra :=\n FreeLieAlgebra R _ ⧸ CartanMatrix.Relations.toIdeal R A", "start": [ 178, 1 ], "end": [ 183, 58 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.ToLieAlgebra.instLieRing", "code": "instance Matrix.ToLieAlgebra.instLieRing : LieRing (Matrix.ToLieAlgebra R A) :=\n inferInstanceAs (LieRing (FreeLieAlgebra R _ ⧸ CartanMatrix.Relations.toIdeal R A))", "start": [ 187, 1 ], "end": [ 188, 86 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.ToLieAlgebra.instInhabited", "code": "instance Matrix.ToLieAlgebra.instInhabited : Inhabited (Matrix.ToLieAlgebra R A) :=\n inferInstanceAs (Inhabited (FreeLieAlgebra R _ ⧸ CartanMatrix.Relations.toIdeal R A))", "start": [ 191, 1 ], "end": [ 192, 88 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.ToLieAlgebra.instLieAlgebra", "code": "instance Matrix.ToLieAlgebra.instLieAlgebra : LieAlgebra R (Matrix.ToLieAlgebra R A) :=\n inferInstanceAs (LieAlgebra R (FreeLieAlgebra R _ ⧸ CartanMatrix.Relations.toIdeal R A))", "start": [ 195, 1 ], "end": [ 196, 91 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.E₆", "code": "def E₆ : Matrix (Fin 6) (Fin 6) ℤ :=\n !![2, 0, -1, 0, 0, 0;\n 0, 2, 0, -1, 0, 0;\n -1, 0, 2, -1, 0, 0;\n 0, -1, -1, 2, -1, 0;\n 0, 0, 0, -1, 2, -1;\n 0, 0, 0, 0, -1, 2]", "start": [ 201, 1 ], "end": [ 216, 23 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.E₇", "code": "def E₇ : Matrix (Fin 7) (Fin 7) ℤ :=\n !![2, 0, -1, 0, 0, 0, 0;\n 0, 2, 0, -1, 0, 0, 0;\n -1, 0, 2, -1, 0, 0, 0;\n 0, -1, -1, 2, -1, 0, 0;\n 0, 0, 0, -1, 2, -1, 0;\n 0, 0, 0, 0, -1, 2, -1;\n 0, 0, 0, 0, 0, -1, 2]", "start": [ 219, 1 ], "end": [ 235, 26 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.E₈", "code": "def E₈ : Matrix (Fin 8) (Fin 8) ℤ :=\n !![2, 0, -1, 0, 0, 0, 0, 0;\n 0, 2, 0, -1, 0, 0, 0, 0;\n -1, 0, 2, -1, 0, 0, 0, 0;\n 0, -1, -1, 2, -1, 0, 0, 0;\n 0, 0, 0, -1, 2, -1, 0, 0;\n 0, 0, 0, 0, -1, 2, -1, 0;\n 0, 0, 0, 0, 0, -1, 2, -1;\n 0, 0, 0, 0, 0, 0, -1, 2]", "start": [ 238, 1 ], "end": [ 255, 29 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.F₄", "code": "def F₄ : Matrix (Fin 4) (Fin 4) ℤ :=\n !![2, -1, 0, 0; -1, 2, -2, 0; 0, -1, 2, -1; 0, 0, -1, 2]", "start": [ 258, 1 ], "end": [ 266, 59 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.G₂", "code": "def G₂ : Matrix (Fin 2) (Fin 2) ℤ :=\n !![2, -3; -1, 2]", "start": [ 269, 1 ], "end": [ 278, 19 ], "kind": "commanddeclaration" }, { "full_name": "LieAlgebra.e₆", "code": "abbrev e₆ :=\n CartanMatrix.E₆.ToLieAlgebra R", "start": [ 285, 1 ], "end": [ 287, 33 ], "kind": "commanddeclaration" }, { "full_name": "LieAlgebra.e₇", "code": "abbrev e₇ :=\n CartanMatrix.E₇.ToLieAlgebra R", "start": [ 290, 1 ], "end": [ 292, 33 ], "kind": "commanddeclaration" }, { "full_name": "LieAlgebra.e₈", "code": "abbrev e₈ :=\n CartanMatrix.E₈.ToLieAlgebra R", "start": [ 295, 1 ], "end": [ 297, 33 ], "kind": "commanddeclaration" }, { "full_name": "LieAlgebra.f₄", "code": "abbrev f₄ :=\n CartanMatrix.F₄.ToLieAlgebra R", "start": [ 300, 1 ], "end": [ 302, 33 ], "kind": "commanddeclaration" }, { "full_name": "LieAlgebra.g₂", "code": "abbrev g₂ :=\n CartanMatrix.G₂.ToLieAlgebra R", "start": [ 305, 1 ], "end": [ 307, 33 ], "kind": "commanddeclaration" } ]
Mathlib/SetTheory/ZFC/Ordinal.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/SetTheory/ZFC/Basic.lean" ]	[ { "full_name": "ZFSet.IsTransitive", "code": "def IsTransitive (x : ZFSet) : Prop :=\n ∀ y ∈ x, y ⊆ x", "start": [ 39, 1 ], "end": [ 41, 17 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.empty_isTransitive", "code": "@[simp]\ntheorem empty_isTransitive : IsTransitive ∅", "start": [ 44, 1 ], "end": [ 45, 85 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.IsTransitive.subset_of_mem", "code": "theorem IsTransitive.subset_of_mem (h : x.IsTransitive) : y ∈ x → y ⊆ x", "start": [ 48, 1 ], "end": [ 49, 6 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.isTransitive_iff_mem_trans", "code": "theorem isTransitive_iff_mem_trans : z.IsTransitive ↔ ∀ {x y : ZFSet}, x ∈ y → y ∈ z → x ∈ z", "start": [ 52, 1 ], "end": [ 53, 73 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.IsTransitive.inter", "code": "protected theorem IsTransitive.inter (hx : x.IsTransitive) (hy : y.IsTransitive) :\n (x ∩ y).IsTransitive", "start": [ 59, 1 ], "end": [ 62, 53 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.IsTransitive.sUnion", "code": "protected theorem IsTransitive.sUnion (h : x.IsTransitive) :\n (⋃₀ x : ZFSet).IsTransitive", "start": [ 65, 1 ], "end": [ 68, 50 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.IsTransitive.sUnion'", "code": "theorem IsTransitive.sUnion' (H : ∀ y ∈ x, IsTransitive y) :\n (⋃₀ x : ZFSet).IsTransitive", "start": [ 71, 1 ], "end": [ 74, 57 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.IsTransitive.union", "code": "protected theorem IsTransitive.union (hx : x.IsTransitive) (hy : y.IsTransitive) :\n (x ∪ y).IsTransitive", "start": [ 77, 1 ], "end": [ 84, 14 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.IsTransitive.powerset", "code": "protected theorem IsTransitive.powerset (h : x.IsTransitive) : (powerset x).IsTransitive", "start": [ 87, 1 ], "end": [ 90, 32 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.isTransitive_iff_sUnion_subset", "code": "theorem isTransitive_iff_sUnion_subset : x.IsTransitive ↔ (⋃₀ x : ZFSet) ⊆ x", "start": [ 93, 1 ], "end": [ 96, 79 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.isTransitive_iff_subset_powerset", "code": "theorem isTransitive_iff_subset_powerset : x.IsTransitive ↔ x ⊆ powerset x", "start": [ 102, 1 ], "end": [ 103, 100 ], "kind": "commanddeclaration" } ]
Mathlib/Analysis/InnerProductSpace/LaxMilgram.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/InnerProductSpace/Dual.lean" ]	[ { "full_name": "IsCoercive.bounded_below", "code": "theorem bounded_below (coercive : IsCoercive B) : ∃ C, 0 < C ∧ ∀ v, C * ‖v‖ ≤ ‖B♯ v‖", "start": [ 51, 1 ], "end": [ 62, 16 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.antilipschitz", "code": "theorem antilipschitz (coercive : IsCoercive B) : ∃ C : ℝ≥0, 0 < C ∧ AntilipschitzWith C B♯", "start": [ 65, 1 ], "end": [ 71, 26 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.ker_eq_bot", "code": "theorem ker_eq_bot (coercive : IsCoercive B) : ker B♯ = ⊥", "start": [ 74, 1 ], "end": [ 77, 32 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.isClosed_range", "code": "theorem isClosed_range (coercive : IsCoercive B) : IsClosed (range B♯ : Set V)", "start": [ 80, 1 ], "end": [ 82, 58 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.range_eq_top", "code": "theorem range_eq_top (coercive : IsCoercive B) : range B♯ = ⊤", "start": [ 87, 1 ], "end": [ 102, 26 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.continuousLinearEquivOfBilin", "code": "def continuousLinearEquivOfBilin (coercive : IsCoercive B) : V ≃L[ℝ] V :=\n ContinuousLinearEquiv.ofBijective B♯ coercive.ker_eq_bot coercive.range_eq_top", "start": [ 105, 1 ], "end": [ 111, 81 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.continuousLinearEquivOfBilin_apply", "code": "@[simp]\ntheorem continuousLinearEquivOfBilin_apply (coercive : IsCoercive B) (v w : V) :\n ⟪coercive.continuousLinearEquivOfBilin v, w⟫_ℝ = B v w", "start": [ 114, 1 ], "end": [ 117, 41 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.unique_continuousLinearEquivOfBilin", "code": "theorem unique_continuousLinearEquivOfBilin (coercive : IsCoercive B) {v f : V}\n (is_lax_milgram : ∀ w, ⟪f, w⟫_ℝ = B v w) : f = coercive.continuousLinearEquivOfBilin v", "start": [ 120, 1 ], "end": [ 122, 53 ], "kind": "commanddeclaration" } ]
Mathlib/Data/Buffer/Basic.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Init/Align.lean" ]	[]
Mathlib/NumberTheory/SiegelsLemma.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Tactic/Rify.lean", "Mathlib/Analysis/Matrix.lean", "Mathlib/Data/Pi/Interval.lean" ]	[ { "full_name": "Int.Matrix.image_T_subset_S", "code": "private lemma image_T_subset_S (v) (hv : v ∈ T) : A ᵥ v ∈ S := by\n rw [mem_Icc] at hv ⊢\n have mulVec_def : A.mulVec v =\n fun i ↦ Finset.sum univ fun j : Fin n ↦ A i j v j := rfl\n rw [mulVec_def]\n refine ⟨fun i ↦ ?_, fun i ↦ ?_⟩\n all_goals\n simp only [mul_neg]\n gcongr ∑ _ : Fin n, ?_ with j _ rw [← mul_comm (v j)] rcases le_total 0 (A i j) with hsign \| hsign· rw [negPart_eq_zero.2 hsign]\n exact mul_nonneg (hv.1 j) hsign\n · rw [negPart_eq_neg.2 hsign]\n simp only [mul_neg, neg_neg]\n exact mul_le_mul_of_nonpos_right (hv.2 j) hsign\n · rw [posPart_eq_self.2 hsign]\n exact mul_le_mul_of_nonneg_right (hv.2 j) hsign\n · rw [posPart_eq_zero.2 hsign]\n exact mul_nonpos_of_nonneg_of_nonpos (hv.1 j) hsign", "start": [ 68, 1 ], "end": [ 87, 56 ], "kind": "lemma" }, { "full_name": "Int.Matrix.card_T_eq", "code": "private lemma card_T_eq : (T).card = (B + 1) ^ n := by\n rw [Pi.card_Icc 0 B']\n simp only [Pi.zero_apply, Int.card_Icc, sub_zero, Int.toNat_ofNat_add_one, prod_const, card_fin]", "start": [ 91, 1 ], "end": [ 93, 99 ], "kind": "lemma" }, { "full_name": "Int.Matrix.N_le_P_add_one", "code": "private lemma N_le_P_add_one (i : Fin m) : N i ≤ P i + 1 := by\n calc N i\n _ ≤ 0 := by\n apply Finset.sum_nonpos\n intro j _\n simp only [mul_neg, Left.neg_nonpos_iff]\n exact mul_nonneg (Nat.cast_nonneg B) (negPart_nonneg (A i j))\n _ ≤ P i + 1 := by\n apply le_trans (Finset.sum_nonneg _) (Int.le_add_one (le_refl P i))\n intro j _\n exact mul_nonneg (Nat.cast_nonneg B) (posPart_nonneg (A i j))", "start": [ 96, 1 ], "end": [ 106, 66 ], "kind": "lemma" }, { "full_name": "Int.Matrix.card_S_eq", "code": "private lemma card_S_eq : (Finset.Icc N P).card = ∏ i : Fin m, (P i - N i + 1) := by\n rw [Pi.card_Icc N P, Nat.cast_prod]\n congr\n ext i\n rw [Int.card_Icc_of_le (N i) (P i) (N_le_P_add_one m n A i)]\n exact add_sub_right_comm (P i) 1 (N i)", "start": [ 108, 1 ], "end": [ 113, 41 ], "kind": "lemma" }, { "full_name": "Int.Matrix.one_le_norm_A_of_ne_zero", "code": "lemma one_le_norm_A_of_ne_zero : 1 ≤ ‖A‖ := by\n by_contra! h\n apply hA\n ext i j\n simp only [zero_apply]\n rw [norm_lt_iff Real.zero_lt_one] at h\n specialize h i j\n rw [Int.norm_eq_abs] at h\n norm_cast at h\n exact Int.abs_lt_one_iff.1 h", "start": [ 117, 1 ], "end": [ 127, 31 ], "kind": "lemma" }, { "full_name": "Int.Matrix.card_S_lt_card_T", "code": "private lemma card_S_lt_card_T : (S).card < (T).card := by\n zify rw [card_T_eq, card_S_eq]\n rify calc\n ∏ x : Fin m, (∑ x_1 : Fin n, ↑B * ↑(A x x_1)⁺ - ∑ x_1 : Fin n, ↑B * -↑(A x x_1)⁻ + 1)\n ≤ (n * ‖A‖ * B + 1) ^ m := by\n rw [← Fin.prod_const m (n * ‖A‖ * B + 1)] refine Finset.prod_le_prod (fun i _ ↦ ?_) (fun i _ ↦ ?_)\n · have h := N_le_P_add_one m n A i\n rify at h\n linarith only [h]\n · simp only [mul_neg, sum_neg_distrib, sub_neg_eq_add, add_le_add_iff_right]\n have h1 : n * ‖A‖ * B = ∑ _ : Fin n, ‖A‖ * B := by\n simp only [sum_const, card_univ, Fintype.card_fin, nsmul_eq_mul, mul_assoc ↑n ‖A‖ ↑B]\n simp_rw [h1, ← Finset.sum_add_distrib, ← mul_add, mul_comm ‖A‖, ← Int.cast_add]\n gcongr with j _\n rw [posPart_add_negPart (A i j), Int.cast_abs]\n exact norm_entry_le_entrywise_sup_norm A\n _ ≤ (n * ‖A‖) ^ m * (B + 1) ^ m := by\n rw [← mul_pow, mul_add, mul_one]\n gcongr\n have H : 1 ≤ (n : ℝ) := mod_cast (hm.trans hn)\n exact one_le_mul_of_one_le_of_one_le H <\| one_le_norm_A_of_ne_zero m n A hA\n _ = ((n * ‖A‖) ^ (m / ((n : ℝ) - m))) ^ ((n : ℝ) - m) * (B + 1) ^ m := by\n congr 1\n rw [← rpow_mul (mul_nonneg n.cast_nonneg (norm_nonneg A)), ← Real.rpow_natCast,\n div_mul_cancel₀]\n exact sub_ne_zero_of_ne (mod_cast hn.ne')\n _ < (B + 1) ^ ((n : ℝ) - m) * (B + 1) ^ m := by\n gcongr\n · exact sub_pos.mpr (mod_cast hn)\n · exact Nat.lt_floor_add_one ((n * ‖A‖) ^ e)\n _ = (B + 1) ^ n := by\n rw [← rpow_natCast, ← rpow_add (Nat.cast_add_one_pos B), ← rpow_natCast, sub_add_cancel]", "start": [ 133, 1 ], "end": [ 167, 97 ], "kind": "lemma" }, { "full_name": "Int.Matrix.exists_ne_zero_int_vec_norm_le", "code": "theorem exists_ne_zero_int_vec_norm_le (hA_nezero : A ≠ 0) : ∃ t : Fin n → ℤ, t ≠ 0 ∧\n A ᵥ t = 0 ∧ ‖t‖ ≤ (n ‖A‖) ^ ((m : ℝ) / (n - m))", "start": [ 171, 1 ], "end": [ 199, 18 ], "kind": "commanddeclaration" } ]
Mathlib/Data/ZMod/Coprime.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/RingTheory/PrincipalIdealDomain.lean", "Mathlib/Data/ZMod/Basic.lean", "Mathlib/RingTheory/Int/Basic.lean" ]	[ { "full_name": "ZMod.eq_zero_iff_gcd_ne_one", "code": "theorem eq_zero_iff_gcd_ne_one {a : ℤ} {p : ℕ} [pp : Fact p.Prime] :\n (a : ZMod p) = 0 ↔ a.gcd p ≠ 1", "start": [ 22, 1 ], "end": [ 28, 34 ], "kind": "commanddeclaration" }, { "full_name": "ZMod.ne_zero_of_gcd_eq_one", "code": "theorem ne_zero_of_gcd_eq_one {a : ℤ} {p : ℕ} (pp : p.Prime) (h : a.gcd p = 1) : (a : ZMod p) ≠ 0", "start": [ 31, 1 ], "end": [ 33, 69 ], "kind": "commanddeclaration" }, { "full_name": "ZMod.eq_zero_of_gcd_ne_one", "code": "theorem eq_zero_of_gcd_ne_one {a : ℤ} {p : ℕ} (pp : p.Prime) (h : a.gcd p ≠ 1) : (a : ZMod p) = 0", "start": [ 36, 1 ], "end": [ 38, 43 ], "kind": "commanddeclaration" } ]
Mathlib/Data/Finset/Functor.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Data/Finset/NAry.lean", "Mathlib/Data/Finset/Lattice.lean", "Mathlib/Data/Multiset/Functor.lean" ]	[ { "full_name": "Finset.functor", "code": "protected instance functor : Functor Finset where map f s := s.image f", "start": [ 37, 1 ], "end": [ 39, 71 ], "kind": "commanddeclaration" }, { "full_name": "Finset.lawfulFunctor", "code": "instance lawfulFunctor : LawfulFunctor Finset where\n id_map s := image_id\n comp_map f g s := image_image.symm\n map_const {α} {β} := by simp only [Functor.mapConst, Functor.map]", "start": [ 41, 1 ], "end": [ 44, 68 ], "kind": "commanddeclaration" }, { "full_name": "Finset.fmap_def", "code": "@[simp]\ntheorem fmap_def {s : Finset α} (f : α → β) : f <$> s = s.image f", "start": [ 46, 1 ], "end": [ 47, 73 ], "kind": "commanddeclaration" }, { "full_name": "Finset.pure", "code": "protected instance pure : Pure Finset :=\n ⟨fun x => {x}⟩", "start": [ 55, 1 ], "end": [ 56, 17 ], "kind": "commanddeclaration" }, { "full_name": "Finset.pure_def", "code": "@[simp]\ntheorem pure_def {α} : (pure : α → Finset α) = singleton", "start": [ 58, 1 ], "end": [ 59, 64 ], "kind": "commanddeclaration" }, { "full_name": "Finset.applicative", "code": "protected instance applicative : Applicative Finset :=\n { Finset.functor, Finset.pure with\n seq := fun t s => t.sup fun f => (s ()).image f\n seqLeft := fun s t => if t () = ∅ then ∅ else s\n seqRight := fun s t => if s = ∅ then ∅ else t () }", "start": [ 69, 1 ], "end": [ 73, 55 ], "kind": "commanddeclaration" }, { "full_name": "Finset.seq_def", "code": "@[simp]\ntheorem seq_def (s : Finset α) (t : Finset (α → β)) : t <> s = t.sup fun f => s.image f", "start": [ 75, 1 ], "end": [ 77, 6 ], "kind": "commanddeclaration" }, { "full_name": "Finset.seqLeft_def", "code": "@[simp]\ntheorem seqLeft_def (s : Finset α) (t : Finset β) : s < t = if t = ∅ then ∅ else s", "start": [ 80, 1 ], "end": [ 82, 6 ], "kind": "commanddeclaration" }, { "full_name": "Finset.seqRight_def", "code": "@[simp]\ntheorem seqRight_def (s : Finset α) (t : Finset β) : s > t = if s = ∅ then ∅ else t", "start": [ 85, 1 ], "end": [ 87, 6 ], "kind": "commanddeclaration" }, { "full_name": "Finset.image₂_def", "code": "theorem image₂_def {α β γ : Type u} (f : α → β → γ) (s : Finset α) (t : Finset β) :\n image₂ f s t = f <$> s <> t", "start": [ 90, 1 ], "end": [ 95, 17 ], "kind": "commanddeclaration" }, { "full_name": "Finset.lawfulApplicative", "code": "instance lawfulApplicative : LawfulApplicative Finset :=\n { Finset.lawfulFunctor with\n seqLeft_eq := fun s t => by\n rw [seq_def, fmap_def, seqLeft_def]\n obtain rfl \| ht := t.eq_empty_or_nonempty\n · simp_rw [image_empty, if_true]\n exact (sup_bot _).symm\n · ext a\n rw [if_neg ht.ne_empty, mem_sup]\n refine ⟨fun ha => ⟨const _ a, mem_image_of_mem _ ha, mem_image_const_self.2 ht⟩, ?_⟩\n rintro ⟨f, hf, ha⟩\n rw [mem_image] at hf ha\n obtain ⟨b, hb, rfl⟩ := hf\n obtain ⟨_, _, rfl⟩ := ha\n exact hb\n seqRight_eq := fun s t => by\n rw [seq_def, fmap_def, seqRight_def]\n obtain rfl \| hs := s.eq_empty_or_nonempty\n · rw [if_pos rfl, image_empty, sup_empty, bot_eq_empty]\n · ext a\n rw [if_neg hs.ne_empty, mem_sup]\n refine ⟨fun ha => ⟨id, mem_image_const_self.2 hs, by rwa [image_id]⟩, ?_⟩\n rintro ⟨f, hf, ha⟩\n rw [mem_image] at hf ha\n obtain ⟨b, hb, rfl⟩ := ha\n obtain ⟨_, _, rfl⟩ := hf\n exact hb\n pure_seq := fun f s => by simp only [pure_def, seq_def, sup_singleton, fmap_def]\n map_pure := fun f a => image_singleton _ _\n seq_pure := fun s a => sup_singleton'' _ _\n seq_assoc := fun s t u => by\n ext a\n simp_rw [seq_def, fmap_def]\n simp only [exists_prop, mem_sup, mem_image]\n constructor\n · rintro ⟨g, hg, b, ⟨f, hf, a, ha, rfl⟩, rfl⟩\n exact ⟨g ∘ f, ⟨comp g, ⟨g, hg, rfl⟩, f, hf, rfl⟩, a, ha, rfl⟩\n · rintro ⟨c, ⟨_, ⟨g, hg, rfl⟩, f, hf, rfl⟩, a, ha, rfl⟩\n exact ⟨g, hg, f a, ⟨f, hf, a, ha, rfl⟩, rfl⟩ }", "start": [ 98, 1 ], "end": [ 136, 55 ], "kind": "commanddeclaration" }, { "full_name": "Finset.commApplicative", "code": "instance commApplicative : CommApplicative Finset :=\n { Finset.lawfulApplicative with\n commutative_prod := fun s t => by\n simp_rw [seq_def, fmap_def, sup_image, sup_eq_biUnion]\n change (s.biUnion fun a => t.image fun b => (a, b))\n = t.biUnion fun b => s.image fun a => (a, b)\n trans s ×ˢ t <;> [rw [product_eq_biUnion]; rw [product_eq_biUnion_right]] }", "start": [ 138, 1 ], "end": [ 144, 82 ], "kind": "commanddeclaration" }, { "full_name": "Finset.bind_def", "code": "@[simp]\ntheorem bind_def {α β} : (· >>= ·) = sup (α := Finset α) (β := β)", "start": [ 158, 1 ], "end": [ 160, 6 ], "kind": "commanddeclaration" }, { "full_name": "Finset.traverse", "code": "def traverse [DecidableEq β] (f : α → F β) (s : Finset α) : F (Finset β) :=\n Multiset.toFinset <$> Multiset.traverse f s.1", "start": [ 194, 1 ], "end": [ 196, 48 ], "kind": "commanddeclaration" }, { "full_name": "Finset.id_traverse", "code": "@[simp]\ntheorem id_traverse [DecidableEq α] (s : Finset α) : traverse (pure : α → Id α) s = s", "start": [ 199, 1 ], "end": [ 202, 23 ], "kind": "commanddeclaration" }, { "full_name": "Finset.map_comp_coe", "code": "@[simp]\ntheorem map_comp_coe (h : α → β) :\n Functor.map h ∘ Multiset.toFinset = Multiset.toFinset ∘ Functor.map h", "start": [ 207, 1 ], "end": [ 210, 33 ], "kind": "commanddeclaration" }, { "full_name": "Finset.map_traverse", "code": "theorem map_traverse (g : α → G β) (h : β → γ) (s : Finset α) :\n Functor.map h <$> traverse g s = traverse (Functor.map h ∘ g) s", "start": [ 213, 1 ], "end": [ 217, 53 ], "kind": "commanddeclaration" } ]
Mathlib/Data/UInt.lean	[ "Mathlib/Data/ZMod/Defs.lean", ".lake/packages/lean4/src/lean/Init.lean" ]	[ { "full_name": "neZero", "code": "instance neZero : NeZero size := ⟨by decide⟩", "start": [ 31, 7 ], "end": [ 31, 51 ], "kind": "commanddeclaration" }, { "full_name": "neg_def", "code": "lemma neg_def (a : $typeName) : -a = ⟨-a.val⟩ := rfl", "start": [ 45, 7 ], "end": [ 45, 59 ], "kind": "lemma" }, { "full_name": "pow_def", "code": "lemma pow_def (a : $typeName) (n : ℕ) : a ^ n = ⟨a.val ^ n⟩ := rfl", "start": [ 47, 7 ], "end": [ 47, 73 ], "kind": "lemma" }, { "full_name": "nsmul_def", "code": "lemma nsmul_def (n : ℕ) (a : $typeName) : n • a = ⟨n • a.val⟩ := rfl", "start": [ 49, 7 ], "end": [ 49, 75 ], "kind": "lemma" }, { "full_name": "zsmul_def", "code": "lemma zsmul_def (z : ℤ) (a : $typeName) : z • a = ⟨z • a.val⟩ := rfl", "start": [ 51, 7 ], "end": [ 51, 75 ], "kind": "lemma" }, { "full_name": "val_injective", "code": "lemma val_injective : Function.Injective val := @eq_of_val_eq", "start": [ 54, 7 ], "end": [ 54, 68 ], "kind": "lemma" }, { "full_name": "instCommMonoid", "code": "instance instCommMonoid : CommMonoid $typeName :=\n Function.Injective.commMonoid val val_injective\n rfl (fun _ _ => rfl) (fun _ _ => rfl)", "start": [ 56, 7 ], "end": [ 58, 48 ], "kind": "commanddeclaration" }, { "full_name": "instNonUnitalCommRing", "code": "instance instNonUnitalCommRing : NonUnitalCommRing $typeName :=\n Function.Injective.nonUnitalCommRing val val_injective\n rfl (fun _ _ => rfl) (fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl)\n (fun _ _ => rfl) (fun _ _ => rfl)", "start": [ 60, 7 ], "end": [ 63, 44 ], "kind": "commanddeclaration" }, { "full_name": "instNatCast", "code": "local instance instNatCast : NatCast $typeName where\n natCast n := mk n", "start": [ 65, 7 ], "end": [ 66, 26 ], "kind": "commanddeclaration" }, { "full_name": "instIntCast", "code": "local instance instIntCast : IntCast $typeName where\n intCast z := mk z", "start": [ 68, 7 ], "end": [ 69, 26 ], "kind": "commanddeclaration" }, { "full_name": "natCast_def", "code": "lemma natCast_def (n : ℕ) : (n : $typeName) = ⟨n⟩ := rfl", "start": [ 71, 7 ], "end": [ 71, 63 ], "kind": "lemma" }, { "full_name": "intCast_def", "code": "lemma intCast_def (z : ℤ) : (z : $typeName) = ⟨z⟩ := rfl", "start": [ 73, 7 ], "end": [ 73, 63 ], "kind": "lemma" }, { "full_name": "instCommRing", "code": "local instance instCommRing : CommRing $typeName :=\n Function.Injective.commRing val val_injective\n rfl rfl (fun _ _ => rfl) (fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl)\n (fun _ _ => rfl) (fun _ _ => rfl) (fun _ _ => rfl) (fun _ => rfl) (fun _ => rfl)", "start": [ 75, 7 ], "end": [ 78, 91 ], "kind": "commanddeclaration" }, { "full_name": "UInt8.isASCIIUpper", "code": "def isASCIIUpper (c : UInt8) : Bool :=\n c ≥ 65 && c ≤ 90", "start": [ 96, 1 ], "end": [ 98, 19 ], "kind": "commanddeclaration" }, { "full_name": "UInt8.isASCIILower", "code": "def isASCIILower (c : UInt8) : Bool :=\n c ≥ 97 && c ≤ 122", "start": [ 100, 1 ], "end": [ 102, 20 ], "kind": "commanddeclaration" }, { "full_name": "UInt8.isASCIIAlpha", "code": "def isASCIIAlpha (c : UInt8) : Bool :=\n c.isASCIIUpper \|\| c.isASCIILower", "start": [ 104, 1 ], "end": [ 106, 35 ], "kind": "commanddeclaration" }, { "full_name": "UInt8.isASCIIDigit", "code": "def isASCIIDigit (c : UInt8) : Bool :=\n c ≥ 48 && c ≤ 57", "start": [ 108, 1 ], "end": [ 110, 19 ], "kind": "commanddeclaration" }, { "full_name": "UInt8.isASCIIAlphanum", "code": "def isASCIIAlphanum (c : UInt8) : Bool :=\n c.isASCIIAlpha \|\| c.isASCIIDigit", "start": [ 112, 1 ], "end": [ 114, 35 ], "kind": "commanddeclaration" }, { "full_name": "UInt8.toChar", "code": "def toChar (n : UInt8) : Char := ⟨n.toUInt32, .inl (n.1.2.trans (by decide))⟩", "start": [ 122, 1 ], "end": [ 123, 78 ], "kind": "commanddeclaration" } ]
Mathlib/Order/Category/OmegaCompletePartialOrder.lean	[ "Mathlib/CategoryTheory/Limits/Shapes/Products.lean", "Mathlib/CategoryTheory/Limits/Constructions/LimitsOfProductsAndEqualizers.lean", "Mathlib/Order/OmegaCompletePartialOrder.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean", "Mathlib/CategoryTheory/ConcreteCategory/BundledHom.lean" ]	[ { "full_name": "ωCPO", "code": "def ωCPO : Type (u + 1) :=\n Bundled OmegaCompletePartialOrder", "start": [ 35, 1 ], "end": [ 37, 36 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.of", "code": "def of (α : Type) [OmegaCompletePartialOrder α] : ωCPO :=\n Bundled.of α", "start": [ 57, 1 ], "end": [ 59, 15 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.coe_of", "code": "@[simp]\ntheorem coe_of (α : Type) [OmegaCompletePartialOrder α] : ↥(of α) = α", "start": [ 62, 1 ], "end": [ 64, 6 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.HasProducts.product", "code": "def product {J : Type v} (f : J → ωCPO.{v}) : Fan f :=\n Fan.mk (of (∀ j, f j)) fun j => .mk (Pi.evalOrderHom j) fun _ => rfl", "start": [ 79, 1 ], "end": [ 81, 71 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.HasProducts.isProduct", "code": "def isProduct (J : Type v) (f : J → ωCPO) : IsLimit (product f) where\n lift s :=\n ⟨⟨fun t j => (s.π.app ⟨j⟩).toFun t, fun x y h j => (s.π.app ⟨j⟩).monotone h⟩,\n fun x => funext fun j => (s.π.app ⟨j⟩).continuous x⟩\n uniq s m w := by\n ext t; funext j change m.toFun t j = (s.π.app ⟨j⟩).toFun t\n rw [← w ⟨j⟩]\n rfl\n fac s j := rfl", "start": [ 84, 1 ], "end": [ 95, 17 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.omegaCompletePartialOrderEqualizer", "code": "instance omegaCompletePartialOrderEqualizer {α β : Type} [OmegaCompletePartialOrder α]\n [OmegaCompletePartialOrder β] (f g : α →𝒄 β) :\n OmegaCompletePartialOrder { a : α // f a = g a } :=\n OmegaCompletePartialOrder.subtype _ fun c hc => by\n rw [f.continuous, g.continuous]\n congr 1\n apply OrderHom.ext; funext x apply hc _ ⟨_, rfl⟩", "start": [ 103, 1 ], "end": [ 110, 24 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.HasEqualizers.equalizerι", "code": "def equalizerι {α β : Type} [OmegaCompletePartialOrder α] [OmegaCompletePartialOrder β]\n (f g : α →𝒄 β) : { a : α // f a = g a } →𝒄 α :=\n .mk (OrderHom.Subtype.val _) fun _ => rfl", "start": [ 115, 1 ], "end": [ 118, 44 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.HasEqualizers.equalizer", "code": "def equalizer {X Y : ωCPO.{v}} (f g : X ⟶ Y) : Fork f g :=\n Fork.ofι (P := ωCPO.of { a // f.toFun a = g.toFun a }) (equalizerι f g)\n (ContinuousHom.ext _ _ fun x => x.2)", "start": [ 121, 1 ], "end": [ 125, 41 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.HasEqualizers.isEqualizer", "code": "def isEqualizer {X Y : ωCPO.{v}} (f g : X ⟶ Y) : IsLimit (equalizer f g) :=\n Fork.IsLimit.mk' _ fun s =>\n ⟨{ toFun := fun x => ⟨s.ι.toFun x, by apply ContinuousHom.congr_fun s.condition⟩\n monotone' := fun x y h => s.ι.monotone h\n cont := fun x => Subtype.ext (s.ι.continuous x) }, by ext; rfl, fun hm => by\n apply ContinuousHom.ext _ _ fun x => Subtype.ext ?_ apply ContinuousHom.congr_fun hm⟩", "start": [ 128, 1 ], "end": [ 136, 40 ], "kind": "commanddeclaration" } ]
Mathlib/Analysis/Calculus/Rademacher.lean	[ "Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean", "Mathlib/MeasureTheory/Measure/Haar/Disintegration.lean", "Mathlib/Analysis/BoundedVariation.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/NormedSpace/FiniteDimension.lean", "Mathlib/MeasureTheory/Group/Integral.lean", "Mathlib/Analysis/Distribution/AEEqOfIntegralContDiff.lean", "Mathlib/Analysis/Calculus/LineDeriv/Measurable.lean" ]	[ { "full_name": "LipschitzWith.ae_lineDifferentiableAt", "code": "theorem ae_lineDifferentiableAt (hf : LipschitzWith C f) (v : E) :\n ∀ᵐ p ∂μ, LineDifferentiableAt ℝ f p v", "start": [ 63, 1 ], "end": [ 77, 77 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.memℒp_lineDeriv", "code": "theorem memℒp_lineDeriv (hf : LipschitzWith C f) (v : E) :\n Memℒp (fun x ↦ lineDeriv ℝ f x v) ∞ μ", "start": [ 79, 1 ], "end": [ 82, 84 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.locallyIntegrable_lineDeriv", "code": "theorem locallyIntegrable_lineDeriv (hf : LipschitzWith C f) (v : E) :\n LocallyIntegrable (fun x ↦ lineDeriv ℝ f x v) μ", "start": [ 84, 1 ], "end": [ 86, 50 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul", "code": "theorem integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul\n (hf : LipschitzWith C f) (hg : Integrable g μ) (v : E) :\n Tendsto (fun (t : ℝ) ↦ ∫ x, (t⁻¹ • (f (x + t • v) - f x)) * g x ∂μ) (𝓝[>] 0)\n (𝓝 (∫ x, lineDeriv ℝ f x v * g x ∂μ))", "start": [ 97, 1 ], "end": [ 117, 76 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul'", "code": "theorem integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul'\n (hf : LipschitzWith C f) (h'f : HasCompactSupport f) (hg : Continuous g) (v : E) :\n Tendsto (fun (t : ℝ) ↦ ∫ x, (t⁻¹ • (f (x + t • v) - f x)) * g x ∂μ) (𝓝[>] 0)\n (𝓝 (∫ x, lineDeriv ℝ f x v * g x ∂μ))", "start": [ 119, 1 ], "end": [ 160, 76 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.integral_lineDeriv_mul_eq", "code": "theorem integral_lineDeriv_mul_eq\n (hf : LipschitzWith C f) (hg : LipschitzWith D g) (h'g : HasCompactSupport g) (v : E) :\n ∫ x, lineDeriv ℝ f x v * g x ∂μ = ∫ x, lineDeriv ℝ g x (-v) * f x ∂μ", "start": [ 162, 1 ], "end": [ 195, 89 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.ae_lineDeriv_sum_eq", "code": "theorem ae_lineDeriv_sum_eq\n (hf : LipschitzWith C f) {ι : Type} (s : Finset ι) (a : ι → ℝ) (v : ι → E) :\n ∀ᵐ x ∂μ, lineDeriv ℝ f x (∑ i ∈ s, a i • v i) = ∑ i ∈ s, a i • lineDeriv ℝ f x (v i)", "start": [ 197, 1 ], "end": [ 233, 54 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.ae_exists_fderiv_of_countable", "code": "theorem ae_exists_fderiv_of_countable\n (hf : LipschitzWith C f) {s : Set E} (hs : s.Countable) :\n ∀ᵐ x ∂μ, ∃ (L : E →L[ℝ] ℝ), ∀ v ∈ s, HasLineDerivAt ℝ f (L v) x v", "start": [ 239, 1 ], "end": [ 253, 44 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.hasFderivAt_of_hasLineDerivAt_of_closure", "code": "theorem hasFderivAt_of_hasLineDerivAt_of_closure {f : E → F}\n (hf : LipschitzWith C f) {s : Set E} (hs : sphere 0 1 ⊆ closure s)\n {L : E →L[ℝ] F} {x : E} (hL : ∀ v ∈ s, HasLineDerivAt ℝ f (L v) x v) :\n HasFDerivAt f L x", "start": [ 255, 1 ], "end": [ 307, 34 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.ae_differentiableAt_of_real", "code": "theorem ae_differentiableAt_of_real (hf : LipschitzWith C f) :\n ∀ᵐ x ∂μ, DifferentiableAt ℝ f x", "start": [ 309, 1 ], "end": [ 320, 77 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzOnWith.ae_differentiableWithinAt_of_mem_of_real", "code": "theorem ae_differentiableWithinAt_of_mem_of_real (hf : LipschitzOnWith C f s) :\n ∀ᵐ x ∂μ, x ∈ s → DifferentiableWithinAt ℝ f s x", "start": [ 328, 1 ], "end": [ 336, 51 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzOnWith.ae_differentiableWithinAt_of_mem_pi", "code": "theorem ae_differentiableWithinAt_of_mem_pi\n {ι : Type} [Fintype ι] {f : E → ι → ℝ} {s : Set E}\n (hf : LipschitzOnWith C f s) : ∀ᵐ x ∂μ, x ∈ s → DifferentiableWithinAt ℝ f s x", "start": [ 338, 1 ], "end": [ 350, 54 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzOnWith.ae_differentiableWithinAt_of_mem", "code": "theorem ae_differentiableWithinAt_of_mem {f : E → F} (hf : LipschitzOnWith C f s) :\n ∀ᵐ x ∂μ, x ∈ s → DifferentiableWithinAt ℝ f s x", "start": [ 352, 1 ], "end": [ 364, 44 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzOnWith.ae_differentiableWithinAt", "code": "theorem ae_differentiableWithinAt {f : E → F} (hf : LipschitzOnWith C f s)\n (hs : MeasurableSet s) :\n ∀ᵐ x ∂(μ.restrict s), DifferentiableWithinAt ℝ f s x", "start": [ 366, 1 ], "end": [ 372, 44 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.ae_differentiableAt", "code": "theorem LipschitzWith.ae_differentiableAt {f : E → F} (h : LipschitzWith C f) :\n ∀ᵐ x ∂μ, DifferentiableAt ℝ f x", "start": [ 376, 1 ], "end": [ 381, 79 ], "kind": "commanddeclaration" } ]
Mathlib/Analysis/Complex/UnitDisc/Basic.lean	[ "Mathlib/Analysis/Complex/Circle.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/NormedSpace/BallAction.lean" ]	[ { "full_name": "Complex.UnitDisc", "code": "def UnitDisc : Type :=\n ball (0 : ℂ) 1 deriving TopologicalSpace", "start": [ 27, 1 ], "end": [ 29, 43 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instCommSemigroup", "code": "instance instCommSemigroup : CommSemigroup UnitDisc := by unfold UnitDisc; infer_instance", "start": [ 37, 1 ], "end": [ 37, 90 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instHasDistribNeg", "code": "instance instHasDistribNeg : HasDistribNeg UnitDisc := by unfold UnitDisc; infer_instance", "start": [ 38, 1 ], "end": [ 38, 90 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instCoe", "code": "instance instCoe : Coe UnitDisc ℂ := ⟨Subtype.val⟩", "start": [ 39, 1 ], "end": [ 39, 51 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_injective", "code": "theorem coe_injective : Injective ((↑) : 𝔻 → ℂ)", "start": [ 41, 1 ], "end": [ 42, 24 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.abs_lt_one", "code": "theorem abs_lt_one (z : 𝔻) : abs (z : ℂ) < 1", "start": [ 45, 1 ], "end": [ 46, 26 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.abs_ne_one", "code": "theorem abs_ne_one (z : 𝔻) : abs (z : ℂ) ≠ 1", "start": [ 49, 1 ], "end": [ 50, 18 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.normSq_lt_one", "code": "theorem normSq_lt_one (z : 𝔻) : normSq z < 1", "start": [ 53, 1 ], "end": [ 55, 25 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_ne_one", "code": "theorem coe_ne_one (z : 𝔻) : (z : ℂ) ≠ 1", "start": [ 58, 1 ], "end": [ 59, 58 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_ne_neg_one", "code": "theorem coe_ne_neg_one (z : 𝔻) : (z : ℂ) ≠ -1", "start": [ 62, 1 ], "end": [ 65, 23 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.one_add_coe_ne_zero", "code": "theorem one_add_coe_ne_zero (z : 𝔻) : (1 + z : ℂ) ≠ 0", "start": [ 68, 1 ], "end": [ 69, 52 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_mul", "code": "@[simp, norm_cast]\ntheorem coe_mul (z w : 𝔻) : ↑(z * w) = (z * w : ℂ)", "start": [ 72, 1 ], "end": [ 74, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.mk", "code": "def mk (z : ℂ) (hz : abs z < 1) : 𝔻 :=\n ⟨z, mem_ball_zero_iff.2 hz⟩", "start": [ 77, 1 ], "end": [ 80, 30 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_mk", "code": "@[simp]\ntheorem coe_mk (z : ℂ) (hz : abs z < 1) : (mk z hz : ℂ) = z", "start": [ 83, 1 ], "end": [ 85, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.mk_coe", "code": "@[simp]\ntheorem mk_coe (z : 𝔻) (hz : abs (z : ℂ) < 1 := z.abs_lt_one) : mk z hz = z", "start": [ 88, 1 ], "end": [ 90, 18 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.mk_neg", "code": "@[simp]\ntheorem mk_neg (z : ℂ) (hz : abs (-z) < 1) : mk (-z) hz = -mk z (abs.map_neg z ▸ hz)", "start": [ 93, 1 ], "end": [ 95, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_zero", "code": "@[simp]\ntheorem coe_zero : ((0 : 𝔻) : ℂ) = 0", "start": [ 104, 1 ], "end": [ 106, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_eq_zero", "code": "@[simp]\ntheorem coe_eq_zero {z : 𝔻} : (z : ℂ) = 0 ↔ z = 0", "start": [ 109, 1 ], "end": [ 111, 33 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.circleAction", "code": "instance circleAction : MulAction circle 𝔻 :=\n mulActionSphereBall", "start": [ 117, 1 ], "end": [ 118, 22 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.isScalarTower_circle_circle", "code": "instance isScalarTower_circle_circle : IsScalarTower circle circle 𝔻 :=\n isScalarTower_sphere_sphere_ball", "start": [ 121, 1 ], "end": [ 122, 35 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.isScalarTower_circle", "code": "instance isScalarTower_circle : IsScalarTower circle 𝔻 𝔻 :=\n isScalarTower_sphere_ball_ball", "start": [ 125, 1 ], "end": [ 126, 33 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instSMulCommClass_circle", "code": "instance instSMulCommClass_circle : SMulCommClass circle 𝔻 𝔻 :=\n instSMulCommClass_sphere_ball_ball", "start": [ 129, 1 ], "end": [ 130, 37 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instSMulCommClass_circle'", "code": "instance instSMulCommClass_circle' : SMulCommClass 𝔻 circle 𝔻 :=\n SMulCommClass.symm _ _ _", "start": [ 133, 1 ], "end": [ 134, 27 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_smul_circle", "code": "@[simp, norm_cast]\ntheorem coe_smul_circle (z : circle) (w : 𝔻) : ↑(z • w) = (z * w : ℂ)", "start": [ 137, 1 ], "end": [ 139, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.closedBallAction", "code": "instance closedBallAction : MulAction (closedBall (0 : ℂ) 1) 𝔻 :=\n mulActionClosedBallBall", "start": [ 142, 1 ], "end": [ 143, 26 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.isScalarTower_closedBall_closedBall", "code": "instance isScalarTower_closedBall_closedBall :\n IsScalarTower (closedBall (0 : ℂ) 1) (closedBall (0 : ℂ) 1) 𝔻 :=\n isScalarTower_closedBall_closedBall_ball", "start": [ 146, 1 ], "end": [ 148, 43 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.isScalarTower_closedBall", "code": "instance isScalarTower_closedBall : IsScalarTower (closedBall (0 : ℂ) 1) 𝔻 𝔻 :=\n isScalarTower_closedBall_ball_ball", "start": [ 151, 1 ], "end": [ 152, 37 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instSMulCommClass_closedBall", "code": "instance instSMulCommClass_closedBall : SMulCommClass (closedBall (0 : ℂ) 1) 𝔻 𝔻 :=\n ⟨fun _ _ _ => Subtype.ext <\| mul_left_comm _ _ _⟩", "start": [ 155, 1 ], "end": [ 156, 52 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instSMulCommClass_closedBall'", "code": "instance instSMulCommClass_closedBall' : SMulCommClass 𝔻 (closedBall (0 : ℂ) 1) 𝔻 :=\n SMulCommClass.symm _ _ _", "start": [ 159, 1 ], "end": [ 160, 27 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instSMulCommClass_circle_closedBall", "code": "instance instSMulCommClass_circle_closedBall : SMulCommClass circle (closedBall (0 : ℂ) 1) 𝔻 :=\n instSMulCommClass_sphere_closedBall_ball", "start": [ 163, 1 ], "end": [ 164, 43 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instSMulCommClass_closedBall_circle", "code": "instance instSMulCommClass_closedBall_circle : SMulCommClass (closedBall (0 : ℂ) 1) circle 𝔻 :=\n SMulCommClass.symm _ _ _", "start": [ 167, 1 ], "end": [ 168, 27 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_smul_closedBall", "code": "@[simp, norm_cast]\ntheorem coe_smul_closedBall (z : closedBall (0 : ℂ) 1) (w : 𝔻) : ↑(z • w) = (z * w : ℂ)", "start": [ 171, 1 ], "end": [ 173, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.re", "code": "def re (z : 𝔻) : ℝ :=\n Complex.re z", "start": [ 176, 1 ], "end": [ 178, 15 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.im", "code": "def im (z : 𝔻) : ℝ :=\n Complex.im z", "start": [ 181, 1 ], "end": [ 183, 15 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.re_coe", "code": "@[simp, norm_cast]\ntheorem re_coe (z : 𝔻) : (z : ℂ).re = z.re", "start": [ 186, 1 ], "end": [ 188, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.im_coe", "code": "@[simp, norm_cast]\ntheorem im_coe (z : 𝔻) : (z : ℂ).im = z.im", "start": [ 191, 1 ], "end": [ 193, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.re_neg", "code": "@[simp]\ntheorem re_neg (z : 𝔻) : (-z).re = -z.re", "start": [ 196, 1 ], "end": [ 198, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.im_neg", "code": "@[simp]\ntheorem im_neg (z : 𝔻) : (-z).im = -z.im", "start": [ 201, 1 ], "end": [ 203, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.conj", "code": "def conj (z : 𝔻) : 𝔻 :=\n mk (conj' ↑z) <\| (abs_conj z).symm ▸ z.abs_lt_one", "start": [ 206, 1 ], "end": [ 208, 52 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_conj", "code": "@[simp]\ntheorem coe_conj (z : 𝔻) : (z.conj : ℂ) = conj' ↑z", "start": [ 213, 1 ], "end": [ 215, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.conj_zero", "code": "@[simp]\ntheorem conj_zero : conj 0 = 0", "start": [ 218, 1 ], "end": [ 220, 33 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.conj_conj", "code": "@[simp]\ntheorem conj_conj (z : 𝔻) : conj (conj z) = z", "start": [ 223, 1 ], "end": [ 225, 45 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.conj_neg", "code": "@[simp]\ntheorem conj_neg (z : 𝔻) : (-z).conj = -z.conj", "start": [ 228, 1 ], "end": [ 230, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.re_conj", "code": "@[simp]\ntheorem re_conj (z : 𝔻) : z.conj.re = z.re", "start": [ 233, 1 ], "end": [ 235, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.im_conj", "code": "@[simp]\ntheorem im_conj (z : 𝔻) : z.conj.im = -z.im", "start": [ 238, 1 ], "end": [ 240, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.conj_mul", "code": "@[simp]\ntheorem conj_mul (z w : 𝔻) : (z * w).conj = z.conj * w.conj", "start": [ 243, 1 ], "end": [ 245, 31 ], "kind": "commanddeclaration" } ]
Mathlib/Algebra/Order/Group/Bounds.lean	[ "Mathlib/Algebra/Order/Group/Defs.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Order/Bounds/Basic.lean" ]	[ { "full_name": "IsGLB.exists_between_self_add", "code": "theorem IsGLB.exists_between_self_add (h : IsGLB s a) (hε : 0 < ε) : ∃ b ∈ s, a ≤ b ∧ b < a + ε", "start": [ 19, 1 ], "end": [ 20, 47 ], "kind": "commanddeclaration" }, { "full_name": "IsGLB.exists_between_self_add'", "code": "theorem IsGLB.exists_between_self_add' (h : IsGLB s a) (h₂ : a ∉ s) (hε : 0 < ε) :\n ∃ b ∈ s, a < b ∧ b < a + ε", "start": [ 23, 1 ], "end": [ 25, 51 ], "kind": "commanddeclaration" }, { "full_name": "IsLUB.exists_between_sub_self", "code": "theorem IsLUB.exists_between_sub_self (h : IsLUB s a) (hε : 0 < ε) : ∃ b ∈ s, a - ε < b ∧ b ≤ a", "start": [ 28, 1 ], "end": [ 29, 39 ], "kind": "commanddeclaration" }, { "full_name": "IsLUB.exists_between_sub_self'", "code": "theorem IsLUB.exists_between_sub_self' (h : IsLUB s a) (h₂ : a ∉ s) (hε : 0 < ε) :\n ∃ b ∈ s, a - ε < b ∧ b < a", "start": [ 32, 1 ], "end": [ 34, 43 ], "kind": "commanddeclaration" } ]
Mathlib/Lean/Expr.lean	[ "Mathlib/Lean/Expr/Basic.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Lean/Expr/ReplaceRec.lean" ]	[]
Mathlib/CategoryTheory/Limits/EpiMono.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean" ]	[ { "full_name": "CategoryTheory.mono_iff_fst_eq_snd", "code": "lemma mono_iff_fst_eq_snd : Mono f ↔ c.fst = c.snd := by\n constructor\n · intro hf\n simpa only [← cancel_mono f] using c.condition\n · intro hf\n constructor\n intro Z g g' h\n obtain ⟨φ, rfl, rfl⟩ := PullbackCone.IsLimit.lift' hc g g' h\n rw [hf]", "start": [ 38, 1 ], "end": [ 46, 12 ], "kind": "lemma" }, { "full_name": "CategoryTheory.mono_iff_isIso_fst", "code": "lemma mono_iff_isIso_fst : Mono f ↔ IsIso c.fst := by\n rw [mono_iff_fst_eq_snd hc]\n constructor\n · intro h\n obtain ⟨φ, hφ₁, hφ₂⟩ := PullbackCone.IsLimit.lift' hc (𝟙 X) (𝟙 X) (by simp)\n refine ⟨φ, PullbackCone.IsLimit.hom_ext hc ?_ ?_, hφ₁⟩\n · dsimp\n simp only [assoc, hφ₁, id_comp, comp_id]\n · dsimp\n simp only [assoc, hφ₂, id_comp, comp_id, h]\n · intro\n obtain ⟨φ, hφ₁, hφ₂⟩ := PullbackCone.IsLimit.lift' hc (𝟙 X) (𝟙 X) (by simp)\n have : IsSplitEpi φ := IsSplitEpi.mk ⟨SplitEpi.mk c.fst (by\n rw [← cancel_mono c.fst, assoc, id_comp, hφ₁, comp_id])⟩\n rw [← cancel_epi φ, hφ₁, hφ₂]", "start": [ 48, 1 ], "end": [ 62, 34 ], "kind": "lemma" }, { "full_name": "CategoryTheory.mono_iff_isIso_snd", "code": "lemma mono_iff_isIso_snd : Mono f ↔ IsIso c.snd :=\n mono_iff_isIso_fst (PullbackCone.flipIsLimit hc)", "start": [ 64, 1 ], "end": [ 65, 51 ], "kind": "lemma" }, { "full_name": "CategoryTheory.mono_iff_isPullback", "code": "lemma mono_iff_isPullback : Mono f ↔ IsPullback (𝟙 X) (𝟙 X) f f := by\n constructor\n · intro\n exact IsPullback.of_isLimit (PullbackCone.isLimitMkIdId f)\n · intro hf\n exact (mono_iff_fst_eq_snd hf.isLimit).2 rfl", "start": [ 69, 1 ], "end": [ 74, 49 ], "kind": "lemma" }, { "full_name": "CategoryTheory.epi_iff_inl_eq_inr", "code": "lemma epi_iff_inl_eq_inr : Epi f ↔ c.inl = c.inr := by\n constructor\n · intro hf\n simpa only [← cancel_epi f] using c.condition\n · intro hf\n constructor\n intro Z g g' h\n obtain ⟨φ, rfl, rfl⟩ := PushoutCocone.IsColimit.desc' hc g g' h\n rw [hf]", "start": [ 82, 1 ], "end": [ 90, 12 ], "kind": "lemma" }, { "full_name": "CategoryTheory.epi_iff_isIso_inl", "code": "lemma epi_iff_isIso_inl : Epi f ↔ IsIso c.inl := by\n rw [epi_iff_inl_eq_inr hc]\n constructor\n · intro h\n obtain ⟨φ, hφ₁, hφ₂⟩ := PushoutCocone.IsColimit.desc' hc (𝟙 Y) (𝟙 Y) (by simp)\n refine ⟨φ, hφ₁, PushoutCocone.IsColimit.hom_ext hc ?_ ?_⟩\n · dsimp\n simp only [comp_id, reassoc_of% hφ₁]\n · dsimp\n simp only [comp_id, h, reassoc_of% hφ₂]\n · intro\n obtain ⟨φ, hφ₁, hφ₂⟩ := PushoutCocone.IsColimit.desc' hc (𝟙 Y) (𝟙 Y) (by simp)\n have : IsSplitMono φ := IsSplitMono.mk ⟨SplitMono.mk c.inl (by\n rw [← cancel_epi c.inl, reassoc_of% hφ₁, comp_id])⟩\n rw [← cancel_mono φ, hφ₁, hφ₂]", "start": [ 92, 1 ], "end": [ 106, 35 ], "kind": "lemma" }, { "full_name": "CategoryTheory.epi_iff_isIso_inr", "code": "lemma epi_iff_isIso_inr : Epi f ↔ IsIso c.inr :=\n epi_iff_isIso_inl (PushoutCocone.flipIsColimit hc)", "start": [ 108, 1 ], "end": [ 109, 53 ], "kind": "lemma" }, { "full_name": "CategoryTheory.epi_iff_isPushout", "code": "lemma epi_iff_isPushout : Epi f ↔ IsPushout f f (𝟙 Y) (𝟙 Y) := by\n constructor\n · intro\n exact IsPushout.of_isColimit (PushoutCocone.isColimitMkIdId f)\n · intro hf\n exact (epi_iff_inl_eq_inr hf.isColimit).2 rfl", "start": [ 113, 1 ], "end": [ 118, 50 ], "kind": "lemma" } ]
Mathlib/Data/Vector/Mem.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Data/Vector/Basic.lean" ]	[ { "full_name": "Vector.get_mem", "code": "@[simp]\ntheorem get_mem (i : Fin n) (v : Vector α n) : v.get i ∈ v.toList", "start": [ 25, 1 ], "end": [ 28, 27 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_iff_get", "code": "theorem mem_iff_get (v : Vector α n) : a ∈ v.toList ↔ ∃ i, v.get i = a", "start": [ 31, 1 ], "end": [ 35, 38 ], "kind": "commanddeclaration" }, { "full_name": "Vector.not_mem_nil", "code": "theorem not_mem_nil : a ∉ (Vector.nil : Vector α 0).toList", "start": [ 38, 1 ], "end": [ 41, 7 ], "kind": "commanddeclaration" }, { "full_name": "Vector.not_mem_zero", "code": "theorem not_mem_zero (v : Vector α 0) : a ∉ v.toList", "start": [ 44, 1 ], "end": [ 45, 41 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_cons_iff", "code": "theorem mem_cons_iff (v : Vector α n) : a' ∈ (a ::ᵥ v).toList ↔ a' = a ∨ a' ∈ v.toList", "start": [ 48, 1 ], "end": [ 49, 41 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_succ_iff", "code": "theorem mem_succ_iff (v : Vector α (n + 1)) : a ∈ v.toList ↔ a = v.head ∨ a ∈ v.tail.toList", "start": [ 52, 1 ], "end": [ 54, 71 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_cons_self", "code": "theorem mem_cons_self (v : Vector α n) : a ∈ (a ::ᵥ v).toList", "start": [ 57, 1 ], "end": [ 58, 67 ], "kind": "commanddeclaration" }, { "full_name": "Vector.head_mem", "code": "@[simp]\ntheorem head_mem (v : Vector α (n + 1)) : v.head ∈ v.toList", "start": [ 61, 1 ], "end": [ 63, 57 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_cons_of_mem", "code": "theorem mem_cons_of_mem (v : Vector α n) (ha' : a' ∈ v.toList) : a' ∈ (a ::ᵥ v).toList", "start": [ 66, 1 ], "end": [ 67, 46 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_of_mem_tail", "code": "theorem mem_of_mem_tail (v : Vector α n) (ha : a ∈ v.tail.toList) : a ∈ v.toList", "start": [ 70, 1 ], "end": [ 73, 43 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_map_iff", "code": "theorem mem_map_iff (b : β) (v : Vector α n) (f : α → β) :\n b ∈ (v.map f).toList ↔ ∃ a : α, a ∈ v.toList ∧ f a = b", "start": [ 76, 1 ], "end": [ 78, 39 ], "kind": "commanddeclaration" }, { "full_name": "Vector.not_mem_map_zero", "code": "theorem not_mem_map_zero (b : β) (v : Vector α 0) (f : α → β) : b ∉ (v.map f).toList", "start": [ 81, 1 ], "end": [ 82, 91 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_map_succ_iff", "code": "theorem mem_map_succ_iff (b : β) (v : Vector α (n + 1)) (f : α → β) :\n b ∈ (v.map f).toList ↔ f v.head = b ∨ ∃ a : α, a ∈ v.tail.toList ∧ f a = b", "start": [ 85, 1 ], "end": [ 87, 67 ], "kind": "commanddeclaration" } ]
Mathlib/CategoryTheory/Functor/Derived/RightDerived.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/CategoryTheory/Localization/Predicate.lean", "Mathlib/CategoryTheory/Functor/KanExtension/Basic.lean" ]	[ { "full_name": "CategoryTheory.Functor.IsRightDerivedFunctor", "code": "class IsRightDerivedFunctor [L.IsLocalization W] : Prop where\n isLeftKanExtension' : RF.IsLeftKanExtension α", "start": [ 47, 1 ], "end": [ 52, 48 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.IsRightDerivedFunctor.isLeftKanExtension", "code": "lemma IsRightDerivedFunctor.isLeftKanExtension\n [L.IsLocalization W] [RF.IsRightDerivedFunctor α W] :\n RF.IsLeftKanExtension α :=\n IsRightDerivedFunctor.isLeftKanExtension' W", "start": [ 54, 1 ], "end": [ 57, 46 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.isRightDerivedFunctor_iff_isLeftKanExtension", "code": "lemma isRightDerivedFunctor_iff_isLeftKanExtension [L.IsLocalization W] :\n RF.IsRightDerivedFunctor α W ↔ RF.IsLeftKanExtension α := by\n constructor\n · exact fun _ => IsRightDerivedFunctor.isLeftKanExtension RF α W\n · exact fun h => ⟨h⟩", "start": [ 59, 1 ], "end": [ 63, 23 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.isRightDerivedFunctor_iff_of_iso", "code": "lemma isRightDerivedFunctor_iff_of_iso (α' : F ⟶ L ⋙ RF') (W : MorphismProperty C)\n [L.IsLocalization W] (e : RF ≅ RF') (comm : α ≫ whiskerLeft L e.hom = α') :\n RF.IsRightDerivedFunctor α W ↔ RF'.IsRightDerivedFunctor α' W := by\n simp only [isRightDerivedFunctor_iff_isLeftKanExtension]\n exact isLeftKanExtension_iff_of_iso e _ _ comm", "start": [ 66, 1 ], "end": [ 70, 49 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerivedDesc", "code": "noncomputable def rightDerivedDesc (G : D ⥤ H) (β : F ⟶ L ⋙ G) : RF ⟶ G :=\n have := IsRightDerivedFunctor.isLeftKanExtension RF α W\n RF.descOfIsLeftKanExtension α G β", "start": [ 77, 1 ], "end": [ 80, 36 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.rightDerived_fac", "code": "@[reassoc (attr := simp)]\nlemma rightDerived_fac (G : D ⥤ H) (β : F ⟶ L ⋙ G) :\n α ≫ whiskerLeft L (RF.rightDerivedDesc α W G β) = β :=\n have := IsRightDerivedFunctor.isLeftKanExtension RF α W\n RF.descOfIsLeftKanExtension_fac α G β", "start": [ 82, 1 ], "end": [ 86, 40 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerived_fac_app", "code": "@[reassoc (attr := simp)]\nlemma rightDerived_fac_app (G : D ⥤ H) (β : F ⟶ L ⋙ G) (X : C):\n α.app X ≫ (RF.rightDerivedDesc α W G β).app (L.obj X) = β.app X :=\n have := IsRightDerivedFunctor.isLeftKanExtension RF α W\n RF.descOfIsLeftKanExtension_fac_app α G β X", "start": [ 88, 1 ], "end": [ 92, 46 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerived_ext", "code": "lemma rightDerived_ext (G : D ⥤ H) (γ₁ γ₂ : RF ⟶ G)\n (hγ : α ≫ whiskerLeft L γ₁ = α ≫ whiskerLeft L γ₂) : γ₁ = γ₂ :=\n have := IsRightDerivedFunctor.isLeftKanExtension RF α W\n RF.hom_ext_of_isLeftKanExtension α γ₁ γ₂ hγ", "start": [ 94, 1 ], "end": [ 97, 46 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerivedNatTrans", "code": "noncomputable def rightDerivedNatTrans (τ : F ⟶ F') : RF ⟶ RF' :=\n RF.rightDerivedDesc α W RF' (τ ≫ α')", "start": [ 99, 1 ], "end": [ 102, 39 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.rightDerivedNatTrans_fac", "code": "@[reassoc (attr := simp)]\nlemma rightDerivedNatTrans_fac (τ : F ⟶ F') :\n α ≫ whiskerLeft L (rightDerivedNatTrans RF RF' α α' W τ) = τ ≫ α' := by\n dsimp only [rightDerivedNatTrans]\n simp", "start": [ 104, 1 ], "end": [ 108, 7 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerivedNatTrans_app", "code": "@[reassoc (attr := simp)]\nlemma rightDerivedNatTrans_app (τ : F ⟶ F') (X : C) :\n α.app X ≫ (rightDerivedNatTrans RF RF' α α' W τ).app (L.obj X) =\n τ.app X ≫ α'.app X := by\n dsimp only [rightDerivedNatTrans]\n simp", "start": [ 110, 1 ], "end": [ 115, 7 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerivedNatTrans_id", "code": "@[simp]\nlemma rightDerivedNatTrans_id :\n rightDerivedNatTrans RF RF α α W (𝟙 F) = 𝟙 RF :=\n rightDerived_ext RF α W _ _ _ (by aesop_cat)", "start": [ 117, 1 ], "end": [ 120, 47 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerivedNatTrans_comp", "code": "@[reassoc (attr:= simp)]\nlemma rightDerivedNatTrans_comp (τ : F ⟶ F') (τ' : F' ⟶ F'') :\n rightDerivedNatTrans RF RF' α α' W τ ≫ rightDerivedNatTrans RF' RF'' α' α'' W τ' =\n rightDerivedNatTrans RF RF'' α α'' W (τ ≫ τ') :=\n rightDerived_ext RF α W _ _ _ (by aesop_cat)", "start": [ 122, 1 ], "end": [ 126, 47 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerivedNatIso", "code": "@[simps]\nnoncomputable def rightDerivedNatIso (τ : F ≅ F') :\n RF ≅ RF' where\n hom := rightDerivedNatTrans RF RF' α α' W τ.hom\n inv := rightDerivedNatTrans RF' RF α' α W τ.inv", "start": [ 128, 1 ], "end": [ 134, 50 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.rightDerivedUnique", "code": "noncomputable abbrev rightDerivedUnique [RF'.IsRightDerivedFunctor α'₂ W] : RF ≅ RF' :=\n rightDerivedNatIso RF RF' α α'₂ W (Iso.refl F)", "start": [ 136, 1 ], "end": [ 138, 49 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.isRightDerivedFunctor_iff_isIso_rightDerivedDesc", "code": "lemma isRightDerivedFunctor_iff_isIso_rightDerivedDesc (G : D ⥤ H) (β : F ⟶ L ⋙ G) :\n G.IsRightDerivedFunctor β W ↔ IsIso (RF.rightDerivedDesc α W G β) := by\n rw [isRightDerivedFunctor_iff_isLeftKanExtension]\n have := IsRightDerivedFunctor.isLeftKanExtension _ α W\n exact isLeftKanExtension_iff_isIso _ α _ (by simp)", "start": [ 140, 1 ], "end": [ 144, 53 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.HasRightDerivedFunctor", "code": "class HasRightDerivedFunctor : Prop where\n hasLeftKanExtension' : HasLeftKanExtension W.Q F", "start": [ 150, 1 ], "end": [ 155, 51 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.hasRightDerivedFunctor_iff", "code": "lemma hasRightDerivedFunctor_iff :\n F.HasRightDerivedFunctor W ↔ HasLeftKanExtension L F := by\n have : HasRightDerivedFunctor F W ↔ HasLeftKanExtension W.Q F :=\n ⟨fun h => h.hasLeftKanExtension', fun h => ⟨h⟩⟩\n rw [this, hasLeftExtension_iff_postcomp₁ (Localization.compUniqFunctor W.Q L W) F]", "start": [ 160, 1 ], "end": [ 164, 85 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.hasRightDerivedFunctor_iff_of_iso", "code": "lemma hasRightDerivedFunctor_iff_of_iso :\n HasRightDerivedFunctor F W ↔ HasRightDerivedFunctor F' W := by\n rw [hasRightDerivedFunctor_iff F W.Q W, hasRightDerivedFunctor_iff F' W.Q W,\n hasLeftExtension_iff_of_iso₂ W.Q e]", "start": [ 168, 1 ], "end": [ 171, 40 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.HasRightDerivedFunctor.hasLeftKanExtension", "code": "lemma HasRightDerivedFunctor.hasLeftKanExtension [HasRightDerivedFunctor F W] :\n HasLeftKanExtension L F := by\n simpa only [← hasRightDerivedFunctor_iff F L W]", "start": [ 175, 1 ], "end": [ 177, 50 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.HasRightDerivedFunctor.mk'", "code": "lemma HasRightDerivedFunctor.mk' [RF.IsRightDerivedFunctor α W] :\n HasRightDerivedFunctor F W := by\n have := IsRightDerivedFunctor.isLeftKanExtension RF α W\n simpa only [hasRightDerivedFunctor_iff F L W] using HasLeftKanExtension.mk RF α", "start": [ 181, 1 ], "end": [ 184, 82 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.totalRightDerived", "code": "noncomputable def totalRightDerived : D ⥤ H :=\n have := HasRightDerivedFunctor.hasLeftKanExtension F L W\n leftKanExtension L F", "start": [ 190, 1 ], "end": [ 195, 23 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.totalRightDerivedUnit", "code": "noncomputable def totalRightDerivedUnit : F ⟶ L ⋙ F.totalRightDerived L W :=\n have := HasRightDerivedFunctor.hasLeftKanExtension F L W\n leftKanExtensionUnit L F", "start": [ 197, 1 ], "end": [ 200, 27 ], "kind": "commanddeclaration" } ]
Mathlib/NumberTheory/Modular.lean	[ "Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup.lean", "Mathlib/Analysis/Complex/UpperHalfPlane/Basic.lean", "Mathlib/Topology/Algebra/Module/FiniteDimension.lean", "Mathlib/LinearAlgebra/GeneralLinearGroup.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Topology/Instances/Matrix.lean" ]	[ { "full_name": "ModularGroup.bottom_row_coprime", "code": "theorem bottom_row_coprime {R : Type} [CommRing R] (g : SL(2, R)) :\n IsCoprime ((↑g : Matrix (Fin 2) (Fin 2) R) 1 0) ((↑g : Matrix (Fin 2) (Fin 2) R) 1 1)", "start": [ 84, 1 ], "end": [ 89, 18 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.bottom_row_surj", "code": "theorem bottom_row_surj {R : Type} [CommRing R] :\n Set.SurjOn (fun g : SL(2, R) => (↑g : Matrix (Fin 2) (Fin 2) R) 1) Set.univ\n {cd \| IsCoprime (cd 0) (cd 1)}", "start": [ 92, 1 ], "end": [ 104, 16 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.tendsto_normSq_coprime_pair", "code": "theorem tendsto_normSq_coprime_pair :\n Filter.Tendsto (fun p : Fin 2 → ℤ => normSq ((p 0 : ℂ) * z + p 1)) cofinite atTop", "start": [ 115, 1 ], "end": [ 161, 76 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.lcRow0", "code": "def lcRow0 (p : Fin 2 → ℤ) : Matrix (Fin 2) (Fin 2) ℝ →ₗ[ℝ] ℝ :=\n ((p 0 : ℝ) • LinearMap.proj (0 : Fin 2) +\n (p 1 : ℝ) • LinearMap.proj (1 : Fin 2) : (Fin 2 → ℝ) →ₗ[ℝ] ℝ).comp\n (LinearMap.proj 0)", "start": [ 164, 1 ], "end": [ 170, 23 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.lcRow0_apply", "code": "@[simp]\ntheorem lcRow0_apply (p : Fin 2 → ℤ) (g : Matrix (Fin 2) (Fin 2) ℝ) :\n lcRow0 p g = p 0 * g 0 0 + p 1 * g 0 1", "start": [ 173, 1 ], "end": [ 176, 6 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.lcRow0Extend", "code": "@[simps!]\ndef lcRow0Extend {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :\n Matrix (Fin 2) (Fin 2) ℝ ≃ₗ[ℝ] Matrix (Fin 2) (Fin 2) ℝ :=\n LinearEquiv.piCongrRight\n ![by\n refine\n LinearMap.GeneralLinearGroup.generalLinearEquiv ℝ (Fin 2 → ℝ)\n (GeneralLinearGroup.toLinear (planeConformalMatrix (cd 0 : ℝ) (-(cd 1 : ℝ)) ?_))\n norm_cast\n rw [neg_sq]\n exact hcd.sq_add_sq_ne_zero, LinearEquiv.refl ℝ (Fin 2 → ℝ)]", "start": [ 179, 1 ], "end": [ 191, 67 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.tendsto_lcRow0", "code": "theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :\n Tendsto (fun g : { g : SL(2, ℤ) // (↑ₘg) 1 = cd } => lcRow0 cd ↑(↑g : SL(2, ℝ))) cofinite\n (cocompact ℝ)", "start": [ 197, 1 ], "end": [ 236, 8 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.smul_eq_lcRow0_add", "code": "theorem smul_eq_lcRow0_add {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) (hg : (↑ₘg) 1 = p) :\n ↑(g • z) =\n (lcRow0 p ↑(g : SL(2, ℝ)) : ℂ) / ((p 0 : ℂ) ^ 2 + (p 1 : ℂ) ^ 2) +\n ((p 1 : ℂ) * z - p 0) / (((p 0 : ℂ) ^ 2 + (p 1 : ℂ) ^ 2) * (p 0 * z + p 1))", "start": [ 239, 1 ], "end": [ 255, 7 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.tendsto_abs_re_smul", "code": "theorem tendsto_abs_re_smul {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) :\n Tendsto\n (fun g : { g : SL(2, ℤ) // (↑ₘg) 1 = p } => \|((g : SL(2, ℤ)) • z).re\|) cofinite atTop", "start": [ 258, 1 ], "end": [ 276, 68 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.exists_max_im", "code": "theorem exists_max_im : ∃ g : SL(2, ℤ), ∀ g' : SL(2, ℤ), (g' • z).im ≤ (g • z).im", "start": [ 287, 1 ], "end": [ 301, 31 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.exists_row_one_eq_and_min_re", "code": "theorem exists_row_one_eq_and_min_re {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :\n ∃ g : SL(2, ℤ), (↑ₘg) 1 = cd ∧ ∀ g' : SL(2, ℤ), (↑ₘg) 1 = (↑ₘg') 1 →\n \|(g • z).re\| ≤ \|(g' • z).re\|", "start": [ 304, 1 ], "end": [ 318, 22 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.coe_T_zpow_smul_eq", "code": "theorem coe_T_zpow_smul_eq {n : ℤ} : (↑(T ^ n • z) : ℂ) = z + n", "start": [ 321, 1 ], "end": [ 323, 43 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.re_T_zpow_smul", "code": "theorem re_T_zpow_smul (n : ℤ) : (T ^ n • z).re = z.re + n", "start": [ 326, 1 ], "end": [ 327, 64 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.im_T_zpow_smul", "code": "theorem im_T_zpow_smul (n : ℤ) : (T ^ n • z).im = z.im", "start": [ 330, 1 ], "end": [ 331, 74 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.re_T_smul", "code": "theorem re_T_smul : (T • z).re = z.re + 1", "start": [ 334, 1 ], "end": [ 334, 79 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.im_T_smul", "code": "theorem im_T_smul : (T • z).im = z.im", "start": [ 337, 1 ], "end": [ 337, 75 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.re_T_inv_smul", "code": "theorem re_T_inv_smul : (T⁻¹ • z).re = z.re - 1", "start": [ 340, 1 ], "end": [ 340, 88 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.im_T_inv_smul", "code": "theorem im_T_inv_smul : (T⁻¹ • z).im = z.im", "start": [ 343, 1 ], "end": [ 343, 84 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.exists_eq_T_zpow_of_c_eq_zero", "code": "theorem exists_eq_T_zpow_of_c_eq_zero (hc : (↑ₘg) 1 0 = 0) :\n ∃ n : ℤ, ∀ z : ℍ, g • z = T ^ n • z", "start": [ 349, 1 ], "end": [ 361, 83 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.g_eq_of_c_eq_one", "code": "theorem g_eq_of_c_eq_one (hc : (↑ₘg) 1 0 = 1) : g = T ^ (↑ₘg) 0 0 * S * T ^ (↑ₘg) 1 1", "start": [ 365, 1 ], "end": [ 372, 37 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.normSq_S_smul_lt_one", "code": "theorem normSq_S_smul_lt_one (h : 1 < normSq z) : normSq ↑(S • z) < 1", "start": [ 375, 1 ], "end": [ 377, 78 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.im_lt_im_S_smul", "code": "theorem im_lt_im_S_smul (h : normSq z < 1) : z.im < (S • z).im", "start": [ 380, 1 ], "end": [ 388, 22 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.fd", "code": "def fd : Set ℍ :=\n {z \| 1 ≤ normSq (z : ℂ) ∧ \|z.re\| ≤ (1 : ℝ) / 2}", "start": [ 391, 1 ], "end": [ 393, 50 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.fdo", "code": "def fdo : Set ℍ :=\n {z \| 1 < normSq (z : ℂ) ∧ \|z.re\| < (1 : ℝ) / 2}", "start": [ 396, 1 ], "end": [ 398, 50 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.abs_two_mul_re_lt_one_of_mem_fdo", "code": "theorem abs_two_mul_re_lt_one_of_mem_fdo (h : z ∈ 𝒟ᵒ) : \|2 * z.re\| < 1", "start": [ 409, 1 ], "end": [ 411, 12 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.three_lt_four_mul_im_sq_of_mem_fdo", "code": "theorem three_lt_four_mul_im_sq_of_mem_fdo (h : z ∈ 𝒟ᵒ) : 3 < 4 * z.im ^ 2", "start": [ 414, 1 ], "end": [ 417, 37 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.one_lt_normSq_T_zpow_smul", "code": "theorem one_lt_normSq_T_zpow_smul (hz : z ∈ 𝒟ᵒ) (n : ℤ) : 1 < normSq (T ^ n • z : ℍ)", "start": [ 420, 1 ], "end": [ 425, 52 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.eq_zero_of_mem_fdo_of_T_zpow_mem_fdo", "code": "theorem eq_zero_of_mem_fdo_of_T_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg : T ^ n • z ∈ 𝒟ᵒ) :\n n = 0", "start": [ 428, 1 ], "end": [ 438, 26 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.exists_smul_mem_fd", "code": "theorem exists_smul_mem_fd (z : ℍ) : ∃ g : SL(2, ℤ), g • z ∈ 𝒟", "start": [ 441, 1 ], "end": [ 472, 83 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.abs_c_le_one", "code": "theorem abs_c_le_one (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : \|(↑ₘg) 1 0\| ≤ 1", "start": [ 477, 1 ], "end": [ 509, 42 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.c_eq_zero", "code": "theorem c_eq_zero (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : (↑ₘg) 1 0 = 0", "start": [ 512, 1 ], "end": [ 531, 71 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.eq_smul_self_of_mem_fdo_mem_fdo", "code": "theorem eq_smul_self_of_mem_fdo_mem_fdo (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : z = g • z", "start": [ 534, 1 ], "end": [ 539, 62 ], "kind": "commanddeclaration" } ]
Mathlib/Topology/ContinuousFunction/Sigma.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Topology/CompactOpen.lean" ]	[ { "full_name": "ContinuousMap.embedding_sigmaMk_comp", "code": "theorem embedding_sigmaMk_comp [Nonempty X] :\n Embedding (fun g : Σ i, C(X, Y i) ↦ (sigmaMk g.1).comp g.2) where", "start": [ 44, 1 ], "end": [ 54, 21 ], "kind": "commanddeclaration" }, { "full_name": "ContinuousMap.exists_lift_sigma", "code": "theorem exists_lift_sigma (f : C(X, Σ i, Y i)) : ∃ i g, f = (sigmaMk i).comp g", "start": [ 60, 1 ], "end": [ 67, 34 ], "kind": "commanddeclaration" }, { "full_name": "ContinuousMap.sigmaCodHomeomorph", "code": "@[simps! symm_apply]\ndef sigmaCodHomeomorph : C(X, Σ i, Y i) ≃ₜ Σ i, C(X, Y i) :=\n .symm <\| Equiv.toHomeomorphOfInducing\n (.ofBijective _ ⟨embedding_sigmaMk_comp.inj, fun f ↦\n let ⟨i, g, hg⟩ := f.exists_lift_sigma; ⟨⟨i, g⟩, hg.symm⟩⟩)\n embedding_sigmaMk_comp.toInducing", "start": [ 71, 1 ], "end": [ 81, 38 ], "kind": "commanddeclaration" } ]
Mathlib/Data/Finset/NatDivisors.lean	[ "Mathlib/Data/Nat/Order/Lemmas.lean", "Mathlib/Data/Finset/Pointwise.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/NumberTheory/Divisors.lean" ]	[ { "full_name": "Nat.divisors_mul", "code": "lemma Nat.divisors_mul (m n : ℕ) : divisors (m * n) = divisors m * divisors n := by\n ext k\n simp_rw [mem_mul, mem_divisors, dvd_mul, mul_ne_zero_iff, ← exists_and_left, ← exists_and_right]\n simp only [and_assoc, and_comm, and_left_comm]", "start": [ 20, 1 ], "end": [ 25, 49 ], "kind": "lemma" }, { "full_name": "Nat.divisorsHom", "code": "@[simps]\ndef Nat.divisorsHom : ℕ →* Finset ℕ where\n toFun := Nat.divisors\n map_mul' := divisors_mul\n map_one' := divisors_one", "start": [ 27, 1 ], "end": [ 32, 27 ], "kind": "commanddeclaration" }, { "full_name": "Nat.Prime.divisors_sq", "code": "lemma Nat.Prime.divisors_sq {p : ℕ} (hp : p.Prime) : (p ^ 2).divisors = {p ^ 2, p, 1} := by\n simp [divisors_prime_pow hp, range_succ]", "start": [ 34, 1 ], "end": [ 35, 43 ], "kind": "lemma" }, { "full_name": "List.nat_divisors_prod", "code": "lemma List.nat_divisors_prod (l : List ℕ) : divisors l.prod = (l.map divisors).prod :=\n map_list_prod Nat.divisorsHom l", "start": [ 37, 1 ], "end": [ 38, 34 ], "kind": "lemma" }, { "full_name": "Multiset.nat_divisors_prod", "code": "lemma Multiset.nat_divisors_prod (s : Multiset ℕ) : divisors s.prod = (s.map divisors).prod :=\n map_multiset_prod Nat.divisorsHom s", "start": [ 40, 1 ], "end": [ 41, 38 ], "kind": "lemma" }, { "full_name": "Finset.nat_divisors_prod", "code": "lemma Finset.nat_divisors_prod {ι : Type*} (s : Finset ι) (f : ι → ℕ) :\n divisors (∏ i ∈ s, f i) = ∏ i ∈ s, divisors (f i) :=\n map_prod Nat.divisorsHom f s", "start": [ 43, 1 ], "end": [ 45, 31 ], "kind": "lemma" } ]
Mathlib/GroupTheory/GroupAction/Sum.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Algebra/Group/Action/Defs.lean" ]	[ { "full_name": "Sum.smul_def", "code": "@[to_additive]\ntheorem smul_def : a • x = x.map (a • ·) (a • ·)", "start": [ 37, 1 ], "end": [ 39, 6 ], "kind": "commanddeclaration" }, { "full_name": "Sum.smul_inl", "code": "@[to_additive (attr := simp)]\ntheorem smul_inl : a • (inl b : Sum α β) = inl (a • b)", "start": [ 43, 1 ], "end": [ 45, 6 ], "kind": "commanddeclaration" }, { "full_name": "Sum.smul_inr", "code": "@[to_additive (attr := simp)]\ntheorem smul_inr : a • (inr c : Sum α β) = inr (a • c)", "start": [ 49, 1 ], "end": [ 51, 6 ], "kind": "commanddeclaration" }, { "full_name": "Sum.smul_swap", "code": "@[to_additive (attr := simp)]\ntheorem smul_swap : (a • x).swap = a • x.swap", "start": [ 55, 1 ], "end": [ 56, 68 ], "kind": "commanddeclaration" }, { "full_name": "Sum.FaithfulSMulLeft", "code": "@[to_additive]\ninstance FaithfulSMulLeft [FaithfulSMul M α] : FaithfulSMul M (Sum α β) :=\n ⟨fun h => eq_of_smul_eq_smul fun a : α => by injection h (inl a)⟩", "start": [ 78, 1 ], "end": [ 80, 68 ], "kind": "commanddeclaration" }, { "full_name": "Sum.FaithfulSMulRight", "code": "@[to_additive]\ninstance FaithfulSMulRight [FaithfulSMul M β] : FaithfulSMul M (Sum α β) :=\n ⟨fun h => eq_of_smul_eq_smul fun b : β => by injection h (inr b)⟩", "start": [ 84, 1 ], "end": [ 86, 68 ], "kind": "commanddeclaration" } ]
Mathlib/Init/Data/Int/Lemmas.lean	[ "Mathlib/Mathport/Rename.lean", ".lake/packages/lean4/src/lean/Init.lean" ]	[]
Mathlib/NumberTheory/PrimesCongruentOne.lean	[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/RingTheory/Polynomial/Cyclotomic/Eval.lean" ]	[ { "full_name": "Nat.exists_prime_gt_modEq_one", "code": "theorem exists_prime_gt_modEq_one {k : ℕ} (n : ℕ) (hk0 : k ≠ 0) :\n ∃ p : ℕ, Nat.Prime p ∧ n < p ∧ p ≡ 1 [MOD k]", "start": [ 24, 1 ], "end": [ 57, 54 ], "kind": "commanddeclaration" }, { "full_name": "Nat.frequently_atTop_modEq_one", "code": "theorem frequently_atTop_modEq_one {k : ℕ} (hk0 : k ≠ 0) :\n ∃ᶠ p in atTop, Nat.Prime p ∧ p ≡ 1 [MOD k]", "start": [ 60, 1 ], "end": [ 64, 39 ], "kind": "commanddeclaration" }, { "full_name": "Nat.infinite_setOf_prime_modEq_one", "code": "theorem infinite_setOf_prime_modEq_one {k : ℕ} (hk0 : k ≠ 0) :\n Set.Infinite {p : ℕ \| Nat.Prime p ∧ p ≡ 1 [MOD k]}", "start": [ 67, 1 ], "end": [ 70, 67 ], "kind": "commanddeclaration" } ]
Mathlib/LinearAlgebra/TensorProduct/Matrix.lean	[ "Mathlib/LinearAlgebra/TensorProduct/Basis.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/LinearAlgebra/Matrix/ToLin.lean", "Mathlib/Data/Matrix/Kronecker.lean" ]	[ { "full_name": "TensorProduct.toMatrix_map", "code": "theorem TensorProduct.toMatrix_map (f : M →ₗ[R] M') (g : N →ₗ[R] N') :\n toMatrix (bM.tensorProduct bN) (bM'.tensorProduct bN') (TensorProduct.map f g) =\n toMatrix bM bM' f ⊗ₖ toMatrix bN bN' g", "start": [ 37, 1 ], "end": [ 44, 65 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.toLin_kronecker", "code": "theorem Matrix.toLin_kronecker (A : Matrix ι' ι R) (B : Matrix κ' κ R) :\n toLin (bM.tensorProduct bN) (bM'.tensorProduct bN') (A ⊗ₖ B) =\n TensorProduct.map (toLin bM bM' A) (toLin bN bN' B)", "start": [ 47, 1 ], "end": [ 53, 20 ], "kind": "commanddeclaration" }, { "full_name": "TensorProduct.toMatrix_comm", "code": "theorem TensorProduct.toMatrix_comm :\n toMatrix (bM.tensorProduct bN) (bN.tensorProduct bM) (TensorProduct.comm R M N) =\n (1 : Matrix (ι × κ) (ι × κ) R).submatrix Prod.swap _root_.id", "start": [ 56, 1 ], "end": [ 64, 75 ], "kind": "commanddeclaration" }, { "full_name": "TensorProduct.toMatrix_assoc", "code": "theorem TensorProduct.toMatrix_assoc :\n toMatrix ((bM.tensorProduct bN).tensorProduct bP) (bM.tensorProduct (bN.tensorProduct bP))\n (TensorProduct.assoc R M N P) =\n (1 : Matrix (ι × κ × τ) (ι × κ × τ) R).submatrix _root_.id (Equiv.prodAssoc _ _ _)", "start": [ 67, 1 ], "end": [ 78, 21 ], "kind": "commanddeclaration" } ]
.lake/packages/lean4/src/lean/Lean/Compiler/IR/LLVMBindings.lean	[ ".lake/packages/lean4/src/lean/Init/System/IO.lean" ]	[ { "full_name": "LLVM.CodegenFileType", "code": "structure CodegenFileType where\n private mk :: val : UInt64", "start": [ 20, 1 ], "end": [ 21, 29 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.CodegenFileType.AssemblyFile", "code": "def CodegenFileType.AssemblyFile : CodegenFileType := { val := 0 }", "start": [ 23, 1 ], "end": [ 23, 67 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.CodegenFileType.ObjectFile", "code": "def CodegenFileType.ObjectFile : CodegenFileType := { val := 1 }", "start": [ 24, 1 ], "end": [ 24, 65 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.IntPredicate", "code": "structure IntPredicate where\n private mk :: val : UInt64", "start": [ 27, 1 ], "end": [ 28, 29 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.IntPredicate.EQ", "code": "def IntPredicate.EQ : IntPredicate := { val := 32 }", "start": [ 30, 1 ], "end": [ 30, 52 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.IntPredicate.NE", "code": "def IntPredicate.NE : IntPredicate := { val := IntPredicate.EQ.val + 1 }", "start": [ 31, 1 ], "end": [ 31, 73 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.IntPredicate.UGT", "code": "def IntPredicate.UGT : IntPredicate := { val := IntPredicate.NE.val + 1 }", "start": [ 32, 1 ], "end": [ 32, 74 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.AttributeIndex", "code": "structure AttributeIndex where\n private mk :: val : UInt64", "start": [ 35, 1 ], "end": [ 36, 29 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.AttributeIndex.AttributeReturnIndex", "code": "def AttributeIndex.AttributeReturnIndex : AttributeIndex := { val := 0 }", "start": [ 38, 1 ], "end": [ 38, 73 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.AttributeIndex.AttributeFunctionIndex", "code": "def AttributeIndex.AttributeFunctionIndex : AttributeIndex := { val := 18446744073709551615 }", "start": [ 40, 1 ], "end": [ 40, 94 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.BasicBlock", "code": "structure BasicBlock (ctx : Context) where\n private mk :: ptr : USize", "start": [ 42, 1 ], "end": [ 43, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Builder", "code": "structure Builder (ctx : Context) where\n private mk :: ptr : USize", "start": [ 46, 1 ], "end": [ 47, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Context", "code": "structure Context where\n private mk :: ptr : USize", "start": [ 50, 1 ], "end": [ 51, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.LLVMType", "code": "structure LLVMType (ctx : Context) where\n private mk :: ptr : USize", "start": [ 54, 1 ], "end": [ 55, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.MemoryBuffer", "code": "structure MemoryBuffer (ctx : Context) where\n private mk :: ptr : USize", "start": [ 58, 1 ], "end": [ 59, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Module", "code": "structure Module (ctx : Context) where\n private mk :: ptr : USize", "start": [ 62, 1 ], "end": [ 63, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.PassManager", "code": "structure PassManager (ctx : Context) where\n private mk :: ptr : USize", "start": [ 66, 1 ], "end": [ 67, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.PassManagerBuilder", "code": "structure PassManagerBuilder (ctx : Context) where\n private mk :: ptr : USize", "start": [ 70, 1 ], "end": [ 71, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Target", "code": "structure Target (ctx : Context) where\n private mk :: ptr : USize", "start": [ 74, 1 ], "end": [ 75, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.TargetMachine", "code": "structure TargetMachine (ctx : Context) where\n private mk :: ptr : USize", "start": [ 78, 1 ], "end": [ 79, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Value", "code": "structure Value (ctx : Context) where\n private mk :: ptr : USize", "start": [ 82, 1 ], "end": [ 83, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Value.isNull", "code": "def Value.isNull (v : Value ctx) : Bool := v.ptr == 0", "start": [ 86, 1 ], "end": [ 87, 54 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Value.getName", "code": "@[extern \"lean_llvm_get_value_name2\"]\nopaque Value.getName {ctx : Context} (value : Value ctx) : BaseIO String", "start": [ 89, 1 ], "end": [ 90, 73 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Attribute", "code": "structure Attribute (ctx : Context) where\n private mk :: ptr : USize", "start": [ 92, 1 ], "end": [ 93, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.llvmInitializeTargetInfo", "code": "@[extern \"lean_llvm_initialize_target_info\"]\nopaque llvmInitializeTargetInfo : BaseIO (Unit)", "start": [ 96, 1 ], "end": [ 97, 48 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createContext", "code": "@[extern \"lean_llvm_create_context\"]\nopaque createContext : BaseIO (Context)", "start": [ 99, 1 ], "end": [ 100, 40 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createModule", "code": "@[extern \"lean_llvm_create_module\"]\nopaque createModule (ctx : Context) (name : @&String) : BaseIO (Module ctx)", "start": [ 102, 1 ], "end": [ 103, 76 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.moduleToString", "code": "@[extern \"lean_llvm_module_to_string\"]\nopaque moduleToString (m : Module ctx) : BaseIO String", "start": [ 105, 1 ], "end": [ 106, 55 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.writeBitcodeToFile", "code": "@[extern \"lean_llvm_write_bitcode_to_file\"]\nopaque writeBitcodeToFile (m : Module ctx) (path : @&String) : BaseIO Unit", "start": [ 108, 1 ], "end": [ 109, 75 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.addFunction", "code": "@[extern \"lean_llvm_add_function\"]\nopaque addFunction (m : Module ctx) (name : @&String) (type : LLVMType ctx) : BaseIO (Value ctx)", "start": [ 111, 1 ], "end": [ 112, 97 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getFirstFunction", "code": "@[extern \"lean_llvm_get_first_function\"]\nopaque getFirstFunction (m : Module ctx) : BaseIO (Value ctx)", "start": [ 114, 1 ], "end": [ 115, 62 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getNextFunction", "code": "@[extern \"lean_llvm_get_next_function\"]\nopaque getNextFunction (glbl : Value ctx) : BaseIO (Value ctx)", "start": [ 117, 1 ], "end": [ 118, 63 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getNamedFunction", "code": "@[extern \"lean_llvm_get_named_function\"]\nopaque getNamedFunction (m : Module ctx) (name : @&String) : BaseIO (Option (Value ctx))", "start": [ 120, 1 ], "end": [ 121, 89 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.addGlobal", "code": "@[extern \"lean_llvm_add_global\"]\nopaque addGlobal (m : Module ctx) (name : @&String) (type : LLVMType ctx) : BaseIO (Value ctx)", "start": [ 123, 1 ], "end": [ 124, 95 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getNamedGlobal", "code": "@[extern \"lean_llvm_get_named_global\"]\nopaque getNamedGlobal (m : Module ctx) (name : @&String) : BaseIO (Option (Value ctx))", "start": [ 126, 1 ], "end": [ 127, 87 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getFirstGlobal", "code": "@[extern \"lean_llvm_get_first_global\"]\nopaque getFirstGlobal (m : Module ctx) : BaseIO (Value ctx)", "start": [ 129, 1 ], "end": [ 130, 60 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getNextGlobal", "code": "@[extern \"lean_llvm_get_next_global\"]\nopaque getNextGlobal (glbl : Value ctx) : BaseIO (Value ctx)", "start": [ 132, 1 ], "end": [ 133, 61 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildGlobalString", "code": "@[extern \"lean_llvm_build_global_string\"]\nopaque buildGlobalString (builder : Builder ctx) (value : @&String) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 135, 1 ], "end": [ 136, 113 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.isDeclaration", "code": "@[extern \"llvm_is_declaration\"]\nopaque isDeclaration (global : Value ctx) : BaseIO Bool", "start": [ 138, 1 ], "end": [ 139, 56 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.setInitializer", "code": "@[extern \"lean_llvm_set_initializer\"]\nopaque setInitializer (glbl : Value ctx) (val : Value ctx) : BaseIO Unit", "start": [ 141, 1 ], "end": [ 142, 73 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.functionType", "code": "@[extern \"lean_llvm_function_type\"]\nopaque functionType (retty : LLVMType ctx) (args : @&Array (LLVMType ctx)) (isVarArg : Bool := false) : BaseIO (LLVMType ctx)", "start": [ 144, 1 ], "end": [ 145, 126 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.voidType", "code": "@[extern \"lean_llvm_void_type_in_context\"]\nopaque voidType (ctx : Context) : BaseIO (LLVMType ctx)", "start": [ 147, 1 ], "end": [ 148, 56 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.intTypeInContext", "code": "@[extern \"lean_llvm_int_type_in_context\"]\nopaque intTypeInContext (ctx : Context) (width : UInt64) : BaseIO (LLVMType ctx)", "start": [ 150, 1 ], "end": [ 151, 81 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.opaquePointerTypeInContext", "code": "@[extern \"lean_llvm_opaque_pointer_type_in_context\"]\nopaque opaquePointerTypeInContext (ctx : Context) (addrspace: UInt64 := 0) : BaseIO (LLVMType ctx)", "start": [ 153, 1 ], "end": [ 154, 99 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.floatTypeInContext", "code": "@[extern \"lean_llvm_float_type_in_context\"]\nopaque floatTypeInContext (ctx : Context) : BaseIO (LLVMType ctx)", "start": [ 156, 1 ], "end": [ 157, 66 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.doubleTypeInContext", "code": "@[extern \"lean_llvm_double_type_in_context\"]\nopaque doubleTypeInContext (ctx : Context) : BaseIO (LLVMType ctx)", "start": [ 159, 1 ], "end": [ 160, 67 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.pointerType", "code": "@[extern \"lean_llvm_pointer_type\"]\nopaque pointerType (elemty : LLVMType ctx) : BaseIO (LLVMType ctx)", "start": [ 162, 1 ], "end": [ 163, 67 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.arrayType", "code": "@[extern \"lean_llvm_array_type\"]\nopaque arrayType (elemty : LLVMType ctx) (nelem : UInt64) : BaseIO (LLVMType ctx)", "start": [ 165, 1 ], "end": [ 166, 82 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constArray", "code": "@[extern \"lean_llvm_const_array\"]\nopaque constArray (elemty : LLVMType ctx) (vals : @&Array (Value ctx)) : BaseIO (LLVMType ctx)", "start": [ 168, 1 ], "end": [ 169, 95 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constString", "code": "@[extern \"lean_llvm_const_string\"]\nopaque constString (ctx : Context) (str : @&String) : BaseIO (Value ctx)", "start": [ 172, 1 ], "end": [ 173, 73 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constPointerNull", "code": "@[extern \"lean_llvm_const_pointer_null\"]\nopaque constPointerNull (elemty : LLVMType ctx) : BaseIO (Value ctx)", "start": [ 175, 1 ], "end": [ 176, 69 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getUndef", "code": "@[extern \"lean_llvm_get_undef\"]\nopaque getUndef (elemty : LLVMType ctx) : BaseIO (Value ctx)", "start": [ 178, 1 ], "end": [ 179, 61 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createBuilderInContext", "code": "@[extern \"lean_llvm_create_builder_in_context\"]\nopaque createBuilderInContext (ctx : Context) : BaseIO (Builder ctx)", "start": [ 181, 1 ], "end": [ 182, 69 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.appendBasicBlockInContext", "code": "@[extern \"lean_llvm_append_basic_block_in_context\"]\nopaque appendBasicBlockInContext (ctx : Context) (fn : Value ctx) (name : @&String) : BaseIO (BasicBlock ctx)", "start": [ 184, 1 ], "end": [ 185, 112 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.countBasicBlocks", "code": "@[extern \"lean_llvm_count_basic_blocks\"]\nopaque countBasicBlocks (fn : Value ctx) : BaseIO UInt64", "start": [ 187, 1 ], "end": [ 188, 57 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getEntryBasicBlock", "code": "@[extern \"lean_llvm_get_entry_basic_block\"]\nopaque getEntryBasicBlock (fn : Value ctx) : BaseIO (BasicBlock ctx)", "start": [ 190, 1 ], "end": [ 191, 69 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getFirstInstruction", "code": "@[extern \"lean_llvm_get_first_instruction\"]\nopaque getFirstInstruction (bb : BasicBlock ctx) : BaseIO (Option (Value ctx))", "start": [ 193, 1 ], "end": [ 194, 79 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.positionBuilderBefore", "code": "@[extern \"lean_llvm_position_builder_before\"]\nopaque positionBuilderBefore (builder : Builder ctx) (instr : Value ctx) : BaseIO Unit", "start": [ 196, 1 ], "end": [ 197, 87 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.positionBuilderAtEnd", "code": "@[extern \"lean_llvm_position_builder_at_end\"]\nopaque positionBuilderAtEnd (builder : Builder ctx) (bb : BasicBlock ctx) : BaseIO Unit", "start": [ 199, 1 ], "end": [ 200, 89 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildCall2", "code": "@[extern \"lean_llvm_build_call2\"]\nopaque buildCall2 (builder : Builder ctx) (ty: LLVMType ctx) (fn : Value ctx) (args : @&Array (Value ctx)) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 202, 1 ], "end": [ 203, 153 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.setTailCall", "code": "@[extern \"lean_llvm_set_tail_call\"]\nopaque setTailCall (fn : Value ctx) (istail : Bool) : BaseIO Unit", "start": [ 205, 1 ], "end": [ 206, 66 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildCondBr", "code": "@[extern \"lean_llvm_build_cond_br\"]\nopaque buildCondBr (builder : Builder ctx) (if_ : Value ctx) (thenbb : BasicBlock ctx) (elsebb : BasicBlock ctx) : BaseIO (Value ctx)", "start": [ 208, 1 ], "end": [ 209, 134 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildBr", "code": "@[extern \"lean_llvm_build_br\"]\nopaque buildBr (builder : Builder ctx) (bb : BasicBlock ctx) : BaseIO (Value ctx)", "start": [ 211, 1 ], "end": [ 212, 82 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildAlloca", "code": "@[extern \"lean_llvm_build_alloca\"]\nopaque buildAlloca (builder : Builder ctx) (ty : LLVMType ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 214, 1 ], "end": [ 215, 108 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildLoad2", "code": "@[extern \"lean_llvm_build_load2\"]\nopaque buildLoad2 (builder : Builder ctx) (ty: LLVMType ctx) (val : Value ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 217, 1 ], "end": [ 218, 124 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildStore", "code": "@[extern \"lean_llvm_build_store\"]\nopaque buildStore (builder : Builder ctx) (val : Value ctx) (store_loc_ptr : Value ctx) : BaseIO Unit", "start": [ 220, 1 ], "end": [ 221, 102 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildRet", "code": "@[extern \"lean_llvm_build_ret\"]\nopaque buildRet (builder : Builder ctx) (val : Value ctx) : BaseIO (Value ctx)", "start": [ 223, 1 ], "end": [ 224, 79 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildUnreachable", "code": "@[extern \"lean_llvm_build_unreachable\"]\nopaque buildUnreachable (builder : Builder ctx) : BaseIO (Value ctx)", "start": [ 226, 1 ], "end": [ 227, 69 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildGEP2", "code": "@[extern \"lean_llvm_build_gep2\"]\nopaque buildGEP2 (builder : Builder ctx) (ty: LLVMType ctx) (base : Value ctx) (ixs : @&Array (Value ctx)) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 229, 1 ], "end": [ 230, 152 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildInBoundsGEP2", "code": "@[extern \"lean_llvm_build_inbounds_gep2\"]\nopaque buildInBoundsGEP2 (builder : Builder ctx) (ty: LLVMType ctx) (base : Value ctx) (ixs : @&Array (Value ctx)) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 232, 1 ], "end": [ 233, 160 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildSext", "code": "@[extern \"lean_llvm_build_sext\"]\nopaque buildSext (builder : Builder ctx) (val : Value ctx) (destTy : LLVMType ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 235, 1 ], "end": [ 236, 128 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildZext", "code": "@[extern \"lean_llvm_build_zext\"]\nopaque buildZext (builder : Builder ctx) (val : Value ctx) (destTy : LLVMType ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 238, 1 ], "end": [ 239, 128 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildSextOrTrunc", "code": "@[extern \"lean_llvm_build_sext_or_trunc\"]\nopaque buildSextOrTrunc (builder : Builder ctx) (val : Value ctx) (destTy : LLVMType ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 241, 1 ], "end": [ 242, 135 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildSwitch", "code": "@[extern \"lean_llvm_build_switch\"]\nopaque buildSwitch (builder : Builder ctx) (val : Value ctx) (elseBB : BasicBlock ctx) (numCasesHint : UInt64) : BaseIO (Value ctx)", "start": [ 244, 1 ], "end": [ 245, 132 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildPtrToInt", "code": "@[extern \"lean_llvm_build_ptr_to_int\"]\nopaque buildPtrToInt (builder : Builder ctx) (ptr : Value ctx) (destTy : LLVMType ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 247, 1 ], "end": [ 248, 132 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildMul", "code": "@[extern \"lean_llvm_build_mul\"]\nopaque buildMul (builder : Builder ctx) (x y : Value ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 250, 1 ], "end": [ 251, 103 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildAdd", "code": "@[extern \"lean_llvm_build_add\"]\nopaque buildAdd (builder : Builder ctx) (x y : Value ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 253, 1 ], "end": [ 254, 103 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildSub", "code": "@[extern \"lean_llvm_build_sub\"]\nopaque buildSub (builder : Builder ctx) (x y : Value ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 256, 1 ], "end": [ 257, 103 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildNot", "code": "@[extern \"lean_llvm_build_not\"]\nopaque buildNot (builder : Builder ctx) (x : Value ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 259, 1 ], "end": [ 260, 101 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildICmp", "code": "@[extern \"lean_llvm_build_icmp\"]\nopaque buildICmp (builder : Builder ctx) (predicate : IntPredicate) (x y : Value ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 262, 1 ], "end": [ 263, 131 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.addCase", "code": "@[extern \"lean_llvm_add_case\"]\nopaque addCase (switch onVal : Value ctx) (destBB : BasicBlock ctx) : BaseIO Unit", "start": [ 265, 1 ], "end": [ 266, 82 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getInsertBlock", "code": "@[extern \"lean_llvm_get_insert_block\"]\nopaque getInsertBlock (builder : Builder ctx) : BaseIO (BasicBlock ctx)", "start": [ 268, 1 ], "end": [ 269, 72 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.clearInsertionPosition", "code": "@[extern \"lean_llvm_clear_insertion_position\"]\nopaque clearInsertionPosition (builder : Builder ctx) : BaseIO Unit", "start": [ 271, 1 ], "end": [ 272, 68 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getBasicBlockParent", "code": "@[extern \"lean_llvm_get_basic_block_parent\"]\nopaque getBasicBlockParent (bb : BasicBlock ctx) : BaseIO (Value ctx)", "start": [ 274, 1 ], "end": [ 275, 70 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.typeOf", "code": "@[extern \"lean_llvm_type_of\"]\nopaque typeOf (val : Value ctx) : BaseIO (LLVMType ctx)", "start": [ 277, 1 ], "end": [ 278, 56 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constInt", "code": "@[extern \"lean_llvm_const_int\"]\nopaque constInt (intty : LLVMType ctx) (value : UInt64) (signExtend : @Bool := false) : BaseIO (Value ctx)", "start": [ 280, 1 ], "end": [ 281, 107 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.printModuletoString", "code": "@[extern \"lean_llvm_print_module_to_string\"]\nopaque printModuletoString (mod : Module ctx) : BaseIO (String)", "start": [ 283, 1 ], "end": [ 284, 64 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.printModuletoFile", "code": "@[extern \"lean_llvm_print_module_to_file\"]\nopaque printModuletoFile (mod : Module ctx) (file : @&String) : BaseIO Unit", "start": [ 286, 1 ], "end": [ 287, 76 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.countParams", "code": "@[extern \"llvm_count_params\"]\nopaque countParams (fn : Value ctx) : BaseIO UInt64", "start": [ 289, 1 ], "end": [ 290, 52 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getParam", "code": "@[extern \"llvm_get_param\"]\nopaque getParam (fn : Value ctx) (ix : UInt64) : BaseIO (Value ctx)", "start": [ 292, 1 ], "end": [ 293, 68 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createMemoryBufferWithContentsOfFile", "code": "@[extern \"lean_llvm_create_memory_buffer_with_contents_of_file\"]\nopaque createMemoryBufferWithContentsOfFile (path : @&String) : BaseIO (MemoryBuffer ctx)", "start": [ 295, 1 ], "end": [ 296, 90 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.parseBitcode", "code": "@[extern \"lean_llvm_parse_bitcode\"]\nopaque parseBitcode (ctx : Context) (membuf : MemoryBuffer ctx) : BaseIO (Module ctx)", "start": [ 298, 1 ], "end": [ 299, 86 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.linkModules", "code": "@[extern \"lean_llvm_link_modules\"]\nopaque linkModules (dest : Module ctx) (src : Module ctx) : BaseIO Unit", "start": [ 301, 1 ], "end": [ 302, 72 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getDefaultTargetTriple", "code": "@[extern \"lean_llvm_get_default_target_triple\"]\nopaque getDefaultTargetTriple : BaseIO String", "start": [ 304, 1 ], "end": [ 305, 46 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getTargetFromTriple", "code": "@[extern \"lean_llvm_get_target_from_triple\"]\nopaque getTargetFromTriple (triple : @&String) : BaseIO (Target ctx)", "start": [ 307, 1 ], "end": [ 308, 69 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createTargetMachine", "code": "@[extern \"lean_llvm_create_target_machine\"]\nopaque createTargetMachine (target : Target ctx) (tripleStr : @&String) (cpu : @&String) (features : @&String) : BaseIO (TargetMachine ctx)", "start": [ 310, 1 ], "end": [ 311, 140 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.targetMachineEmitToFile", "code": "@[extern \"lean_llvm_target_machine_emit_to_file\"]\nopaque targetMachineEmitToFile (targetMachine : TargetMachine ctx) (module : Module ctx) (filepath : @&String) (codegenType : LLVM.CodegenFileType) : BaseIO Unit", "start": [ 313, 1 ], "end": [ 314, 162 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createPassManager", "code": "@[extern \"lean_llvm_create_pass_manager\"]\nopaque createPassManager : BaseIO (PassManager ctx)", "start": [ 316, 1 ], "end": [ 317, 52 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.disposePassManager", "code": "@[extern \"lean_llvm_dispose_pass_manager\"]\nopaque disposePassManager (pm : PassManager ctx) : BaseIO Unit", "start": [ 319, 1 ], "end": [ 320, 63 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.runPassManager", "code": "@[extern \"lean_llvm_run_pass_manager\"]\nopaque runPassManager (pm : PassManager ctx) (mod : Module ctx): BaseIO Unit", "start": [ 322, 1 ], "end": [ 323, 77 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createPassManagerBuilder", "code": "@[extern \"lean_llvm_create_pass_manager_builder\"]\nopaque createPassManagerBuilder : BaseIO (PassManagerBuilder ctx)", "start": [ 325, 1 ], "end": [ 326, 66 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.disposePassManagerBuilder", "code": "@[extern \"lean_llvm_dispose_pass_manager_builder\"]\nopaque disposePassManagerBuilder (pmb : PassManagerBuilder ctx) : BaseIO Unit", "start": [ 328, 1 ], "end": [ 329, 78 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.PassManagerBuilder.setOptLevel", "code": "@[extern \"lean_llvm_pass_manager_builder_set_opt_level\"]\nopaque PassManagerBuilder.setOptLevel (pmb : PassManagerBuilder ctx) (optLevel : unsigned) : BaseIO Unit", "start": [ 331, 1 ], "end": [ 332, 105 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.PassManagerBuilder.populateModulePassManager", "code": "@[extern \"lean_llvm_pass_manager_builder_populate_module_pass_manager\"]\nopaque PassManagerBuilder.populateModulePassManager (pmb : PassManagerBuilder ctx) (pm : PassManager ctx): BaseIO Unit", "start": [ 334, 1 ], "end": [ 335, 119 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.disposeTargetMachine", "code": "@[extern \"lean_llvm_dispose_target_machine\"]\nopaque disposeTargetMachine (tm : TargetMachine ctx) : BaseIO Unit", "start": [ 337, 1 ], "end": [ 338, 67 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.disposeModule", "code": "@[extern \"lean_llvm_dispose_module\"]\nopaque disposeModule (m : Module ctx) : BaseIO Unit", "start": [ 340, 1 ], "end": [ 341, 52 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.verifyModule", "code": "@[extern \"lean_llvm_verify_module\"]\nopaque verifyModule (m : Module ctx) : BaseIO (Option String)", "start": [ 343, 1 ], "end": [ 344, 62 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createStringAttribute", "code": "@[extern \"lean_llvm_create_string_attribute\"]\nopaque createStringAttribute (key : String) (value : String) : BaseIO (Attribute ctx)", "start": [ 346, 1 ], "end": [ 347, 86 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.addAttributeAtIndex", "code": "@[extern \"lean_llvm_add_attribute_at_index\"]\nopaque addAttributeAtIndex (fn : Value ctx) (idx: AttributeIndex) (attr: Attribute ctx) : BaseIO Unit", "start": [ 349, 1 ], "end": [ 350, 102 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Visibility", "code": "structure Visibility where\n private mk :: val : UInt64", "start": [ 354, 1 ], "end": [ 355, 29 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Visibility.default", "code": "def Visibility.default : Visibility := { val := 0 }", "start": [ 357, 1 ], "end": [ 357, 54 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Visibility.hidden", "code": "def Visibility.hidden : Visibility := { val := 1 }", "start": [ 358, 1 ], "end": [ 358, 54 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Visibility.protected", "code": "def Visibility.protected : Visibility := { val := 2 }", "start": [ 359, 1 ], "end": [ 359, 54 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.setVisibility", "code": "@[extern \"lean_llvm_set_visibility\"]\nopaque setVisibility {ctx : Context} (value : Value ctx) (visibility : Visibility) : BaseIO Unit", "start": [ 361, 1 ], "end": [ 362, 97 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.DLLStorageClass", "code": "structure DLLStorageClass where\n private mk :: val : UInt64", "start": [ 365, 1 ], "end": [ 366, 29 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.DLLStorageClass.default", "code": "def DLLStorageClass.default : DLLStorageClass := { val := 0 }", "start": [ 368, 1 ], "end": [ 368, 62 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.DLLStorageClass.import", "code": "def DLLStorageClass.import : DLLStorageClass := { val := 1 }", "start": [ 369, 1 ], "end": [ 369, 62 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.DLLStorageClass.export", "code": "def DLLStorageClass.export : DLLStorageClass := { val := 2 }", "start": [ 370, 1 ], "end": [ 370, 62 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.setDLLStorageClass", "code": "@[extern \"lean_llvm_set_dll_storage_class\"]\nopaque setDLLStorageClass {ctx : Context} (value : Value ctx) (dllStorageClass : DLLStorageClass) : BaseIO Unit", "start": [ 372, 1 ], "end": [ 373, 112 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage", "code": "structure Linkage where\n private mk :: val : UInt64", "start": [ 376, 1 ], "end": [ 377, 29 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.external", "code": "def Linkage.external : Linkage := { val := 0 }", "start": [ 379, 1 ], "end": [ 380, 47 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.availableExternally", "code": "def Linkage.availableExternally : Linkage := { val := 1 }", "start": [ 381, 1 ], "end": [ 381, 58 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.linkOnceAny", "code": "def Linkage.linkOnceAny : Linkage := { val := 2 }", "start": [ 382, 1 ], "end": [ 383, 50 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.linkOnceODR", "code": "def Linkage.linkOnceODR : Linkage := { val := 3 }", "start": [ 384, 1 ], "end": [ 385, 50 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.linkOnceODRAutoHide", "code": "def Linkage.linkOnceODRAutoHide : Linkage := { val := 4 }", "start": [ 386, 1 ], "end": [ 387, 58 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.weakAny", "code": "def Linkage.weakAny : Linkage := { val := 5 }", "start": [ 388, 1 ], "end": [ 389, 46 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.weakODR", "code": "def Linkage.weakODR : Linkage := { val := 6 }", "start": [ 390, 1 ], "end": [ 391, 46 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.appending", "code": "def Linkage.appending : Linkage := { val := 7 }", "start": [ 392, 1 ], "end": [ 393, 48 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.internal", "code": "def Linkage.internal : Linkage := { val := 8 }", "start": [ 394, 1 ], "end": [ 395, 47 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.private", "code": "def Linkage.private : Linkage := { val := 9 }", "start": [ 396, 1 ], "end": [ 397, 46 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.dllImport", "code": "def Linkage.dllImport : Linkage := { val := 10 }", "start": [ 398, 1 ], "end": [ 399, 49 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.dllExport", "code": "def Linkage.dllExport : Linkage := { val := 11 }", "start": [ 400, 1 ], "end": [ 401, 49 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.externalWeak", "code": "def Linkage.externalWeak : Linkage := { val := 12 }", "start": [ 402, 1 ], "end": [ 403, 52 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.ghost", "code": "def Linkage.ghost : Linkage := { val := 13 }", "start": [ 404, 1 ], "end": [ 405, 45 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.common", "code": "def Linkage.common : Linkage := { val := 14 }", "start": [ 406, 1 ], "end": [ 407, 46 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.linkerPrivate", "code": "def Linkage.linkerPrivate : Linkage := { val := 15 }", "start": [ 408, 1 ], "end": [ 409, 53 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.linkerPrivateWeak", "code": "def Linkage.linkerPrivateWeak : Linkage := { val := 16 }", "start": [ 410, 1 ], "end": [ 411, 57 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.setLinkage", "code": "@[extern \"lean_llvm_set_linkage\"]\nopaque setLinkage {ctx : Context} (value : Value ctx) (linkage : Linkage) : BaseIO Unit", "start": [ 413, 1 ], "end": [ 414, 88 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.i1Type", "code": "def i1Type (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n LLVM.intTypeInContext ctx 1", "start": [ 417, 1 ], "end": [ 418, 30 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.i8Type", "code": "def i8Type (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n LLVM.intTypeInContext ctx 8", "start": [ 420, 1 ], "end": [ 421, 30 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.i16Type", "code": "def i16Type (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n LLVM.intTypeInContext ctx 16", "start": [ 423, 1 ], "end": [ 424, 31 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.i32Type", "code": "def i32Type (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n LLVM.intTypeInContext ctx 32", "start": [ 426, 1 ], "end": [ 427, 31 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.i64Type", "code": "def i64Type (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n LLVM.intTypeInContext ctx 64", "start": [ 429, 1 ], "end": [ 430, 31 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.voidPtrType", "code": "def voidPtrType (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n do LLVM.pointerType (← LLVM.intTypeInContext ctx 8)", "start": [ 432, 1 ], "end": [ 433, 54 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.i8PtrType", "code": "def i8PtrType (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n voidPtrType ctx", "start": [ 435, 1 ], "end": [ 436, 18 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constTrue", "code": "def constTrue (ctx : Context) : BaseIO (Value ctx) :=\n do constInt (← i1Type ctx) 1 (signExtend := false)", "start": [ 438, 1 ], "end": [ 439, 53 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constFalse", "code": "def constFalse (ctx : Context) : BaseIO (Value ctx) :=\n do constInt (← i1Type ctx) 0 (signExtend := false)", "start": [ 441, 1 ], "end": [ 442, 53 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constInt'", "code": "def constInt' (ctx : Context) (width : UInt64) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n do constInt (← LLVM.intTypeInContext ctx width) value signExtend", "start": [ 444, 1 ], "end": [ 445, 66 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constInt1", "code": "def constInt1 (ctx : Context) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n constInt' ctx 1 value signExtend", "start": [ 447, 1 ], "end": [ 448, 35 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constInt8", "code": "def constInt8 (ctx : Context) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n constInt' ctx 8 value signExtend", "start": [ 450, 1 ], "end": [ 451, 35 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constInt32", "code": "def constInt32 (ctx : Context) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n constInt' ctx 32 value signExtend", "start": [ 453, 1 ], "end": [ 454, 36 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constInt64", "code": "def constInt64 (ctx : Context) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n constInt' ctx 64 value signExtend", "start": [ 456, 1 ], "end": [ 457, 36 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constIntSizeT", "code": "def constIntSizeT (ctx : Context) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n constInt' ctx 64 value signExtend", "start": [ 459, 1 ], "end": [ 461, 36 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constIntUnsigned", "code": "def constIntUnsigned (ctx : Context) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n constInt' ctx 32 value signExtend", "start": [ 463, 1 ], "end": [ 465, 36 ], "kind": "commanddeclaration" } ]
.lake/packages/lean4/src/lean/lake/Lake.lean	[ ".lake/packages/lean4/src/lean/lake/Lake/Config.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/lean4/src/lean/lake/Lake/Toml.lean", ".lake/packages/lean4/src/lean/lake/Lake/DSL.lean", ".lake/packages/lean4/src/lean/lake/Lake/Version.lean", ".lake/packages/lean4/src/lean/lake/Lake/Build.lean", ".lake/packages/lean4/src/lean/lake/Lake/CLI/Actions.lean" ]	[]
.lake/packages/lean4/src/lean/lake/Lake/CLI.lean	[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/lean4/src/lean/lake/Lake/CLI/Main.lean" ]	[]
Mathlib.lean	[ "Mathlib/Data/Finset/Union.lean", "Mathlib/LinearAlgebra/TensorProduct/Matrix.lean", "Mathlib/NumberTheory/PrimesCongruentOne.lean", "Mathlib/Init/Data/Int/Lemmas.lean", "Mathlib/Topology/Homotopy/Equiv.lean", "Mathlib/CategoryTheory/Functor/Functorial.lean", "Mathlib/GroupTheory/GroupAction/Sum.lean", "Mathlib/Analysis/InnerProductSpace/Calculus.lean", "Mathlib/Data/Rat/Cast/Lemmas.lean", "Mathlib/Algebra/Category/ModuleCat/Presheaf/Sheafification.lean", "Mathlib/Topology/Connected/LocallyConnected.lean", "Mathlib/ModelTheory/Encoding.lean", "Mathlib/Tactic/Linarith/Oracle/SimplexAlgorithm/SimplexAlgorithm.lean", "Mathlib/LinearAlgebra/FreeModule/StrongRankCondition.lean", "Mathlib/RingTheory/Ideal/Basic.lean", "Mathlib/Data/Finset/NatDivisors.lean", "Mathlib/NumberTheory/LegendreSymbol/QuadraticReciprocity.lean", "Mathlib/Tactic/CC/Datatypes.lean", "Mathlib/Topology/ContinuousFunction/Sigma.lean", "Mathlib/Tactic/PPWithUniv.lean", "Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean", "Mathlib/MeasureTheory/Integral/ExpDecay.lean", "Mathlib/Analysis/InnerProductSpace/NormPow.lean", "Mathlib/ModelTheory/Skolem.lean", "Mathlib/Analysis/LocallyConvex/Basic.lean", "Mathlib/NumberTheory/Modular.lean", "Mathlib/Algebra/GroupWithZero/Hom.lean", "Mathlib/Topology/Algebra/Module/Multilinear/Basic.lean", "Mathlib/Order/CompactlyGenerated/Basic.lean", "Mathlib/AlgebraicTopology/DoldKan/Homotopies.lean", "Mathlib/Data/Multiset/NatAntidiagonal.lean", "Mathlib/Analysis/Distribution/AEEqOfIntegralContDiff.lean", "Mathlib/Algebra/Order/BigOperators/Group/Multiset.lean", "Mathlib/RingTheory/FiniteStability.lean", "Mathlib/Control/Fix.lean", "Mathlib/Topology/ContinuousFunction/Algebra.lean", "Mathlib/CategoryTheory/Sites/Coherent/ExtensiveSheaves.lean", "Mathlib/CategoryTheory/Functor/Derived/RightDerived.lean", "Mathlib/Deprecated/Group.lean", "Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean", "Mathlib/Topology/Order/Hom/Basic.lean", "Mathlib/Data/Sign.lean", "Mathlib/ModelTheory/Satisfiability.lean", "Mathlib/Data/Vector/Mem.lean", "Mathlib/Topology/MetricSpace/Dilation.lean", "Mathlib/Topology/Order/IntermediateValue.lean", "Mathlib/Analysis/Convex/Between.lean", "Mathlib/Topology/Algebra/Group/Basic.lean", "Mathlib/Topology/Sheaves/Limits.lean", "Mathlib/Logic/IsEmpty.lean", "Mathlib/Algebra/GroupWithZero/Divisibility.lean", "Mathlib/CategoryTheory/Limits/EpiMono.lean", "Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean", "Mathlib/CategoryTheory/Shift/CommShift.lean", "Mathlib/Tactic/Choose.lean", "Mathlib/Control/Basic.lean", "Mathlib/Tactic/Sat/FromLRAT.lean", "Mathlib/GroupTheory/Transfer.lean", "Mathlib/LinearAlgebra/DirectSum/Finsupp.lean", "Mathlib/Algebra/Category/Grp/Basic.lean", "Mathlib/RingTheory/Polynomial/Cyclotomic/Eval.lean", "Mathlib/Topology/Order/T5.lean", "Mathlib/Algebra/MvPolynomial/Cardinal.lean", "Mathlib/Lean/Expr.lean", "Mathlib/Algebra/Group/Semiconj/Units.lean", "Mathlib/Data/List/TFAE.lean", "Mathlib/Order/Filter/ENNReal.lean", "Mathlib/Order/Filter/CountableSeparatingOn.lean", "Mathlib/Algebra/Category/FGModuleCat/Basic.lean", "Mathlib/Data/Matroid/Basic.lean", "Mathlib/LinearAlgebra/Dimension/Finrank.lean", "Mathlib/Algebra/Order/Group/Bounds.lean", "Mathlib/Data/Fin/Tuple/Sort.lean", "Mathlib/Tactic/Positivity.lean", "Mathlib/Topology/MetricSpace/Thickening.lean", "Mathlib/Analysis/Complex/UnitDisc/Basic.lean", "Mathlib/Analysis/Calculus/Rademacher.lean", "Mathlib/Order/Category/OmegaCompletePartialOrder.lean", "Mathlib/Logic/Pairwise.lean", "Mathlib/Analysis/PSeriesComplex.lean", "Mathlib/CategoryTheory/LiftingProperties/Adjunction.lean", "Mathlib/CategoryTheory/Sites/Coherent/Basic.lean", "Mathlib/Combinatorics/SimpleGraph/Hasse.lean", "Mathlib/Computability/PartrecCode.lean", "Mathlib/Control/Monad/Basic.lean", "Mathlib/Algebra/Category/Ring/Constructions.lean", "Mathlib/Data/Complex/BigOperators.lean", "Mathlib/Data/UInt.lean", "Mathlib/MeasureTheory/OuterMeasure/AE.lean", "Mathlib/ModelTheory/Syntax.lean", "Mathlib/Order/Filter/AtTopBot.lean", "Mathlib/NumberTheory/Zsqrtd/Basic.lean", "Mathlib/Tactic/Conv.lean", "Mathlib/Combinatorics/Derangements/Basic.lean", "Mathlib/Topology/UrysohnsBounded.lean", "Mathlib/Data/Finset/Functor.lean", "Mathlib/LinearAlgebra/DirectSum/TensorProduct.lean", "Mathlib/Topology/Order/Bornology.lean", "Mathlib/Topology/ContinuousFunction/FunctionalCalculus.lean", "Mathlib/CategoryTheory/Filtered/Final.lean", "Mathlib/RingTheory/Coprime/Lemmas.lean", "Mathlib/Data/ZMod/Coprime.lean", "Mathlib/MeasureTheory/Integral/Bochner.lean", "Mathlib/MeasureTheory/Function/ConditionalExpectation/CondexpL1.lean", "Mathlib/NumberTheory/SiegelsLemma.lean", "Mathlib/CategoryTheory/Sites/ConcreteSheafification.lean", "Mathlib/Data/Buffer/Basic.lean", "Mathlib/Analysis/InnerProductSpace/LaxMilgram.lean", "Mathlib/SetTheory/ZFC/Ordinal.lean", "Mathlib/Data/Nat/ModEq.lean", "Mathlib/GroupTheory/CoprodI.lean", "Mathlib/Data/Nat/Log.lean", "Mathlib/Algebra/Homology/ComplexShape.lean", "Mathlib/FieldTheory/IsAlgClosed/AlgebraicClosure.lean", "Mathlib/NumberTheory/NumberField/Embeddings.lean", "Mathlib/Algebra/Lie/CartanMatrix.lean", "Mathlib/LinearAlgebra/Span.lean", "Mathlib/Algebra/Homology/HomotopyCategory/SingleFunctors.lean", "Mathlib/Algebra/Star/Unitary.lean", "Mathlib/CategoryTheory/Limits/Shapes/ZeroObjects.lean", "Mathlib/RingTheory/TensorProduct/MvPolynomial.lean", "Mathlib/RepresentationTheory/Character.lean", "Mathlib/Algebra/Order/Positive/Ring.lean", "Mathlib/Lean/EnvExtension.lean", "Mathlib/Algebra/Group/Pi/Basic.lean", "Mathlib/Algebra/ContinuedFractions/Computation/CorrectnessTerminating.lean", "Mathlib/CategoryTheory/Limits/Shapes/BinaryProducts.lean", "Mathlib/Data/Subtype.lean", "Mathlib/Tactic/Ring/PNat.lean", "Mathlib/Topology/Category/Locale.lean", "Mathlib/Algebra/Ring/Subsemiring/Pointwise.lean", "Mathlib/Util/CountHeartbeats.lean", "Mathlib/CategoryTheory/IsomorphismClasses.lean", "Mathlib/LinearAlgebra/LinearPMap.lean", "Mathlib/Algebra/EuclideanDomain/Basic.lean", "Mathlib/Analysis/Convex/StrictConvexBetween.lean", "Mathlib/RingTheory/WittVector/DiscreteValuationRing.lean", "Mathlib/Algebra/Squarefree/Basic.lean", "Mathlib/Algebra/Order/CauSeq/Basic.lean", "Mathlib/Analysis/Convex/Radon.lean", "Mathlib/Data/Nat/Factors.lean", "Mathlib/Data/Set/Function.lean", "Mathlib/Order/BoundedOrder.lean", "Mathlib/Order/Closure.lean", "Mathlib/RingTheory/IntegralClosure.lean", "Mathlib/CategoryTheory/Limits/Preserves/FunctorCategory.lean", "Mathlib/Analysis/Analytic/Composition.lean", "Mathlib/Analysis/Calculus/InverseFunctionTheorem/FiniteDimensional.lean", "Mathlib/CategoryTheory/Adjunction/Unique.lean", "Mathlib/Algebra/Order/Ring/Abs.lean", "Mathlib/Condensed/Light/Module.lean", "Mathlib/Algebra/Order/GroupWithZero/Unbundled.lean", "Mathlib/Analysis/Fourier/RiemannLebesgueLemma.lean", "Mathlib/RingTheory/MvPowerSeries/Inverse.lean", "Mathlib/Topology/Semicontinuous.lean", "Mathlib/Data/Complex/Cardinality.lean", "Mathlib/LinearAlgebra/Matrix/Trace.lean", "Mathlib/Algebra/Algebra/Subalgebra/Basic.lean", "Mathlib/Data/Multiset/Antidiagonal.lean", "Mathlib/Algebra/Lie/EngelSubalgebra.lean", "Mathlib/CategoryTheory/MorphismProperty/Concrete.lean", "Mathlib/Analysis/NormedSpace/Star/ContinuousFunctionalCalculus/Instances.lean", "Mathlib/Algebra/Category/ModuleCat/Adjunctions.lean", "Mathlib/Algebra/Module/Injective.lean", "Mathlib/Data/Finset/Card.lean", "Mathlib/CategoryTheory/Localization/FiniteProducts.lean", "Mathlib/CategoryTheory/Limits/HasLimits.lean", "Mathlib/AlgebraicGeometry/OpenImmersion.lean", "Mathlib/Algebra/Star/Prod.lean", "Mathlib/CategoryTheory/Limits/Shapes/FiniteProducts.lean", "Mathlib/CategoryTheory/Limits/FinallySmall.lean", "Mathlib/Tactic/ComputeDegree.lean", 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"Mathlib/NumberTheory/EllipticDivisibilitySequence.lean", "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean", "Mathlib/Tactic/FunProp/ToBatteries.lean", "Mathlib/RingTheory/Polynomial/ScaleRoots.lean", "Mathlib/CategoryTheory/Limits/Opposites.lean", "Mathlib/Geometry/Euclidean/Sphere/Basic.lean", "Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean", "Mathlib/Data/Vector/Basic.lean", "Mathlib/RingTheory/OreLocalization/Ring.lean", "Mathlib/CategoryTheory/EqToHom.lean", "Mathlib/Algebra/Group/Aut.lean", "Mathlib/Init/Order/Defs.lean", "Mathlib/Tactic/ProdAssoc.lean", "Mathlib/Data/Holor.lean", "Mathlib/Algebra/Homology/ShortComplex/QuasiIso.lean", "Mathlib/Data/Matroid/Init.lean", "Mathlib/ModelTheory/Substructures.lean", "Mathlib/Data/Real/Sqrt.lean", "Mathlib/Algebra/Category/ModuleCat/Presheaf/Abelian.lean", "Mathlib/Geometry/Manifold/Algebra/Monoid.lean", "Mathlib/LinearAlgebra/Matrix/Permutation.lean", "Mathlib/Data/List/Defs.lean", "Mathlib/Analysis/Complex/UpperHalfPlane/Basic.lean", "Mathlib/Data/Nat/PrimeNormNum.lean", "Mathlib/Topology/Algebra/Valuation.lean", "Mathlib/Data/Set/Pointwise/Support.lean", "Mathlib/Analysis/Calculus/Deriv/Shift.lean", "Mathlib/Analysis/NormedSpace/Spectrum.lean", "Mathlib/Algebra/Group/Indicator.lean", "Mathlib/RepresentationTheory/GroupCohomology/Basic.lean", "Mathlib/Analysis/InnerProductSpace/MeanErgodic.lean", "Mathlib/Order/OrdContinuous.lean", "Mathlib/Testing/SlimCheck/Gen.lean", "Mathlib/Topology/MetricSpace/GromovHausdorff.lean", "Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean", "Mathlib/Analysis/NormedSpace/MatrixExponential.lean", "Mathlib/Topology/Algebra/Nonarchimedean/AdicTopology.lean", "Mathlib/Analysis/SpecialFunctions/Trigonometric/Bounds.lean", "Mathlib/Data/Nat/Factorization/PrimePow.lean", "Mathlib/Probability/Kernel/CondDistrib.lean", "Mathlib/Tactic/SuccessIfFailWithMsg.lean", "Mathlib/Data/String/Basic.lean", "Mathlib/NumberTheory/Cyclotomic/Discriminant.lean", "Mathlib/LinearAlgebra/Matrix/DotProduct.lean", "Mathlib/Algebra/GroupWithZero/InjSurj.lean", "Mathlib/Data/Fintype/Fin.lean", "Mathlib/Tactic/ExtractLets.lean", "Mathlib/Data/Sym/Sym2.lean", "Mathlib/Topology/UniformSpace/Compact.lean", "Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean", "Mathlib/MeasureTheory/Function/Jacobian.lean", "Mathlib/Algebra/RingQuot.lean", "Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean", "Mathlib/Algebra/Homology/Augment.lean", "Mathlib/CategoryTheory/Limits/IsConnected.lean", "Mathlib/RingTheory/Filtration.lean", "Mathlib/Analysis/Complex/Convex.lean", "Mathlib/Geometry/Manifold/InteriorBoundary.lean", "Mathlib/Algebra/Homology/Factorizations/Basic.lean" ]	[]
.lake/packages/proofwidgets/ProofWidgets/Demos/Conv.lean	[ ".lake/packages/lean4/src/lean/Lean/Meta/ExprLens.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/MakeEditLink.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/Basic.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/OfRpcMethod.lean", ".lake/packages/proofwidgets/ProofWidgets/Data/Html.lean" ]	[ { "full_name": "NewCursorPos", "code": "structure NewCursorPos where\n newCursorPos? : Option Lsp.Position\n uri? : Option String\n deriving ToJson, FromJson", "start": [ 17, 1 ], "end": [ 20, 28 ], "kind": "commanddeclaration" }, { "full_name": "SolveReturn", "code": "private structure SolveReturn where\n expr : Expr\n val? : Option String\n listRest : List Nat", "start": [ 22, 1 ], "end": [ 25, 22 ], "kind": "commanddeclaration" }, { "full_name": "solveLevel", "code": "private def solveLevel (expr : Expr) (path : List Nat) : MetaM SolveReturn := match expr with\n \| Expr.app _ _ => do\n let mut descExp := expr\n let mut count := 0\n let mut explicitList := []\n\n while descExp.isApp do\n if (←Lean.Meta.inferType descExp.appFn!).bindingInfo!.isExplicit then\n explicitList := true::explicitList\n count := count + 1\n else\n explicitList := false::explicitList\n descExp := descExp.appFn!\n\n let mut mutablePath := path\n let mut length := count\n explicitList := List.reverse explicitList\n while !mutablePath.isEmpty && mutablePath.head! == 0 do\n if explicitList.head! == true then\n count := count - 1\n explicitList := explicitList.tail!\n mutablePath := mutablePath.tail!\n\n let mut nextExp := expr\n while length > count do\n nextExp := nextExp.appFn!\n length := length - 1\n nextExp := nextExp.appArg!\n\n let pathRest := if mutablePath.isEmpty then [] else mutablePath.tail!\n\n return { expr := nextExp, val? := toString count , listRest := pathRest }\n\n \| Expr.lam n _ b _ => do\n let name := match n with\n \| Name.str _ s => s\n \| _ => panic! \"no name found\"\n return { expr := b, val? := name, listRest := path.tail! }\n\n \| Expr.forallE n _ b _ => do\n let name := match n with\n \| Name.str _ s => s\n \| _ => panic! \"no name found\"\n return { expr := b, val? := name, listRest := path.tail! }\n\n \| Expr.mdata _ b => do\n match b with\n \| Expr.mdata _ _ => return { expr := b, val? := none, listRest := path }\n \| _ => return { expr := b.appFn!.appArg!, val? := none, listRest := path.tail!.tail! }\n\n \| _ => do\n return { expr := ←(Lean.Core.viewSubexpr path.head! expr), val? := toString (path.head! + 1), listRest := path.tail! }", "start": [ 27, 1 ], "end": [ 81, 123 ], "kind": "commanddeclaration" }, { "full_name": "reprint!", "code": "def reprint! (stx : Syntax) : String :=\n match stx.reprint with\n \| some x => x\n \| none => panic! \"Could not reprint syntax\"", "start": [ 84, 1 ], "end": [ 87, 49 ], "kind": "commanddeclaration" }, { "full_name": "LocateReturn", "code": "structure LocateReturn where\n pathBeforeConv : List Nat\n pathAfterConv : List Nat\n deriving Inhabited", "start": [ 89, 1 ], "end": [ 92, 21 ], "kind": "commanddeclaration" }, { "full_name": "locate", "code": "private def locate (stx : Syntax) (pos : String.Pos) : LocateReturn := Id.run do\n let mut t := Syntax.Traverser.fromSyntax stx\n let mut path := []\n let mut rangeList := []\n\n while !t.cur.getArgs.isEmpty do\n let mut args := t.cur.getArgs\n let mut i := 0\n let mut newT := t\n let mut found := false\n rangeList := []\n for arg in args do\n let mut range := match arg.getRange? with\n \| some x => x\n \| none => { start := 0, stop := 0 }\n rangeList := range::rangeList\n if range.start < pos && pos <= range.stop then do\n newT := t.down i\n path := i::path\n found := true\n i := i + 1\n if !found then break\n t := newT\n\n let mut pathAfterConv := []\n while !(t.cur.getKind == `Lean.Parser.Tactic.Conv.conv\n \|\| t.cur.getKind == `Lean.Parser.Tactic.Conv.convConvSeq\n \|\| t.cur.getKind == `Lean.Widget.conv!)\n && path.length > 0 do\n t := t.up\n pathAfterConv := path.head!::pathAfterConv\n path := path.tail!\n\n if pathAfterConv == [] \|\| pathAfterConv.length == 1 then\n pathAfterConv := [t.cur.getArgs.size - 2]\n\n else if pathAfterConv.length == 3 then\n let mut rangeList' := rangeList.reverse\n let mut ctr := 0\n while rangeList'.head!.stop < pos do\n ctr := ctr + 1\n rangeList' := rangeList'.tail!\n pathAfterConv := List.append pathAfterConv ((ctr-2)::[0])\n\n return {pathBeforeConv := path.reverse, pathAfterConv := pathAfterConv }", "start": [ 94, 1 ], "end": [ 142, 75 ], "kind": "commanddeclaration" }, { "full_name": "extractIndentation", "code": "private partial def extractIndentation (input : String) : String := match \" \".isPrefixOf input with\n \| true => \" \" ++ extractIndentation (input.drop 2)\n \| false => \"\"", "start": [ 144, 1 ], "end": [ 146, 16 ], "kind": "commanddeclaration" }, { "full_name": "InsertReturn", "code": "private structure InsertReturn where\n stx : Syntax\n newPath : List Nat\n newCursorPos : Lsp.Position", "start": [ 148, 1 ], "end": [ 151, 30 ], "kind": "commanddeclaration" }, { "full_name": "insertAfterArrow", "code": "private def insertAfterArrow (stx : Syntax) (pathBeforeConvParam : List Nat) (pathAfterConvParam : List Nat) (value : String) (text : FileMap) : InsertReturn := Id.run do\n let mut t := Syntax.Traverser.fromSyntax stx\n let mut pathBeforeConv := pathBeforeConvParam\n while pathBeforeConv.length > 0 do\n t := t.down pathBeforeConv.head!\n pathBeforeConv := pathBeforeConv.tail!\n let mut pathAfterConv := pathAfterConvParam\n\nlet mut pathBeforeConv' := pathBeforeConvParam.reverse\n let mut returnPath := []\n for _ in [:4] do\n t := t.up\n returnPath := pathBeforeConv'.head!::returnPath\n pathBeforeConv' := pathBeforeConv'.tail!\n t := t.up\n\n let argNr := pathBeforeConv'.head! - 1\n let prevArg := reprint! t.cur.getArgs[argNr]!\n let mut previousIndentation := extractIndentation (prevArg.splitOn \"\\n\").reverse.head!\n\n t := t.down pathBeforeConv'.head!\n while returnPath.length > 0 do\n t := t.down returnPath.head!\n returnPath := returnPath.tail!\n\n let arrow := reprint! t.cur.getArgs[pathAfterConv.head!]!\n let mut arrowIndentation := extractIndentation (arrow.splitOn \"\\n\").reverse.head!\n let mut newCursorPos := match t.cur.getArgs[pathAfterConv.head!]!.getRange? with\n \| some range => text.utf8PosToLspPos range.stop\n \| none => text.utf8PosToLspPos 0\n\n let mut newNode := Syntax.missing\n if reprint! t.cur.getArgs[pathAfterConv.head! + 1]! == \"\" \|\| previousIndentation == arrowIndentation then\n let newArrow := Syntax.atom (SourceInfo.original \"\".toSubstring 0 \"\".toSubstring 0) \"=>\\n\"\n t := t.setCur (t.cur.setArgs (List.append (t.cur.getArgs.toList.take pathAfterConv.head!) (newArrow::t.cur.getArgs.toList.drop (pathAfterConv.head! + 1))).toArray)\n newNode := Syntax.atom (SourceInfo.original \"\".toSubstring 0 \"\".toSubstring 0) (\" \" ++ previousIndentation ++ value ++ \"\\n\" ++ arrowIndentation)\n newCursorPos := { line := newCursorPos.line + 1, character := 2 + previousIndentation.length + value.length }\n else\n newNode := Syntax.atom (SourceInfo.original \"\".toSubstring 0 \"\".toSubstring 0) (value ++ \"\\n\" ++ arrowIndentation)\n newCursorPos := { line := newCursorPos.line + 1, character := arrowIndentation.length + value.length }\n\n t := t.down (pathAfterConv.head! + 1)\n t := t.down 0\n t := t.down 0\n\n let newArgList := newNode::t.cur.getArgs.toList\n t := t.setCur (t.cur.setArgs newArgList.toArray)\n while t.parents.size > 0 do\n t := t.up\n\n let newPath := pathBeforeConvParam ++ (pathAfterConv.head! + 1)::0::0::[0]\n\n return { stx := t.cur, newPath := newPath, newCursorPos }", "start": [ 153, 1 ], "end": [ 212, 60 ], "kind": "commanddeclaration" }, { "full_name": "insertAnywhereElse", "code": "private def insertAnywhereElse (stx : Syntax) (pathBeforeConvParam : List Nat) (pathAfterConvParam : List Nat) (value : String) (text : FileMap): InsertReturn := Id.run do\n let mut t := Syntax.Traverser.fromSyntax stx\n let mut pathBeforeConv := pathBeforeConvParam\n while pathBeforeConv.length > 0 do\n t := t.down pathBeforeConv.head!\n pathBeforeConv := pathBeforeConv.tail!\n let mut pathAfterConv := pathAfterConvParam\n\nlet nothingAfterConv := t.up.cur.getArgs.size - 1 == pathBeforeConvParam.reverse.head!\n\n for _ in [:3] do\n t := t.down pathAfterConv.head!\n pathAfterConv := pathAfterConv.tail!\n\n let argAsString := reprint! t.cur.getArgs[pathAfterConv.head!]!\n let mut newval := value\n let mut entersMerged := false\n if toString t.cur.getArgs[pathAfterConv.head!]!.getKind == \"Lean.Parser.Tactic.Conv.«convEnter[__]»\" then\n let mut additionalArgs := (argAsString.splitOn \"\\n\").head!\n additionalArgs := (additionalArgs.drop \"enter [\".length).dropRight 1\n\n let left := value.take \"enter [\".length\n let right := value.drop \"enter [\".length\n newval := left ++ additionalArgs ++ \", \" ++ right\n entersMerged := true\n\n let mut newCursorPos := match t.cur.getArgs[pathAfterConv.head!]!.getRange? with\n \| some range => text.utf8PosToLspPos range.stop\n \| none => text.utf8PosToLspPos 0\n\n let mut argNr := pathAfterConv.head!\n let mut indentation := \"\"\n if argNr == 0 then\n indentation := extractIndentation ((reprint! t.up.up.up.cur).splitOn \"\\n\").tail!.head!\n else\n argNr := argNr - 2\n let mut prevArg := reprint! t.cur.getArgs[argNr]!\n let mut split := prevArg.splitOn \"\\n\"\n while split.length == 1 do\n argNr := argNr + 2\n prevArg := reprint! t.cur.getArgs[argNr]!\n split := prevArg.splitOn \"\\n\"\n\n let mut indentationLine := split.reverse.head!\n indentation := extractIndentation indentationLine\n\n newCursorPos := match entersMerged with\n \| true => { line := newCursorPos.line, character := indentation.length + newval.length }\n \| false => { line := newCursorPos.line + 1, character := indentation.length + newval.length }\n\n let mut frontIndentation := \"\"\n if pathAfterConv.head! == t.cur.getArgs.size - 1 then\n let lastArg := reprint! t.cur.getArgs[ t.cur.getArgs.size - 1]!\n let mut lastArgIndentation := extractIndentation (lastArg.splitOn \"\\n\").reverse.head!\n let numOfWhitespace := indentation.length - lastArgIndentation.length\n for _ in [:numOfWhitespace] do\n frontIndentation := frontIndentation ++ \" \"\n indentation := indentation.drop numOfWhitespace\n\n let mut argList := []\n if nothingAfterConv then\n let mut adjustedLastLine := reprint! t.cur.getArgs[t.cur.getArgs.size - 1]!\n while adjustedLastLine.takeRight 1 == \"\\n\" do\n adjustedLastLine := adjustedLastLine.dropRight 1\n adjustedLastLine := adjustedLastLine ++ \"\\n\"\n let adjustedLastNode := Syntax.atom (SourceInfo.original \"\".toSubstring 0 \"\".toSubstring 0) adjustedLastLine\n argList := (adjustedLastNode::t.cur.getArgs.toList.reverse.tail!).reverse\n else\n argList := t.cur.getArgs.toList\n\n let newNode := match entersMerged with\n \| true => Syntax.atom (SourceInfo.original \"\".toSubstring 0 \"\".toSubstring 0) (newval ++ \"\\n\" ++ indentation)\n \| false => Syntax.atom (SourceInfo.original \"\".toSubstring 0 \"\".toSubstring 0) (frontIndentation ++ newval ++ \"\\n\" ++ indentation)\n let newArgList := match entersMerged with\n \| true => List.append (argList.take (pathAfterConv.head!) ) (newNode::(argList.drop (pathAfterConv.head! + 1)))\n \| false => List.append (argList.take (pathAfterConv.head! + 1) ) (newNode::(argList.drop (pathAfterConv.head! + 1)))\n let newPath := match entersMerged with\n \| true => pathBeforeConvParam ++ (pathAfterConvParam.take 4)\n \| false => pathBeforeConvParam ++ (pathAfterConvParam.take 3) ++ [(pathAfterConvParam.get! 3) + 2]\n\n t := t.setCur (t.cur.setArgs newArgList.toArray)\n while t.parents.size > 0 do\n t := t.up\n\n return { stx := t.cur, newPath := newPath, newCursorPos := newCursorPos }", "start": [ 214, 1 ], "end": [ 309, 76 ], "kind": "commanddeclaration" }, { "full_name": "syntaxInsert", "code": "private def syntaxInsert (stx : Syntax) (pathBeforeConvParam : List Nat) (pathAfterConvParam : List Nat) (value : String) (text : FileMap): InsertReturn := Id.run do\n if value == \"\" then return { stx := stx, newPath := pathBeforeConvParam ++ pathAfterConvParam, newCursorPos := {line := 0, character := 0} }\n if pathAfterConvParam.length == 1 then\n return insertAfterArrow stx pathBeforeConvParam pathAfterConvParam value text\n else\n return insertAnywhereElse stx pathBeforeConvParam pathAfterConvParam value text", "start": [ 311, 1 ], "end": [ 316, 84 ], "kind": "commanddeclaration" }, { "full_name": "InsertEnterResponse", "code": "structure InsertEnterResponse where\n \n label : String\n edit : Lsp.TextDocumentEdit\n \n newCursorPos : Lsp.Position\n deriving FromJson, ToJson", "start": [ 318, 1 ], "end": [ 324, 28 ], "kind": "commanddeclaration" }, { "full_name": "insertEnter", "code": "def insertEnter (subexprPos : SubExpr.Pos) (goalType : Expr) (cmdStx : Syntax)\n (cursorPos : String.Pos) (doc : Lean.Server.FileWorker.EditableDocument) : MetaM InsertEnterResponse := do\n let mut list := (SubExpr.Pos.toArray subexprPos).toList\n let mut expr := goalType\n let mut retList := []\n while !list.isEmpty do\n let res ← solveLevel expr list\n expr := res.expr\n retList := match res.val? with\n \| none => retList\n \| some val => val::retList\n list := res.listRest\n\n retList := List.reverse retList\n let mut enterval := \"enter \" ++ toString retList\n if enterval.contains '0' then enterval := \"Error: Not a valid conv target\"\n if retList.isEmpty then enterval := \"\"\n\n let range := match cmdStx.getRange? with\n \| some x => x\n \| none => panic! \"could not get range\"\n\n let text := doc.meta.text\n\n let located := locate cmdStx { byteIdx := (min cursorPos.byteIdx range.stop.byteIdx) }\n let inserted := syntaxInsert cmdStx located.pathBeforeConv located.pathAfterConv enterval text\n let mut newSyntax := reprint! inserted.stx\n\n let mut syntaxAsList := newSyntax.data.reverse\n while syntaxAsList.head! == '\\n' \|\| syntaxAsList.head! == ' ' do\n newSyntax := newSyntax.dropRight 1\n syntaxAsList := syntaxAsList.tail!\n\n let textEdit : Lsp.TextEdit := { range := { start := text.utf8PosToLspPos range.start, «end» := text.utf8PosToLspPos { byteIdx := range.stop.byteIdx } }, newText := newSyntax }\n let edit : Lsp.TextDocumentEdit := { textDocument := { uri := doc.meta.uri, version? := doc.meta.version }, edits := [textEdit].toArray }\n\n return { label := enterval, edit, newCursorPos := inserted.newCursorPos }", "start": [ 326, 1 ], "end": [ 367, 76 ], "kind": "commanddeclaration" }, { "full_name": "ConvButtonProps", "code": "structure ConvButtonProps where\n pos : Lsp.Position\n goal : Widget.InteractiveGoal\n loc : SubExpr.GoalLocation\n deriving RpcEncodable", "start": [ 373, 1 ], "end": [ 377, 24 ], "kind": "commanddeclaration" }, { "full_name": "ConvButton.rpc", "code": "@[server_rpc_method]\ndef ConvButton.rpc (props : ConvButtonProps) : RequestM (RequestTask Html) :=\n RequestM.withWaitFindSnapAtPos props.pos fun snap => do\n if props.goal.goalPrefix != \"\| \" then\n throw $ .invalidParams s!\"The current goal is not a conv goal.\"\n let .target subexprPos := props.loc\n \| throw $ .invalidParams s!\"Select something in the target type.\"\n let doc ← RequestM.readDoc\n let cursorPos := doc.meta.text.lspPosToUtf8Pos props.pos\n props.goal.ctx.val.runMetaM {} do\n let md ← props.goal.mvarId.getDecl\n let lctx := md.lctx \|>.sanitizeNames.run' {options := (← getOptions)}\n Meta.withLCtx lctx md.localInstances do\n let resp ← insertEnter subexprPos md.type snap.stx cursorPos doc\n return <div><MakeEditLink\n edit={resp.edit}\n newSelection?={some ⟨resp.newCursorPos, resp.newCursorPos⟩}\n title?={resp.label}\n >\n {.text resp.label}\n </MakeEditLink></div>", "start": [ 380, 1 ], "end": [ 400, 32 ], "kind": "commanddeclaration" }, { "full_name": "ConvButton", "code": "@[widget_module]\ndef ConvButton : Component ConvButtonProps :=\n mk_rpc_widget% ConvButton.rpc", "start": [ 402, 1 ], "end": [ 404, 32 ], "kind": "commanddeclaration" }, { "full_name": "findGoalForLocation", "code": "def findGoalForLocation (goals : Array Widget.InteractiveGoal) (loc : SubExpr.GoalsLocation) :\n Option Widget.InteractiveGoal :=\n goals.find? (·.mvarId == loc.mvarId)", "start": [ 406, 1 ], "end": [ 408, 39 ], "kind": "commanddeclaration" }, { "full_name": "ConvPanel.rpc", "code": "@[server_rpc_method]\ndef ConvPanel.rpc (props : PanelWidgetProps) : RequestM (RequestTask Html) :=\n RequestM.asTask do\n let inner : Html ← (do\n if props.selectedLocations.isEmpty then\n return <span>No actions available. You can use shift-click to select an expression in the goal state.</span>\n let buttons : Array Html ← props.selectedLocations.mapM fun loc => do\n let some g := findGoalForLocation props.goals loc\n \| throw $ .invalidParams s!\"could not find goal for location {toJson loc}\"\n return <ConvButton pos={props.pos} goal={g} loc={loc.loc} />\n return Html.element \"div\" #[] buttons)\n return <details «open»={true}>\n <summary className=\"mv2 pointer\">Conv 🔍</summary>\n <div className=\"ml1\">{inner}</div>\n </details>", "start": [ 411, 1 ], "end": [ 425, 17 ], "kind": "commanddeclaration" }, { "full_name": "ConvPanel", "code": "@[widget_module]\ndef ConvPanel : Component PanelWidgetProps :=\n mk_rpc_widget% ConvPanel.rpc", "start": [ 427, 1 ], "end": [ 429, 31 ], "kind": "commanddeclaration" }, { "full_name": "test_sorry", "code": "axiom test_sorry {α} : α", "start": [ 434, 1 ], "end": [ 434, 25 ], "kind": "commanddeclaration" } ]
.lake/packages/proofwidgets/ProofWidgets/Demos/SelectInsertConv.lean	[ ".lake/packages/lean4/src/lean/Lean/Meta/ExprLens.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/MakeEditLink.lean", ".lake/packages/batteries/Batteries/Lean/Position.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/Basic.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/OfRpcMethod.lean", ".lake/packages/proofwidgets/ProofWidgets/Data/Html.lean" ]	[ { "full_name": "SolveReturn", "code": "private structure SolveReturn where\n expr : Expr\n val? : Option String\n listRest : List Nat", "start": [ 23, 1 ], "end": [ 26, 22 ], "kind": "commanddeclaration" }, { "full_name": "solveLevel", "code": "private def solveLevel (expr : Expr) (path : List Nat) : MetaM SolveReturn := match expr with\n \| Expr.app _ _ => do\n let mut descExp := expr\n let mut count := 0\n let mut explicitList := []\n\n while descExp.isApp do\n if (←Lean.Meta.inferType descExp.appFn!).bindingInfo!.isExplicit then\n explicitList := true::explicitList\n count := count + 1\n else\n explicitList := false::explicitList\n descExp := descExp.appFn!\n\n let mut mutablePath := path\n let mut length := count\n explicitList := List.reverse explicitList\n while !mutablePath.isEmpty && mutablePath.head! == 0 do\n if explicitList.head! == true then\n count := count - 1\n explicitList := explicitList.tail!\n mutablePath := mutablePath.tail!\n\n let mut nextExp := expr\n while length > count do\n nextExp := nextExp.appFn!\n length := length - 1\n nextExp := nextExp.appArg!\n\n let pathRest := if mutablePath.isEmpty then [] else mutablePath.tail!\n\n return { expr := nextExp, val? := toString count , listRest := pathRest }\n\n \| Expr.lam n _ b _ => do\n let name := match n with\n \| Name.str _ s => s\n \| _ => panic! \"no name found\"\n return { expr := b, val? := name, listRest := path.tail! }\n\n \| Expr.forallE n _ b _ => do\n let name := match n with\n \| Name.str _ s => s\n \| _ => panic! \"no name found\"\n return { expr := b, val? := name, listRest := path.tail! }\n\n \| Expr.mdata _ b => do\n match b with\n \| Expr.mdata _ _ => return { expr := b, val? := none, listRest := path }\n \| _ => return { expr := b.appFn!.appArg!, val? := none, listRest := path.tail!.tail! }\n\n \| _ => do\n return {\n expr := ←(Lean.Core.viewSubexpr path.head! expr)\n val? := toString (path.head! + 1)\n listRest := path.tail!\n }", "start": [ 28, 1 ], "end": [ 86, 6 ], "kind": "commanddeclaration" }, { "full_name": "insertEnter", "code": "def insertEnter (locations : Array Lean.SubExpr.GoalsLocation) (goalType : Expr) : MetaM String := do\n let some pos := locations[0]? \| throwError \"You must select something.\"\n let ⟨_, .target subexprPos⟩ := pos \| throwError \"You must select something in the goal.\"\n let mut list := (SubExpr.Pos.toArray subexprPos).toList\n let mut expr := goalType\n let mut retList := []\n while !list.isEmpty do\n let res ← solveLevel expr list\n expr := res.expr\n retList := match res.val? with\n \| none => retList\n \| some val => val::retList\n list := res.listRest\n\n retList := List.reverse retList\n let mut enterval := \"conv => enter \" ++ toString retList\n if enterval.contains '0' then enterval := \"Error: Not a valid conv target\"\n if retList.isEmpty then enterval := \"\"\n return enterval", "start": [ 89, 1 ], "end": [ 109, 18 ], "kind": "commanddeclaration" }, { "full_name": "findGoalForLocation", "code": "def findGoalForLocation (goals : Array Widget.InteractiveGoal) (loc : SubExpr.GoalsLocation) :\n Option Widget.InteractiveGoal :=\n goals.find? (·.mvarId == loc.mvarId)", "start": [ 111, 1 ], "end": [ 113, 39 ], "kind": "commanddeclaration" }, { "full_name": "ConvSelectionPanelProps", "code": "structure ConvSelectionPanelProps extends PanelWidgetProps where\n \n replaceRange : Lsp.Range\n deriving RpcEncodable", "start": [ 115, 1 ], "end": [ 118, 24 ], "kind": "commanddeclaration" }, { "full_name": "ConvSelectionPanel.rpc", "code": "@[server_rpc_method]\ndef ConvSelectionPanel.rpc (props : ConvSelectionPanelProps) : RequestM (RequestTask Html) :=\n RequestM.asTask do\n let doc ← RequestM.readDoc\n let inner : Html ← (do\n if props.selectedLocations.isEmpty then\n return <span>Use shift-click to select one sub-expression in the goal that you want to zoom on.</span>\n let some selectedLoc := props.selectedLocations[0]? \| unreachable!\n\n let some g := findGoalForLocation props.goals selectedLoc\n \| throw $ .invalidParams\n s!\"could not find goal for location {toJson selectedLoc}\"\n g.ctx.val.runMetaM {} do\n let md ← g.mvarId.getDecl\n let lctx := md.lctx \|>.sanitizeNames.run' {options := (← getOptions)}\n Meta.withLCtx lctx md.localInstances do\n let newCode ← insertEnter props.selectedLocations md.type\n return .ofComponent\n MakeEditLink\n (.ofReplaceRange doc.meta props.replaceRange newCode)\n #[ .text newCode ])\n return <details «open»={true}>\n <summary className=\"mv2 pointer\">Conv 🔍</summary>\n <div className=\"ml1\">{inner}</div>\n </details>", "start": [ 121, 1 ], "end": [ 145, 17 ], "kind": "commanddeclaration" }, { "full_name": "ConvSelectionPanel", "code": "@[widget_module]\ndef ConvSelectionPanel : Component ConvSelectionPanelProps :=\n mk_rpc_widget% ConvSelectionPanel.rpc", "start": [ 147, 1 ], "end": [ 149, 40 ], "kind": "commanddeclaration" }, { "full_name": "test_sorry", "code": "axiom test_sorry {α} : α", "start": [ 158, 1 ], "end": [ 158, 25 ], "kind": "commanddeclaration" } ]
.lake/packages/proofwidgets/ProofWidgets/Demos/Plot.lean	[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Recharts.lean" ]	[ { "full_name": "fn", "code": "def fn (t : Float) (x : Float): Float :=\n 50 * (x - 0.25) * (x - 0.5) * (x - 0.7) + 0.1 * (x * 40 - t * 2 * 3.141).sin", "start": [ 6, 1 ], "end": [ 7, 80 ], "kind": "commanddeclaration" }, { "full_name": "Plot", "code": "def Plot (fn : Float → Float) (steps := 100) : Html :=\n let jsonData : Array Json :=\n Nat.fold (flip Array.push) (steps + 1) #[]\n \|> Array.map (fun (x : Nat) => let x : Float := x.toFloat / steps.toFloat; (x, fn x))\n \|> Array.map (fun (x,y) => json% {x: $(toJson x) , y: $(toJson y)});\n <LineChart width={400} height={400} data={jsonData}>\n <XAxis domain?={#[toJson 0, toJson 1]} dataKey?=\"x\" />\n <YAxis domain?={#[toJson (-1), toJson 1]} allowDataOverflow={Bool.false} />\n <Line type={.monotone} dataKey=\"y\" stroke=\"#8884d8\" dot?={Bool.false} />\n </LineChart>", "start": [ 10, 1 ], "end": [ 19, 15 ], "kind": "commanddeclaration" }, { "full_name": "mkFrames", "code": "def mkFrames (fn : Float → Float → Float) (steps := 100) : Array Html:=\n List.range (steps + 1) \|>.toArray \|>.map (fun t => Plot (fn (t.toFloat / steps.toFloat)))", "start": [ 30, 1 ], "end": [ 31, 92 ], "kind": "commanddeclaration" }, { "full_name": "AnimatedHtmlProps", "code": "structure AnimatedHtmlProps where\n frames : Array Html\n framesPerSecond? : Option Nat := none\n deriving Server.RpcEncodable", "start": [ 33, 1 ], "end": [ 36, 31 ], "kind": "commanddeclaration" }, { "full_name": "AnimatedHtml", "code": "@[widget_module]\ndef AnimatedHtml : Component AnimatedHtmlProps where\n javascript := include_str \"..\" / \"..\" / \".lake\" / \"build\" / \"js\" / \"animatedHtml.js\"", "start": [ 38, 1 ], "end": [ 40, 87 ], "kind": "commanddeclaration" } ]
.lake/packages/proofwidgets/ProofWidgets/Demos/InteractiveSvg.lean	[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/InteractiveSvg.lean" ]	[ { "full_name": "State", "code": "abbrev State := Array (Float × Float)", "start": [ 7, 1 ], "end": [ 7, 38 ], "kind": "commanddeclaration" }, { "full_name": "isvg", "code": "def isvg : InteractiveSvg State where\n init := #[(-0.5, -0.5), (0.5, -0.5), (0.5, 0.5), (-0.5, 0.5)]\n\n frame :=\n { xmin := -1\n ymin := -1\n xSize := 2\n width := 400\n height := 400 }\n\n update _time _Δt _action _mouseStart mouseEnd _selected getData state :=\n match getData Nat, mouseEnd with\n \| some id, some p => state.set! id p.toAbsolute\n \| _, _ => state\n\n render _time mouseStart mouseEnd state :=\n {\n elements :=\n let mousePointer :=\n match mouseStart, mouseEnd with\n \| some s, some e =>\n #[\n Svg.circle e (.px 5) \|>.setFill (1.,1.,1.),\n Svg.line s e \|>.setStroke (1.,1.,1.) (.px 2)\n ]\n \| _, _ => #[]\n let circles := (state.mapIdx fun idx (p : Float × Float) =>\n Svg.circle p (.abs 0.2) \|>.setFill (0.7,0.7,0.7) \|>.setId s!\"circle{idx}\" \|>.setData idx.1\n )\n mousePointer.append circles\n }", "start": [ 9, 1 ], "end": [ 39, 6 ], "kind": "commanddeclaration" }, { "full_name": "updateSvg", "code": "@[server_rpc_method]\ndef updateSvg (params : UpdateParams State) : RequestM (RequestTask (UpdateResult State)) := isvg.serverRpcMethod params", "start": [ 42, 1 ], "end": [ 43, 121 ], "kind": "commanddeclaration" }, { "full_name": "SvgWidget", "code": "@[widget_module]\ndef SvgWidget : Component (UpdateResult State) where\n javascript := include_str \"..\" / \"..\" / \".lake\" / \"build\" / \"js\" / \"interactiveSvg.js\"", "start": [ 45, 1 ], "end": [ 47, 89 ], "kind": "commanddeclaration" }, { "full_name": "init", "code": "def init : UpdateResult State := {\n html := <div>Init!!!</div>,\n state := { state := isvg.init\n time := 0\n selected := none\n mousePos := none\n idToData := isvg.render 0 none none isvg.init \|>.idToDataList}\n}", "start": [ 49, 1 ], "end": [ 56, 2 ], "kind": "commanddeclaration" } ]
.lake/packages/proofwidgets/ProofWidgets/Demos/Venn.lean	[ ".lake/packages/proofwidgets/ProofWidgets/Component/PenroseDiagram.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean", ".lake/packages/lean4/src/lean/Lean/Data/HashMap.lean", ".lake/packages/lean4/src/lean/Lean/Elab/Tactic.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/Basic.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/OfRpcMethod.lean" ]	[ { "full_name": "Set", "code": "def Set (α : Type u) := α → Prop", "start": [ 12, 1 ], "end": [ 12, 33 ], "kind": "commanddeclaration" }, { "full_name": "Set.Mem", "code": "protected def Mem (a : α) (s : Set α) : Prop :=\n s a", "start": [ 16, 1 ], "end": [ 18, 6 ], "kind": "commanddeclaration" }, { "full_name": "Set.ext", "code": "theorem ext {a b : Set α} (h : ∀ (x : α), x ∈ a ↔ x ∈ b) : a = b", "start": [ 23, 1 ], "end": [ 24, 33 ], "kind": "commanddeclaration" }, { "full_name": "Set.Subset", "code": "protected def Subset (s₁ s₂ : Set α) :=\n ∀ ⦃a⦄, a ∈ s₁ → a ∈ s₂", "start": [ 26, 1 ], "end": [ 27, 25 ], "kind": "commanddeclaration" }, { "full_name": "isSubsetPred?", "code": "def isSubsetPred? (e : Expr) : Option (Expr × Expr) := do\n let some (_, _, S, T) := e.app4? ``HasSubset.Subset \| none\n return (S, T)", "start": [ 41, 1 ], "end": [ 44, 16 ], "kind": "commanddeclaration" }, { "full_name": "ExprEmbeds", "code": "abbrev ExprEmbeds := Array (String × Expr)", "start": [ 46, 1 ], "end": [ 47, 43 ], "kind": "commanddeclaration" }, { "full_name": "mkSetDiag", "code": "def mkSetDiag (sub : String) (embeds : ExprEmbeds) : MetaM Html := do\n let embeds ← embeds.mapM fun (s, h) =>\n return (s, <InteractiveCode fmt={← Widget.ppExprTagged h} />)\n return <PenroseDiagram\n embeds={embeds}\n dsl={include_str \"..\"/\"..\"/\"widget\"/\"penrose\"/\"setTheory.dsl\"}\n sty={include_str \"..\"/\"..\"/\"widget\"/\"penrose\"/\"venn.sty\"}\n sub={sub} />", "start": [ 50, 1 ], "end": [ 57, 19 ], "kind": "commanddeclaration" }, { "full_name": "isSetGoal?", "code": "def isSetGoal? (hyps : Array LocalDecl) : MetaM (Option Html) := do\n let mut sub := \"AutoLabel All\\n\"\n let mut sets : HashMap String Expr := .empty\n for assm in hyps do\n let tp ← instantiateMVars assm.type\n if let some (S, T) := isSubsetPred? tp then\n let sS ← toString <$> Lean.Meta.ppExpr S\n let sT ← toString <$> Lean.Meta.ppExpr T\n let (sets', cS) := sets.insert' sS S\n let (sets', cT) := sets'.insert' sT T\n sets := sets'\n if !cS then\n sub := sub ++ s!\"Set {sS}\\n\"\n if !cT then\n sub := sub ++ s!\"Set {sT}\\n\"\n sub := sub ++ s!\"IsSubset({sS}, {sT})\\n\"\n if sets.isEmpty then return none\n some <$> mkSetDiag sub sets.toArray", "start": [ 59, 1 ], "end": [ 76, 38 ], "kind": "commanddeclaration" }, { "full_name": "findGoalForLocation", "code": "def findGoalForLocation (goals : Array Widget.InteractiveGoal) (loc : SubExpr.GoalsLocation) :\n Option Widget.InteractiveGoal :=\n goals.find? (·.mvarId == loc.mvarId)", "start": [ 80, 1 ], "end": [ 82, 39 ], "kind": "commanddeclaration" }, { "full_name": "VennDisplay.rpc", "code": "@[server_rpc_method]\ndef VennDisplay.rpc (props : PanelWidgetProps) : RequestM (RequestTask Html) :=\n RequestM.asTask do\n let inner : Html ← (do\n if props.selectedLocations.isEmpty then\n return <span>Use shift-click to select hypotheses to include in the diagram.</span>\n let some selectedLoc := props.selectedLocations[0]? \| unreachable!\n\n let some g := findGoalForLocation props.goals selectedLoc\n \| throw $ .invalidParams\n s!\"could not find goal for location {toJson selectedLoc}\"\n g.ctx.val.runMetaM {} do\n let md ← g.mvarId.getDecl\n let lctx := md.lctx \|>.sanitizeNames.run' {options := (← getOptions)}\n Meta.withLCtx lctx md.localInstances do\n let locs : Array LocalDecl ← props.selectedLocations.filterMapM fun\n \| ⟨mv, .hyp fv⟩ \| ⟨mv, .hypType fv _⟩ =>\n if mv == g.mvarId then return some (← fv.getDecl) else return none\n \| _ => return none\n match ← isSetGoal? locs with\n \| some html => return html\n \| none => return <span>No set goal.</span>)\n return <details «open»={true}>\n <summary className=\"mv2 pointer\">Venn diagram</summary>\n <div className=\"ml1\">{inner}</div>\n </details>", "start": [ 85, 1 ], "end": [ 110, 17 ], "kind": "commanddeclaration" }, { "full_name": "VennDisplay", "code": "@[widget_module]\ndef VennDisplay : Component PanelWidgetProps :=\n mk_rpc_widget% VennDisplay.rpc", "start": [ 112, 1 ], "end": [ 114, 33 ], "kind": "commanddeclaration" } ]
.lake/packages/proofwidgets/ProofWidgets/Demos/Euclidean.lean	[ ".lake/packages/proofwidgets/ProofWidgets/Component/PenroseDiagram.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/MakeEditLink.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean", ".lake/packages/lean4/src/lean/Lean/Data/HashMap.lean", ".lake/packages/lean4/src/lean/Lean/Elab/Tactic.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/Basic.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/OfRpcMethod.lean" ]	[ { "full_name": "IncidenceGeometry", "code": "class IncidenceGeometry where\n Point : Type u₁\n Line : Type u₂\n Circle : Type u₃\n\n between : Point → Point → Point → Prop onLine : Point → Line → Prop\n onCircle : Point → Circle → Prop\n inCircle : Point → Circle → Prop\n centerCircle : Point → Circle → Prop\n circlesInter : Circle → Circle → Prop\n\n ne_23_of_between : ∀ {a b c : Point}, between a b c → b ≠ c\n line_unique_of_pts : ∀ {a b : Point}, ∀ {L M : Line},\n a ≠ b → onLine a L → onLine b L → onLine a M → onLine b M → L = M\n onLine_2_of_between : ∀ {a b c : Point}, ∀ {L : Line},\n between a b c → onLine a L → onLine c L → onLine b L\n line_of_pts : ∀ a b, ∃ L, onLine a L ∧ onLine b L\n circle_of_ne : ∀ a b, a ≠ b → ∃ C, centerCircle a C ∧ onCircle b C\n circlesInter_of_onCircle_inCircle :\n ∀ {a b α β}, onCircle b α → onCircle a β → inCircle a α →\n inCircle b β → circlesInter α β\n pts_of_circlesInter : ∀ {α β}, circlesInter α β →\n ∃ a b, a ≠ b ∧ onCircle a α ∧ onCircle a β ∧ onCircle b α ∧ onCircle b β\n inCircle_of_centerCircle : ∀ {a α}, centerCircle a α → inCircle a α", "start": [ 25, 1 ], "end": [ 49, 70 ], "kind": "commanddeclaration" }, { "full_name": "isBetweenPred?", "code": "def isBetweenPred? (e : Expr) : Option (Expr × Expr × Expr) := do\n let some (_, a, b, c) := e.app4? ``between \| none\n return (a, b, c)", "start": [ 55, 1 ], "end": [ 58, 19 ], "kind": "commanddeclaration" }, { "full_name": "isOnLinePred?", "code": "def isOnLinePred? (e : Expr) : Option (Expr × Expr) := do\n let some (_, a, L) := e.app3? ``onLine \| none\n return (a, L)", "start": [ 60, 1 ], "end": [ 63, 16 ], "kind": "commanddeclaration" }, { "full_name": "isOnCirclePred?", "code": "def isOnCirclePred? (e : Expr) : Option (Expr × Expr) := do\n let some (_, a, C) := e.app3? ``onCircle \| none\n return (a, C)", "start": [ 65, 1 ], "end": [ 68, 16 ], "kind": "commanddeclaration" }, { "full_name": "isInCirclePred?", "code": "def isInCirclePred? (e : Expr) : Option (Expr × Expr) := do\n let some (_, a, C) := e.app3? ``inCircle \| none\n return (a, C)", "start": [ 70, 1 ], "end": [ 73, 16 ], "kind": "commanddeclaration" }, { "full_name": "isCenterCirclePred?", "code": "def isCenterCirclePred? (e : Expr) : Option (Expr × Expr) := do\n let some (_, a, C) := e.app3? ``centerCircle \| none\n return (a, C)", "start": [ 75, 1 ], "end": [ 78, 16 ], "kind": "commanddeclaration" }, { "full_name": "isCirclesInterPred?", "code": "def isCirclesInterPred? (e : Expr) : Option (Expr × Expr) := do\n let some (_, a, C) := e.app3? ``circlesInter \| none\n return (a, C)", "start": [ 80, 1 ], "end": [ 83, 16 ], "kind": "commanddeclaration" }, { "full_name": "isPoint?", "code": "def isPoint? (e : Expr) : Bool :=\n e.isAppOf ``Point", "start": [ 85, 1 ], "end": [ 86, 20 ], "kind": "commanddeclaration" }, { "full_name": "isLine?", "code": "def isLine? (e : Expr) : Bool :=\n e.isAppOf ``Line", "start": [ 88, 1 ], "end": [ 89, 19 ], "kind": "commanddeclaration" }, { "full_name": "addHypotheses", "code": "def addHypotheses (hyps : Array LocalDecl) : DiagramBuilderM Unit := do\n for h in hyps do\n let tp ← instantiateMVars h.type\n if isPoint? tp then\n discard $ addExpr \"Point\" h.toExpr\n if isLine? tp then\n discard $ addExpr \"Line\" h.toExpr\n if let some (a, b, c) := isBetweenPred? tp then\n let sa ← addExpr \"Point\" a\n let sb ← addExpr \"Point\" b\n let sc ← addExpr \"Point\" c\n addInstruction s!\"Between({sa}, {sb}, {sc})\"\n if let some (a, L) := isOnLinePred? tp then\n let sa ← addExpr \"Point\" a\n let sL ← addExpr \"Line\" L\n addInstruction s!\"OnLine({sa}, {sL})\"\n if let some (a, C) := isOnCirclePred? tp then\n let sa ← addExpr \"Point\" a\n let sC ← addExpr \"Circle\" C\n addInstruction s!\"OnCircle({sa}, {sC})\"\n if let some (a, C) := isInCirclePred? tp then\n let sa ← addExpr \"Point\" a\n let sC ← addExpr \"Circle\" C\n addInstruction s!\"InCircle({sa}, {sC})\"\n if let some (a, C) := isCenterCirclePred? tp then\n let sa ← addExpr \"Point\" a\n let sC ← addExpr \"Circle\" C\n addInstruction s!\"CenterCircle({sa}, {sC})\"\n if let some (C, D) := isCirclesInterPred? tp then\n let sC ← addExpr \"Circle\" C\n let sD ← addExpr \"Circle\" D\n addInstruction s!\"CirclesInter({sC}, {sD})\"", "start": [ 94, 1 ], "end": [ 125, 50 ], "kind": "commanddeclaration" }, { "full_name": "EuclideanDisplay.dsl", "code": "def EuclideanDisplay.dsl :=\n include_str \"..\"/\"..\"/\"widget\"/\"penrose\"/\"euclidean.dsl\"", "start": [ 129, 1 ], "end": [ 130, 59 ], "kind": "commanddeclaration" }, { "full_name": "EuclideanDisplay.sty", "code": "def EuclideanDisplay.sty :=\n include_str \"..\"/\"..\"/\"widget\"/\"penrose\"/\"euclidean.sty\"", "start": [ 132, 1 ], "end": [ 133, 59 ], "kind": "commanddeclaration" }, { "full_name": "EuclideanDisplay.rpc", "code": "@[server_rpc_method]\ndef EuclideanDisplay.rpc (props : PanelWidgetProps) : RequestM (RequestTask Html) :=\n RequestM.asTask do\n let inner : Html ← (do\n if props.goals.isEmpty then\n return <span>No goals.</span>\n let some g := props.goals[0]? \| unreachable!\n\n g.ctx.val.runMetaM {} do\n let md ← g.mvarId.getDecl\n let lctx := md.lctx \|>.sanitizeNames.run' {options := (← getOptions)}\n Meta.withLCtx lctx md.localInstances do\n let mut hiddenLocs : HashSet FVarId := mkHashSet props.selectedLocations.size\n for l in props.selectedLocations do\n match l with\n \| ⟨mv, .hyp fv⟩ \| ⟨mv, .hypType fv _⟩ =>\n if mv == g.mvarId then\n hiddenLocs := hiddenLocs.insert fv\n \| _ => continue\n let locs := (← getLCtx).decls.toArray.filterMap (fun d? =>\n if let some d := d? then\n if !hiddenLocs.contains d.fvarId then some d else none\n else\n none)\n DiagramBuilderM.run do\n addHypotheses locs\n match ← DiagramBuilderM.buildDiagram dsl sty with\n \| some html => return html\n \| none => return <span>No Euclidean goal.</span>)\n\n return <details «open»={true}>\n <summary className=\"mv2 pointer\">Euclidean diagram</summary>\n <div className=\"ml1\">{inner}</div>\n </details>", "start": [ 136, 1 ], "end": [ 175, 17 ], "kind": "commanddeclaration" }, { "full_name": "EuclideanDisplay", "code": "@[widget_module]\ndef EuclideanDisplay : Component PanelWidgetProps :=\n mk_rpc_widget% EuclideanDisplay.rpc", "start": [ 177, 1 ], "end": [ 179, 38 ], "kind": "commanddeclaration" }, { "full_name": "constructLines", "code": "def constructLines (hyps : Array LocalDecl) (meta : Server.DocumentMeta) (cursorPos : Lsp.Position)\n : DiagramBuilderM Unit := do\n let mut points : Array LocalDecl := {}\n let mut circleInters : Array (LocalDecl × LocalDecl × LocalDecl) := {}\n for h in hyps do\n let tp ← instantiateMVars h.type\n if isPoint? tp then\n points := points.push h\n if let some (.fvar C, .fvar D) := isCirclesInterPred? tp then\n circleInters := circleInters.push (h, ← C.getDecl, ← D.getDecl)\n\n let addConstruction (nm tp ctr : String) : DiagramBuilderM Unit := do\n addEmbed nm tp (\n <span>\n <b>{.text nm}</b> ({\n .ofComponent MakeEditLink\n (MakeEditLinkProps.ofReplaceRange meta ⟨cursorPos, cursorPos⟩ ctr)\n #[.text \"insert\"]\n })\n </span>)\n addInstruction s!\"Emphasize({nm})\"\n\n for hi : i in [0:points.size] do\n let p := points[i]\n let sp ← addExpr \"Point\" p.toExpr\n for hj : j in [i+1:points.size] do\n let q := points[j]\n let sq ← addExpr \"Point\" q.toExpr\n\n let nm := s!\"{sp}{sq}\"\n addConstruction nm \"Line\" s!\"let ⟨{nm}, _, _⟩ := line_of_pts {sp} {sq}\"\n addInstruction s!\"OnLine({sp}, {nm})\"\n addInstruction s!\"OnLine({sq}, {nm})\"\n\n let nm := s!\"C{sp}{sq}\"\n addConstruction nm \"Circle\" s!\"let ⟨{nm}, _, _⟩ := circle_of_ne {sp} {sq} (by assumption)\"\n addInstruction s!\"CenterCircle({sp}, {nm})\"\n addInstruction s!\"OnCircle({sq}, {nm})\"\n\n let nm := s!\"C{sq}{sp}\"\n addConstruction nm \"Circle\" s!\"let ⟨{nm}, _, _⟩ := circle_of_ne {sq} {sp} (by assumption)\"\n addInstruction s!\"CenterCircle({sq}, {nm})\"\n addInstruction s!\"OnCircle({sp}, {nm})\"\n\n for hi : i in [0:circleInters.size] do\n let (h, C, D) := circleInters[i]\n let sC ← addExpr \"Circle\" C.toExpr\n let sD ← addExpr \"Circle\" D.toExpr\n let nm := s!\"{sC}{sD}\"\n let nm' := s!\"{sD}{sC}\"\n addConstruction nm \"Point\" s!\"let ⟨{nm}, {nm'}, _, _, _, _, _⟩ := pts_of_circlesInter {h.userName}\"\n addEmbed nm' \"Point\" <b>{.text nm'}</b>\n addInstruction s!\"OnCircle({nm'}, {sC})\"\n addInstruction s!\"OnCircle({nm}, {sD})\"\n addInstruction s!\"OnCircle({nm}, {sC})\"\n addInstruction s!\"OnCircle({nm'}, {sD})\"", "start": [ 197, 1 ], "end": [ 261, 45 ], "kind": "commanddeclaration" }, { "full_name": "EuclideanConstructions.rpc", "code": "@[server_rpc_method]\ndef EuclideanConstructions.rpc (props : PanelWidgetProps) : RequestM (RequestTask Html) :=\n RequestM.asTask do\n let doc ← RequestM.readDoc\n let inner : Html ← (do\n if props.goals.isEmpty then\n return <span>No goals.</span>\n let some g := props.goals[0]? \| unreachable!\n\n g.ctx.val.runMetaM {} do\n let md ← g.mvarId.getDecl\n let lctx := md.lctx \|>.sanitizeNames.run' {options := (← getOptions)}\n Meta.withLCtx lctx md.localInstances do\n\n let allHyps := (← getLCtx).decls.toArray.filterMap id\n\n let selectedHyps ← props.selectedLocations.filterMapM fun\n \| ⟨mv, .hyp fv⟩ \| ⟨mv, .hypType fv _⟩ =>\n if mv == g.mvarId then return some (← fv.getDecl) else return none\n \| _ =>\n return none\n\n DiagramBuilderM.run do\n addHypotheses allHyps\n constructLines selectedHyps doc.meta props.pos\n match ← DiagramBuilderM.buildDiagram EuclideanDisplay.dsl EuclideanDisplay.sty 1500 with\n \| some html => return html\n \| none => return <span>No Euclidean goal.</span>)\n\n return <details «open»={true}>\n <summary className=\"mv2 pointer\">Euclidean constructions</summary>\n <div className=\"ml1\">{inner}</div>\n </details>", "start": [ 264, 1 ], "end": [ 302, 17 ], "kind": "commanddeclaration" }, { "full_name": "EuclideanConstructions", "code": "@[widget_module]\ndef EuclideanConstructions : Component PanelWidgetProps :=\n mk_rpc_widget% EuclideanConstructions.rpc", "start": [ 304, 1 ], "end": [ 306, 44 ], "kind": "commanddeclaration" }, { "full_name": "test_sorry", "code": "axiom test_sorry {α} : α", "start": [ 308, 1 ], "end": [ 308, 25 ], "kind": "commanddeclaration" } ]
.lake/packages/proofwidgets/ProofWidgets/Demos/Rubiks.lean	[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean" ]	[ { "full_name": "RubiksProps", "code": "structure RubiksProps where\n seq : Array String := #[]\n deriving ToJson, FromJson, Inhabited", "start": [ 6, 1 ], "end": [ 8, 39 ], "kind": "commanddeclaration" }, { "full_name": "Rubiks", "code": "@[widget_module]\ndef Rubiks : Component RubiksProps where\n javascript := include_str \"..\" / \"..\" / \".lake\" / \"build\" / \"js\" / \"rubiks.js\"", "start": [ 10, 1 ], "end": [ 12, 81 ], "kind": "commanddeclaration" }, { "full_name": "eg", "code": "def eg := #[\"L\", \"L\", \"D⁻¹\", \"U⁻¹\", \"L\", \"D\", \"D\", \"L\", \"U⁻¹\", \"R\", \"D\", \"F\", \"F\", \"D\"]", "start": [ 14, 1 ], "end": [ 14, 88 ], "kind": "commanddeclaration" } ]
.lake/packages/proofwidgets/ProofWidgets/Demos/Macro.lean	[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean" ]	[ { "full_name": "Lean.SourceInfo.mkCanonical", "code": "def Lean.SourceInfo.mkCanonical : SourceInfo → SourceInfo\n \| .synthetic s e _ => .synthetic s e true\n \| si => si", "start": [ 13, 1 ], "end": [ 15, 13 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Syntax.mkInfoCanonical", "code": "def Lean.Syntax.mkInfoCanonical : Syntax → Syntax\n \| .missing => .missing\n \| .node i k a => .node i.mkCanonical k a\n \| .atom i v => .atom i.mkCanonical v\n \| .ident i r v p => .ident i.mkCanonical r v p", "start": [ 17, 1 ], "end": [ 21, 49 ], "kind": "commanddeclaration" }, { "full_name": "Lean.TSyntax.mkInfoCanonical", "code": "def Lean.TSyntax.mkInfoCanonical : TSyntax k → TSyntax k :=\n (.mk ·.raw.mkInfoCanonical)", "start": [ 23, 1 ], "end": [ 24, 30 ], "kind": "commanddeclaration" } ]
.lake/packages/proofwidgets/ProofWidgets/Demos/Jsx.lean	[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean" ]	[ { "full_name": "htmlLetters", "code": "def htmlLetters : Array ProofWidgets.Html := #[\n <span style={json% {color: \"red\"}}>H</span>,\n <span style={json% {color: \"yellow\"}}>T</span>,\n <span style={json% {color: \"green\"}}>M</span>,\n <span style={json% {color: \"blue\"}}>L</span>\n ]", "start": [ 13, 1 ], "end": [ 18, 4 ], "kind": "commanddeclaration" }, { "full_name": "x", "code": "def x := <b>You can use {...htmlLetters} in Lean {.text s!\"{1 + 3}\"}! <hr/> </b>", "start": [ 21, 1 ], "end": [ 21, 81 ], "kind": "commanddeclaration" } ]
.lake/packages/proofwidgets/ProofWidgets/Demos/LazyComputation.lean	[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Basic.lean" ]	[ { "full_name": "MetaMStringCont", "code": "structure MetaMStringCont where\n ci : Elab.ContextInfo\n lctx : LocalContext\n k : MetaM String\n deriving TypeName", "start": [ 6, 1 ], "end": [ 12, 20 ], "kind": "commanddeclaration" }, { "full_name": "RunnerWidgetProps", "code": "structure RunnerWidgetProps where\n \n k : WithRpcRef MetaMStringCont\n deriving RpcEncodable", "start": [ 14, 1 ], "end": [ 18, 24 ], "kind": "commanddeclaration" }, { "full_name": "runMetaMStringCont", "code": "@[server_rpc_method]\ndef runMetaMStringCont : RunnerWidgetProps → RequestM (RequestTask String)\n \| {k := ⟨{ci, lctx, k}⟩} => RequestM.asTask do\n ci.runMetaM lctx k", "start": [ 20, 1 ], "end": [ 23, 23 ], "kind": "commanddeclaration" }, { "full_name": "runnerWidget", "code": "@[widget_module]\ndef runnerWidget : Component RunnerWidgetProps where\n javascript := \"\n import { RpcContext, mapRpcError } from '@leanprover/infoview'\n import * as React from 'react';\n const e = React.createElement;\n\n export default function(props) {\n const [contents, setContents] = React.useState('Run!')\n const rs = React.useContext(RpcContext)\n return e('button', { onClick: () => {\n setContents('Running..')\n rs.call('runMetaMStringCont', props)\n .then(setContents)\n .catch(e => { setContents(mapRpcError(e).message) })\n }}, contents)\n }\n \"", "start": [ 25, 1 ], "end": [ 42, 4 ], "kind": "commanddeclaration" }, { "full_name": "makeRunner", "code": "@[tactic makeRunnerTac] def makeRunner : Tactic\n \| `(tactic\| make_runner%$tk) => do\n let x : MetaM String := do\n return \"Hello, world!\"\n let props : RunnerWidgetProps := {\n k := ⟨{\n ci := { ← CommandContextInfo.save with }\n lctx := (← getLCtx)\n k := x\n }⟩}\n Widget.savePanelWidgetInfo runnerWidget.javascriptHash (rpcEncode props) tk\n \| _ => throwUnsupportedSyntax", "start": [ 46, 1 ], "end": [ 59, 32 ], "kind": "commanddeclaration" } ]
.lake/packages/proofwidgets/ProofWidgets/Demos/Dynkin.lean	[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean" ]	[ { "full_name": "List.product", "code": "def List.product : List α → List β → List (α × β)\n \| [], _ => []\n \| a::as, bs => bs.map ((a, ·)) ++ as.product bs", "start": [ 6, 1 ], "end": [ 8, 50 ], "kind": "commanddeclaration" }, { "full_name": "Matrix", "code": "def Matrix (n m α : Type) := n → m → α", "start": [ 10, 1 ], "end": [ 10, 39 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.nat_index", "code": "def nat_index (i j : Nat) : Int :=\n if h : i < n ∧ j < n then A ⟨i, h.1⟩ ⟨j, h.2⟩ else 999", "start": [ 19, 1 ], "end": [ 20, 57 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_node_pos_E", "code": "def get_node_pos_E : Nat → Nat × Nat\n \| 0 => ⟨0, 0⟩\n \| 1 => ⟨2, 1⟩\n \| (i+1) => ⟨i, 0⟩", "start": [ 22, 1 ], "end": [ 26, 20 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_node_pos", "code": "def get_node_pos (n : Nat) : Nat → Nat × Nat := if n < 6 then ((·, 0)) else get_node_pos_E", "start": [ 28, 1 ], "end": [ 29, 91 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_node_cx", "code": "def get_node_cx (n i : Nat) : Int := 20 + (get_node_pos n i).1 * 40", "start": [ 31, 1 ], "end": [ 31, 68 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_node_cy", "code": "def get_node_cy (n i : Nat) : Int := 20 + (get_node_pos n i).2 * 40", "start": [ 33, 1 ], "end": [ 33, 68 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_node_html", "code": "def get_node_html (n i : Nat) : Html :=\n <circle\n cx={toString <\| get_node_cx n i}\n cy={toString <\| get_node_cy n i}\n r=\"10\"\n fill=\"white\"\n stroke=\"black\" />", "start": [ 35, 1 ], "end": [ 41, 22 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_edge_html", "code": "def get_edge_html : Nat × Nat → List Html\n \| (i, j) => if A.nat_index i j = 0 then [] else\n [<line\n x1={toString <\| get_node_cx n i}\n y1={toString <\| get_node_cy n i}\n x2={toString <\| get_node_cx n j}\n y2={toString <\| get_node_cy n j}\n fill=\"black\"\n stroke=\"black\" />]", "start": [ 43, 1 ], "end": [ 56, 24 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_nodes_html", "code": "def get_nodes_html (n : Nat) : List Html :=\n (List.range n).map (get_node_html n)", "start": [ 58, 1 ], "end": [ 59, 39 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_edges_html", "code": "def get_edges_html : List Html := Id.run do\n let mut out := []\n for j in [:n] do\n for i in [:j] do\n out := A.get_edge_html (i, j) ++ out\n return out", "start": [ 61, 1 ], "end": [ 66, 13 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.toHtml", "code": "def toHtml (M : Matrix (Fin n) (Fin n) Int) : Html :=\n <div style={json% { height: \"100px\", width: \"300px\", background: \"grey\" }}>\n {Html.element \"svg\" #[] (M.get_edges_html ++ Matrix.get_nodes_html n).toArray}\n </div>", "start": [ 68, 1 ], "end": [ 71, 9 ], "kind": "commanddeclaration" }, { "full_name": "cartanMatrix.E₈", "code": "def cartanMatrix.E₈ : Matrix (Fin 8) (Fin 8) Int :=\n fun i j =>\n [[ 2, 0, -1, 0, 0, 0, 0, 0],\n [ 0, 2, 0, -1, 0, 0, 0, 0],\n [-1, 0, 2, -1, 0, 0, 0, 0],\n [ 0, -1, -1, 2, -1, 0, 0, 0],\n [ 0, 0, 0, -1, 2, -1, 0, 0],\n [ 0, 0, 0, 0, -1, 2, -1, 0],\n [ 0, 0, 0, 0, 0, -1, 2, -1],\n [ 0, 0, 0, 0, 0, 0, -1, 2]].get! i \|>.get! j", "start": [ 75, 1 ], "end": [ 84, 56 ], "kind": "commanddeclaration" } ]
.lake/packages/proofwidgets/ProofWidgets/Demos/ExprPresentation.lean	[ ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/SelectionPanel.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/GoalTypePanel.lean" ]	[ { "full_name": "presenter", "code": "@[expr_presenter]\ndef presenter : ExprPresenter where\n userName := \"With octopodes\"\n layoutKind := .inline\n present e :=\n return <span>\n {.text \"🐙 \"}<InteractiveCode fmt={← Lean.Widget.ppExprTagged e} />{.text \" 🐙\"}\n </span>", "start": [ 6, 1 ], "end": [ 13, 14 ], "kind": "commanddeclaration" } ]
.lake/packages/proofwidgets/ProofWidgets/Demos/RbTree.lean	[ ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/SelectionPanel.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Presentation/Expr.lean" ]	[ { "full_name": "RBColour", "code": "inductive RBColour where\n \| red \| black", "start": [ 7, 1 ], "end": [ 8, 16 ], "kind": "commanddeclaration" }, { "full_name": "RBTree", "code": "inductive RBTree (α : Type u) where\n \| empty : RBTree α\n \| node (color : RBColour) (l : RBTree α) (a : α) (r : RBTree α) : RBTree α", "start": [ 10, 1 ], "end": [ 12, 77 ], "kind": "commanddeclaration" }, { "full_name": "RBTree.contains", "code": "def contains [Ord α] (a : α) : RBTree α → Bool\n \| empty => false\n \| node _ l b r => match compare a b with\n \| .lt => l.contains a\n \| .eq => true\n \| .gt => r.contains a", "start": [ 16, 1 ], "end": [ 21, 26 ], "kind": "commanddeclaration" }, { "full_name": "RBTree.balance", "code": "def balance : RBColour → RBTree α → α → RBTree α → RBTree α\n \| .black, (node .red (node .red a x b) y c), z, d\n \| .black, (node .red a x (node .red b y c)), z, d\n \| .black, a, x, (node .red (node .red b y c) z d)\n \| .black, a, x, (node .red b y (node .red c z d)) =>\n node .red (node .black a x b) y (node .black c z d)\n \| color, a, x, b => node color a x b", "start": [ 23, 1 ], "end": [ 29, 39 ], "kind": "commanddeclaration" }, { "full_name": "RBTree.insert", "code": "def insert [Ord α] (a : α) (s : RBTree α) : RBTree α :=\n makeBlack (ins s)\nwhere\n ins : RBTree α → RBTree α\n \| empty => node .red empty a empty\n \| node c l b r => match compare a b with\n \| .lt => balance c (ins l) b r\n \| .eq => node c l b r\n \| .gt => balance c l b (ins r)\n makeBlack : RBTree α → RBTree α\n \| empty => empty\n \| node _ l b r => node .black l b r", "start": [ 31, 1 ], "end": [ 42, 40 ], "kind": "commanddeclaration" }, { "full_name": "empty?", "code": "def empty? (e : Expr) : Bool :=\n e.app1? ``RBTree.empty matches some _", "start": [ 50, 1 ], "end": [ 51, 40 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Expr.app5?", "code": "@[inline] def Lean.Expr.app5? (e : Expr) (fName : Name) : Option (Expr × Expr × Expr × Expr × Expr) :=\n if e.isAppOfArity fName 5 then\n some (\n e.appFn!.appFn!.appFn!.appFn!.appArg!,\n e.appFn!.appFn!.appFn!.appArg!,\n e.appFn!.appFn!.appArg!,\n e.appFn!.appArg!,\n e.appArg!)\n else\n none", "start": [ 53, 1 ], "end": [ 62, 9 ], "kind": "commanddeclaration" }, { "full_name": "node?", "code": "def node? (e : Expr) : Option (Expr × Expr × Expr × Expr) := do\n let some (_, color, l, a, r) := e.app5? ``RBTree.node \| none\n return (color, l, a, r)", "start": [ 64, 1 ], "end": [ 66, 26 ], "kind": "commanddeclaration" }, { "full_name": "evalColourUnsafe", "code": "unsafe def evalColourUnsafe (e : Expr) : MetaM RBColour :=\n Lean.Meta.evalExpr' RBColour ``RBColour e", "start": [ 68, 1 ], "end": [ 69, 44 ], "kind": "commanddeclaration" }, { "full_name": "evalColour", "code": "@[implemented_by evalColourUnsafe]\nopaque evalColour (e : Expr) : MetaM RBColour", "start": [ 71, 1 ], "end": [ 72, 46 ], "kind": "commanddeclaration" }, { "full_name": "RBTreeVarsColour", "code": "inductive RBTreeVarsColour where\n \| red \| black \| blue\n deriving FromJson, ToJson", "start": [ 74, 1 ], "end": [ 77, 28 ], "kind": "commanddeclaration" }, { "full_name": "RBTreeVars", "code": "inductive RBTreeVars where\n \| empty : RBTreeVars\n \| var : CodeWithInfos → RBTreeVars\n \| node (color : RBTreeVarsColour) (l : RBTreeVars) (a : CodeWithInfos) (r : RBTreeVars) : RBTreeVars\n deriving Server.RpcEncodable", "start": [ 80, 1 ], "end": [ 89, 31 ], "kind": "commanddeclaration" }, { "full_name": "RBDisplayProps", "code": "structure RBDisplayProps where\n tree : RBTreeVars\n deriving Server.RpcEncodable", "start": [ 93, 1 ], "end": [ 95, 31 ], "kind": "commanddeclaration" }, { "full_name": "RBDisplay", "code": "@[widget_module]\ndef RBDisplay : Component RBDisplayProps where\n javascript := include_str \"..\" / \"..\" / \".lake\" / \"build\" / \"js\" / \"rbTree.js\"", "start": [ 99, 1 ], "end": [ 101, 81 ], "kind": "commanddeclaration" }, { "full_name": "drawTree?", "code": "partial def drawTree? (e : Expr) : MetaM (Option Html) := do\n if let some _ := node? e then\n return some <RBDisplay tree={← go e}/>\n else if empty? e then\n return some <RBDisplay tree={← go e}/>\n else\n return none\nwhere go (e : Expr) : MetaM RBTreeVars := do\n if let some (color, l, a, r) := node? e then\n let color ← try\n match ← evalColour color with\n \| .red => pure .red\n \| .black => pure .black\n catch _ => pure .blue\n return .node color (← go l) (← Widget.ppExprTagged a) (← go r)\n else if empty? e then\n return .empty\n else\n return .var (← Widget.ppExprTagged e)", "start": [ 104, 1 ], "end": [ 122, 42 ], "kind": "commanddeclaration" }, { "full_name": "RBTree.presenter", "code": "@[expr_presenter]\ndef RBTree.presenter : ExprPresenter where\n userName := \"Red-black tree\"\n present e := do\n let some t ← drawTree? e\n \| throwError \"not a tree :(\"\n return t", "start": [ 124, 1 ], "end": [ 130, 13 ], "kind": "commanddeclaration" } ]
.lake/packages/proofwidgets/ProofWidgets/Demos/Svg.lean	[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean", ".lake/packages/proofwidgets/ProofWidgets/Data/Svg.lean" ]	[ { "full_name": "frame", "code": "private def frame : Frame where\n xmin := -2\n ymin := -2\n xSize := 4\n width := 400\n height := 400", "start": [ 6, 1 ], "end": [ 11, 16 ], "kind": "commanddeclaration" }, { "full_name": "svg", "code": "private def svg : Svg frame :=\n { elements :=\n #[line (0.,0.) (1.,0.) \|>.setStroke (1.,0.,0.) (.px 2),\n line (1.,0.) (0.,1.) \|>.setStroke (0.,1.,0.) (.px 2),\n line (0.,1.) (0.,0.) \|>.setStroke (0.,0.,1.) (.px 2),\n circle (0.,0.) (.abs 0.1) \|>.setStroke (0.,0.,0.) (.px 2) \|>.setFill (0.,1.,1.) \|>.setId \"point1\",\n circle (1.,0.) (.abs 0.1) \|>.setStroke (0.,0.,0.) (.px 2) \|>.setFill (1.,0.,1.) \|>.setId \"point2\",\n circle (0.,1.) (.abs 0.1) \|>.setStroke (0.,0.,0.) (.px 2) \|>.setFill (1.,1.,0.) \|>.setId \"point3\"] }", "start": [ 13, 1 ], "end": [ 20, 109 ], "kind": "commanddeclaration" } ]
.lake/packages/lean4/src/lean/Lean/Compiler/IR/EmitLLVM.lean	[ ".lake/packages/lean4/src/lean/Lean/Compiler/ExportAttr.lean", ".lake/packages/lean4/src/lean/Lean/Runtime.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/EmitUtil.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/ResetReuse.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/Boxing.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/SimpCase.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/NameMangling.lean", ".lake/packages/lean4/src/lean/Lean/Data/HashMap.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/InitAttr.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/NormIds.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/CompilerM.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/LLVMBindings.lean" ]	[ { "full_name": "Lean.IR.leanMainFn", "code": "def leanMainFn := \"_lean_main\"", "start": [ 24, 1 ], "end": [ 24, 31 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.LLVM.size_tType", "code": "def size_tType (llvmctx : LLVM.Context) : BaseIO (LLVM.LLVMType llvmctx) :=\n LLVM.i64Type llvmctx", "start": [ 28, 1 ], "end": [ 29, 23 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.LLVM.unsignedType", "code": "def unsignedType (llvmctx : LLVM.Context) : BaseIO (LLVM.LLVMType llvmctx) :=\n LLVM.i32Type llvmctx", "start": [ 32, 1 ], "end": [ 33, 23 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.LLVM.getOrAddFunction", "code": "def getOrAddFunction (m : LLVM.Module ctx) (name : String) (type : LLVM.LLVMType ctx) : BaseIO (LLVM.Value ctx) := do\n match (← LLVM.getNamedFunction m name) with\n \| some fn => return fn\n \| none =>\n \n let fn ← LLVM.addFunction m name type\n let attr ← LLVM.createStringAttribute \"probe-stack\" \"inline-asm\"\n LLVM.addAttributeAtIndex fn LLVM.AttributeIndex.AttributeFunctionIndex attr\n return fn", "start": [ 36, 1 ], "end": [ 48, 14 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.LLVM.getOrAddGlobal", "code": "def getOrAddGlobal (m : LLVM.Module ctx) (name : String) (type : LLVM.LLVMType ctx) : BaseIO (LLVM.Value ctx) := do\n match (← LLVM.getNamedGlobal m name) with\n \| .some fn => return fn\n \| .none => LLVM.addGlobal m name type", "start": [ 50, 1 ], "end": [ 53, 40 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.Context", "code": "structure Context (llvmctx : LLVM.Context) where\n env : Environment\n modName : Name\n jpMap : JPParamsMap := {}\n mainFn : FunId := default\n mainParams : Array Param := #[]\n llvmmodule : LLVM.Module llvmctx", "start": [ 59, 1 ], "end": [ 65, 35 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.State", "code": "structure State (llvmctx : LLVM.Context) where\n var2val : HashMap VarId (LLVM.LLVMType llvmctx × LLVM.Value llvmctx)\n jp2bb : HashMap JoinPointId (LLVM.BasicBlock llvmctx)", "start": [ 67, 1 ], "end": [ 69, 58 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.Error", "code": "abbrev Error := String", "start": [ 71, 1 ], "end": [ 71, 23 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.M", "code": "abbrev M (llvmctx : LLVM.Context) :=\n StateRefT (State llvmctx) (ReaderT (Context llvmctx) (ExceptT Error IO))", "start": [ 73, 1 ], "end": [ 74, 75 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.addVartoState", "code": "def addVartoState (x : VarId) (v : LLVM.Value llvmctx) (ty : LLVM.LLVMType llvmctx) : M llvmctx Unit := do\n modify (fun s => { s with var2val := s.var2val.insert x (ty, v) })", "start": [ 79, 1 ], "end": [ 80, 69 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.addJpTostate", "code": "def addJpTostate (jp : JoinPointId) (bb : LLVM.BasicBlock llvmctx) : M llvmctx Unit :=\n modify (fun s => { s with jp2bb := s.jp2bb.insert jp bb })", "start": [ 82, 1 ], "end": [ 83, 61 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitJp", "code": "def emitJp (jp : JoinPointId) : M llvmctx (LLVM.BasicBlock llvmctx) := do\n let state ← get\n match state.jp2bb.find? jp with\n \| .some bb => return bb\n \| .none => throw s!\"unable to find join point {jp}\"", "start": [ 85, 1 ], "end": [ 89, 54 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getLLVMModule", "code": "def getLLVMModule : M llvmctx (LLVM.Module llvmctx) := Context.llvmmodule <$> read", "start": [ 91, 1 ], "end": [ 91, 83 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getEnv", "code": "def getEnv : M llvmctx Environment := Context.env <$> read", "start": [ 93, 1 ], "end": [ 93, 59 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getModName", "code": "def getModName : M llvmctx Name := Context.modName <$> read", "start": [ 95, 1 ], "end": [ 95, 61 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getDecl", "code": "def getDecl (n : Name) : M llvmctx Decl := do\n let env ← getEnv\n match findEnvDecl env n with\n \| some d => pure d\n \| none => throw s!\"unknown declaration {n}\"", "start": [ 97, 1 ], "end": [ 101, 48 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.constInt8", "code": "def constInt8 (n : Nat) : M llvmctx (LLVM.Value llvmctx) := do\n LLVM.constInt8 llvmctx (UInt64.ofNat n)", "start": [ 103, 1 ], "end": [ 104, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.constInt64", "code": "def constInt64 (n : Nat) : M llvmctx (LLVM.Value llvmctx) := do\n LLVM.constInt64 llvmctx (UInt64.ofNat n)", "start": [ 106, 1 ], "end": [ 107, 45 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.constIntSizeT", "code": "def constIntSizeT (n : Nat) : M llvmctx (LLVM.Value llvmctx) := do\n LLVM.constIntSizeT llvmctx (UInt64.ofNat n)", "start": [ 109, 1 ], "end": [ 110, 48 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.constIntUnsigned", "code": "def constIntUnsigned (n : Nat) : M llvmctx (LLVM.Value llvmctx) := do\n LLVM.constIntUnsigned llvmctx (UInt64.ofNat n)", "start": [ 112, 1 ], "end": [ 113, 51 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getOrCreateFunctionPrototype", "code": "def getOrCreateFunctionPrototype (mod : LLVM.Module llvmctx)\n (retty : LLVM.LLVMType llvmctx) (name : String) (args : Array (LLVM.LLVMType llvmctx)) : M llvmctx (LLVM.Value llvmctx) := do\n LLVM.getOrAddFunction mod name $ ← LLVM.functionType retty args (isVarArg := false)", "start": [ 115, 1 ], "end": [ 117, 86 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanBox", "code": "def callLeanBox (builder : LLVM.Builder llvmctx)\n (arg : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_box\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[ ← LLVM.size_tType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[arg] name", "start": [ 119, 1 ], "end": [ 126, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanMarkPersistentFn", "code": "def callLeanMarkPersistentFn (builder : LLVM.Builder llvmctx) (arg : LLVM.Value llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_mark_persistent\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[arg]", "start": [ 128, 1 ], "end": [ 134, 52 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.RefcountKind", "code": "inductive RefcountKind where\n \| inc \| dec", "start": [ 137, 1 ], "end": [ 138, 14 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanRefcountFn", "code": "def callLeanRefcountFn (builder : LLVM.Builder llvmctx)\n (kind : RefcountKind) (checkRef? : Bool) (arg : LLVM.Value llvmctx)\n (delta : Option (LLVM.Value llvmctx) := Option.none) : M llvmctx Unit := do\n let fnName := s!\"lean_{kind}{if checkRef? then \"\" else \"_ref\"}{if delta.isNone then \"\" else \"_n\"}\"\n let retty ← LLVM.voidType llvmctx\n let argtys ← if delta.isNone then pure #[← LLVM.voidPtrType llvmctx] else pure #[← LLVM.voidPtrType llvmctx, ← LLVM.size_tType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n match delta with\n \| .none => do\n let _ ← LLVM.buildCall2 builder fnty fn #[arg]\n \| .some n => do\n let _ ← LLVM.buildCall2 builder fnty fn #[arg, n]", "start": [ 145, 1 ], "end": [ 158, 54 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanDecRef", "code": "def callLeanDecRef (builder : LLVM.Builder llvmctx) (res : LLVM.Value llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_dec_ref\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.i8PtrType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[res]", "start": [ 163, 1 ], "end": [ 169, 50 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanUnsignedToNatFn", "code": "def callLeanUnsignedToNatFn (builder : LLVM.Builder llvmctx)\n (n : Nat) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let mod ← getLLVMModule\n let argtys := #[← LLVM.i32Type llvmctx]\n let retty ← LLVM.voidPtrType llvmctx\n let f ← getOrCreateFunctionPrototype mod retty \"lean_unsigned_to_nat\" argtys\n let fnty ← LLVM.functionType retty argtys\n let nv ← constIntUnsigned n\n LLVM.buildCall2 builder fnty f #[nv] name", "start": [ 171, 1 ], "end": [ 179, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanMkStringUncheckedFn", "code": "def callLeanMkStringUncheckedFn (builder : LLVM.Builder llvmctx)\n (strPtr nBytes nChars : LLVM.Value llvmctx) (name : String) : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_mk_string_unchecked\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[← LLVM.voidPtrType llvmctx, ← LLVM.size_tType llvmctx, ← LLVM.size_tType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[strPtr, nBytes, nChars] name", "start": [ 181, 1 ], "end": [ 188, 65 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanMkString", "code": "def callLeanMkString (builder : LLVM.Builder llvmctx)\n (strPtr : LLVM.Value llvmctx) (name : String) : M llvmctx (LLVM.Value llvmctx) := do\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty \"lean_mk_string\" argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[strPtr] name", "start": [ 190, 1 ], "end": [ 196, 49 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanCStrToNatFn", "code": "def callLeanCStrToNatFn (builder : LLVM.Builder llvmctx)\n (n : Nat) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_cstr_to_nat\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let s ← LLVM.buildGlobalString builder (value := toString n)\n LLVM.buildCall2 builder fnty fn #[s] name", "start": [ 198, 1 ], "end": [ 206, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOMkWorld", "code": "def callLeanIOMkWorld (builder : LLVM.Builder llvmctx) : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_io_mk_world\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[] \"mk_io_out\"", "start": [ 208, 1 ], "end": [ 214, 50 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOResultIsError", "code": "def callLeanIOResultIsError (builder : LLVM.Builder llvmctx)\n (arg : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_io_result_is_error\"\n let retty ← LLVM.i1Type llvmctx\n let argtys := #[← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[arg] name", "start": [ 216, 1 ], "end": [ 223, 46 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanAllocCtor", "code": "def callLeanAllocCtor (builder : LLVM.Builder llvmctx)\n (tag num_objs scalar_sz : Nat) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_alloc_ctor\"\n let retty ← LLVM.voidPtrType llvmctx\n let i32 ← LLVM.i32Type llvmctx\n let argtys := #[i32, i32, i32]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n\n let tag ← constIntUnsigned tag\n let num_objs ← constIntUnsigned num_objs\n let scalar_sz ← constIntUnsigned scalar_sz\n LLVM.buildCall2 builder fnty fn #[tag, num_objs, scalar_sz] name", "start": [ 225, 1 ], "end": [ 237, 67 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanCtorSet", "code": "def callLeanCtorSet (builder : LLVM.Builder llvmctx)\n (o i v : LLVM.Value llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_ctor_set\"\n let retty ← LLVM.voidType llvmctx\n let voidptr ← LLVM.voidPtrType llvmctx\n let unsigned ← LLVM.unsignedType llvmctx\n let argtys := #[voidptr, unsigned, voidptr]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n _ <- LLVM.buildCall2 builder fnty fn #[o, i, v]", "start": [ 239, 1 ], "end": [ 248, 51 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOResultMKOk", "code": "def callLeanIOResultMKOk (builder : LLVM.Builder llvmctx)\n (v : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_io_result_mk_ok\"\n let voidptr ← LLVM.voidPtrType llvmctx\n let retty := voidptr\n let argtys := #[voidptr]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[v] name", "start": [ 250, 1 ], "end": [ 258, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanAllocClosureFn", "code": "def callLeanAllocClosureFn (builder : LLVM.Builder llvmctx)\n (f arity nys : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_alloc_closure\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx, ← LLVM.unsignedType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[f, arity, nys] retName", "start": [ 260, 1 ], "end": [ 267, 60 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanClosureSetFn", "code": "def callLeanClosureSetFn (builder : LLVM.Builder llvmctx)\n (closure ix arg : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx Unit := do\n let fnName := \"lean_closure_set\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx, ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[closure, ix, arg] retName", "start": [ 269, 1 ], "end": [ 276, 71 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanObjTag", "code": "def callLeanObjTag (builder : LLVM.Builder llvmctx)\n (closure : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_obj_tag\"\n let retty ← LLVM.i32Type llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let out ← LLVM.buildCall2 builder fnty fn #[closure] retName\n LLVM.buildSextOrTrunc builder out (← LLVM.i64Type llvmctx)", "start": [ 278, 1 ], "end": [ 286, 61 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOResultGetValue", "code": "def callLeanIOResultGetValue (builder : LLVM.Builder llvmctx)\n (v : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_io_result_get_value\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[v] name", "start": [ 288, 1 ], "end": [ 295, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanCtorRelease", "code": "def callLeanCtorRelease (builder : LLVM.Builder llvmctx)\n (closure i : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx Unit := do\n let fnName := \"lean_ctor_release\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[closure, i] retName", "start": [ 297, 1 ], "end": [ 304, 65 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanCtorSetTag", "code": "def callLeanCtorSetTag (builder : LLVM.Builder llvmctx)\n (closure i : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx Unit := do\n let fnName := \"lean_ctor_set_tag\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.i8Type llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[closure, i] retName", "start": [ 306, 1 ], "end": [ 313, 65 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.toLLVMType", "code": "def toLLVMType (t : IRType) : M llvmctx (LLVM.LLVMType llvmctx) := do\n match t with\n \| IRType.float => LLVM.doubleTypeInContext llvmctx\n \| IRType.uint8 => LLVM.intTypeInContext llvmctx 8\n \| IRType.uint16 => LLVM.intTypeInContext llvmctx 16\n \| IRType.uint32 => LLVM.intTypeInContext llvmctx 32\n \| IRType.uint64 => LLVM.intTypeInContext llvmctx 64\n \| IRType.usize => LLVM.size_tType llvmctx\n \| IRType.object => do LLVM.pointerType (← LLVM.i8Type llvmctx)\n \| IRType.tobject => do LLVM.pointerType (← LLVM.i8Type llvmctx)\n \| IRType.irrelevant => do LLVM.pointerType (← LLVM.i8Type llvmctx)\n \| IRType.struct _ _ => panic! \"not implemented yet\"\n \| IRType.union _ _ => panic! \"not implemented yet\"", "start": [ 315, 1 ], "end": [ 328, 54 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.throwInvalidExportName", "code": "def throwInvalidExportName {α : Type} (n : Name) : M llvmctx α := do\n throw s!\"invalid export name {n.toString}\"", "start": [ 330, 1 ], "end": [ 331, 45 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.toCName", "code": "def toCName (n : Name) : M llvmctx String := do\n match getExportNameFor? (← getEnv) n with\n \| some (.str .anonymous s) => pure s\n \| some _ => throwInvalidExportName n\n \| none => if n == `main then pure leanMainFn else pure n.mangle", "start": [ 333, 1 ], "end": [ 337, 86 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.toCInitName", "code": "def toCInitName (n : Name) : M llvmctx String := do\n match getExportNameFor? (← getEnv) n with\n \| some (.str .anonymous s) => return \"_init_\" ++ s\n \| some _ => throwInvalidExportName n\n \| none => pure (\"_init_\" ++ n.mangle)", "start": [ 339, 1 ], "end": [ 343, 60 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.ShouldForwardControlFlow", "code": "inductive ShouldForwardControlFlow where\n\| yes \| no", "start": [ 345, 1 ], "end": [ 352, 11 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.builderGetInsertionFn", "code": "def builderGetInsertionFn (builder : LLVM.Builder llvmctx) : M llvmctx (LLVM.Value llvmctx) := do\n let builderBB ← LLVM.getInsertBlock builder\n LLVM.getBasicBlockParent builderBB", "start": [ 355, 1 ], "end": [ 357, 37 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.builderAppendBasicBlock", "code": "def builderAppendBasicBlock (builder : LLVM.Builder llvmctx) (name : String) : M llvmctx (LLVM.BasicBlock llvmctx) := do\n let fn ← builderGetInsertionFn builder\n LLVM.appendBasicBlockInContext llvmctx fn name", "start": [ 359, 1 ], "end": [ 361, 49 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.buildPrologueAlloca", "code": "def buildPrologueAlloca (builder : LLVM.Builder llvmctx) (ty : LLVM.LLVMType llvmctx) (name : @&String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let origBB ← LLVM.getInsertBlock builder\n\n let fn ← builderGetInsertionFn builder\n if (← LLVM.countBasicBlocks fn) == 0 then\n throw \"Attempt to obtain first BB of function without BBs\"\n\n let entryBB ← LLVM.getEntryBasicBlock fn\n match ← LLVM.getFirstInstruction entryBB with\n \| some instr => LLVM.positionBuilderBefore builder instr\n \| none => LLVM.positionBuilderAtEnd builder entryBB\n\n let alloca ← LLVM.buildAlloca builder ty name\n LLVM.positionBuilderAtEnd builder origBB\n return alloca", "start": [ 363, 1 ], "end": [ 385, 16 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.buildWhile_", "code": "def buildWhile_ (builder : LLVM.Builder llvmctx) (name : String)\n (condcodegen : LLVM.Builder llvmctx → M llvmctx (LLVM.Value llvmctx))\n (bodycodegen : LLVM.Builder llvmctx → M llvmctx Unit) : M llvmctx Unit := do\n let fn ← builderGetInsertionFn builder\n\n let nameHeader := name ++ \"header\"\n let nameBody := name ++ \"body\"\n let nameMerge := name ++ \"merge\"\n\n let headerbb ← LLVM.appendBasicBlockInContext llvmctx fn nameHeader\n let _ ← LLVM.buildBr builder headerbb\n\n let bodybb ← LLVM.appendBasicBlockInContext llvmctx fn nameBody\n let mergebb ← LLVM.appendBasicBlockInContext llvmctx fn nameMerge\n\n LLVM.positionBuilderAtEnd builder headerbb\n let cond ← condcodegen builder\n let _ ← LLVM.buildCondBr builder cond bodybb mergebb\n\n LLVM.positionBuilderAtEnd builder bodybb\n bodycodegen builder\n let _ ← LLVM.buildBr builder headerbb\n\n LLVM.positionBuilderAtEnd builder mergebb", "start": [ 388, 1 ], "end": [ 415, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.buildIfThen_", "code": "def buildIfThen_ (builder : LLVM.Builder llvmctx) (name : String) (brval : LLVM.Value llvmctx)\n (thencodegen : LLVM.Builder llvmctx → M llvmctx ShouldForwardControlFlow) : M llvmctx Unit := do\n let fn ← builderGetInsertionFn builder\n\n let nameThen := name ++ \"Then\"\n let nameElse := name ++ \"Else\"\n let nameMerge := name ++ \"Merge\"\n\n let thenbb ← LLVM.appendBasicBlockInContext llvmctx fn nameThen\n let elsebb ← LLVM.appendBasicBlockInContext llvmctx fn nameElse\n let mergebb ← LLVM.appendBasicBlockInContext llvmctx fn nameMerge\n let _ ← LLVM.buildCondBr builder brval thenbb elsebb\n LLVM.positionBuilderAtEnd builder thenbb\n let fwd? ← thencodegen builder\n match fwd? with\n \| .yes => let _ ← LLVM.buildBr builder mergebb\n \| .no => pure ()\n LLVM.positionBuilderAtEnd builder elsebb\n let _ ← LLVM.buildBr builder mergebb\n LLVM.positionBuilderAtEnd builder mergebb", "start": [ 419, 1 ], "end": [ 441, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.buildIfThenElse_", "code": "def buildIfThenElse_ (builder : LLVM.Builder llvmctx) (name : String) (brval : LLVM.Value llvmctx)\n (thencodegen : LLVM.Builder llvmctx → M llvmctx ShouldForwardControlFlow)\n (elsecodegen : LLVM.Builder llvmctx → M llvmctx ShouldForwardControlFlow) : M llvmctx Unit := do\n let fn ← LLVM.getBasicBlockParent (← LLVM.getInsertBlock builder)\n let thenbb ← LLVM.appendBasicBlockInContext llvmctx fn (name ++ \"Then\")\n let elsebb ← LLVM.appendBasicBlockInContext llvmctx fn (name ++ \"Else\")\n let mergebb ← LLVM.appendBasicBlockInContext llvmctx fn (name ++ \"Merge\")\n let _ ← LLVM.buildCondBr builder brval thenbb elsebb\n LLVM.positionBuilderAtEnd builder thenbb\n let fwd? ← thencodegen builder\n match fwd? with\n \| .yes => let _ ← LLVM.buildBr builder mergebb\n \| .no => pure ()\n LLVM.positionBuilderAtEnd builder elsebb\n let fwd? ← elsecodegen builder\n match fwd? with\n \| .yes => let _ ← LLVM.buildBr builder mergebb\n \| .no => pure ()\n LLVM.positionBuilderAtEnd builder mergebb", "start": [ 443, 1 ], "end": [ 464, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.buildLeanBoolTrue?", "code": "def buildLeanBoolTrue? (builder : LLVM.Builder llvmctx)\n (b : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n LLVM.buildICmp builder LLVM.IntPredicate.NE b (← constInt8 0) name", "start": [ 467, 1 ], "end": [ 469, 69 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFnDeclAux", "code": "def emitFnDeclAux (mod : LLVM.Module llvmctx)\n (decl : Decl) (cppBaseName : String) (isExternal : Bool) : M llvmctx (LLVM.Value llvmctx) := do\n let ps := decl.params\n let env ← getEnv\n let global ←\n if ps.isEmpty then\n let retty ← (toLLVMType decl.resultType)\n let global ← LLVM.getOrAddGlobal mod cppBaseName retty\n if !isExternal then\n LLVM.setInitializer global (← LLVM.getUndef retty)\n pure global\n else\n let retty ← (toLLVMType decl.resultType)\n let mut argtys := #[]\n for p in ps do\n if !(isExternC env decl.name) \|\| !p.ty.isIrrelevant then\n argtys := argtys.push (← toLLVMType p.ty)\n if argtys.size > closureMaxArgs && isBoxedName decl.name then\n argtys := #[← LLVM.pointerType (← LLVM.voidPtrType llvmctx)]\n let fnty ← LLVM.functionType retty argtys (isVarArg := false)\n LLVM.getOrAddFunction mod cppBaseName fnty\n if ps.isEmpty then\n if isClosedTermName env decl.name then LLVM.setVisibility global LLVM.Visibility.hidden else if isExternal then pure () else LLVM.setDLLStorageClass global LLVM.DLLStorageClass.export else if !isExternal\n then LLVM.setDLLStorageClass global LLVM.DLLStorageClass.export\n return global", "start": [ 471, 1 ], "end": [ 507, 16 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFnDecl", "code": "def emitFnDecl (decl : Decl) (isExternal : Bool) : M llvmctx Unit := do\n let cppBaseName ← toCName decl.name\n let _ ← emitFnDeclAux (← getLLVMModule) decl cppBaseName isExternal", "start": [ 510, 1 ], "end": [ 512, 70 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitExternDeclAux", "code": "def emitExternDeclAux (decl : Decl) (cNameStr : String) : M llvmctx Unit := do\n let env ← getEnv\n let extC := isExternC env decl.name\n let _ ← emitFnDeclAux (← getLLVMModule) decl cNameStr extC", "start": [ 514, 1 ], "end": [ 517, 61 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFnDecls", "code": "def emitFnDecls : M llvmctx Unit := do\n let env ← getEnv\n let decls := getDecls env\n let modDecls : NameSet := decls.foldl (fun s d => s.insert d.name) {}\n let usedDecls : NameSet := decls.foldl (fun s d => collectUsedDecls env d (s.insert d.name)) {}\n let usedDecls := usedDecls.toList\n for n in usedDecls do\n let decl ← getDecl n\n match getExternNameFor env `c decl.name with\n \| some cName => emitExternDeclAux decl cName\n \| none => emitFnDecl decl (!modDecls.contains n)\n return ()", "start": [ 519, 1 ], "end": [ 530, 12 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitLhsSlot_", "code": "def emitLhsSlot_ (x : VarId) : M llvmctx (LLVM.LLVMType llvmctx × LLVM.Value llvmctx) := do\n let state ← get\n match state.var2val.find? x with\n \| .some v => return v\n \| .none => throw s!\"unable to find variable {x}\"", "start": [ 532, 1 ], "end": [ 536, 51 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitLhsVal", "code": "def emitLhsVal (builder : LLVM.Builder llvmctx)\n (x : VarId) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let (xty, xslot) ← emitLhsSlot_ x\n LLVM.buildLoad2 builder xty xslot name", "start": [ 538, 1 ], "end": [ 541, 41 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitLhsSlotStore", "code": "def emitLhsSlotStore (builder : LLVM.Builder llvmctx)\n (x : VarId) (v : LLVM.Value llvmctx) : M llvmctx Unit := do\n let (_, slot) ← emitLhsSlot_ x\n LLVM.buildStore builder v slot", "start": [ 543, 1 ], "end": [ 546, 33 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitArgSlot_", "code": "def emitArgSlot_ (builder : LLVM.Builder llvmctx)\n (x : Arg) : M llvmctx (LLVM.LLVMType llvmctx × LLVM.Value llvmctx) := do\n match x with\n \| Arg.var x => emitLhsSlot_ x\n \| _ => do\n let slotty ← LLVM.voidPtrType llvmctx\n let slot ← buildPrologueAlloca builder slotty \"irrelevant_slot\"\n let v ← callLeanBox builder (← constIntSizeT 0) \"irrelevant_val\"\n let _ ← LLVM.buildStore builder v slot\n return (slotty, slot)", "start": [ 548, 1 ], "end": [ 557, 26 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitArgVal", "code": "def emitArgVal (builder : LLVM.Builder llvmctx)\n (x : Arg) (name : String := \"\") : M llvmctx (LLVM.LLVMType llvmctx × LLVM.Value llvmctx) := do\n let (xty, xslot) ← emitArgSlot_ builder x\n let xval ← LLVM.buildLoad2 builder xty xslot name\n return (xty, xval)", "start": [ 559, 1 ], "end": [ 563, 21 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitAllocCtor", "code": "def emitAllocCtor (builder : LLVM.Builder llvmctx)\n (c : CtorInfo) : M llvmctx (LLVM.Value llvmctx) := do\n let hackSizeofVoidPtr := 8\n let scalarSize := hackSizeofVoidPtr * c.usize + c.ssize\n callLeanAllocCtor builder c.cidx c.size scalarSize \"lean_alloc_ctor_out\"", "start": [ 565, 1 ], "end": [ 570, 75 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitCtorSetArgs", "code": "def emitCtorSetArgs (builder : LLVM.Builder llvmctx)\n (z : VarId) (ys : Array Arg) : M llvmctx Unit := do\n ys.size.forM fun i => do\n let zv ← emitLhsVal builder z\n let (_yty, yv) ← emitArgVal builder ys[i]!\n let iv ← constIntUnsigned i\n callLeanCtorSet builder zv iv yv\n emitLhsSlotStore builder z zv\n pure ()", "start": [ 572, 1 ], "end": [ 580, 12 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitCtor", "code": "def emitCtor (builder : LLVM.Builder llvmctx)\n (z : VarId) (c : CtorInfo) (ys : Array Arg) : M llvmctx Unit := do\n let (_llvmty, slot) ← emitLhsSlot_ z\n if c.size == 0 && c.usize == 0 && c.ssize == 0 then do\n let v ← callLeanBox builder (← constIntSizeT c.cidx) \"lean_box_outv\"\n let _ ← LLVM.buildStore builder v slot\n else do\n let v ← emitAllocCtor builder c\n let _ ← LLVM.buildStore builder v slot\n emitCtorSetArgs builder z ys", "start": [ 582, 1 ], "end": [ 591, 33 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitInc", "code": "def emitInc (builder : LLVM.Builder llvmctx)\n (x : VarId) (n : Nat) (checkRef? : Bool) : M llvmctx Unit := do\n let xv ← emitLhsVal builder x\n if n != 1\n then do\n let nv ← constIntSizeT n\n callLeanRefcountFn builder (kind := RefcountKind.inc) (checkRef? := checkRef?) (delta := nv) xv\n else callLeanRefcountFn builder (kind := RefcountKind.inc) (checkRef? := checkRef?) xv", "start": [ 593, 1 ], "end": [ 600, 89 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitDec", "code": "def emitDec (builder : LLVM.Builder llvmctx)\n (x : VarId) (n : Nat) (checkRef? : Bool) : M llvmctx Unit := do\n let xv ← emitLhsVal builder x\n if n != 1\n then throw \"expected n = 1 for emitDec\"\n else callLeanRefcountFn builder (kind := RefcountKind.dec) (checkRef? := checkRef?) xv", "start": [ 602, 1 ], "end": [ 607, 89 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitNumLit", "code": "def emitNumLit (builder : LLVM.Builder llvmctx)\n (t : IRType) (v : Nat) : M llvmctx (LLVM.Value llvmctx) := do\n if t.isObj then\n if v < UInt32.size then\n callLeanUnsignedToNatFn builder v\n else\n callLeanCStrToNatFn builder v\n else\n LLVM.constInt (← toLLVMType t) (UInt64.ofNat v)", "start": [ 609, 1 ], "end": [ 617, 52 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.toHexDigit", "code": "def toHexDigit (c : Nat) : String :=\n String.singleton c.digitChar", "start": [ 619, 1 ], "end": [ 620, 31 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.quoteString", "code": "def quoteString (s : String) : String :=\n let q := \"\\\"\";\n let q := s.foldl\n (fun q c => q ++\n if c == '\\n' then \"\\\\n\"\n else if c == '\\r' then \"\\\\r\"\n else if c == '\\t' then \"\\\\t\"\n else if c == '\\\\' then \"\\\\\\\\\"\n else if c == '\\\"' then \"\\\\\\\"\"\n else if c.toNat <= 31 then\n \"\\\\x\" ++ toHexDigit (c.toNat / 16) ++ toHexDigit (c.toNat % 16)\n else String.singleton c)\n q;\n q ++ \"\\\"\"", "start": [ 623, 1 ], "end": [ 637, 12 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitSimpleExternalCall", "code": "def emitSimpleExternalCall (builder : LLVM.Builder llvmctx)\n (f : String)\n (ps : Array Param)\n (ys : Array Arg)\n (retty : IRType)\n (name : String) : M llvmctx (LLVM.Value llvmctx) := do\n let mut args := #[]\n let mut argTys := #[]\n for (p, y) in ps.zip ys do\n if !p.ty.isIrrelevant then\n let (_yty, yv) ← emitArgVal builder y \"\"\n argTys := argTys.push (← toLLVMType p.ty)\n args := args.push yv\n let fnty ← LLVM.functionType (← toLLVMType retty) argTys\n let fn ← LLVM.getOrAddFunction (← getLLVMModule) f fnty\n LLVM.buildCall2 builder fnty fn args name", "start": [ 639, 1 ], "end": [ 654, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitExternCall", "code": "def emitExternCall (builder : LLVM.Builder llvmctx)\n (f : FunId)\n (ps : Array Param)\n (extData : ExternAttrData)\n (ys : Array Arg) (retty : IRType)\n (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) :=\n match getExternEntryFor extData `c with\n \| some (ExternEntry.standard _ extFn) => emitSimpleExternalCall builder extFn ps ys retty name\n \| some (ExternEntry.inline `llvm _pat) => throw \"Unimplemented codegen of inline LLVM\"\n \| some (ExternEntry.inline _ pat) => throw s!\"Cannot codegen non-LLVM inline code '{pat}'.\"\n \| some (ExternEntry.foreign _ extFn) => emitSimpleExternalCall builder extFn ps ys retty name\n \| _ => throw s!\"Failed to emit extern application '{f}'.\"", "start": [ 658, 1 ], "end": [ 669, 60 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getFunIdTy", "code": "def getFunIdTy (f : FunId) : M llvmctx (LLVM.LLVMType llvmctx) := do\n let decl ← getDecl f\n let retty ← toLLVMType decl.resultType\n let argtys ← decl.params.mapM (fun p => do toLLVMType p.ty)\n LLVM.functionType retty argtys", "start": [ 671, 1 ], "end": [ 675, 33 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getOrAddFunIdValue", "code": "def getOrAddFunIdValue (builder : LLVM.Builder llvmctx) (f : FunId) : M llvmctx (LLVM.Value llvmctx) := do\n let decl ← getDecl f\n let fcname ← toCName f\n let retty ← toLLVMType decl.resultType\n if decl.params.isEmpty then\n let gslot ← LLVM.getOrAddGlobal (← getLLVMModule) fcname retty\n LLVM.buildLoad2 builder retty gslot\n else\n let argtys ← decl.params.mapM (fun p => do toLLVMType p.ty)\n let fnty ← LLVM.functionType retty argtys\n LLVM.getOrAddFunction (← getLLVMModule) fcname fnty", "start": [ 677, 1 ], "end": [ 694, 56 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitPartialApp", "code": "def emitPartialApp (builder : LLVM.Builder llvmctx) (z : VarId) (f : FunId) (ys : Array Arg) : M llvmctx Unit := do\n let decl ← getDecl f\n let fv ← getOrAddFunIdValue builder f\n let arity := decl.params.size\n let (_zty, zslot) ← emitLhsSlot_ z\n let zval ← callLeanAllocClosureFn builder fv\n (← constIntUnsigned arity)\n (← constIntUnsigned ys.size)\n LLVM.buildStore builder zval zslot\n ys.size.forM fun i => do\n let (yty, yslot) ← emitArgSlot_ builder ys[i]!\n let yval ← LLVM.buildLoad2 builder yty yslot\n callLeanClosureSetFn builder zval (← constIntUnsigned i) yval", "start": [ 696, 1 ], "end": [ 708, 66 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitApp", "code": "def emitApp (builder : LLVM.Builder llvmctx) (z : VarId) (f : VarId) (ys : Array Arg) : M llvmctx Unit := do\n if ys.size > closureMaxArgs then do\n let aargs ← buildPrologueAlloca builder (← LLVM.arrayType (← LLVM.voidPtrType llvmctx) (UInt64.ofNat ys.size)) \"aargs\"\n for i in List.range ys.size do\n let (yty, yv) ← emitArgVal builder ys[i]!\n let aslot ← LLVM.buildInBoundsGEP2 builder yty aargs #[← constIntUnsigned 0, ← constIntUnsigned i] s!\"param_{i}_slot\"\n LLVM.buildStore builder yv aslot\n let fnName := s!\"lean_apply_m\"\n let retty ← LLVM.voidPtrType llvmctx\n let args := #[← emitLhsVal builder f, ← constIntUnsigned ys.size, aargs]\n let argtys := #[← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx, ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let zv ← LLVM.buildCall2 builder fnty fn args\n emitLhsSlotStore builder z zv\n else do\n\n let fnName := s!\"lean_apply_{ys.size}\"\n let retty ← LLVM.voidPtrType llvmctx\n let args : Array (LLVM.Value llvmctx) := #[← emitLhsVal builder f] ++ (← ys.mapM (fun y => Prod.snd <$> (emitArgVal builder y)))\n let argtys := (List.replicate (1 + ys.size) (← LLVM.voidPtrType llvmctx)).toArray\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let zv ← LLVM.buildCall2 builder fnty fn args\n emitLhsSlotStore builder z zv", "start": [ 710, 1 ], "end": [ 736, 34 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFullApp", "code": "def emitFullApp (builder : LLVM.Builder llvmctx)\n (z : VarId) (f : FunId) (ys : Array Arg) : M llvmctx Unit := do\n let (__zty, zslot) ← emitLhsSlot_ z\n let decl ← getDecl f\n match decl with\n \| Decl.extern _ ps retty extData =>\n let zv ← emitExternCall builder f ps extData ys retty\n LLVM.buildStore builder zv zslot\n \| Decl.fdecl .. =>\n if ys.size > 0 then\n let fv ← getOrAddFunIdValue builder f\n let ys ← ys.mapM (fun y => do\n let (yty, yslot) ← emitArgSlot_ builder y\n let yv ← LLVM.buildLoad2 builder yty yslot\n return yv)\n let zv ← LLVM.buildCall2 builder (← getFunIdTy f) fv ys\n LLVM.buildStore builder zv zslot\n else\n let zv ← getOrAddFunIdValue builder f\n LLVM.buildStore builder zv zslot", "start": [ 738, 1 ], "end": [ 757, 40 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitLit", "code": "def emitLit (builder : LLVM.Builder llvmctx)\n (z : VarId) (t : IRType) (v : LitVal) : M llvmctx (LLVM.Value llvmctx) := do\n let llvmty ← toLLVMType t\n let zslot ← buildPrologueAlloca builder llvmty\n addVartoState z zslot llvmty\n let zv ← match v with\n \| LitVal.num v => emitNumLit builder t v\n \| LitVal.str v =>\n let zero ← constIntUnsigned 0\n let str_global ← LLVM.buildGlobalString builder v\n let strPtr ← LLVM.buildInBoundsGEP2 builder\n (← LLVM.opaquePointerTypeInContext llvmctx)\n str_global #[zero] \"\"\n let nbytes ← constIntSizeT v.utf8ByteSize\n let nchars ← constIntSizeT v.length\n callLeanMkStringUncheckedFn builder strPtr nbytes nchars \"\"\n LLVM.buildStore builder zv zslot\n return zslot", "start": [ 760, 1 ], "end": [ 778, 15 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanCtorGet", "code": "def callLeanCtorGet (builder : LLVM.Builder llvmctx)\n (x i : LLVM.Value llvmctx) (retName : String) : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_ctor_get\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.i32Type llvmctx]\n let fnty ← LLVM.functionType retty argtys\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let i ← LLVM.buildSextOrTrunc builder i (← LLVM.i32Type llvmctx)\n LLVM.buildCall2 builder fnty fn #[x, i] retName", "start": [ 780, 1 ], "end": [ 788, 51 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitProj", "code": "def emitProj (builder : LLVM.Builder llvmctx) (z : VarId) (i : Nat) (x : VarId) : M llvmctx Unit := do\n let xval ← emitLhsVal builder x\n let zval ← callLeanCtorGet builder xval (← constIntUnsigned i) \"\"\n emitLhsSlotStore builder z zval", "start": [ 790, 1 ], "end": [ 793, 34 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanCtorGetUsize", "code": "def callLeanCtorGetUsize (builder : LLVM.Builder llvmctx)\n (x i : LLVM.Value llvmctx) (retName : String) : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_ctor_get_usize\"\n let retty ← LLVM.size_tType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx]\n let fnty ← LLVM.functionType retty argtys\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n LLVM.buildCall2 builder fnty fn #[x, i] retName", "start": [ 795, 1 ], "end": [ 802, 51 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitUProj", "code": "def emitUProj (builder : LLVM.Builder llvmctx) (z : VarId) (i : Nat) (x : VarId) : M llvmctx Unit := do\n let xval ← emitLhsVal builder x\n let zval ← callLeanCtorGetUsize builder xval (← constIntUnsigned i) \"\"\n emitLhsSlotStore builder z zval", "start": [ 804, 1 ], "end": [ 807, 34 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitOffset", "code": "def emitOffset (builder : LLVM.Builder llvmctx)\n (n : Nat) (offset : Nat) : M llvmctx (LLVM.Value llvmctx) := do\n let out ← constIntUnsigned 8\n let out ← LLVM.buildMul builder out (← constIntUnsigned n) \"\" LLVM.buildAdd builder out (← constIntUnsigned offset) \"\"", "start": [ 809, 1 ], "end": [ 814, 60 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitSProj", "code": "def emitSProj (builder : LLVM.Builder llvmctx)\n (z : VarId) (t : IRType) (n offset : Nat) (x : VarId) : M llvmctx Unit := do\n let (fnName, retty) ←\n match t with\n \| IRType.float => pure (\"lean_ctor_get_float\", ← LLVM.doubleTypeInContext llvmctx)\n \| IRType.uint8 => pure (\"lean_ctor_get_uint8\", ← LLVM.i8Type llvmctx)\n \| IRType.uint16 => pure (\"lean_ctor_get_uint16\", ← LLVM.i16Type llvmctx)\n \| IRType.uint32 => pure (\"lean_ctor_get_uint32\", ← LLVM.i32Type llvmctx)\n \| IRType.uint64 => pure (\"lean_ctor_get_uint64\", ← LLVM.i64Type llvmctx)\n \| _ => throw s!\"Invalid type for lean_ctor_get: '{t}'\"\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let xval ← emitLhsVal builder x\n let offset ← emitOffset builder n offset\n let fnty ← LLVM.functionType retty argtys\n let zval ← LLVM.buildCall2 builder fnty fn #[xval, offset]\n emitLhsSlotStore builder z zval", "start": [ 816, 1 ], "end": [ 832, 34 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIsExclusive", "code": "def callLeanIsExclusive (builder : LLVM.Builder llvmctx)\n (closure : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_is_exclusive\"\n let retty ← LLVM.i1Type llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let out ← LLVM.buildCall2 builder fnty fn #[closure] retName\n LLVM.buildSextOrTrunc builder out (← LLVM.i8Type llvmctx)", "start": [ 834, 1 ], "end": [ 842, 60 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIsScalar", "code": "def callLeanIsScalar (builder : LLVM.Builder llvmctx)\n (closure : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_is_scalar\"\n let retty ← LLVM.i8Type llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[closure] retName", "start": [ 844, 1 ], "end": [ 851, 54 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitIsShared", "code": "def emitIsShared (builder : LLVM.Builder llvmctx) (z : VarId) (x : VarId) : M llvmctx Unit := do\n let xv ← emitLhsVal builder x\n let exclusive? ← callLeanIsExclusive builder xv\n let exclusive? ← LLVM.buildSextOrTrunc builder exclusive? (← LLVM.i1Type llvmctx)\n let shared? ← LLVM.buildNot builder exclusive?\n let shared? ← LLVM.buildSext builder shared? (← LLVM.i8Type llvmctx)\n emitLhsSlotStore builder z shared?", "start": [ 853, 1 ], "end": [ 859, 39 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitBox", "code": "def emitBox (builder : LLVM.Builder llvmctx) (z : VarId) (x : VarId) (xType : IRType) : M llvmctx Unit := do\n let xv ← emitLhsVal builder x\n let (fnName, argTy, xv) ←\n match xType with\n \| IRType.usize => pure (\"lean_box_usize\", ← LLVM.size_tType llvmctx, xv)\n \| IRType.uint32 => pure (\"lean_box_uint32\", ← LLVM.i32Type llvmctx, xv)\n \| IRType.uint64 => pure (\"lean_box_uint64\", ← LLVM.size_tType llvmctx, xv)\n \| IRType.float => pure (\"lean_box_float\", ← LLVM.doubleTypeInContext llvmctx, xv)\n \| _ => do\n let xv ← LLVM.buildSext builder xv (← LLVM.size_tType llvmctx)\n pure (\"lean_box\", ← LLVM.size_tType llvmctx, xv)\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[argTy]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let zv ← LLVM.buildCall2 builder fnty fn #[xv]\n emitLhsSlotStore builder z zv", "start": [ 861, 1 ], "end": [ 878, 32 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.IRType.isIntegerType", "code": "def IRType.isIntegerType (t : IRType) : Bool :=\n match t with\n \| .uint8 => true\n \| .uint16 => true\n \| .uint32 => true\n \| .uint64 => true\n \| .usize => true\n \| _ => false", "start": [ 880, 1 ], "end": [ 887, 15 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callUnboxForType", "code": "def callUnboxForType (builder : LLVM.Builder llvmctx)\n (t : IRType)\n (v : LLVM.Value llvmctx)\n (retName : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let (fnName, retty) ←\n match t with\n \| IRType.usize => pure (\"lean_unbox_usize\", ← toLLVMType t)\n \| IRType.uint32 => pure (\"lean_unbox_uint32\", ← toLLVMType t)\n \| IRType.uint64 => pure (\"lean_unbox_uint64\", ← toLLVMType t)\n \| IRType.float => pure (\"lean_unbox_float\", ← toLLVMType t)\n \| _ => pure (\"lean_unbox\", ← LLVM.size_tType llvmctx)\n let argtys := #[← LLVM.voidPtrType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[v] retName", "start": [ 889, 1 ], "end": [ 903, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitUnbox", "code": "def emitUnbox (builder : LLVM.Builder llvmctx)\n (z : VarId) (t : IRType) (x : VarId) (retName : String := \"\") : M llvmctx Unit := do\n let zval ← callUnboxForType builder t (← emitLhsVal builder x) retName\n let zval ←\n if IRType.isIntegerType t\n then LLVM.buildSextOrTrunc builder zval (← toLLVMType t)\n else pure zval\n emitLhsSlotStore builder z zval", "start": [ 907, 1 ], "end": [ 916, 34 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitReset", "code": "def emitReset (builder : LLVM.Builder llvmctx) (z : VarId) (n : Nat) (x : VarId) : M llvmctx Unit := do\n let xv ← emitLhsVal builder x\n let isExclusive ← callLeanIsExclusive builder xv\n let isExclusive ← buildLeanBoolTrue? builder isExclusive\n buildIfThenElse_ builder \"isExclusive\" isExclusive\n (fun builder => do\n let xv ← emitLhsVal builder x\n n.forM fun i => do\n callLeanCtorRelease builder xv (← constIntUnsigned i)\n emitLhsSlotStore builder z xv\n return ShouldForwardControlFlow.yes\n )\n (fun builder => do\n let xv ← emitLhsVal builder x\n callLeanDecRef builder xv\n let box0 ← callLeanBox builder (← constIntSizeT 0) \"box0\"\n emitLhsSlotStore builder z box0\n return ShouldForwardControlFlow.yes\n )", "start": [ 918, 1 ], "end": [ 936, 5 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitReuse", "code": "def emitReuse (builder : LLVM.Builder llvmctx)\n (z : VarId) (x : VarId) (c : CtorInfo) (updtHeader : Bool) (ys : Array Arg) : M llvmctx Unit := do\n let xv ← emitLhsVal builder x\n let isScalar ← callLeanIsScalar builder xv\n let isScalar ← buildLeanBoolTrue? builder isScalar\n buildIfThenElse_ builder \"isScalar\" isScalar\n (fun builder => do\n let cv ← emitAllocCtor builder c\n emitLhsSlotStore builder z cv\n return ShouldForwardControlFlow.yes\n )\n (fun builder => do\n let xv ← emitLhsVal builder x\n emitLhsSlotStore builder z xv\n if updtHeader then\n let zv ← emitLhsVal builder z\n callLeanCtorSetTag builder zv (← constInt8 c.cidx)\n return ShouldForwardControlFlow.yes\n )\n emitCtorSetArgs builder z ys", "start": [ 938, 1 ], "end": [ 957, 31 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitVDecl", "code": "def emitVDecl (builder : LLVM.Builder llvmctx) (z : VarId) (t : IRType) (v : Expr) : M llvmctx Unit := do\n match v with\n \| Expr.ctor c ys => emitCtor builder z c ys\n \| Expr.reset n x => emitReset builder z n x\n \| Expr.reuse x c u ys => emitReuse builder z x c u ys\n \| Expr.proj i x => emitProj builder z i x\n \| Expr.uproj i x => emitUProj builder z i x\n \| Expr.sproj n o x => emitSProj builder z t n o x\n \| Expr.fap c ys => emitFullApp builder z c ys\n \| Expr.pap c ys => emitPartialApp builder z c ys\n \| Expr.ap x ys => emitApp builder z x ys\n \| Expr.box t x => emitBox builder z x t\n \| Expr.unbox x => emitUnbox builder z t x\n \| Expr.isShared x => emitIsShared builder z x\n \| Expr.lit v => let _ ← emitLit builder z t v", "start": [ 959, 1 ], "end": [ 973, 57 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.declareVar", "code": "def declareVar (builder : LLVM.Builder llvmctx) (x : VarId) (t : IRType) : M llvmctx Unit := do\n let llvmty ← toLLVMType t\n let alloca ← buildPrologueAlloca builder llvmty \"varx\"\n addVartoState x alloca llvmty", "start": [ 975, 1 ], "end": [ 978, 32 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.declareVars", "code": "partial def declareVars (builder : LLVM.Builder llvmctx) (f : FnBody) : M llvmctx Unit := do\n match f with\n \| FnBody.vdecl x t _ b => do\n declareVar builder x t\n declareVars builder b\n \| FnBody.jdecl _ xs _ b => do\n for param in xs do declareVar builder param.x param.ty\n declareVars builder b\n \| e => do\n if e.isTerminal then pure () else declareVars builder e.body", "start": [ 980, 1 ], "end": [ 989, 67 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitTag", "code": "def emitTag (builder : LLVM.Builder llvmctx) (x : VarId) (xType : IRType) : M llvmctx (LLVM.Value llvmctx) := do\n if xType.isObj then do\n let xval ← emitLhsVal builder x\n callLeanObjTag builder xval\n else if xType.isScalar then do\n emitLhsVal builder x\n else\n throw \"Do not know how to `emitTag` in general.\"", "start": [ 991, 1 ], "end": [ 998, 53 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitSet", "code": "def emitSet (builder : LLVM.Builder llvmctx) (x : VarId) (i : Nat) (y : Arg) : M llvmctx Unit := do\n let fnName := \"lean_ctor_set\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx , ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[← emitLhsVal builder x, ← constIntUnsigned i, (← emitArgVal builder y).2]", "start": [ 1000, 1 ], "end": [ 1006, 119 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitUSet", "code": "def emitUSet (builder : LLVM.Builder llvmctx) (x : VarId) (i : Nat) (y : VarId) : M llvmctx Unit := do\n let fnName := \"lean_ctor_set_usize\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx, ← LLVM.size_tType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[← emitLhsVal builder x, ← constIntUnsigned i, (← emitLhsVal builder y)]", "start": [ 1008, 1 ], "end": [ 1014, 117 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitTailCall", "code": "def emitTailCall (builder : LLVM.Builder llvmctx) (f : FunId) (v : Expr) : M llvmctx Unit := do\n match v with\n \| Expr.fap _ ys => do\n let llvmctx ← read\n let ps := llvmctx.mainParams\n unless ps.size == ys.size do throw s!\"Invalid tail call. f:'{f}' v:'{v}'\"\n let args ← ys.mapM (fun y => Prod.snd <$> emitArgVal builder y)\n let fn ← builderGetInsertionFn builder\n let call ← LLVM.buildCall2 builder (← getFunIdTy f) fn args\n LLVM.setTailCall call true let _ ← LLVM.buildRet builder call\n \| _ => throw s!\"EmitTailCall expects function application, found '{v}'\"", "start": [ 1016, 1 ], "end": [ 1028, 74 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitJmp", "code": "def emitJmp (builder : LLVM.Builder llvmctx) (jp : JoinPointId) (xs : Array Arg) : M llvmctx Unit := do\n let llvmctx ← read\n let ps ← match llvmctx.jpMap.find? jp with\n \| some ps => pure ps\n \| none => throw s!\"Unknown join point {jp}\"\n unless xs.size == ps.size do throw s!\"Invalid goto, mismatched sizes between arguments, formal parameters.\"\n for (p, x) in ps.zip xs do\n let (_xty, xv) ← emitArgVal builder x\n emitLhsSlotStore builder p.x xv\n let _ ← LLVM.buildBr builder (← emitJp jp)", "start": [ 1030, 1 ], "end": [ 1039, 45 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitSSet", "code": "def emitSSet (builder : LLVM.Builder llvmctx) (x : VarId) (n : Nat) (offset : Nat) (y : VarId) (t : IRType) : M llvmctx Unit := do\n let (fnName, setty) ←\n match t with\n \| IRType.float => pure (\"lean_ctor_set_float\", ← LLVM.doubleTypeInContext llvmctx)\n \| IRType.uint8 => pure (\"lean_ctor_set_uint8\", ← LLVM.i8Type llvmctx)\n \| IRType.uint16 => pure (\"lean_ctor_set_uint16\", ← LLVM.i16Type llvmctx)\n \| IRType.uint32 => pure (\"lean_ctor_set_uint32\", ← LLVM.i32Type llvmctx)\n \| IRType.uint64 => pure (\"lean_ctor_set_uint64\", ← LLVM.i64Type llvmctx)\n \| _ => throw s!\"invalid type for 'lean_ctor_set': '{t}'\"\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx, setty]\n let retty ← LLVM.voidType llvmctx\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let xv ← emitLhsVal builder x\n let offset ← emitOffset builder n offset\n let yv ← emitLhsVal builder y\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[xv, offset, yv]", "start": [ 1041, 1 ], "end": [ 1057, 61 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitDel", "code": "def emitDel (builder : LLVM.Builder llvmctx) (x : VarId) : M llvmctx Unit := do\n let argtys := #[ ← LLVM.voidPtrType llvmctx]\n let retty ← LLVM.voidType llvmctx\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty \"lean_free_object\" argtys\n let xv ← emitLhsVal builder x\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[xv]", "start": [ 1059, 1 ], "end": [ 1065, 49 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitSetTag", "code": "def emitSetTag (builder : LLVM.Builder llvmctx) (x : VarId) (i : Nat) : M llvmctx Unit := do\n let argtys := #[← LLVM.voidPtrType llvmctx, ← LLVM.i8Type llvmctx]\n let retty ← LLVM.voidType llvmctx\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty \"lean_ctor_set_tag\" argtys\n let xv ← emitLhsVal builder x\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[xv, ← constInt8 i]", "start": [ 1067, 1 ], "end": [ 1073, 64 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.ensureHasDefault'", "code": "def ensureHasDefault' (alts : Array Alt) : Array Alt :=\n if alts.any Alt.isDefault then alts\n else\n let last := alts.back\n let alts := alts.pop\n alts.push (Alt.default last.body)", "start": [ 1075, 1 ], "end": [ 1080, 38 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitCase", "code": "partial def emitCase (builder : LLVM.Builder llvmctx)\n (x : VarId) (xType : IRType) (alts : Array Alt) : M llvmctx Unit := do\n let oldBB ← LLVM.getInsertBlock builder\n let tag ← emitTag builder x xType\n let tag ← LLVM.buildZext builder tag (← LLVM.i64Type llvmctx)\n let alts := ensureHasDefault' alts\n let defaultBB ← builderAppendBasicBlock builder s!\"case_{xType}_default\"\n let numCasesHint := alts.size\n let switch ← LLVM.buildSwitch builder tag defaultBB (UInt64.ofNat numCasesHint)\n alts.forM fun alt => do\n match alt with\n \| Alt.ctor c b =>\n let destbb ← builderAppendBasicBlock builder s!\"case_{xType}_{c.name}_{c.cidx}\"\n LLVM.addCase switch (← constIntSizeT c.cidx) destbb\n LLVM.positionBuilderAtEnd builder destbb\n emitFnBody builder b\n \| Alt.default b =>\n LLVM.positionBuilderAtEnd builder defaultBB\n emitFnBody builder b\n LLVM.clearInsertionPosition builder\n LLVM.positionBuilderAtEnd builder oldBB", "start": [ 1083, 1 ], "end": [ 1106, 42 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitJDecl", "code": "partial def emitJDecl (builder : LLVM.Builder llvmctx)\n (jp : JoinPointId) (_ps : Array Param) (b : FnBody) : M llvmctx Unit := do\n let oldBB ← LLVM.getInsertBlock builder\n let jpbb ← builderAppendBasicBlock builder s!\"jp_{jp.idx}\"\n addJpTostate jp jpbb\n LLVM.positionBuilderAtEnd builder jpbb\n declareVars builder b\n emitBlock builder b\n LLVM.positionBuilderAtEnd builder oldBB", "start": [ 1109, 1 ], "end": [ 1122, 42 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitUnreachable", "code": "partial def emitUnreachable (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let retty ← LLVM.voidType llvmctx\n let argtys := #[]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty \"lean_internal_panic_unreachable\" argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[]\n let _ ← LLVM.buildUnreachable builder", "start": [ 1124, 1 ], "end": [ 1130, 40 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitBlock", "code": "partial def emitBlock (builder : LLVM.Builder llvmctx) (b : FnBody) : M llvmctx Unit := do\n match b with\n \| FnBody.jdecl j xs v b =>\n emitJDecl builder j xs v\n emitBlock builder b\n \| d@(FnBody.vdecl x t v b) => do\n let llvmctx ← read\n if isTailCallTo llvmctx.mainFn d then\n emitTailCall builder llvmctx.mainFn v\n else\n emitVDecl builder x t v\n emitBlock builder b\n \| FnBody.inc x n c p b =>\n unless p do emitInc builder x n c\n emitBlock builder b\n \| FnBody.dec x n c p b =>\n unless p do emitDec builder x n c\n emitBlock builder b\n \| FnBody.del x b => emitDel builder x; emitBlock builder b\n \| FnBody.setTag x i b => emitSetTag builder x i; emitBlock builder b\n \| FnBody.set x i y b => emitSet builder x i y; emitBlock builder b\n \| FnBody.uset x i y b => emitUSet builder x i y; emitBlock builder b\n \| FnBody.sset x i o y t b => emitSSet builder x i o y t; emitBlock builder b\n \| FnBody.mdata _ b => emitBlock builder b\n \| FnBody.ret x => do\n let (_xty, xv) ← emitArgVal builder x \"ret_val\"\n let _ ← LLVM.buildRet builder xv\n \| FnBody.case _ x xType alts =>\n emitCase builder x xType alts\n \| FnBody.jmp j xs =>\n emitJmp builder j xs\n \| FnBody.unreachable => emitUnreachable builder", "start": [ 1132, 1 ], "end": [ 1163, 58 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFnBody", "code": "partial def emitFnBody (builder : LLVM.Builder llvmctx) (b : FnBody) : M llvmctx Unit := do\n declareVars builder b\n emitBlock builder b", "start": [ 1165, 1 ], "end": [ 1167, 22 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFnArgs", "code": "def emitFnArgs (builder : LLVM.Builder llvmctx)\n (needsPackedArgs? : Bool) (llvmfn : LLVM.Value llvmctx) (params : Array Param) : M llvmctx Unit := do\n if needsPackedArgs? then do\n let argsp ← LLVM.getParam llvmfn 0 for i in List.range params.size do\n let param := params[i]!\n let argsi ← LLVM.buildGEP2 builder (← LLVM.voidPtrType llvmctx) argsp #[← constIntUnsigned i] s!\"packed_arg_{i}_slot\"\n let llvmty ← toLLVMType param.ty\n let pv ← LLVM.buildLoad2 builder llvmty argsi\n let alloca ← buildPrologueAlloca builder llvmty s!\"arg_{i}\"\n LLVM.buildStore builder pv alloca\n addVartoState params[i]!.x alloca llvmty\n else\n let n ← LLVM.countParams llvmfn\n for i in (List.range n.toNat) do\n let llvmty ← toLLVMType params[i]!.ty\n let alloca ← buildPrologueAlloca builder llvmty s!\"arg_{i}\"\n let arg ← LLVM.getParam llvmfn (UInt64.ofNat i)\n let _ ← LLVM.buildStore builder arg alloca\n addVartoState params[i]!.x alloca llvmty", "start": [ 1171, 1 ], "end": [ 1193, 49 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitDeclAux", "code": "def emitDeclAux (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) (d : Decl) : M llvmctx Unit := do\n let env ← getEnv\n let (_, jpMap) := mkVarJPMaps d\n withReader (fun llvmctx => { llvmctx with jpMap := jpMap }) do\n unless hasInitAttr env d.name do\n match d with\n \| .fdecl (f := f) (xs := xs) (type := t) (body := b) .. =>\n let baseName ← toCName f\n let name := if xs.size > 0 then baseName else \"_init_\" ++ baseName\n let retty ← toLLVMType t\n let mut argtys := #[]\n let needsPackedArgs? := xs.size > closureMaxArgs && isBoxedName d.name\n if needsPackedArgs? then\n argtys := #[← LLVM.pointerType (← LLVM.voidPtrType llvmctx)]\n else\n for x in xs do\n argtys := argtys.push (← toLLVMType x.ty)\n let fnty ← LLVM.functionType retty argtys (isVarArg := false)\n let llvmfn ← LLVM.getOrAddFunction mod name fnty\n if xs.size == 0 then\n LLVM.setVisibility llvmfn LLVM.Visibility.hidden else\n LLVM.setDLLStorageClass llvmfn LLVM.DLLStorageClass.export withReader (fun llvmctx => { llvmctx with mainFn := f, mainParams := xs }) do\n set { var2val := default, jp2bb := default : EmitLLVM.State llvmctx } let bb ← LLVM.appendBasicBlockInContext llvmctx llvmfn \"entry\"\n LLVM.positionBuilderAtEnd builder bb\n emitFnArgs builder needsPackedArgs? llvmfn xs\n emitFnBody builder b\n pure ()\n \| _ => pure ()", "start": [ 1195, 1 ], "end": [ 1229, 19 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitDecl", "code": "def emitDecl (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) (d : Decl) : M llvmctx Unit := do\n let d := d.normalizeIds try\n emitDeclAux mod builder d\n return ()\n catch err =>\n throw (s!\"emitDecl:\\ncompiling:\\n{d}\\nerr:\\n{err}\\n\")", "start": [ 1231, 1 ], "end": [ 1237, 58 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFns", "code": "def emitFns (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let env ← getEnv\n let decls := getDecls env\n decls.reverse.forM (emitDecl mod builder)", "start": [ 1239, 1 ], "end": [ 1242, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callIODeclInitFn", "code": "def callIODeclInitFn (builder : LLVM.Builder llvmctx)\n (initFnName : String)\n (world : LLVM.Value llvmctx): M llvmctx (LLVM.Value llvmctx) := do\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty initFnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[world]", "start": [ 1244, 1 ], "end": [ 1251, 43 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callPureDeclInitFn", "code": "def callPureDeclInitFn (builder : LLVM.Builder llvmctx)\n (initFnName : String)\n (retty : LLVM.LLVMType llvmctx): M llvmctx (LLVM.Value llvmctx) := do\n let argtys := #[]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty initFnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[]", "start": [ 1253, 1 ], "end": [ 1259, 38 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitDeclInit", "code": "def emitDeclInit (builder : LLVM.Builder llvmctx)\n (parentFn : LLVM.Value llvmctx) (d : Decl) : M llvmctx Unit := do\n let env ← getEnv\n if isIOUnitInitFn env d.name then do\n let world ← callLeanIOMkWorld builder\n let resv ← callIODeclInitFn builder (← toCName d.name) world\n let err? ← callLeanIOResultIsError builder resv \"is_error\"\n buildIfThen_ builder s!\"init_{d.name}_isError\" err?\n (fun builder => do\n let _ ← LLVM.buildRet builder resv\n pure ShouldForwardControlFlow.no)\n else if d.params.size == 0 then\n match getInitFnNameFor? env d.name with\n \| some initFn =>\n let llvmty ← toLLVMType d.resultType\n let dslot ← LLVM.getOrAddGlobal (← getLLVMModule) (← toCName d.name) llvmty\n LLVM.setInitializer dslot (← LLVM.getUndef llvmty)\n let initBB ← builderAppendBasicBlock builder s!\"do_{d.name}_init\"\n let restBB ← builderAppendBasicBlock builder s!\"post_{d.name}_init\"\n let checkBuiltin? := getBuiltinInitFnNameFor? env d.name \|>.isSome\n if checkBuiltin? then\n let builtinParam ← LLVM.getParam parentFn 0\n let cond ← buildLeanBoolTrue? builder builtinParam \"is_builtin_true\"\n let _ ← LLVM.buildCondBr builder cond initBB restBB\n else\n let _ ← LLVM.buildBr builder initBB\n LLVM.positionBuilderAtEnd builder initBB\n let world ← callLeanIOMkWorld builder\n let resv ← callIODeclInitFn builder (← toCName initFn) world\n let err? ← callLeanIOResultIsError builder resv s!\"{d.name}_is_error\"\n buildIfThen_ builder s!\"init_{d.name}_isError\" err?\n (fun builder => do\n let _ ← LLVM.buildRet builder resv\n pure ShouldForwardControlFlow.no)\n if d.resultType.isScalar then\n let dval ← callLeanIOResultGetValue builder resv s!\"{d.name}_res\"\n let dval ← callUnboxForType builder d.resultType dval\n LLVM.buildStore builder dval dslot\n else\n let dval ← callLeanIOResultGetValue builder resv s!\"{d.name}_res\"\n LLVM.buildStore builder dval dslot\n callLeanMarkPersistentFn builder dval\n let _ ← LLVM.buildBr builder restBB\n LLVM.positionBuilderAtEnd builder restBB\n \| none => do\n let llvmty ← toLLVMType d.resultType\n let dslot ← LLVM.getOrAddGlobal (← getLLVMModule) (← toCName d.name) llvmty\n LLVM.setInitializer dslot (← LLVM.getUndef llvmty)\n let dval ← callPureDeclInitFn builder (← toCInitName d.name) (← toLLVMType d.resultType)\n LLVM.buildStore builder dval dslot\n if d.resultType.isObj then\n callLeanMarkPersistentFn builder dval", "start": [ 1261, 1 ], "end": [ 1315, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callModInitFn", "code": "def callModInitFn (builder : LLVM.Builder llvmctx)\n (modName : Name) (input world : LLVM.Value llvmctx) (retName : String): M llvmctx (LLVM.Value llvmctx) := do\n let fnName := mkModuleInitializationFunctionName modName\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[ (← LLVM.i8Type llvmctx), (← LLVM.voidPtrType llvmctx)]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[input, world] retName", "start": [ 1317, 1 ], "end": [ 1324, 58 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitInitFn", "code": "def emitInitFn (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let env ← getEnv\n let modName ← getModName\n\n let initFnTy ← LLVM.functionType (← LLVM.voidPtrType llvmctx) #[ (← LLVM.i8Type llvmctx), (← LLVM.voidPtrType llvmctx)] (isVarArg := false)\n let initFn ← LLVM.getOrAddFunction mod (mkModuleInitializationFunctionName modName) initFnTy\n LLVM.setDLLStorageClass initFn LLVM.DLLStorageClass.export let entryBB ← LLVM.appendBasicBlockInContext llvmctx initFn \"entry\"\n LLVM.positionBuilderAtEnd builder entryBB\n let ginit?ty := ← LLVM.i1Type llvmctx\n let ginit?slot ← LLVM.getOrAddGlobal mod (modName.mangle ++ \"_G_initialized\") ginit?ty\n LLVM.setVisibility ginit?slot LLVM.Visibility.hidden LLVM.setInitializer ginit?slot (← LLVM.constFalse llvmctx)\n let ginit?v ← LLVM.buildLoad2 builder ginit?ty ginit?slot \"init_v\"\n buildIfThen_ builder \"isGInitialized\" ginit?v\n (fun builder => do\n let box0 ← callLeanBox builder (← constIntSizeT 0) \"box0\"\n let out ← callLeanIOResultMKOk builder box0 \"retval\"\n let _ ← LLVM.buildRet builder out\n pure ShouldForwardControlFlow.no)\n LLVM.buildStore builder (← LLVM.constTrue llvmctx) ginit?slot\n\n env.imports.forM fun import_ => do\n let builtin ← LLVM.getParam initFn 0\n let world ← callLeanIOMkWorld builder\n let res ← callModInitFn builder import_.module builtin world (\"res_\" ++ import_.module.mangle)\n let err? ← callLeanIOResultIsError builder res (\"res_is_error_\" ++ import_.module.mangle)\n buildIfThen_ builder (\"IsError\" ++ import_.module.mangle) err?\n (fun builder => do\n let _ ← LLVM.buildRet builder res\n pure ShouldForwardControlFlow.no)\n callLeanDecRef builder res\n let decls := getDecls env\n decls.reverse.forM (emitDeclInit builder initFn)\n let box0 ← callLeanBox builder (← constIntSizeT 0) \"box0\"\n let out ← callLeanIOResultMKOk builder box0 \"retval\"\n let _ ← LLVM.buildRet builder out", "start": [ 1326, 1 ], "end": [ 1362, 36 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanInitialize", "code": "def callLeanInitialize (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_initialize\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[]\n let fnty ← LLVM.functionType retty argtys\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[]", "start": [ 1364, 1 ], "end": [ 1370, 46 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanInitializeRuntimeModule", "code": "def callLeanInitializeRuntimeModule (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_initialize_runtime_module\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[]\n let fnty ← LLVM.functionType retty argtys\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[]", "start": [ 1372, 1 ], "end": [ 1378, 46 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanSetPanicMessages", "code": "def callLeanSetPanicMessages (builder : LLVM.Builder llvmctx)\n (enable? : LLVM.Value llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_set_panic_messages\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.i1Type llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[enable?]", "start": [ 1380, 1 ], "end": [ 1387, 53 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOMarkEndInitialization", "code": "def callLeanIOMarkEndInitialization (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_io_mark_end_initialization\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[]", "start": [ 1389, 1 ], "end": [ 1395, 46 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOResultIsOk", "code": "def callLeanIOResultIsOk (builder : LLVM.Builder llvmctx)\n (arg : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_io_result_is_ok\"\n let retty ← LLVM.i1Type llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[arg] name", "start": [ 1397, 1 ], "end": [ 1404, 46 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanInitTaskManager", "code": "def callLeanInitTaskManager (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_init_task_manager\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[]", "start": [ 1406, 1 ], "end": [ 1412, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanFinalizeTaskManager", "code": "def callLeanFinalizeTaskManager (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_finalize_task_manager\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[]", "start": [ 1414, 1 ], "end": [ 1420, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanUnboxUint32", "code": "def callLeanUnboxUint32 (builder : LLVM.Builder llvmctx)\n (v : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_unbox_uint32\"\n let retty ← LLVM.i32Type llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[v] name", "start": [ 1422, 1 ], "end": [ 1429, 45 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOResultShowError", "code": "def callLeanIOResultShowError (builder : LLVM.Builder llvmctx)\n (v : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx Unit := do\n let fnName := \"lean_io_result_show_error\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[v] name", "start": [ 1431, 1 ], "end": [ 1438, 52 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanMainFn", "code": "def callLeanMainFn (builder : LLVM.Builder llvmctx)\n (argv? : Option (LLVM.Value llvmctx))\n (world : LLVM.Value llvmctx)\n (name : String) : M llvmctx (LLVM.Value llvmctx) := do\n let retty ← LLVM.voidPtrType llvmctx\n let voidptr ← LLVM.voidPtrType llvmctx\n let argtys := if argv?.isSome then #[ voidptr, voidptr ] else #[ voidptr ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty leanMainFn argtys\n let fnty ← LLVM.functionType retty argtys\n let args := match argv? with\n \| .some argv => #[argv, world]\n \| .none => #[world]\n LLVM.buildCall2 builder fnty fn args name", "start": [ 1440, 1 ], "end": [ 1452, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitMainFn", "code": "def emitMainFn (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let d ← getDecl `main\n let xs ← match d with\n \| .fdecl (xs := xs) .. => pure xs\n \| _ => throw \"Function declaration expected for 'main'\"\n\n unless xs.size == 2 \|\| xs.size == 1 do throw s!\"Invalid main function, main expected to have '2' or '1' arguments, found '{xs.size}' arguments\"\n let env ← getEnv\n let usesLeanAPI := usesModuleFrom env `Lean\n let mainTy ← LLVM.functionType (← LLVM.i64Type llvmctx)\n #[(← LLVM.i64Type llvmctx), (← LLVM.pointerType (← LLVM.voidPtrType llvmctx))]\n let main ← LLVM.getOrAddFunction mod \"main\" mainTy\n let entry ← LLVM.appendBasicBlockInContext llvmctx main \"entry\"\n LLVM.positionBuilderAtEnd builder entry\n \n let inty ← LLVM.voidPtrType llvmctx\n let inslot ← buildPrologueAlloca builder (← LLVM.pointerType inty) \"in\"\n let resty ← LLVM.voidPtrType llvmctx\n let res ← buildPrologueAlloca builder (← LLVM.pointerType resty) \"res\"\n if usesLeanAPI then callLeanInitialize builder else callLeanInitializeRuntimeModule builder\n \n callLeanSetPanicMessages builder (← LLVM.constFalse llvmctx)\n let world ← callLeanIOMkWorld builder\n let resv ← callModInitFn builder (← getModName) (← constInt8 1) world ((← getModName).toString ++ \"_init_out\")\n let _ ← LLVM.buildStore builder resv res\n\n callLeanSetPanicMessages builder (← LLVM.constTrue llvmctx)\n callLeanIOMarkEndInitialization builder\n\n let resv ← LLVM.buildLoad2 builder resty res \"resv\"\n let res_is_ok ← callLeanIOResultIsOk builder resv \"res_is_ok\"\n buildIfThen_ builder \"resIsOkBranches\" res_is_ok\n (fun builder => do callLeanDecRef builder resv\n callLeanInitTaskManager builder\n if xs.size == 2 then\n let inv ← callLeanBox builder (← constIntSizeT 0) \"inv\"\n let _ ← LLVM.buildStore builder inv inslot\n let ity ← LLVM.size_tType llvmctx\n let islot ← buildPrologueAlloca builder ity \"islot\"\n let argcval ← LLVM.getParam main 0\n let argvval ← LLVM.getParam main 1\n LLVM.buildStore builder argcval islot\n buildWhile_ builder \"argv\"\n (condcodegen := fun builder => do\n let iv ← LLVM.buildLoad2 builder ity islot \"iv\"\n let i_gt_1 ← LLVM.buildICmp builder LLVM.IntPredicate.UGT iv (← constIntSizeT 1) \"i_gt_1\"\n return i_gt_1)\n (bodycodegen := fun builder => do\n let iv ← LLVM.buildLoad2 builder ity islot \"iv\"\n let iv_next ← LLVM.buildSub builder iv (← constIntSizeT 1) \"iv.next\"\n LLVM.buildStore builder iv_next islot\n let nv ← callLeanAllocCtor builder 1 2 0 \"nv\"\n let argv_i_next_slot ← LLVM.buildGEP2 builder (← LLVM.voidPtrType llvmctx) argvval #[iv_next] \"argv.i.next.slot\"\n let argv_i_next_val ← LLVM.buildLoad2 builder (← LLVM.voidPtrType llvmctx) argv_i_next_slot \"argv.i.next.val\"\n let argv_i_next_val_str ← callLeanMkString builder argv_i_next_val \"arg.i.next.val.str\"\n callLeanCtorSet builder nv (← constIntUnsigned 0) argv_i_next_val_str\n let inv ← LLVM.buildLoad2 builder inty inslot \"inv\"\n callLeanCtorSet builder nv (← constIntUnsigned 1) inv\n LLVM.buildStore builder nv inslot)\n let world ← callLeanIOMkWorld builder\n let inv ← LLVM.buildLoad2 builder inty inslot \"inv\"\n let resv ← callLeanMainFn builder (argv? := .some inv) (world := world) \"resv\"\n let _ ← LLVM.buildStore builder resv res\n pure ShouldForwardControlFlow.yes\n else\n let world ← callLeanIOMkWorld builder\n let resv ← callLeanMainFn builder (argv? := .none) (world := world) \"resv\"\n let _ ← LLVM.buildStore builder resv res\n pure ShouldForwardControlFlow.yes\n )\n\n let retTy := env.find? `main \|>.get! \|>.type \|>.getForallBody\n let retTy := retTy.appArg!\n callLeanFinalizeTaskManager builder\n let resv ← LLVM.buildLoad2 builder resty res \"resv\"\n let res_is_ok ← callLeanIOResultIsOk builder resv \"res_is_ok\"\n buildIfThenElse_ builder \"res.is.ok\" res_is_ok\n (fun builder => if retTy.constName? == some ``UInt32 then do\n let resv ← LLVM.buildLoad2 builder resty res \"resv\"\n let retv ← callLeanUnboxUint32 builder (← callLeanIOResultGetValue builder resv \"io_val\") \"retv\"\n let retv ← LLVM.buildSext builder retv (← LLVM.i64Type llvmctx) \"retv_sext\"\n callLeanDecRef builder resv\n let _ ← LLVM.buildRet builder retv\n pure ShouldForwardControlFlow.no\n else do\n callLeanDecRef builder resv\n let _ ← LLVM.buildRet builder (← constInt64 0)\n pure ShouldForwardControlFlow.no\n\n )\n (fun builder => do let resv ← LLVM.buildLoad2 builder resty res \"resv\"\n callLeanIOResultShowError builder resv\n callLeanDecRef builder resv\n let _ ← LLVM.buildRet builder (← constInt64 1)\n pure ShouldForwardControlFlow.no)\n let _ ← LLVM.buildUnreachable builder", "start": [ 1454, 1 ], "end": [ 1562, 40 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.hasMainFn", "code": "def hasMainFn : M llvmctx Bool := do\n let env ← getEnv\n let decls := getDecls env\n return decls.any (fun d => d.name == `main)", "start": [ 1564, 1 ], "end": [ 1567, 46 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitMainFnIfNeeded", "code": "def emitMainFnIfNeeded (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n if (← hasMainFn) then emitMainFn mod builder", "start": [ 1569, 1 ], "end": [ 1570, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.main", "code": "def main : M llvmctx Unit := do\n emitFnDecls\n let builder ← LLVM.createBuilderInContext llvmctx\n emitFns (← getLLVMModule) builder\n emitInitFn (← getLLVMModule) builder\n emitMainFnIfNeeded (← getLLVMModule) builder", "start": [ 1572, 1 ], "end": [ 1577, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.getLeanHBcPath", "code": "def getLeanHBcPath : IO System.FilePath := do\n return (← getLibDir (← getBuildDir)) / \"lean.h.bc\"", "start": [ 1580, 1 ], "end": [ 1581, 53 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.getModuleGlobals", "code": "partial def getModuleGlobals (mod : LLVM.Module llvmctx) : IO (Array (LLVM.Value llvmctx)) := do\n let rec go (v : LLVM.Value llvmctx) (acc : Array (LLVM.Value llvmctx)) : IO (Array (LLVM.Value llvmctx)) := do\n if v.isNull then return acc\n else go (← LLVM.getNextGlobal v) (acc.push v)\n go (← LLVM.getFirstGlobal mod) #[]", "start": [ 1583, 1 ], "end": [ 1588, 37 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.getModuleFunctions", "code": "partial def getModuleFunctions (mod : LLVM.Module llvmctx) : IO (Array (LLVM.Value llvmctx)) := do\n let rec go (v : LLVM.Value llvmctx) (acc : Array (LLVM.Value llvmctx)) : IO (Array (LLVM.Value llvmctx)) := do\n if v.isNull then return acc\n else go (← LLVM.getNextFunction v) (acc.push v)\n go (← LLVM.getFirstFunction mod) #[]", "start": [ 1590, 1 ], "end": [ 1595, 39 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.emitLLVM", "code": "@[export lean_ir_emit_llvm]\ndef emitLLVM (env : Environment) (modName : Name) (filepath : String) : IO Unit := do\n LLVM.llvmInitializeTargetInfo\n let llvmctx ← LLVM.createContext\n let module ← LLVM.createModule llvmctx modName.toString\n let emitLLVMCtx : EmitLLVM.Context llvmctx := {env := env, modName := modName, llvmmodule := module}\n let initState := { var2val := default, jp2bb := default : EmitLLVM.State llvmctx}\n let out? ← ((EmitLLVM.main (llvmctx := llvmctx)).run initState).run emitLLVMCtx\n match out? with\n \| .ok _ => do\n let membuf ← LLVM.createMemoryBufferWithContentsOfFile (← getLeanHBcPath).toString\n let modruntime ← LLVM.parseBitcode llvmctx membuf\n \n let runtimeGlobals ← (← getModuleGlobals modruntime).mapM (·.getName)\n let filter func := do\n if (← LLVM.isDeclaration func) then\n return none\n else\n return some (← func.getName)\n let runtimeFunctions ← (← getModuleFunctions modruntime).filterMapM filter\n LLVM.linkModules (dest := emitLLVMCtx.llvmmodule) (src := modruntime)\n for name in runtimeGlobals do\n let some global ← LLVM.getNamedGlobal emitLLVMCtx.llvmmodule name\n \| throw <\| IO.Error.userError s!\"ERROR: linked module must have global from runtime module: '{name}'\"\n LLVM.setLinkage global LLVM.Linkage.internal\n for name in runtimeFunctions do\n let some fn ← LLVM.getNamedFunction emitLLVMCtx.llvmmodule name\n \| throw <\| IO.Error.userError s!\"ERROR: linked module must have function from runtime module: '{name}'\"\n LLVM.setLinkage fn LLVM.Linkage.internal\n if let some err ← LLVM.verifyModule emitLLVMCtx.llvmmodule then\n throw <\| .userError err\n LLVM.writeBitcodeToFile emitLLVMCtx.llvmmodule filepath\n LLVM.disposeModule emitLLVMCtx.llvmmodule\n \| .error err => throw (IO.Error.userError err)", "start": [ 1597, 1 ], "end": [ 1638, 49 ], "kind": "commanddeclaration" } ]
.lake/packages/lean4/src/lean/lake/Lake/Main.lean	[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/lean4/src/lean/lake/Lake/CLI.lean", ".lake/packages/lean4/src/lean/lake/Lake.lean" ]	[ { "full_name": "main", "code": "def main (args : List String) : IO UInt32 := do\n Lake.cli args", "start": [ 9, 1 ], "end": [ 10, 16 ], "kind": "commanddeclaration" } ]
.lake/packages/lean4/src/lean/Lean/Compiler/LCNF/Probing.lean	[ ".lake/packages/lean4/src/lean/Lean/Compiler/LCNF/ForEachExpr.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/LCNF/CompilerM.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/LCNF/PassManager.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/LCNF/PhaseExt.lean" ]	[ { "full_name": "Lean.Compiler.LCNF.Probe", "code": "abbrev Probe α β := Array α → CompilerM (Array β)", "start": [ 14, 1 ], "end": [ 14, 50 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.map", "code": "@[inline]\ndef map (f : α → CompilerM β) : Probe α β := fun data => data.mapM f", "start": [ 18, 1 ], "end": [ 19, 69 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filter", "code": "@[inline]\ndef filter (f : α → CompilerM Bool) : Probe α α := fun data => data.filterM f", "start": [ 21, 1 ], "end": [ 22, 78 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.sorted", "code": "@[inline]\ndef sorted [Inhabited α] [inst : LT α] [DecidableRel inst.lt] : Probe α α := fun data => return data.qsort (· < ·)", "start": [ 24, 1 ], "end": [ 25, 115 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.sortedBySize", "code": "@[inline]\ndef sortedBySize : Probe Decl (Nat × Decl) := fun decls =>\n let decls := decls.map fun decl => (decl.size, decl)\n return decls.qsort fun (sz₁, decl₁) (sz₂, decl₂) =>\n if sz₁ == sz₂ then Name.lt decl₁.name decl₂.name else sz₁ < sz₂", "start": [ 27, 1 ], "end": [ 31, 68 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.countUnique", "code": "def countUnique [ToString α] [BEq α] [Hashable α] : Probe α (α × Nat) := fun data => do\n let mut map := HashMap.empty\n for d in data do\n if let some count := map.find? d then\n map := map.insert d (count + 1)\n else\n map := map.insert d 1\n return map.toArray", "start": [ 33, 1 ], "end": [ 40, 21 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.countUniqueSorted", "code": "@[inline]\ndef countUniqueSorted [ToString α] [BEq α] [Hashable α] [Inhabited α] : Probe α (α × Nat) :=\n countUnique >=> fun data => return data.qsort (fun l r => l.snd < r.snd)", "start": [ 42, 1 ], "end": [ 44, 75 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.getLetValues", "code": "partial def getLetValues : Probe Decl LetValue := fun decls => do\n let (_, res) ← start decls \|>.run #[]\n return res\nwhere\n go (c : Code) : StateRefT (Array LetValue) CompilerM Unit := do\n match c with\n \| .let (decl : LetDecl) (k : Code) =>\n modify fun s => s.push decl.value\n go k\n \| .fun decl k \| .jp decl k =>\n go decl.value\n go k\n \| .cases (cases : CasesCore Code) => cases.alts.forM (go ·.getCode)\n \| .jmp .. \| .return .. \| .unreach .. => return ()\n start (decls : Array Decl) : StateRefT (Array LetValue) CompilerM Unit :=\n decls.forM (go ·.value)", "start": [ 46, 1 ], "end": [ 61, 28 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.getJps", "code": "partial def getJps : Probe Decl FunDecl := fun decls => do\n let (_, res) ← start decls \|>.run #[]\n return res\nwhere\n go (code : Code) : StateRefT (Array FunDecl) CompilerM Unit := do\n match code with\n \| .let _ k => go k\n \| .fun decl k => go decl.value; go k\n \| .jp decl k => modify (·.push decl); go decl.value; go k\n \| .cases cs => cs.alts.forM (go ·.getCode)\n \| .jmp .. \| .return .. \| .unreach .. => return ()\n\n start (decls : Array Decl) : StateRefT (Array FunDecl) CompilerM Unit :=\n decls.forM fun decl => go decl.value", "start": [ 63, 1 ], "end": [ 76, 41 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByLet", "code": "partial def filterByLet (f : LetDecl → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n \| .let decl k => do if (← f decl) then return true else go k\n \| .fun decl k \| .jp decl k => go decl.value <\|\|> go k\n \| .cases cs => cs.alts.anyM (go ·.getCode)\n \| .jmp .. \| .return .. \| .unreach .. => return false", "start": [ 78, 1 ], "end": [ 85, 55 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByFun", "code": "partial def filterByFun (f : FunDecl → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n \| .let _ k \| .jp _ k => go k\n \| .fun decl k => do if (← f decl) then return true else go decl.value <\|\|> go k\n \| .cases cs => cs.alts.anyM (go ·.getCode)\n \| .jmp .. \| .return .. \| .unreach .. => return false", "start": [ 87, 1 ], "end": [ 94, 55 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByJp", "code": "partial def filterByJp (f : FunDecl → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n \| .let _ k => go k\n \| .fun decl k => go decl.value <\|\|> go k\n \| .jp decl k => do if (← f decl) then return true else go decl.value <\|\|> go k\n \| .cases cs => cs.alts.anyM (go ·.getCode)\n \| .jmp .. \| .return .. \| .unreach .. => return false", "start": [ 96, 1 ], "end": [ 104, 55 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByFunDecl", "code": "partial def filterByFunDecl (f : FunDecl → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n \| .let _ k => go k\n \| .fun decl k \| .jp decl k => do if (← f decl) then return true else go decl.value <\|\|> go k\n \| .cases cs => cs.alts.anyM (go ·.getCode)\n \| .jmp .. \| .return .. \| .unreach .. => return false", "start": [ 106, 1 ], "end": [ 113, 55 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByCases", "code": "partial def filterByCases (f : Cases → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n \| .let _ k => go k\n \| .fun decl k \| .jp decl k => go decl.value <\|\|> go k\n \| .cases cs => do if (← f cs) then return true else cs.alts.anyM (go ·.getCode)\n \| .jmp .. \| .return .. \| .unreach .. => return false", "start": [ 115, 1 ], "end": [ 122, 55 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByJmp", "code": "partial def filterByJmp (f : FVarId → Array Arg → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n \| .let _ k => go k\n \| .fun decl k \| .jp decl k => go decl.value <\|\|> go k\n \| .cases cs => cs.alts.anyM (go ·.getCode)\n \| .jmp fn var => f fn var\n \| .return .. \| .unreach .. => return false", "start": [ 124, 1 ], "end": [ 132, 45 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByReturn", "code": "partial def filterByReturn (f : FVarId → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n \| .let _ k => go k\n \| .fun decl k \| .jp decl k => go decl.value <\|\|> go k\n \| .cases cs => cs.alts.anyM (go ·.getCode)\n \| .jmp .. \| .unreach .. => return false\n \| .return var => f var", "start": [ 134, 1 ], "end": [ 142, 26 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByUnreach", "code": "partial def filterByUnreach (f : Expr → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n \| .let _ k => go k\n \| .fun decl k \| .jp decl k => go decl.value <\|\|> go k\n \| .cases cs => cs.alts.anyM (go ·.getCode)\n \| .jmp .. \| .return .. => return false\n \| .unreach typ => f typ", "start": [ 144, 1 ], "end": [ 152, 27 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.declNames", "code": "@[inline]\ndef declNames : Probe Decl Name :=\n Probe.map (fun decl => return decl.name)", "start": [ 154, 1 ], "end": [ 156, 43 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.toString", "code": "@[inline]\ndef toString [ToString α] : Probe α String :=\n Probe.map (return ToString.toString ·)", "start": [ 158, 1 ], "end": [ 160, 41 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.count", "code": "@[inline]\ndef count : Probe α Nat := fun data => return #[data.size]", "start": [ 162, 1 ], "end": [ 163, 59 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.sum", "code": "@[inline]\ndef sum : Probe Nat Nat := fun data => return #[data.foldl (init := 0) (·+·)]", "start": [ 165, 1 ], "end": [ 166, 78 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.tail", "code": "@[inline]\ndef tail (n : Nat) : Probe α α := fun data => return data[data.size - n:]", "start": [ 168, 1 ], "end": [ 169, 74 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.head", "code": "@[inline]\ndef head (n : Nat) : Probe α α := fun data => return data[:n]", "start": [ 171, 1 ], "end": [ 172, 62 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.runOnModule", "code": "def runOnModule (moduleName : Name) (probe : Probe Decl β) (phase : Phase := Phase.base): CoreM (Array β) := do\n let ext := getExt phase\n let env ← getEnv\n let some modIdx := env.getModuleIdx? moduleName \| throwError \"module `{moduleName}` not found\"\n let decls := ext.getModuleEntries env modIdx\n probe decls \|>.run (phase := phase)", "start": [ 174, 1 ], "end": [ 179, 38 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.runGlobally", "code": "def runGlobally (probe : Probe Decl β) (phase : Phase := Phase.base) : CoreM (Array β) := do\n let ext := getExt phase\n let env ← getEnv\n let mut decls := #[]\n for modIdx in [:env.allImportedModuleNames.size] do\n decls := decls.append <\| ext.getModuleEntries env modIdx\n probe decls \|>.run (phase := phase)", "start": [ 181, 1 ], "end": [ 187, 38 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.toPass", "code": "def toPass [ToString β] (probe : Probe Decl β) (phase : Phase) : Pass where\n phase := phase\n name := `probe\n run := fun decls => do\n let res ← probe decls\n trace[Compiler.probe] s!\"{res}\"\n return decls", "start": [ 189, 1 ], "end": [ 195, 17 ], "kind": "commanddeclaration" } ]
.lake/packages/lean4/src/lean/Lean/Meta/Match/MatcherApp.lean	[ ".lake/packages/lean4/src/lean/Lean/Meta/Match/MatcherApp/Basic.lean", ".lake/packages/lean4/src/lean/Lean/Meta/Match/MatcherApp/Transform.lean" ]	[]
.lake/packages/lean4/src/lean/Lean/Meta/Match/MVarRenaming.lean	[ ".lake/packages/lean4/src/lean/Lean/Util/ReplaceExpr.lean" ]	[ { "full_name": "Lean.Meta.MVarRenaming", "code": "structure MVarRenaming where\n map : MVarIdMap MVarId := {}", "start": [ 11, 1 ], "end": [ 13, 31 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Meta.MVarRenaming.isEmpty", "code": "def MVarRenaming.isEmpty (s : MVarRenaming) : Bool :=\n s.map.isEmpty", "start": [ 15, 1 ], "end": [ 16, 16 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Meta.MVarRenaming.find?", "code": "def MVarRenaming.find? (s : MVarRenaming) (mvarId : MVarId) : Option MVarId :=\n s.map.find? mvarId", "start": [ 18, 1 ], "end": [ 19, 21 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Meta.MVarRenaming.find!", "code": "def MVarRenaming.find! (s : MVarRenaming) (mvarId : MVarId) : MVarId :=\n (s.find? mvarId).get!", "start": [ 21, 1 ], "end": [ 22, 24 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Meta.MVarRenaming.insert", "code": "def MVarRenaming.insert (s : MVarRenaming) (mvarId mvarId' : MVarId) : MVarRenaming :=\n { s with map := s.map.insert mvarId mvarId' }", "start": [ 24, 1 ], "end": [ 25, 48 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Meta.MVarRenaming.apply", "code": "def MVarRenaming.apply (s : MVarRenaming) (e : Expr) : Expr :=\n if !e.hasMVar then e\n else if s.map.isEmpty then e\n else e.replace fun e => match e with\n \| Expr.mvar mvarId => match s.map.find? mvarId with\n \| none => e\n \| some newMVarId => mkMVar newMVarId\n \| _ => none", "start": [ 27, 1 ], "end": [ 34, 16 ], "kind": "commanddeclaration" } ]
.lake/packages/lean4/src/lean/Lean/Data/Lsp/Window.lean	[ ".lake/packages/lean4/src/lean/Lean/Data/Json.lean" ]	[ { "full_name": "MessageType", "code": "inductive MessageType where\n \| error\n \| warning\n \| info\n \| log", "start": [ 11, 1 ], "end": [ 15, 8 ], "kind": "commanddeclaration" }, { "full_name": "ShowMessageParams", "code": "structure ShowMessageParams where\n type : MessageType\n message : String\n deriving FromJson, ToJson", "start": [ 32, 1 ], "end": [ 35, 28 ], "kind": "commanddeclaration" }, { "full_name": "MessageActionItem", "code": "structure MessageActionItem where\n title : String\n deriving FromJson, ToJson", "start": [ 37, 1 ], "end": [ 39, 28 ], "kind": "commanddeclaration" }, { "full_name": "ShowMessageRequestParams", "code": "structure ShowMessageRequestParams where\n type : MessageType\n message : String\n actions? : Option (Array MessageActionItem)\n deriving FromJson, ToJson", "start": [ 41, 1 ], "end": [ 45, 28 ], "kind": "commanddeclaration" }, { "full_name": "ShowMessageResponse", "code": "def ShowMessageResponse := Option MessageActionItem\n deriving FromJson, ToJson", "start": [ 47, 1 ], "end": [ 48, 28 ], "kind": "commanddeclaration" } ]
.lake/packages/lean4/src/lean/Std.lean	[ ".lake/packages/lean4/src/lean/Init.lean" ]	[]

Mathlib/Data/Rbtree/Find.lean

[ "Mathlib/Mathport/Rename.lean", ".lake/packages/lean4/src/lean/Init.lean" ]

[]

Mathlib/Combinatorics/SimpleGraph/StronglyRegular.lean

[ "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean", "Mathlib/Combinatorics/SimpleGraph/Basic.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Data/Set/Finite.lean", "Mathlib/Combinatorics/SimpleGraph/AdjMatrix.lean" ]

[ { "full_name": "SimpleGraph.IsSRGWith", "code": "structure IsSRGWith (n k ℓ μ : ℕ) : Prop where\n card : Fintype.card V = n\n regular : G.IsRegularOfDegree k\n of_adj : ∀ v w : V, G.Adj v w → Fintype.card (G.commonNeighbors v w) = ℓ\n of_not_adj : Pairwise fun v w => ¬G.Adj v w → Fintype.card (G.commonNeighbors v w) = μ", "start": [ 43, 1 ], "end": [ 53, 89 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.bot_strongly_regular", "code": "theorem bot_strongly_regular : (⊥ : SimpleGraph V).IsSRGWith (Fintype.card V) 0 ℓ 0 where", "start": [ 59, 1 ], "end": [ 68, 31 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.top", "code": "theorem IsSRGWith.top :\n (⊤ : SimpleGraph V).IsSRGWith (Fintype.card V) (Fintype.card V - 1) (Fintype.card V - 2) μ where", "start": [ 71, 1 ], "end": [ 80, 68 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.card_neighborFinset_union_eq", "code": "theorem IsSRGWith.card_neighborFinset_union_eq {v w : V} (h : G.IsSRGWith n k ℓ μ) :\n (G.neighborFinset v ∪ G.neighborFinset w).card =\n 2 * k - Fintype.card (G.commonNeighbors v w)", "start": [ 84, 1 ], "end": [ 95, 40 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.card_neighborFinset_union_of_not_adj", "code": "theorem IsSRGWith.card_neighborFinset_union_of_not_adj {v w : V} (h : G.IsSRGWith n k ℓ μ)\n (hne : v ≠ w) (ha : ¬G.Adj v w) :\n (G.neighborFinset v ∪ G.neighborFinset w).card = 2 * k - μ", "start": [ 99, 1 ], "end": [ 106, 39 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.card_neighborFinset_union_of_adj", "code": "theorem IsSRGWith.card_neighborFinset_union_of_adj {v w : V} (h : G.IsSRGWith n k ℓ μ)\n (ha : G.Adj v w) : (G.neighborFinset v ∪ G.neighborFinset w).card = 2 * k - ℓ", "start": [ 110, 1 ], "end": [ 113, 39 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.compl_neighborFinset_sdiff_inter_eq", "code": "theorem compl_neighborFinset_sdiff_inter_eq {v w : V} :\n (G.neighborFinset v)ᶜ \\ {v} ∩ ((G.neighborFinset w)ᶜ \\ {w}) =\n ((G.neighborFinset v)ᶜ ∩ (G.neighborFinset w)ᶜ) \\ ({w} ∪ {v})", "start": [ 117, 1 ], "end": [ 122, 57 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.sdiff_compl_neighborFinset_inter_eq", "code": "theorem sdiff_compl_neighborFinset_inter_eq {v w : V} (h : G.Adj v w) :\n ((G.neighborFinset v)ᶜ ∩ (G.neighborFinset w)ᶜ) \\ ({w} ∪ {v}) =\n (G.neighborFinset v)ᶜ ∩ (G.neighborFinset w)ᶜ", "start": [ 125, 1 ], "end": [ 134, 19 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.compl_is_regular", "code": "theorem IsSRGWith.compl_is_regular (h : G.IsSRGWith n k ℓ μ) :\n Gᶜ.IsRegularOfDegree (n - k - 1)", "start": [ 137, 1 ], "end": [ 140, 24 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_adj_compl", "code": "theorem IsSRGWith.card_commonNeighbors_eq_of_adj_compl (h : G.IsSRGWith n k ℓ μ) {v w : V}\n (ha : Gᶜ.Adj v w) : Fintype.card (Gᶜ.commonNeighbors v w) = n - (2 * k - μ) - 2", "start": [ 144, 1 ], "end": [ 156, 55 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl", "code": "theorem IsSRGWith.card_commonNeighbors_eq_of_not_adj_compl (h : G.IsSRGWith n k ℓ μ) {v w : V}\n (hn : v ≠ w) (hna : ¬Gᶜ.Adj v w) :\n Fintype.card (Gᶜ.commonNeighbors v w) = n - (2 * k - ℓ)", "start": [ 160, 1 ], "end": [ 168, 87 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.compl", "code": "theorem IsSRGWith.compl (h : G.IsSRGWith n k ℓ μ) :\n Gᶜ.IsSRGWith n (n - k - 1) (n - (2 * k - μ) - 2) (n - (2 * k - ℓ)) where", "start": [ 172, 1 ], "end": [ 178, 86 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.param_eq", "code": "theorem IsSRGWith.param_eq (h : G.IsSRGWith n k ℓ μ) (hn : 0 < n) :\n k * (k - ℓ - 1) = (n - k - 1) * μ", "start": [ 182, 1 ], "end": [ 215, 11 ], "kind": "commanddeclaration" }, { "full_name": "SimpleGraph.IsSRGWith.matrix_eq", "code": "theorem IsSRGWith.matrix_eq {α : Type*} [Semiring α] (h : G.IsSRGWith n k ℓ μ) :\n G.adjMatrix α ^ 2 = k • (1 : Matrix V V α) + ℓ • G.adjMatrix α + μ • Gᶜ.adjMatrix α", "start": [ 217, 1 ], "end": [ 235, 30 ], "kind": "commanddeclaration" } ]

Mathlib/LinearAlgebra/TensorProduct/DirectLimit.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Algebra/DirectLimit.lean" ]

[ { "full_name": "TensorProduct.fromDirectLimit", "code": "noncomputable def fromDirectLimit :\n DirectLimit (G · ⊗[R] M) (f ▷ M) →ₗ[R] DirectLimit G f ⊗[R] M :=\n DirectLimit.lift _ _ _ _ (fun _ ↦ (of _ _ _ _ _).rTensor M)\n fun _ _ _ x ↦ by refine x.induction_on ?_ ?_ ?_ <;> aesop", "start": [ 39, 1 ], "end": [ 46, 62 ], "kind": "commanddeclaration" }, { "full_name": "TensorProduct.fromDirectLimit_of_tmul", "code": "@[simp] lemma fromDirectLimit_of_tmul {i : ι} (g : G i) (m : M) :\n fromDirectLimit f M (of _ _ _ _ i (g ⊗ₜ m)) = (of _ _ _ f i g) ⊗ₜ m :=\n lift_of (G := (G · ⊗[R] M)) _ _ (g ⊗ₜ m)", "start": [ 49, 1 ], "end": [ 51, 43 ], "kind": "lemma" }, { "full_name": "TensorProduct.toDirectLimit", "code": "noncomputable def toDirectLimit : DirectLimit G f ⊗[R] M →ₗ[R] DirectLimit (G · ⊗[R] M) (f ▷ M) :=\n TensorProduct.lift <| DirectLimit.lift _ _ _ _\n (fun i ↦\n (TensorProduct.mk R _ _).compr₂ (of R ι _ (fun _i _j h ↦ (f _ _ h).rTensor M) i))\n fun _ _ _ g ↦ DFunLike.ext _ _ (of_f (G := (G · ⊗[R] M)) (x := g ⊗ₜ ·))", "start": [ 53, 1 ], "end": [ 62, 76 ], "kind": "commanddeclaration" }, { "full_name": "TensorProduct.toDirectLimit_tmul_of", "code": "@[simp] lemma toDirectLimit_tmul_of\n {i : ι} (g : G i) (m : M) :\n (toDirectLimit f M <| (of _ _ G f i g) ⊗ₜ m) = (of _ _ _ _ i (g ⊗ₜ m)) := by\n rw [toDirectLimit, lift.tmul, lift_of]\n rfl", "start": [ 65, 1 ], "end": [ 69, 6 ], "kind": "lemma" }, { "full_name": "TensorProduct.directLimitLeft", "code": "noncomputable def directLimitLeft :\n DirectLimit G f ⊗[R] M ≃ₗ[R] DirectLimit (G · ⊗[R] M) (f ▷ M) := by\n refine LinearEquiv.ofLinear (toDirectLimit f M) (fromDirectLimit f M) ?_ ?_\n <;> cases isEmpty_or_nonempty ι\n · ext; apply Subsingleton.elim\n · refine DFunLike.ext _ _ fun x ↦ x.induction_on fun i g ↦ g.induction_on ?_ ?_ ?_ <;> aesop\n · ext; apply Subsingleton.elim\n · exact ext (DFunLike.ext _ _ fun g ↦ DFunLike.ext _ _ fun _ ↦ g.induction_on <| by aesop)", "start": [ 73, 1 ], "end": [ 83, 93 ], "kind": "commanddeclaration" }, { "full_name": "TensorProduct.directLimitLeft_tmul_of", "code": "@[simp] lemma directLimitLeft_tmul_of {i : ι} (g : G i) (m : M) :\n directLimitLeft f M (of _ _ _ _ _ g ⊗ₜ m) = of _ _ _ (f ▷ M) _ (g ⊗ₜ m) :=\n toDirectLimit_tmul_of f g m", "start": [ 85, 1 ], "end": [ 87, 30 ], "kind": "lemma" }, { "full_name": "TensorProduct.directLimitLeft_symm_of_tmul", "code": "@[simp] lemma directLimitLeft_symm_of_tmul {i : ι} (g : G i) (m : M) :\n (directLimitLeft f M).symm (of _ _ _ _ _ (g ⊗ₜ m)) = of _ _ _ f _ g ⊗ₜ m :=\n fromDirectLimit_of_tmul f g m", "start": [ 89, 1 ], "end": [ 91, 32 ], "kind": "lemma" }, { "full_name": "TensorProduct.directLimitRight", "code": "noncomputable def directLimitRight :\n M ⊗[R] DirectLimit G f ≃ₗ[R] DirectLimit (M ⊗[R] G ·) (M ◁ f) :=\n TensorProduct.comm _ _ _ ≪≫ₗ directLimitLeft f M ≪≫ₗ\n Module.DirectLimit.congr (fun i ↦ TensorProduct.comm _ _ _)\n (fun i j h ↦ TensorProduct.ext <| DFunLike.ext _ _ <| by aesop)", "start": [ 93, 1 ], "end": [ 100, 70 ], "kind": "commanddeclaration" }, { "full_name": "TensorProduct.directLimitRight_tmul_of", "code": "@[simp] lemma directLimitRight_tmul_of {i : ι} (m : M) (g : G i):\n directLimitRight f M (m ⊗ₜ of _ _ _ _ _ g) = of _ _ _ _ i (m ⊗ₜ g) := by\n simp [directLimitRight, congr_apply_of]", "start": [ 102, 1 ], "end": [ 104, 42 ], "kind": "lemma" }, { "full_name": "TensorProduct.directLimitRight_symm_of_tmul", "code": "@[simp] lemma directLimitRight_symm_of_tmul {i : ι} (m : M) (g : G i) :\n (directLimitRight f M).symm (of _ _ _ _ _ (m ⊗ₜ g)) = m ⊗ₜ of _ _ _ f _ g := by\n simp [directLimitRight, congr_symm_apply_of]", "start": [ 106, 1 ], "end": [ 108, 47 ], "kind": "lemma" } ]

Mathlib/Analysis/Convex/Quasiconvex.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/Convex/Function.lean" ]

[ { "full_name": "QuasiconvexOn", "code": "def QuasiconvexOn : Prop :=\n ∀ r, Convex 𝕜 ({ x ∈ s | f x ≤ r })", "start": [ 48, 1 ], "end": [ 51, 38 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconcaveOn", "code": "def QuasiconcaveOn : Prop :=\n ∀ r, Convex 𝕜 ({ x ∈ s | r ≤ f x })", "start": [ 54, 1 ], "end": [ 57, 38 ], "kind": "commanddeclaration" }, { "full_name": "QuasilinearOn", "code": "def QuasilinearOn : Prop :=\n QuasiconvexOn 𝕜 s f ∧ QuasiconcaveOn 𝕜 s f", "start": [ 60, 1 ], "end": [ 64, 45 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconvexOn.dual", "code": "theorem QuasiconvexOn.dual : QuasiconvexOn 𝕜 s f → QuasiconcaveOn 𝕜 s (toDual ∘ f)", "start": [ 69, 1 ], "end": [ 70, 5 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconcaveOn.dual", "code": "theorem QuasiconcaveOn.dual : QuasiconcaveOn 𝕜 s f → QuasiconvexOn 𝕜 s (toDual ∘ f)", "start": [ 73, 1 ], "end": [ 74, 5 ], "kind": "commanddeclaration" }, { "full_name": "QuasilinearOn.dual", "code": "theorem QuasilinearOn.dual : QuasilinearOn 𝕜 s f → QuasilinearOn 𝕜 s (toDual ∘ f)", "start": [ 77, 1 ], "end": [ 78, 11 ], "kind": "commanddeclaration" }, { "full_name": "Convex.quasiconvexOn_of_convex_le", "code": "theorem Convex.quasiconvexOn_of_convex_le (hs : Convex 𝕜 s) (h : ∀ r, Convex 𝕜 { x | f x ≤ r }) :\n QuasiconvexOn 𝕜 s f", "start": [ 81, 1 ], "end": [ 82, 51 ], "kind": "commanddeclaration" }, { "full_name": "Convex.quasiconcaveOn_of_convex_ge", "code": "theorem Convex.quasiconcaveOn_of_convex_ge (hs : Convex 𝕜 s) (h : ∀ r, Convex 𝕜 { x | r ≤ f x }) :\n QuasiconcaveOn 𝕜 s f", "start": [ 85, 1 ], "end": [ 87, 62 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconvexOn.convex", "code": "theorem QuasiconvexOn.convex [IsDirected β (· ≤ ·)] (hf : QuasiconvexOn 𝕜 s f) : Convex 𝕜 s", "start": [ 90, 1 ], "end": [ 93, 41 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconcaveOn.convex", "code": "theorem QuasiconcaveOn.convex [IsDirected β (· ≥ ·)] (hf : QuasiconcaveOn 𝕜 s f) : Convex 𝕜 s", "start": [ 96, 1 ], "end": [ 97, 17 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconvexOn.sup", "code": "theorem QuasiconvexOn.sup [SemilatticeSup β] (hf : QuasiconvexOn 𝕜 s f)\n (hg : QuasiconvexOn 𝕜 s g) : QuasiconvexOn 𝕜 s (f ⊔ g)", "start": [ 106, 1 ], "end": [ 110, 28 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconcaveOn.inf", "code": "theorem QuasiconcaveOn.inf [SemilatticeInf β] (hf : QuasiconcaveOn 𝕜 s f)\n (hg : QuasiconcaveOn 𝕜 s g) : QuasiconcaveOn 𝕜 s (f ⊓ g)", "start": [ 113, 1 ], "end": [ 115, 17 ], "kind": "commanddeclaration" }, { "full_name": "quasiconvexOn_iff_le_max", "code": "theorem quasiconvexOn_iff_le_max : QuasiconvexOn 𝕜 s f ↔ Convex 𝕜 s ∧ ∀ ⦃x⦄, x ∈ s → ∀ ⦃y⦄,\n y ∈ s → ∀ ⦃a b : 𝕜⦄, 0 ≤ a → 0 ≤ b → a + b = 1 → f (a • x + b • y) ≤ max (f x) (f y)", "start": [ 124, 1 ], "end": [ 130, 86 ], "kind": "commanddeclaration" }, { "full_name": "quasiconcaveOn_iff_min_le", "code": "theorem quasiconcaveOn_iff_min_le : QuasiconcaveOn 𝕜 s f ↔ Convex 𝕜 s ∧ ∀ ⦃x⦄, x ∈ s → ∀ ⦃y⦄,\n y ∈ s → ∀ ⦃a b : 𝕜⦄, 0 ≤ a → 0 ≤ b → a + b = 1 → min (f x) (f y) ≤ f (a • x + b • y)", "start": [ 133, 1 ], "end": [ 135, 48 ], "kind": "commanddeclaration" }, { "full_name": "quasilinearOn_iff_mem_uIcc", "code": "theorem quasilinearOn_iff_mem_uIcc : QuasilinearOn 𝕜 s f ↔ Convex 𝕜 s ∧ ∀ ⦃x⦄, x ∈ s → ∀ ⦃y⦄,\n y ∈ s → ∀ ⦃a b : 𝕜⦄, 0 ≤ a → 0 ≤ b → a + b = 1 → f (a • x + b • y) ∈ uIcc (f x) (f y)", "start": [ 138, 1 ], "end": [ 143, 59 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconvexOn.convex_lt", "code": "theorem QuasiconvexOn.convex_lt (hf : QuasiconvexOn 𝕜 s f) (r : β) :\n Convex 𝕜 ({ x ∈ s | f x < r })", "start": [ 146, 1 ], "end": [ 150, 48 ], "kind": "commanddeclaration" }, { "full_name": "QuasiconcaveOn.convex_gt", "code": "theorem QuasiconcaveOn.convex_gt (hf : QuasiconcaveOn 𝕜 s f) (r : β) :\n Convex 𝕜 ({ x ∈ s | r < f x })", "start": [ 153, 1 ], "end": [ 155, 22 ], "kind": "commanddeclaration" }, { "full_name": "ConvexOn.quasiconvexOn", "code": "theorem ConvexOn.quasiconvexOn (hf : ConvexOn 𝕜 s f) : QuasiconvexOn 𝕜 s f", "start": [ 165, 1 ], "end": [ 166, 15 ], "kind": "commanddeclaration" }, { "full_name": "ConcaveOn.quasiconcaveOn", "code": "theorem ConcaveOn.quasiconcaveOn (hf : ConcaveOn 𝕜 s f) : QuasiconcaveOn 𝕜 s f", "start": [ 169, 1 ], "end": [ 170, 15 ], "kind": "commanddeclaration" }, { "full_name": "MonotoneOn.quasiconvexOn", "code": "theorem MonotoneOn.quasiconvexOn (hf : MonotoneOn f s) (hs : Convex 𝕜 s) : QuasiconvexOn 𝕜 s f", "start": [ 182, 1 ], "end": [ 183, 18 ], "kind": "commanddeclaration" }, { "full_name": "MonotoneOn.quasiconcaveOn", "code": "theorem MonotoneOn.quasiconcaveOn (hf : MonotoneOn f s) (hs : Convex 𝕜 s) : QuasiconcaveOn 𝕜 s f", "start": [ 186, 1 ], "end": [ 187, 18 ], "kind": "commanddeclaration" }, { "full_name": "MonotoneOn.quasilinearOn", "code": "theorem MonotoneOn.quasilinearOn (hf : MonotoneOn f s) (hs : Convex 𝕜 s) : QuasilinearOn 𝕜 s f", "start": [ 190, 1 ], "end": [ 191, 46 ], "kind": "commanddeclaration" }, { "full_name": "AntitoneOn.quasiconvexOn", "code": "theorem AntitoneOn.quasiconvexOn (hf : AntitoneOn f s) (hs : Convex 𝕜 s) : QuasiconvexOn 𝕜 s f", "start": [ 194, 1 ], "end": [ 195, 18 ], "kind": "commanddeclaration" }, { "full_name": "AntitoneOn.quasiconcaveOn", "code": "theorem AntitoneOn.quasiconcaveOn (hf : AntitoneOn f s) (hs : Convex 𝕜 s) : QuasiconcaveOn 𝕜 s f", "start": [ 198, 1 ], "end": [ 199, 18 ], "kind": "commanddeclaration" }, { "full_name": "AntitoneOn.quasilinearOn", "code": "theorem AntitoneOn.quasilinearOn (hf : AntitoneOn f s) (hs : Convex 𝕜 s) : QuasilinearOn 𝕜 s f", "start": [ 202, 1 ], "end": [ 203, 46 ], "kind": "commanddeclaration" }, { "full_name": "Monotone.quasiconvexOn", "code": "theorem Monotone.quasiconvexOn (hf : Monotone f) : QuasiconvexOn 𝕜 univ f", "start": [ 206, 1 ], "end": [ 207, 46 ], "kind": "commanddeclaration" }, { "full_name": "Monotone.quasiconcaveOn", "code": "theorem Monotone.quasiconcaveOn (hf : Monotone f) : QuasiconcaveOn 𝕜 univ f", "start": [ 210, 1 ], "end": [ 211, 47 ], "kind": "commanddeclaration" }, { "full_name": "Monotone.quasilinearOn", "code": "theorem Monotone.quasilinearOn (hf : Monotone f) : QuasilinearOn 𝕜 univ f", "start": [ 214, 1 ], "end": [ 215, 40 ], "kind": "commanddeclaration" }, { "full_name": "Antitone.quasiconvexOn", "code": "theorem Antitone.quasiconvexOn (hf : Antitone f) : QuasiconvexOn 𝕜 univ f", "start": [ 218, 1 ], "end": [ 219, 46 ], "kind": "commanddeclaration" }, { "full_name": "Antitone.quasiconcaveOn", "code": "theorem Antitone.quasiconcaveOn (hf : Antitone f) : QuasiconcaveOn 𝕜 univ f", "start": [ 222, 1 ], "end": [ 223, 47 ], "kind": "commanddeclaration" }, { "full_name": "Antitone.quasilinearOn", "code": "theorem Antitone.quasilinearOn (hf : Antitone f) : QuasilinearOn 𝕜 univ f", "start": [ 226, 1 ], "end": [ 227, 40 ], "kind": "commanddeclaration" }, { "full_name": "QuasilinearOn.monotoneOn_or_antitoneOn", "code": "theorem QuasilinearOn.monotoneOn_or_antitoneOn [LinearOrder β] (hf : QuasilinearOn 𝕜 s f) :\n MonotoneOn f s ∨ AntitoneOn f s", "start": [ 238, 1 ], "end": [ 242, 97 ], "kind": "commanddeclaration" }, { "full_name": "quasilinearOn_iff_monotoneOn_or_antitoneOn", "code": "theorem quasilinearOn_iff_monotoneOn_or_antitoneOn [LinearOrderedAddCommMonoid β]\n (hs : Convex 𝕜 s) : QuasilinearOn 𝕜 s f ↔ MonotoneOn f s ∨ AntitoneOn f s", "start": [ 245, 1 ], "end": [ 248, 70 ], "kind": "commanddeclaration" } ]

Mathlib/Algebra/AddConstMap/Basic.lean

[ "Mathlib/Algebra/Module/Defs.lean", "Mathlib/Algebra/Order/Group/Instances.lean", "Mathlib/Logic/Function/Iterate.lean", "Mathlib/Algebra/GroupPower/IterateHom.lean", "Mathlib/GroupTheory/GroupAction/Pi.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Algebra/Order/Archimedean.lean" ]

[ { "full_name": "AddConstMap", "code": "structure AddConstMap (G H : Type*) [Add G] [Add H] (a : G) (b : H) where\n \n protected toFun : G → H\n \n map_add_const' (x : G) : toFun (x + a) = toFun x + b", "start": [ 33, 1 ], "end": [ 41, 55 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass", "code": "class AddConstMapClass (F : Type*) (G H : outParam Type*) [Add G] [Add H]\n (a : outParam G) (b : outParam H) [FunLike F G H] : Prop where\n \n map_add_const (f : F) (x : G) : f (x + a) = f x + b", "start": [ 46, 1 ], "end": [ 55, 54 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.semiconj", "code": "protected theorem semiconj [Add G] [Add H] [AddConstMapClass F G H a b] (f : F) :\n Semiconj f (· + a) (· + b)", "start": [ 69, 1 ], "end": [ 71, 18 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_nsmul", "code": "@[scoped simp]\ntheorem map_add_nsmul [AddMonoid G] [AddMonoid H] [AddConstMapClass F G H a b]\n (f : F) (x : G) (n : ℕ) : f (x + n • a) = f x + n • b", "start": [ 73, 1 ], "end": [ 76, 62 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_nat'", "code": "@[scoped simp]\ntheorem map_add_nat' [AddMonoidWithOne G] [AddMonoid H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) (n : ℕ) : f (x + n) = f x + n • b", "start": [ 78, 1 ], "end": [ 80, 83 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_one", "code": "theorem map_add_one [AddMonoidWithOne G] [Add H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) : f (x + 1) = f x + b", "start": [ 82, 1 ], "end": [ 83, 63 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_ofNat'", "code": "@[scoped simp]\ntheorem map_add_ofNat' [AddMonoidWithOne G] [AddMonoid H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) (n : ℕ) [n.AtLeastTwo] :\n f (x + no_index (OfNat.ofNat n)) = f x + (OfNat.ofNat n : ℕ) • b", "start": [ 85, 1 ], "end": [ 89, 21 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_nat", "code": "theorem map_add_nat [AddMonoidWithOne G] [AddMonoidWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (x : G) (n : ℕ) : f (x + n) = f x + n", "start": [ 91, 1 ], "end": [ 92, 61 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_ofNat", "code": "theorem map_add_ofNat [AddMonoidWithOne G] [AddMonoidWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (x : G) (n : ℕ) [n.AtLeastTwo] :\n f (x + OfNat.ofNat n) = f x + OfNat.ofNat n", "start": [ 94, 1 ], "end": [ 96, 69 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_const", "code": "@[scoped simp]\ntheorem map_const [AddZeroClass G] [Add H] [AddConstMapClass F G H a b] (f : F) :\n f a = f 0 + b", "start": [ 98, 1 ], "end": [ 101, 32 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_one", "code": "theorem map_one [AddZeroClass G] [One G] [Add H] [AddConstMapClass F G H 1 b] (f : F) :\n f 1 = f 0 + b", "start": [ 103, 1 ], "end": [ 105, 14 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_nsmul_const", "code": "@[scoped simp]\ntheorem map_nsmul_const [AddMonoid G] [AddMonoid H] [AddConstMapClass F G H a b]\n (f : F) (n : ℕ) : f (n • a) = f 0 + n • b", "start": [ 107, 1 ], "end": [ 110, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_nat'", "code": "@[scoped simp]\ntheorem map_nat' [AddMonoidWithOne G] [AddMonoid H] [AddConstMapClass F G H 1 b]\n (f : F) (n : ℕ) : f n = f 0 + n • b", "start": [ 112, 1 ], "end": [ 115, 33 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_ofNat'", "code": "theorem map_ofNat' [AddMonoidWithOne G] [AddMonoid H] [AddConstMapClass F G H 1 b]\n (f : F) (n : ℕ) [n.AtLeastTwo] :\n f (OfNat.ofNat n) = f 0 + (OfNat.ofNat n : ℕ) • b", "start": [ 117, 1 ], "end": [ 120, 15 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_nat", "code": "theorem map_nat [AddMonoidWithOne G] [AddMonoidWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (n : ℕ) : f n = f 0 + n", "start": [ 122, 1 ], "end": [ 123, 47 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_ofNat", "code": "theorem map_ofNat [AddMonoidWithOne G] [AddMonoidWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (n : ℕ) [n.AtLeastTwo] :\n f (OfNat.ofNat n) = f 0 + OfNat.ofNat n", "start": [ 125, 1 ], "end": [ 127, 59 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_const_add", "code": "@[scoped simp]\ntheorem map_const_add [AddCommSemigroup G] [Add H] [AddConstMapClass F G H a b]\n (f : F) (x : G) : f (a + x) = f x + b", "start": [ 129, 1 ], "end": [ 132, 31 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_one_add", "code": "theorem map_one_add [AddCommMonoidWithOne G] [Add H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) : f (1 + x) = f x + b", "start": [ 134, 1 ], "end": [ 135, 63 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_nsmul_add", "code": "@[scoped simp]\ntheorem map_nsmul_add [AddCommMonoid G] [AddMonoid H] [AddConstMapClass F G H a b]\n (f : F) (n : ℕ) (x : G) : f (n • a + x) = f x + n • b", "start": [ 137, 1 ], "end": [ 140, 31 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_nat_add'", "code": "@[scoped simp]\ntheorem map_nat_add' [AddCommMonoidWithOne G] [AddMonoid H] [AddConstMapClass F G H 1 b]\n (f : F) (n : ℕ) (x : G) : f (↑n + x) = f x + n • b", "start": [ 142, 1 ], "end": [ 145, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_ofNat_add'", "code": "theorem map_ofNat_add' [AddCommMonoidWithOne G] [AddMonoid H] [AddConstMapClass F G H 1 b]\n (f : F) (n : ℕ) [n.AtLeastTwo] (x : G) :\n f (OfNat.ofNat n + x) = f x + OfNat.ofNat n • b", "start": [ 147, 1 ], "end": [ 150, 21 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_nat_add", "code": "theorem map_nat_add [AddCommMonoidWithOne G] [AddMonoidWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (n : ℕ) (x : G) : f (↑n + x) = f x + n", "start": [ 152, 1 ], "end": [ 153, 62 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_ofNat_add", "code": "theorem map_ofNat_add [AddCommMonoidWithOne G] [AddMonoidWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (n : ℕ) [n.AtLeastTwo] (x : G) :\n f (OfNat.ofNat n + x) = f x + OfNat.ofNat n", "start": [ 155, 1 ], "end": [ 158, 20 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_nsmul", "code": "@[scoped simp]\ntheorem map_sub_nsmul [AddGroup G] [AddGroup H] [AddConstMapClass F G H a b]\n (f : F) (x : G) (n : ℕ) : f (x - n • a) = f x - n • b", "start": [ 160, 1 ], "end": [ 163, 83 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_const", "code": "@[scoped simp]\ntheorem map_sub_const [AddGroup G] [AddGroup H] [AddConstMapClass F G H a b]\n (f : F) (x : G) : f (x - a) = f x - b", "start": [ 165, 1 ], "end": [ 168, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_one", "code": "theorem map_sub_one [AddGroup G] [One G] [AddGroup H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) : f (x - 1) = f x - b", "start": [ 170, 1 ], "end": [ 172, 20 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_nat'", "code": "@[scoped simp]\ntheorem map_sub_nat' [AddGroupWithOne G] [AddGroup H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) (n : ℕ) : f (x - n) = f x - n • b", "start": [ 174, 1 ], "end": [ 177, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_ofNat'", "code": "@[scoped simp]\ntheorem map_sub_ofNat' [AddGroupWithOne G] [AddGroup H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) (n : ℕ) [n.AtLeastTwo] :\n f (x - no_index (OfNat.ofNat n)) = f x - OfNat.ofNat n • b", "start": [ 179, 1 ], "end": [ 183, 21 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_zsmul", "code": "@[scoped simp]\ntheorem map_add_zsmul [AddGroup G] [AddGroup H] [AddConstMapClass F G H a b]\n (f : F) (x : G) : ∀ n : ℤ, f (x + n • a) = f x + n • b", "start": [ 185, 1 ], "end": [ 189, 45 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_zsmul_const", "code": "@[scoped simp]\ntheorem map_zsmul_const [AddGroup G] [AddGroup H] [AddConstMapClass F G H a b]\n (f : F) (n : ℤ) : f (n • a) = f 0 + n • b", "start": [ 191, 1 ], "end": [ 194, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_int'", "code": "@[scoped simp]\ntheorem map_add_int' [AddGroupWithOne G] [AddGroup H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) (n : ℤ) : f (x + n) = f x + n • b", "start": [ 196, 1 ], "end": [ 199, 40 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_add_int", "code": "theorem map_add_int [AddGroupWithOne G] [AddGroupWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (x : G) (n : ℤ) : f (x + n) = f x + n", "start": [ 201, 1 ], "end": [ 202, 61 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_zsmul", "code": "@[scoped simp]\ntheorem map_sub_zsmul [AddGroup G] [AddGroup H] [AddConstMapClass F G H a b]\n (f : F) (x : G) (n : ℤ) : f (x - n • a) = f x - n • b", "start": [ 204, 1 ], "end": [ 207, 54 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_int'", "code": "@[scoped simp]\ntheorem map_sub_int' [AddGroupWithOne G] [AddGroup H] [AddConstMapClass F G H 1 b]\n (f : F) (x : G) (n : ℤ) : f (x - n) = f x - n • b", "start": [ 209, 1 ], "end": [ 212, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_sub_int", "code": "theorem map_sub_int [AddGroupWithOne G] [AddGroupWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (x : G) (n : ℤ) : f (x - n) = f x - n", "start": [ 214, 1 ], "end": [ 215, 61 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_zsmul_add", "code": "@[scoped simp]\ntheorem map_zsmul_add [AddCommGroup G] [AddGroup H] [AddConstMapClass F G H a b]\n (f : F) (n : ℤ) (x : G) : f (n • a + x) = f x + n • b", "start": [ 217, 1 ], "end": [ 220, 31 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_int_add'", "code": "@[scoped simp]\ntheorem map_int_add' [AddCommGroupWithOne G] [AddGroup H] [AddConstMapClass F G H 1 b]\n (f : F) (n : ℤ) (x : G) : f (↑n + x) = f x + n • b", "start": [ 222, 1 ], "end": [ 225, 34 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_int_add", "code": "theorem map_int_add [AddCommGroupWithOne G] [AddGroupWithOne H] [AddConstMapClass F G H 1 1]\n (f : F) (n : ℤ) (x : G) : f (↑n + x) = f x + n", "start": [ 227, 1 ], "end": [ 228, 62 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.map_fract", "code": "theorem map_fract {R : Type*} [LinearOrderedRing R] [FloorRing R] [AddGroup H]\n [FunLike F R H] [AddConstMapClass F R H 1 b] (f : F) (x : R) :\n f (Int.fract x) = f x - ⌊x⌋ • b", "start": [ 230, 1 ], "end": [ 233, 18 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.rel_map_of_Icc", "code": "protected theorem rel_map_of_Icc [LinearOrderedAddCommGroup G] [Archimedean G] [AddGroup H]\n [AddConstMapClass F G H a b] {f : F} {R : H → H → Prop} [IsTrans H R]\n [hR : CovariantClass H H (fun x y ↦ y + x) R] (ha : 0 < a) {l : G}\n (hf : ∀ x ∈ Icc l (l + a), ∀ y ∈ Icc l (l + a), x < y → R (f x) (f y)) :\n ((· < ·) ⇒ R) f f", "start": [ 235, 1 ], "end": [ 276, 19 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.monotone_iff_Icc", "code": "theorem monotone_iff_Icc [LinearOrderedAddCommGroup G] [Archimedean G] [OrderedAddCommGroup H]\n [AddConstMapClass F G H a b] {f : F} (ha : 0 < a) (l : G) :\n Monotone f ↔ MonotoneOn f (Icc l (l + a))", "start": [ 278, 1 ], "end": [ 282, 78 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.antitone_iff_Icc", "code": "theorem antitone_iff_Icc [LinearOrderedAddCommGroup G] [Archimedean G] [OrderedAddCommGroup H]\n [AddConstMapClass F G H a b] {f : F} (ha : 0 < a) (l : G) :\n Antitone f ↔ AntitoneOn f (Icc l (l + a))", "start": [ 284, 1 ], "end": [ 287, 35 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.strictMono_iff_Icc", "code": "theorem strictMono_iff_Icc [LinearOrderedAddCommGroup G] [Archimedean G] [OrderedAddCommGroup H]\n [AddConstMapClass F G H a b] {f : F} (ha : 0 < a) (l : G) :\n StrictMono f ↔ StrictMonoOn f (Icc l (l + a))", "start": [ 289, 1 ], "end": [ 292, 70 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMapClass.strictAnti_iff_Icc", "code": "theorem strictAnti_iff_Icc [LinearOrderedAddCommGroup G] [Archimedean G] [OrderedAddCommGroup H]\n [AddConstMapClass F G H a b] {f : F} (ha : 0 < a) (l : G) :\n StrictAnti f ↔ StrictAntiOn f (Icc l (l + a))", "start": [ 294, 1 ], "end": [ 297, 37 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.coe_mk", "code": "@[scoped simp] theorem coe_mk (f : G → H) (hf) : ⇑(mk f hf : G →+c[a, b] H) = f", "start": [ 317, 1 ], "end": [ 317, 87 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.mk_coe", "code": "@[scoped simp] theorem mk_coe (f : G →+c[a, b] H) : mk f f.2 = f", "start": [ 318, 1 ], "end": [ 318, 72 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.toFun_eq_coe", "code": "@[scoped simp] theorem toFun_eq_coe (f : G →+c[a, b] H) : f.toFun = f", "start": [ 319, 1 ], "end": [ 319, 77 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.ext", "code": "@[ext] protected theorem ext {f g : G →+c[a, b] H} (h : ∀ x, f x = g x) : f = g", "start": [ 324, 1 ], "end": [ 325, 21 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.id", "code": "@[simps (config := .asFn)]\nprotected def id : G →+c[a, a] G := ⟨id, fun _ ↦ rfl⟩", "start": [ 333, 1 ], "end": [ 335, 54 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.comp", "code": "@[simps (config := .asFn)]\ndef comp {K : Type*} [Add K] {c : K} (g : H →+c[b, c] K) (f : G →+c[a, b] H) :\n G →+c[a, c] K :=\n ⟨g ∘ f, by simp⟩", "start": [ 339, 1 ], "end": [ 343, 19 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.comp_id", "code": "@[scoped simp] theorem comp_id (f : G →+c[a, b] H) : f.comp .id = f", "start": [ 345, 1 ], "end": [ 345, 75 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.id_comp", "code": "@[scoped simp] theorem id_comp (f : G →+c[a, b] H) : .comp .id f = f", "start": [ 346, 1 ], "end": [ 346, 76 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.replaceConsts", "code": "@[simps (config := .asFn)]\ndef replaceConsts (f : G →+c[a, b] H) (a' b') (ha : a = a') (hb : b = b') :\n G →+c[a', b'] H where\n toFun := f\n map_add_const' := ha ▸ hb ▸ f.map_add_const'", "start": [ 348, 1 ], "end": [ 353, 47 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.coe_vadd", "code": "@[scoped simp]\ntheorem coe_vadd {K : Type*} [VAdd K H] [VAddAssocClass K H H] (c : K) (f : G →+c[a, b] H) :\n ⇑(c +ᵥ f) = c +ᵥ ⇑f", "start": [ 363, 1 ], "end": [ 366, 6 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.mul_def", "code": "theorem mul_def (f g : G →+c[a, a] G) : f * g = f.comp g", "start": [ 385, 1 ], "end": [ 385, 64 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.coe_mul", "code": "@[scoped simp] theorem coe_mul (f g : G →+c[a, a] G) : ⇑(f * g) = f ∘ g", "start": [ 386, 1 ], "end": [ 386, 79 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.one_def", "code": "theorem one_def : (1 : G →+c[a, a] G) = .id", "start": [ 388, 1 ], "end": [ 388, 51 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.coe_one", "code": "@[scoped simp] theorem coe_one : ⇑(1 : G →+c[a, a] G) = id", "start": [ 389, 1 ], "end": [ 389, 66 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.coe_pow", "code": "@[scoped simp] theorem coe_pow (f : G →+c[a, a] G) (n : ℕ) : ⇑(f ^ n) = f^[n]", "start": [ 391, 1 ], "end": [ 391, 85 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.pow_apply", "code": "theorem pow_apply (f : G →+c[a, a] G) (n : ℕ) (x : G) : (f ^ n) x = f^[n] x", "start": [ 393, 1 ], "end": [ 393, 83 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.smul", "code": "@[simps (config := .asFn)]\ndef smul [DistribSMul K H] (c : K) (f : G →+c[a, b] H) : G →+c[a, c • b] H where\n toFun := c • ⇑f\n map_add_const' x := by simp [smul_add]", "start": [ 411, 1 ], "end": [ 415, 41 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.addLeftHom", "code": "@[simps! (config := .asFn)]\ndef addLeftHom : Multiplicative G →* (G →+c[a, a] G) where\n toFun c := Multiplicative.toAdd c +ᵥ .id\n map_one' := by ext; apply zero_add\n map_mul' _ _ := by ext; apply add_assoc", "start": [ 423, 1 ], "end": [ 429, 42 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.conjNeg", "code": "@[simps! apply_coe]\ndef conjNeg : (G →+c[a, b] H) ≃ (G →+c[a, b] H) :=\n Involutive.toPerm (fun f ↦ ⟨fun x ↦ - f (-x), fun _ ↦ by simp [neg_add_eq_sub]⟩) fun _ ↦\n AddConstMap.ext fun _ ↦ by simp", "start": [ 437, 1 ], "end": [ 441, 36 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.conjNeg_symm", "code": "@[scoped simp] theorem conjNeg_symm : (conjNeg (a := a) (b := b)).symm = conjNeg", "start": [ 443, 1 ], "end": [ 443, 88 ], "kind": "commanddeclaration" }, { "full_name": "AddConstMap.mkFract", "code": "def mkFract : (Ico (0 : R) 1 → G) ≃ (R →+c[1, a] G) where\n toFun f := ⟨fun x ↦ f ⟨Int.fract x, Int.fract_nonneg _, Int.fract_lt_one _⟩ + ⌊x⌋ • a, fun x ↦ by\n simp [add_one_zsmul, add_assoc]⟩\n invFun f x := f x\n left_inv _ := by ext x; simp [Int.fract_eq_self.2 x.2, Int.floor_eq_zero_iff.2 x.2]\n right_inv f := by ext x; simp [map_fract]", "start": [ 451, 1 ], "end": [ 457, 44 ], "kind": "commanddeclaration" } ]

Mathlib/Probability/BorelCantelli.lean

[ "Mathlib/Probability/ConditionalExpectation.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Probability/Martingale/BorelCantelli.lean", "Mathlib/Probability/Independence/Basic.lean" ]

[ { "full_name": "ProbabilityTheory.iIndepFun.indep_comap_natural_of_lt", "code": "theorem iIndepFun.indep_comap_natural_of_lt (hf : ∀ i, StronglyMeasurable (f i))\n (hfi : iIndepFun (fun _ => mβ) f μ) (hij : i < j) :\n Indep (MeasurableSpace.comap (f j) mβ) (Filtration.natural f hf i) μ", "start": [ 43, 1 ], "end": [ 48, 84 ], "kind": "commanddeclaration" }, { "full_name": "ProbabilityTheory.iIndepFun.condexp_natural_ae_eq_of_lt", "code": "theorem iIndepFun.condexp_natural_ae_eq_of_lt [SecondCountableTopology β] [CompleteSpace β]\n [NormedSpace ℝ β] (hf : ∀ i, StronglyMeasurable (f i)) (hfi : iIndepFun (fun _ => mβ) f μ)\n (hij : i < j) : μ[f j|Filtration.natural f hf i] =ᵐ[μ] fun _ => μ[f j]", "start": [ 52, 1 ], "end": [ 56, 88 ], "kind": "commanddeclaration" }, { "full_name": "ProbabilityTheory.iIndepSet.condexp_indicator_filtrationOfSet_ae_eq", "code": "theorem iIndepSet.condexp_indicator_filtrationOfSet_ae_eq (hsm : ∀ n, MeasurableSet (s n))\n (hs : iIndepSet s μ) (hij : i < j) :\n μ[(s j).indicator (fun _ => 1 : Ω → ℝ)|filtrationOfSet hsm i] =ᵐ[μ]\n fun _ => (μ (s j)).toReal", "start": [ 60, 1 ], "end": [ 66, 87 ], "kind": "commanddeclaration" }, { "full_name": "ProbabilityTheory.measure_limsup_eq_one", "code": "theorem measure_limsup_eq_one {s : ℕ → Set Ω} (hsm : ∀ n, MeasurableSet (s n)) (hs : iIndepSet s μ)\n (hs' : (∑' n, μ (s n)) = ∞) : μ (limsup s atTop) = 1", "start": [ 72, 1 ], "end": [ 105, 44 ], "kind": "commanddeclaration" } ]

Mathlib/Combinatorics/SetFamily/Compression/UV.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Combinatorics/SetFamily/Shadow.lean" ]

[ { "full_name": "sup_sdiff_injOn", "code": "theorem sup_sdiff_injOn [GeneralizedBooleanAlgebra α] (u v : α) :\n { x | Disjoint u x ∧ v ≤ x }.InjOn fun x => (x ⊔ u) \\ v", "start": [ 56, 1 ], "end": [ 64, 89 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress", "code": "def compress (u v a : α) : α :=\n if Disjoint u a ∧ v ≤ a then (a ⊔ u) \\ v else a", "start": [ 78, 1 ], "end": [ 82, 50 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_of_disjoint_of_le", "code": "theorem compress_of_disjoint_of_le (hua : Disjoint u a) (hva : v ≤ a) :\n compress u v a = (a ⊔ u) \\ v", "start": [ 85, 1 ], "end": [ 87, 20 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_of_disjoint_of_le'", "code": "theorem compress_of_disjoint_of_le' (hva : Disjoint v a) (hua : u ≤ a) :\n compress u v ((a ⊔ v) \\ u) = a", "start": [ 90, 1 ], "end": [ 94, 79 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_self", "code": "@[simp]\ntheorem compress_self (u a : α) : compress u u a = a", "start": [ 97, 1 ], "end": [ 102, 8 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_sdiff_sdiff", "code": "@[simp]\ntheorem compress_sdiff_sdiff (a b : α) : compress (a \\ b) (b \\ a) b = a", "start": [ 105, 1 ], "end": [ 110, 23 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_idem", "code": "@[simp]\ntheorem compress_idem (u v a : α) : compress u v (compress u v a) = compress u v a", "start": [ 113, 1 ], "end": [ 120, 8 ], "kind": "commanddeclaration" }, { "full_name": "UV.compression", "code": "def compression (u v : α) (s : Finset α) :=\n (s.filter (compress u v · ∈ s)) ∪ (s.image <| compress u v).filter (· ∉ s)", "start": [ 125, 1 ], "end": [ 128, 77 ], "kind": "commanddeclaration" }, { "full_name": "UV.IsCompressed", "code": "def IsCompressed (u v : α) (s : Finset α) :=\n 𝓒 u v s = s", "start": [ 136, 1 ], "end": [ 138, 14 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_injOn", "code": "theorem compress_injOn : Set.InjOn (compress u v) ↑(s.filter (compress u v · ∉ s))", "start": [ 141, 1 ], "end": [ 151, 27 ], "kind": "commanddeclaration" }, { "full_name": "UV.mem_compression", "code": "theorem mem_compression :\n a ∈ 𝓒 u v s ↔ a ∈ s ∧ compress u v a ∈ s ∨ a ∉ s ∧ ∃ b ∈ s, compress u v b = a", "start": [ 154, 1 ], "end": [ 158, 68 ], "kind": "commanddeclaration" }, { "full_name": "UV.IsCompressed.eq", "code": "protected theorem IsCompressed.eq (h : IsCompressed u v s) : 𝓒 u v s = s", "start": [ 161, 1 ], "end": [ 161, 78 ], "kind": "commanddeclaration" }, { "full_name": "UV.compression_self", "code": "@[simp]\ntheorem compression_self (u : α) (s : Finset α) : 𝓒 u u s = s", "start": [ 164, 1 ], "end": [ 173, 17 ], "kind": "commanddeclaration" }, { "full_name": "UV.isCompressed_self", "code": "theorem isCompressed_self (u : α) (s : Finset α) : IsCompressed u u s", "start": [ 176, 1 ], "end": [ 177, 94 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_disjoint", "code": "theorem compress_disjoint :\n Disjoint (s.filter (compress u v · ∈ s)) ((s.image <| compress u v).filter (· ∉ s))", "start": [ 180, 1 ], "end": [ 182, 77 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_mem_compression", "code": "theorem compress_mem_compression (ha : a ∈ s) : compress u v a ∈ 𝓒 u v s", "start": [ 185, 1 ], "end": [ 190, 33 ], "kind": "commanddeclaration" }, { "full_name": "UV.compress_mem_compression_of_mem_compression", "code": "theorem compress_mem_compression_of_mem_compression (ha : a ∈ 𝓒 u v s) :\n compress u v a ∈ 𝓒 u v s", "start": [ 194, 1 ], "end": [ 200, 77 ], "kind": "commanddeclaration" }, { "full_name": "UV.compression_idem", "code": "@[simp]\ntheorem compression_idem (u v : α) (s : Finset α) : 𝓒 u v (𝓒 u v s) = 𝓒 u v s", "start": [ 203, 1 ], "end": [ 209, 57 ], "kind": "commanddeclaration" }, { "full_name": "UV.card_compression", "code": "@[simp]\ntheorem card_compression (u v : α) (s : Finset α) : (𝓒 u v s).card = s.card", "start": [ 212, 1 ], "end": [ 217, 32 ], "kind": "commanddeclaration" }, { "full_name": "UV.le_of_mem_compression_of_not_mem", "code": "theorem le_of_mem_compression_of_not_mem (h : a ∈ 𝓒 u v s) (ha : a ∉ s) : u ≤ a", "start": [ 220, 1 ], "end": [ 228, 41 ], "kind": "commanddeclaration" }, { "full_name": "UV.disjoint_of_mem_compression_of_not_mem", "code": "theorem disjoint_of_mem_compression_of_not_mem (h : a ∈ 𝓒 u v s) (ha : a ∉ s) : Disjoint v a", "start": [ 231, 1 ], "end": [ 239, 41 ], "kind": "commanddeclaration" }, { "full_name": "UV.sup_sdiff_mem_of_mem_compression_of_not_mem", "code": "theorem sup_sdiff_mem_of_mem_compression_of_not_mem (h : a ∈ 𝓒 u v s) (ha : a ∉ s) :\n (a ⊔ v) \\ u ∈ s", "start": [ 242, 1 ], "end": [ 251, 41 ], "kind": "commanddeclaration" }, { "full_name": "UV.sup_sdiff_mem_of_mem_compression", "code": "theorem sup_sdiff_mem_of_mem_compression (ha : a ∈ 𝓒 u v s) (hva : v ≤ a) (hua : Disjoint u a) :\n (a ⊔ u) \\ v ∈ s", "start": [ 254, 1 ], "end": [ 271, 53 ], "kind": "commanddeclaration" }, { "full_name": "UV.mem_of_mem_compression", "code": "theorem mem_of_mem_compression (ha : a ∈ 𝓒 u v s) (hva : v ≤ a) (hvu : v = ⊥ → u = ⊥) :\n a ∈ s", "start": [ 274, 1 ], "end": [ 285, 14 ], "kind": "commanddeclaration" }, { "full_name": "UV.card_compress", "code": "theorem card_compress (huv : u.card = v.card) (a : Finset α) : (compress u v a).card = a.card", "start": [ 296, 1 ], "end": [ 302, 8 ], "kind": "commanddeclaration" }, { "full_name": "Set.Sized.uvCompression", "code": "lemma _root_.Set.Sized.uvCompression (huv : u.card = v.card) (h𝒜 : (𝒜 : Set (Finset α)).Sized r) :\n (𝓒 u v 𝒜 : Set (Finset α)).Sized r := by\n simp_rw [Set.Sized, mem_coe, mem_compression]\n rintro s (hs | ⟨huvt, t, ht, rfl⟩)\n · exact h𝒜 hs.1\n · rw [card_compress huv, h𝒜 ht]", "start": [ 305, 1 ], "end": [ 310, 34 ], "kind": "lemma" }, { "full_name": "UV.aux", "code": "private theorem aux (huv : ∀ x ∈ u, ∃ y ∈ v, IsCompressed (u.erase x) (v.erase y) 𝒜) :\n v = ∅ → u = ∅", "start": [ 312, 1 ], "end": [ 314, 93 ], "kind": "commanddeclaration" }, { "full_name": "UV.shadow_compression_subset_compression_shadow", "code": "theorem shadow_compression_subset_compression_shadow (u v : Finset α)\n (huv : ∀ x ∈ u, ∃ y ∈ v, IsCompressed (u.erase x) (v.erase y) 𝒜) :\n ∂ (𝓒 u v 𝒜) ⊆ 𝓒 u v (∂ 𝒜)", "start": [ 316, 1 ], "end": [ 420, 93 ], "kind": "commanddeclaration" }, { "full_name": "UV.card_shadow_compression_le", "code": "theorem card_shadow_compression_le (u v : Finset α)\n (huv : ∀ x ∈ u, ∃ y ∈ v, IsCompressed (u.erase x) (v.erase y) 𝒜) :\n (∂ (𝓒 u v 𝒜)).card ≤ (∂ 𝒜).card", "start": [ 423, 1 ], "end": [ 430, 32 ], "kind": "commanddeclaration" } ]

Mathlib/LinearAlgebra/AffineSpace/Pointwise.lean

[ "Mathlib/LinearAlgebra/AffineSpace/AffineSubspace.lean", ".lake/packages/lean4/src/lean/Init.lean" ]

[ { "full_name": "AffineSubspace.pointwiseAddAction", "code": "protected def pointwiseAddAction : AddAction V (AffineSubspace k P) where\n vadd x S := S.map (AffineEquiv.constVAdd k P x)\n zero_vadd p := ((congr_arg fun f => p.map f) <| AffineMap.ext <| zero_vadd _).trans p.map_id\n add_vadd _ _ p :=\n ((congr_arg fun f => p.map f) <| AffineMap.ext <| add_vadd _ _).trans (p.map_map _ _).symm", "start": [ 30, 1 ], "end": [ 37, 95 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.pointwise_vadd_eq_map", "code": "theorem pointwise_vadd_eq_map (v : V) (s : AffineSubspace k P) :\n v +ᵥ s = s.map (AffineEquiv.constVAdd k P v)", "start": [ 44, 1 ], "end": [ 46, 6 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.coe_pointwise_vadd", "code": "@[simp]\ntheorem coe_pointwise_vadd (v : V) (s : AffineSubspace k P) :\n ((v +ᵥ s : AffineSubspace k P) : Set P) = v +ᵥ (s : Set P)", "start": [ 48, 1 ], "end": [ 51, 6 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.vadd_mem_pointwise_vadd_iff", "code": "theorem vadd_mem_pointwise_vadd_iff {v : V} {s : AffineSubspace k P} {p : P} :\n v +ᵥ p ∈ v +ᵥ s ↔ p ∈ s", "start": [ 54, 1 ], "end": [ 56, 24 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.pointwise_vadd_bot", "code": "theorem pointwise_vadd_bot (v : V) : v +ᵥ (⊥ : AffineSubspace k P) = ⊥", "start": [ 59, 1 ], "end": [ 60, 45 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.pointwise_vadd_direction", "code": "theorem pointwise_vadd_direction (v : V) (s : AffineSubspace k P) :\n (v +ᵥ s).direction = s.direction", "start": [ 63, 1 ], "end": [ 66, 27 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.pointwise_vadd_span", "code": "theorem pointwise_vadd_span (v : V) (s : Set P) : v +ᵥ affineSpan k s = affineSpan k (v +ᵥ s)", "start": [ 69, 1 ], "end": [ 70, 15 ], "kind": "commanddeclaration" }, { "full_name": "AffineSubspace.map_pointwise_vadd", "code": "theorem map_pointwise_vadd (f : P₁ →ᵃ[k] P₂) (v : V₁) (s : AffineSubspace k P₁) :\n (v +ᵥ s).map f = f.linear v +ᵥ s.map f", "start": [ 73, 1 ], "end": [ 78, 23 ], "kind": "commanddeclaration" } ]

Mathlib/Lean/CoreM.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Tactic/ToExpr.lean" ]

[ { "full_name": "CoreM.withImportModules", "code": "def CoreM.withImportModules (modules : Array Name) (run : CoreM α)\n (searchPath : Option SearchPath := none) (options : Options := {})\n (trustLevel : UInt32 := 0) (fileName := \"\") :\n IO α := unsafe do\n if let some sp := searchPath then searchPathRef.set sp\n Lean.withImportModules (modules.map (Import.mk · false)) options trustLevel fun env =>\n let ctx := {fileName, options, fileMap := default}\n let state := {env}\n Prod.fst <$> (CoreM.toIO · ctx state) do\n run", "start": [ 16, 1 ], "end": [ 28, 10 ], "kind": "commanddeclaration" } ]

Mathlib/Algebra/Algebra/Subalgebra/Rank.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/LinearAlgebra/Dimension/Free.lean", "Mathlib/LinearAlgebra/FreeModule/StrongRankCondition.lean", "Mathlib/LinearAlgebra/Dimension/Finite.lean" ]

[ { "full_name": "Subalgebra.rank_sup_eq_rank_left_mul_rank_of_free", "code": "theorem rank_sup_eq_rank_left_mul_rank_of_free :\n Module.rank R ↥(A ⊔ B) = Module.rank R A * Module.rank A (Algebra.adjoin A (B : Set S))", "start": [ 30, 1 ], "end": [ 41, 43 ], "kind": "commanddeclaration" }, { "full_name": "Subalgebra.rank_sup_eq_rank_right_mul_rank_of_free", "code": "theorem rank_sup_eq_rank_right_mul_rank_of_free :\n Module.rank R ↥(A ⊔ B) = Module.rank R B * Module.rank B (Algebra.adjoin B (A : Set S))", "start": [ 43, 1 ], "end": [ 45, 56 ], "kind": "commanddeclaration" }, { "full_name": "Subalgebra.finrank_sup_eq_finrank_left_mul_finrank_of_free", "code": "theorem finrank_sup_eq_finrank_left_mul_finrank_of_free :\n finrank R ↥(A ⊔ B) = finrank R A * finrank A (Algebra.adjoin A (B : Set S))", "start": [ 47, 1 ], "end": [ 49, 97 ], "kind": "commanddeclaration" }, { "full_name": "Subalgebra.finrank_sup_eq_finrank_right_mul_finrank_of_free", "code": "theorem finrank_sup_eq_finrank_right_mul_finrank_of_free :\n finrank R ↥(A ⊔ B) = finrank R B * finrank B (Algebra.adjoin B (A : Set S))", "start": [ 51, 1 ], "end": [ 53, 65 ], "kind": "commanddeclaration" }, { "full_name": "Subalgebra.finrank_left_dvd_finrank_sup_of_free", "code": "theorem finrank_left_dvd_finrank_sup_of_free :\n finrank R A ∣ finrank R ↥(A ⊔ B)", "start": [ 55, 1 ], "end": [ 56, 97 ], "kind": "commanddeclaration" }, { "full_name": "Subalgebra.finrank_right_dvd_finrank_sup_of_free", "code": "theorem finrank_right_dvd_finrank_sup_of_free :\n finrank R B ∣ finrank R ↥(A ⊔ B)", "start": [ 58, 1 ], "end": [ 59, 98 ], "kind": "commanddeclaration" } ]

Mathlib/Analysis/Convex/SimplicialComplex/Basic.lean

[ "Mathlib/Analysis/Convex/Hull.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/LinearAlgebra/AffineSpace/Independent.lean" ]

[ { "full_name": "Geometry.SimplicialComplex", "code": "@[ext]\nstructure SimplicialComplex where\n \n faces : Set (Finset E)\n \n not_empty_mem : ∅ ∉ faces\n \n indep : ∀ {s}, s ∈ faces → AffineIndependent 𝕜 ((↑) : s → E)\n \n down_closed : ∀ {s t}, s ∈ faces → t ⊆ s → t ≠ ∅ → t ∈ faces\n inter_subset_convexHull : ∀ {s t}, s ∈ faces → t ∈ faces →\n convexHull 𝕜 ↑s ∩ convexHull 𝕜 ↑t ⊆ convexHull 𝕜 (s ∩ t : Set E)", "start": [ 53, 1 ], "end": [ 68, 69 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.space", "code": "def space (K : SimplicialComplex 𝕜 E) : Set E :=\n ⋃ s ∈ K.faces, convexHull 𝕜 (s : Set E)", "start": [ 80, 1 ], "end": [ 82, 42 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.mem_space_iff", "code": "theorem mem_space_iff : x ∈ K.space ↔ ∃ s ∈ K.faces, x ∈ convexHull 𝕜 (s : Set E)", "start": [ 86, 1 ], "end": [ 87, 15 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.convexHull_subset_space", "code": "theorem convexHull_subset_space (hs : s ∈ K.faces) : convexHull 𝕜 ↑s ⊆ K.space", "start": [ 91, 1 ], "end": [ 93, 6 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.subset_space", "code": "protected theorem subset_space (hs : s ∈ K.faces) : (s : Set E) ⊆ K.space", "start": [ 96, 1 ], "end": [ 97, 62 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.convexHull_inter_convexHull", "code": "theorem convexHull_inter_convexHull (hs : s ∈ K.faces) (ht : t ∈ K.faces) :\n convexHull 𝕜 ↑s ∩ convexHull 𝕜 ↑t = convexHull 𝕜 (s ∩ t : Set E)", "start": [ 100, 1 ], "end": [ 104, 45 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.disjoint_or_exists_inter_eq_convexHull", "code": "theorem disjoint_or_exists_inter_eq_convexHull (hs : s ∈ K.faces) (ht : t ∈ K.faces) :\n Disjoint (convexHull 𝕜 (s : Set E)) (convexHull 𝕜 ↑t) ∨\n ∃ u ∈ K.faces, convexHull 𝕜 (s : Set E) ∩ convexHull 𝕜 ↑t = convexHull 𝕜 ↑u", "start": [ 107, 1 ], "end": [ 119, 54 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.ofErase", "code": "@[simps]\ndef ofErase (faces : Set (Finset E)) (indep : ∀ s ∈ faces, AffineIndependent 𝕜 ((↑) : s → E))\n (down_closed : ∀ s ∈ faces, ∀ t ⊆ s, t ∈ faces)\n (inter_subset_convexHull : ∀ᵉ (s ∈ faces) (t ∈ faces),\n convexHull 𝕜 ↑s ∩ convexHull 𝕜 ↑t ⊆ convexHull 𝕜 (s ∩ t : Set E)) :\n SimplicialComplex 𝕜 E where\n faces := faces \\ {∅}\n not_empty_mem h := h.2 (mem_singleton _)\n indep hs := indep _ hs.1\n down_closed hs hts ht := ⟨down_closed _ hs.1 _ hts, ht⟩\n inter_subset_convexHull hs ht := inter_subset_convexHull _ hs.1 _ ht.1", "start": [ 122, 1 ], "end": [ 133, 73 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.ofSubcomplex", "code": "@[simps]\ndef ofSubcomplex (K : SimplicialComplex 𝕜 E) (faces : Set (Finset E)) (subset : faces ⊆ K.faces)\n (down_closed : ∀ {s t}, s ∈ faces → t ⊆ s → t ∈ faces) : SimplicialComplex 𝕜 E :=\n { faces\n not_empty_mem := fun h => K.not_empty_mem (subset h)\n indep := fun hs => K.indep (subset hs)\n down_closed := fun hs hts _ => down_closed hs hts\n inter_subset_convexHull := fun hs ht => K.inter_subset_convexHull (subset hs) (subset ht) }", "start": [ 136, 1 ], "end": [ 144, 96 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.vertices", "code": "def vertices (K : SimplicialComplex 𝕜 E) : Set E :=\n { x | {x} ∈ K.faces }", "start": [ 150, 1 ], "end": [ 152, 24 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.mem_vertices", "code": "theorem mem_vertices : x ∈ K.vertices ↔ {x} ∈ K.faces", "start": [ 155, 1 ], "end": [ 155, 65 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.vertices_eq", "code": "theorem vertices_eq : K.vertices = ⋃ k ∈ K.faces, (k : Set E)", "start": [ 158, 1 ], "end": [ 162, 96 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.vertices_subset_space", "code": "theorem vertices_subset_space : K.vertices ⊆ K.space", "start": [ 165, 1 ], "end": [ 166, 86 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.vertex_mem_convexHull_iff", "code": "theorem vertex_mem_convexHull_iff (hx : x ∈ K.vertices) (hs : s ∈ K.faces) :\n x ∈ convexHull 𝕜 (s : Set E) ↔ x ∈ s", "start": [ 169, 1 ], "end": [ 176, 38 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.face_subset_face_iff", "code": "theorem face_subset_face_iff (hs : s ∈ K.faces) (ht : t ∈ K.faces) :\n convexHull 𝕜 (s : Set E) ⊆ convexHull 𝕜 ↑t ↔ s ⊆ t", "start": [ 179, 1 ], "end": [ 186, 21 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.facets", "code": "def facets (K : SimplicialComplex 𝕜 E) : Set (Finset E) :=\n { s ∈ K.faces | ∀ ⦃t⦄, t ∈ K.faces → s ⊆ t → s = t }", "start": [ 192, 1 ], "end": [ 194, 55 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.mem_facets", "code": "theorem mem_facets : s ∈ K.facets ↔ s ∈ K.faces ∧ ∀ t ∈ K.faces, s ⊆ t → s = t", "start": [ 197, 1 ], "end": [ 198, 14 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.facets_subset", "code": "theorem facets_subset : K.facets ⊆ K.faces", "start": [ 201, 1 ], "end": [ 201, 63 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.not_facet_iff_subface", "code": "theorem not_facet_iff_subface (hs : s ∈ K.faces) : s ∉ K.facets ↔ ∃ t, t ∈ K.faces ∧ s ⊂ t", "start": [ 204, 1 ], "end": [ 212, 33 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.hasBot", "code": "instance hasBot : Bot (SimplicialComplex 𝕜 E) :=\n ⟨{ faces := ∅\n not_empty_mem := Set.not_mem_empty ∅\n indep := fun hs => (Set.not_mem_empty _ hs).elim\n down_closed := fun hs => (Set.not_mem_empty _ hs).elim\n inter_subset_convexHull := fun hs => (Set.not_mem_empty _ hs).elim }⟩", "start": [ 241, 1 ], "end": [ 246, 76 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.faces_bot", "code": "theorem faces_bot : (⊥ : SimplicialComplex 𝕜 E).faces = ∅", "start": [ 256, 1 ], "end": [ 256, 65 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.space_bot", "code": "theorem space_bot : (⊥ : SimplicialComplex 𝕜 E).space = ∅", "start": [ 259, 1 ], "end": [ 260, 22 ], "kind": "commanddeclaration" }, { "full_name": "Geometry.SimplicialComplex.facets_bot", "code": "theorem facets_bot : (⊥ : SimplicialComplex 𝕜 E).facets = ∅", "start": [ 263, 1 ], "end": [ 264, 41 ], "kind": "commanddeclaration" } ]

Mathlib/Analysis/Calculus/Gradient/Basic.lean

[ "Mathlib/Analysis/Calculus/FDeriv/Basic.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/InnerProductSpace/Dual.lean", "Mathlib/Analysis/Calculus/Deriv/Basic.lean" ]

[ { "full_name": "HasGradientAtFilter", "code": "def HasGradientAtFilter (f : F → 𝕜) (f' x : F) (L : Filter F) :=\n HasFDerivAtFilter f (toDual 𝕜 F f') x L", "start": [ 48, 1 ], "end": [ 51, 42 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt", "code": "def HasGradientWithinAt (f : F → 𝕜) (f' : F) (s : Set F) (x : F) :=\n HasGradientAtFilter f f' x (𝓝[s] x)", "start": [ 53, 1 ], "end": [ 56, 38 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt", "code": "def HasGradientAt (f : F → 𝕜) (f' x : F) :=\n HasGradientAtFilter f f' x (𝓝 x)", "start": [ 58, 1 ], "end": [ 61, 35 ], "kind": "commanddeclaration" }, { "full_name": "gradientWithin", "code": "def gradientWithin (f : F → 𝕜) (s : Set F) (x : F) : F :=\n (toDual 𝕜 F).symm (fderivWithin 𝕜 f s x)", "start": [ 63, 1 ], "end": [ 68, 43 ], "kind": "commanddeclaration" }, { "full_name": "gradient", "code": "def gradient (f : F → 𝕜) (x : F) : F :=\n (toDual 𝕜 F).symm (fderiv 𝕜 f x)", "start": [ 70, 1 ], "end": [ 75, 35 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_iff_hasFDerivWithinAt", "code": "theorem hasGradientWithinAt_iff_hasFDerivWithinAt {s : Set F} :\n HasGradientWithinAt f f' s x ↔ HasFDerivWithinAt f (toDual 𝕜 F f') s x", "start": [ 86, 1 ], "end": [ 88, 10 ], "kind": "commanddeclaration" }, { "full_name": "hasFDerivWithinAt_iff_hasGradientWithinAt", "code": "theorem hasFDerivWithinAt_iff_hasGradientWithinAt {frechet : F →L[𝕜] 𝕜} {s : Set F} :\n HasFDerivWithinAt f frechet s x ↔ HasGradientWithinAt f ((toDual 𝕜 F).symm frechet) s x", "start": [ 90, 1 ], "end": [ 92, 88 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAt_iff_hasFDerivAt", "code": "theorem hasGradientAt_iff_hasFDerivAt :\n HasGradientAt f f' x ↔ HasFDerivAt f (toDual 𝕜 F f') x", "start": [ 94, 1 ], "end": [ 96, 10 ], "kind": "commanddeclaration" }, { "full_name": "hasFDerivAt_iff_hasGradientAt", "code": "theorem hasFDerivAt_iff_hasGradientAt {frechet : F →L[𝕜] 𝕜} :\n HasFDerivAt f frechet x ↔ HasGradientAt f ((toDual 𝕜 F).symm frechet) x", "start": [ 98, 1 ], "end": [ 100, 76 ], "kind": "commanddeclaration" }, { "full_name": "gradient_eq_zero_of_not_differentiableAt", "code": "theorem gradient_eq_zero_of_not_differentiableAt (h : ¬DifferentiableAt 𝕜 f x) : ∇ f x = 0", "start": [ 110, 1 ], "end": [ 111, 65 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.unique", "code": "theorem HasGradientAt.unique {gradf gradg : F}\n (hf : HasGradientAt f gradf x) (hg : HasGradientAt f gradg x) :\n gradf = gradg", "start": [ 113, 1 ], "end": [ 116, 64 ], "kind": "commanddeclaration" }, { "full_name": "DifferentiableAt.hasGradientAt", "code": "theorem DifferentiableAt.hasGradientAt (h : DifferentiableAt 𝕜 f x) :\n HasGradientAt f (∇ f x) x", "start": [ 118, 1 ], "end": [ 121, 22 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.differentiableAt", "code": "theorem HasGradientAt.differentiableAt (h : HasGradientAt f f' x) :\n DifferentiableAt 𝕜 f x", "start": [ 123, 1 ], "end": [ 125, 33 ], "kind": "commanddeclaration" }, { "full_name": "DifferentiableWithinAt.hasGradientWithinAt", "code": "theorem DifferentiableWithinAt.hasGradientWithinAt (h : DifferentiableWithinAt 𝕜 f s x) :\n HasGradientWithinAt f (gradientWithin f s x) s x", "start": [ 127, 1 ], "end": [ 131, 28 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.differentiableWithinAt", "code": "theorem HasGradientWithinAt.differentiableWithinAt (h : HasGradientWithinAt f f' s x) :\n DifferentiableWithinAt 𝕜 f s x", "start": [ 133, 1 ], "end": [ 135, 45 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_univ", "code": "@[simp]\ntheorem hasGradientWithinAt_univ : HasGradientWithinAt f f' univ x ↔ HasGradientAt f f' x", "start": [ 137, 1 ], "end": [ 140, 31 ], "kind": "commanddeclaration" }, { "full_name": "DifferentiableOn.hasGradientAt", "code": "theorem DifferentiableOn.hasGradientAt (h : DifferentiableOn 𝕜 f s) (hs : s ∈ 𝓝 x) :\n HasGradientAt f (∇ f x) x", "start": [ 142, 1 ], "end": [ 144, 35 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.gradient", "code": "theorem HasGradientAt.gradient (h : HasGradientAt f f' x) : ∇ f x = f'", "start": [ 146, 1 ], "end": [ 147, 44 ], "kind": "commanddeclaration" }, { "full_name": "gradient_eq", "code": "theorem gradient_eq {f' : F → F} (h : ∀ x, HasGradientAt f (f' x) x) : ∇ f = f'", "start": [ 149, 1 ], "end": [ 150, 33 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAtFilter.hasDerivAtFilter", "code": "theorem HasGradientAtFilter.hasDerivAtFilter (h : HasGradientAtFilter g g' u L') :\n HasDerivAtFilter g (starRingEnd 𝕜 g') u L'", "start": [ 156, 1 ], "end": [ 160, 31 ], "kind": "commanddeclaration" }, { "full_name": "HasDerivAtFilter.hasGradientAtFilter", "code": "theorem HasDerivAtFilter.hasGradientAtFilter (h : HasDerivAtFilter g g' u L') :\n HasGradientAtFilter g (starRingEnd 𝕜 g') u L'", "start": [ 162, 1 ], "end": [ 166, 36 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.hasDerivAt", "code": "theorem HasGradientAt.hasDerivAt (h : HasGradientAt g g' u) :\n HasDerivAt g (starRingEnd 𝕜 g') u", "start": [ 168, 1 ], "end": [ 171, 16 ], "kind": "commanddeclaration" }, { "full_name": "HasDerivAt.hasGradientAt", "code": "theorem HasDerivAt.hasGradientAt (h : HasDerivAt g g' u) :\n HasGradientAt g (starRingEnd 𝕜 g') u", "start": [ 173, 1 ], "end": [ 176, 8 ], "kind": "commanddeclaration" }, { "full_name": "gradient_eq_deriv", "code": "theorem gradient_eq_deriv : ∇ g u = starRingEnd 𝕜 (deriv g u)", "start": [ 178, 1 ], "end": [ 181, 100 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAtFilter.hasDerivAtFilter'", "code": "theorem HasGradientAtFilter.hasDerivAtFilter' (h : HasGradientAtFilter g g' u L') :\n HasDerivAtFilter g g' u L'", "start": [ 189, 1 ], "end": [ 190, 53 ], "kind": "commanddeclaration" }, { "full_name": "HasDerivAtFilter.hasGradientAtFilter'", "code": "theorem HasDerivAtFilter.hasGradientAtFilter' (h : HasDerivAtFilter g g' u L') :\n HasGradientAtFilter g g' u L'", "start": [ 192, 1 ], "end": [ 193, 59 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.hasDerivAt'", "code": "theorem HasGradientAt.hasDerivAt' (h : HasGradientAt g g' u) :\n HasDerivAt g g' u", "start": [ 195, 1 ], "end": [ 196, 38 ], "kind": "commanddeclaration" }, { "full_name": "HasDerivAt.hasGradientAt'", "code": "theorem HasDerivAt.hasGradientAt' (h : HasDerivAt g g' u) :\n HasGradientAt g g' u", "start": [ 198, 1 ], "end": [ 199, 44 ], "kind": "commanddeclaration" }, { "full_name": "gradient_eq_deriv'", "code": "theorem gradient_eq_deriv' : ∇ g u = deriv g u", "start": [ 201, 1 ], "end": [ 201, 68 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAtFilter_iff_isLittleO", "code": "theorem hasGradientAtFilter_iff_isLittleO :\n HasGradientAtFilter f f' x L ↔\n (fun x' : F => f x' - f x - ⟪f', x' - x⟫) =o[L] fun x' => x' - x", "start": [ 209, 1 ], "end": [ 212, 37 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_iff_isLittleO", "code": "theorem hasGradientWithinAt_iff_isLittleO :\n HasGradientWithinAt f f' s x ↔\n (fun x' : F => f x' - f x - ⟪f', x' - x⟫) =o[𝓝[s] x] fun x' => x' - x", "start": [ 214, 1 ], "end": [ 217, 36 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_iff_tendsto", "code": "theorem hasGradientWithinAt_iff_tendsto :\n HasGradientWithinAt f f' s x ↔\n Tendsto (fun x' => ‖x' - x‖⁻¹ * ‖f x' - f x - ⟪f', x' - x⟫‖) (𝓝[s] x) (𝓝 0)", "start": [ 219, 1 ], "end": [ 222, 32 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAt_iff_isLittleO", "code": "theorem hasGradientAt_iff_isLittleO : HasGradientAt f f' x ↔\n (fun x' : F => f x' - f x - ⟪f', x' - x⟫) =o[𝓝 x] fun x' => x' - x", "start": [ 224, 1 ], "end": [ 226, 36 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAt_iff_tendsto", "code": "theorem hasGradientAt_iff_tendsto :\n HasGradientAt f f' x ↔\n Tendsto (fun x' => ‖x' - x‖⁻¹ * ‖f x' - f x - ⟪f', x' - x⟫‖) (𝓝 x) (𝓝 0)", "start": [ 228, 1 ], "end": [ 231, 32 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAtFilter.isBigO_sub", "code": "theorem HasGradientAtFilter.isBigO_sub (h : HasGradientAtFilter f f' x L) :\n (fun x' => f x' - f x) =O[L] fun x' => x' - x", "start": [ 233, 1 ], "end": [ 235, 33 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_congr_set'", "code": "theorem hasGradientWithinAt_congr_set' {s t : Set F} (y : F) (h : s =ᶠ[𝓝[{y}ᶜ] x] t) :\n HasGradientWithinAt f f' s x ↔ HasGradientWithinAt f f' t x", "start": [ 237, 1 ], "end": [ 239, 35 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_congr_set", "code": "theorem hasGradientWithinAt_congr_set {s t : Set F} (h : s =ᶠ[𝓝 x] t) :\n HasGradientWithinAt f f' s x ↔ HasGradientWithinAt f f' t x", "start": [ 241, 1 ], "end": [ 243, 32 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAt_iff_isLittleO_nhds_zero", "code": "theorem hasGradientAt_iff_isLittleO_nhds_zero : HasGradientAt f f' x ↔\n (fun h => f (x + h) - f x - ⟪f', h⟫) =o[𝓝 0] fun h => h", "start": [ 245, 1 ], "end": [ 247, 38 ], "kind": "commanddeclaration" }, { "full_name": "Filter.EventuallyEq.hasGradientAtFilter_iff", "code": "theorem Filter.EventuallyEq.hasGradientAtFilter_iff (h₀ : f₀ =ᶠ[L] f₁) (hx : f₀ x = f₁ x)\n (h₁ : f₀' = f₁') : HasGradientAtFilter f₀ f₀' x L ↔ HasGradientAtFilter f₁ f₁' x L", "start": [ 257, 1 ], "end": [ 259, 45 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAtFilter.congr_of_eventuallyEq", "code": "theorem HasGradientAtFilter.congr_of_eventuallyEq (h : HasGradientAtFilter f f' x L)\n (hL : f₁ =ᶠ[L] f) (hx : f₁ x = f x) : HasGradientAtFilter f₁ f' x L", "start": [ 261, 1 ], "end": [ 263, 42 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.congr_mono", "code": "theorem HasGradientWithinAt.congr_mono (h : HasGradientWithinAt f f' s x) (ht : ∀ x ∈ t, f₁ x = f x)\n (hx : f₁ x = f x) (h₁ : t ⊆ s) : HasGradientWithinAt f₁ f' t x", "start": [ 265, 1 ], "end": [ 267, 42 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.congr", "code": "theorem HasGradientWithinAt.congr (h : HasGradientWithinAt f f' s x) (hs : ∀ x ∈ s, f₁ x = f x)\n (hx : f₁ x = f x) : HasGradientWithinAt f₁ f' s x", "start": [ 269, 1 ], "end": [ 271, 32 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.congr_of_mem", "code": "theorem HasGradientWithinAt.congr_of_mem (h : HasGradientWithinAt f f' s x)\n (hs : ∀ x ∈ s, f₁ x = f x) (hx : x ∈ s) : HasGradientWithinAt f₁ f' s x", "start": [ 273, 1 ], "end": [ 275, 23 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.congr_of_eventuallyEq", "code": "theorem HasGradientWithinAt.congr_of_eventuallyEq (h : HasGradientWithinAt f f' s x)\n (h₁ : f₁ =ᶠ[𝓝[s] x] f) (hx : f₁ x = f x) : HasGradientWithinAt f₁ f' s x", "start": [ 277, 1 ], "end": [ 279, 52 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.congr_of_eventuallyEq_of_mem", "code": "theorem HasGradientWithinAt.congr_of_eventuallyEq_of_mem (h : HasGradientWithinAt f f' s x)\n (h₁ : f₁ =ᶠ[𝓝[s] x] f) (hx : x ∈ s) : HasGradientWithinAt f₁ f' s x", "start": [ 281, 1 ], "end": [ 283, 54 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.congr_of_eventuallyEq", "code": "theorem HasGradientAt.congr_of_eventuallyEq (h : HasGradientAt f f' x) (h₁ : f₁ =ᶠ[𝓝 x] f) :\n HasGradientAt f₁ f' x", "start": [ 285, 1 ], "end": [ 287, 74 ], "kind": "commanddeclaration" }, { "full_name": "Filter.EventuallyEq.gradient_eq", "code": "theorem Filter.EventuallyEq.gradient_eq (hL : f₁ =ᶠ[𝓝 x] f) : ∇ f₁ x = ∇ f x", "start": [ 289, 1 ], "end": [ 291, 38 ], "kind": "commanddeclaration" }, { "full_name": "Filter.EventuallyEq.gradient", "code": "protected theorem Filter.EventuallyEq.gradient (h : f₁ =ᶠ[𝓝 x] f) : ∇ f₁ =ᶠ[𝓝 x] ∇ f", "start": [ 293, 1 ], "end": [ 294, 52 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAtFilter_const", "code": "theorem hasGradientAtFilter_const : HasGradientAtFilter (fun _ => c) 0 x L", "start": [ 304, 1 ], "end": [ 305, 74 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientWithinAt_const", "code": "theorem hasGradientWithinAt_const : HasGradientWithinAt (fun _ => c) 0 s x", "start": [ 307, 1 ], "end": [ 308, 34 ], "kind": "commanddeclaration" }, { "full_name": "hasGradientAt_const", "code": "theorem hasGradientAt_const : HasGradientAt (fun _ => c) 0 x", "start": [ 310, 1 ], "end": [ 311, 34 ], "kind": "commanddeclaration" }, { "full_name": "gradient_const", "code": "theorem gradient_const : ∇ (fun _ => c) x = 0", "start": [ 313, 1 ], "end": [ 314, 55 ], "kind": "commanddeclaration" }, { "full_name": "gradient_const'", "code": "@[simp]\ntheorem gradient_const' : (∇ fun _ : 𝕜 => c) = fun _ => 0", "start": [ 316, 1 ], "end": [ 318, 37 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAtFilter.tendsto_nhds", "code": "nonrec theorem HasGradientAtFilter.tendsto_nhds (hL : L ≤ 𝓝 x) (h : HasGradientAtFilter f f' x L) :\n Tendsto f L (𝓝 (f x))", "start": [ 326, 1 ], "end": [ 328, 20 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientWithinAt.continuousWithinAt", "code": "theorem HasGradientWithinAt.continuousWithinAt (h : HasGradientWithinAt f f' s x) :\n ContinuousWithinAt f s x", "start": [ 330, 1 ], "end": [ 332, 49 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.continuousAt", "code": "theorem HasGradientAt.continuousAt (h : HasGradientAt f f' x) : ContinuousAt f x", "start": [ 334, 1 ], "end": [ 335, 44 ], "kind": "commanddeclaration" }, { "full_name": "HasGradientAt.continuousOn", "code": "protected theorem HasGradientAt.continuousOn {f' : F → F} (h : ∀ x ∈ s, HasGradientAt f (f' x) x) :\n ContinuousOn f s", "start": [ 337, 1 ], "end": [ 339, 55 ], "kind": "commanddeclaration" } ]

Mathlib/LinearAlgebra/TensorAlgebra/Grading.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/RingTheory/GradedAlgebra/Basic.lean", "Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean" ]

[ { "full_name": "TensorAlgebra.GradedAlgebra.ι", "code": "nonrec def GradedAlgebra.ι : M →ₗ[R] ⨁ i : ℕ, ↥(LinearMap.range (ι R : M →ₗ[_] _) ^ i) :=\n DirectSum.lof R ℕ (fun i => ↥(LinearMap.range (ι R : M →ₗ[_] _) ^ i)) 1 ∘ₗ\n (ι R).codRestrict _ fun m => by simpa only [pow_one] using LinearMap.mem_range_self _ m", "start": [ 28, 1 ], "end": [ 32, 92 ], "kind": "commanddeclaration" }, { "full_name": "TensorAlgebra.GradedAlgebra.ι_apply", "code": "theorem GradedAlgebra.ι_apply (m : M) :\n GradedAlgebra.ι R M m =\n DirectSum.of (fun (i : ℕ) => ↥(LinearMap.range (TensorAlgebra.ι R : M →ₗ[_] _) ^ i)) 1\n ⟨TensorAlgebra.ι R m, by simpa only [pow_one] using LinearMap.mem_range_self _ m⟩", "start": [ 35, 1 ], "end": [ 39, 6 ], "kind": "commanddeclaration" }, { "full_name": "TensorAlgebra.gradedAlgebra", "code": "instance gradedAlgebra :\n GradedAlgebra ((LinearMap.range (ι R : M →ₗ[R] TensorAlgebra R M) ^ ·) : ℕ → Submodule R _) :=\n GradedAlgebra.ofAlgHom _ (lift R <| GradedAlgebra.ι R M)\n (by\n ext m\n dsimp only [LinearMap.comp_apply, AlgHom.toLinearMap_apply, AlgHom.comp_apply,\n AlgHom.id_apply]\n rw [lift_ι_apply, GradedAlgebra.ι_apply R M, DirectSum.coeAlgHom_of, Subtype.coe_mk])\n fun i x => by\n cases' x with x hx\n dsimp only [Subtype.coe_mk, DirectSum.lof_eq_of]\n induction hx using Submodule.pow_induction_on_left' with\n | algebraMap r =>\n rw [AlgHom.commutes, DirectSum.algebraMap_apply]; rfl\n | add x y i hx hy ihx ihy =>\n rw [AlgHom.map_add, ihx, ihy, ← AddMonoidHom.map_add]\n rfl\n | mem_mul m hm i x hx ih =>\n obtain ⟨_, rfl⟩ := hm\n rw [AlgHom.map_mul, ih, lift_ι_apply, GradedAlgebra.ι_apply R M, DirectSum.of_mul_of]\n exact DirectSum.of_eq_of_gradedMonoid_eq (Sigma.subtype_ext (add_comm _ _) rfl)", "start": [ 44, 1 ], "end": [ 68, 86 ], "kind": "commanddeclaration" } ]

Mathlib/Data/QPF/Multivariate/Constructions/Const.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Control/Functor/Multivariate.lean", "Mathlib/Data/QPF/Multivariate/Basic.lean" ]

[ { "full_name": "MvQPF.Const", "code": "@[nolint unusedArguments]\ndef Const (A : Type*) (_v : TypeVec.{u} n) : Type _ := A", "start": [ 30, 1 ], "end": [ 32, 57 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.inhabited", "code": "instance Const.inhabited {A α} [Inhabited A] : Inhabited (Const n A α) := ⟨(default : A)⟩", "start": [ 35, 1 ], "end": [ 35, 90 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.mk", "code": "protected def mk (x : A) : Const n A α := x", "start": [ 44, 1 ], "end": [ 45, 44 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.get", "code": "protected def get (x : Const n A α) : A := x", "start": [ 48, 1 ], "end": [ 49, 45 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.mk_get", "code": "@[simp]\nprotected theorem mk_get (x : Const n A α) : Const.mk (Const.get x) = x", "start": [ 52, 1 ], "end": [ 53, 79 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.get_mk", "code": "@[simp]\nprotected theorem get_mk (x : A) : Const.get (Const.mk x : Const n A α) = x", "start": [ 56, 1 ], "end": [ 57, 83 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.map", "code": "protected def map : Const n A α → Const n A β := fun x => x", "start": [ 60, 1 ], "end": [ 61, 60 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.MvFunctor", "code": "instance MvFunctor : MvFunctor (Const n A) where map _f := Const.map", "start": [ 64, 1 ], "end": [ 64, 69 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.map_mk", "code": "theorem map_mk (x : A) : f <$$> Const.mk x = Const.mk x", "start": [ 66, 1 ], "end": [ 66, 63 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.get_map", "code": "theorem get_map (x : (Const n A) α) : Const.get (f <$$> x) = Const.get x", "start": [ 69, 1 ], "end": [ 69, 80 ], "kind": "commanddeclaration" }, { "full_name": "MvQPF.Const.mvqpf", "code": "instance mvqpf : @MvQPF _ (Const n A) where\n P := MvPFunctor.const n A\n abs x := MvPFunctor.const.get x\n repr x := MvPFunctor.const.mk n x\n abs_repr := fun _ => const.get_mk _\n abs_map := fun _ => const.get_map _", "start": [ 72, 1 ], "end": [ 77, 38 ], "kind": "commanddeclaration" } ]

Mathlib/Combinatorics/Configuration.lean

[ "Mathlib/Combinatorics/Hall/Basic.lean", "Mathlib/Data/Fintype/BigOperators.lean", "Mathlib/SetTheory/Cardinal/Finite.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Algebra/Order/BigOperators/Group/Finset.lean" ]

[ { "full_name": "Configuration.Dual", "code": "def Dual :=\n P", "start": [ 44, 1 ], "end": [ 46, 4 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.Nondegenerate", "code": "class Nondegenerate : Prop where\n exists_point : ∀ l : L, ∃ p, p ∉ l\n exists_line : ∀ p, ∃ l : L, p ∉ l\n eq_or_eq : ∀ {p₁ p₂ : P} {l₁ l₂ : L}, p₁ ∈ l₁ → p₂ ∈ l₁ → p₁ ∈ l₂ → p₂ ∈ l₂ → p₁ = p₂ ∨ l₁ = l₂", "start": [ 65, 1 ], "end": [ 74, 98 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasPoints", "code": "class HasPoints extends Nondegenerate P L where\n mkPoint : ∀ {l₁ l₂ : L}, l₁ ≠ l₂ → P\n mkPoint_ax : ∀ {l₁ l₂ : L} (h : l₁ ≠ l₂), mkPoint h ∈ l₁ ∧ mkPoint h ∈ l₂", "start": [ 77, 1 ], "end": [ 80, 76 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines", "code": "class HasLines extends Nondegenerate P L where\n mkLine : ∀ {p₁ p₂ : P}, p₁ ≠ p₂ → L\n mkLine_ax : ∀ {p₁ p₂ : P} (h : p₁ ≠ p₂), p₁ ∈ mkLine h ∧ p₂ ∈ mkLine h", "start": [ 83, 1 ], "end": [ 86, 73 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.Dual.Nondegenerate", "code": "instance Dual.Nondegenerate [Nondegenerate P L] : Nondegenerate (Dual L) (Dual P) where\n exists_point := @exists_line P L _ _\n exists_line := @exists_point P L _ _\n eq_or_eq := @fun l₁ l₂ p₁ p₂ h₁ h₂ h₃ h₄ => (@eq_or_eq P L _ _ p₁ p₂ l₁ l₂ h₁ h₃ h₂ h₄).symm", "start": [ 95, 1 ], "end": [ 98, 95 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.Dual.hasLines", "code": "instance Dual.hasLines [HasPoints P L] : HasLines (Dual L) (Dual P) :=\n { Dual.Nondegenerate _ _ with\n mkLine := @mkPoint P L _ _\n mkLine_ax := @mkPoint_ax P L _ _ }", "start": [ 100, 1 ], "end": [ 103, 39 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.Dual.hasPoints", "code": "instance Dual.hasPoints [HasLines P L] : HasPoints (Dual L) (Dual P) :=\n { Dual.Nondegenerate _ _ with\n mkPoint := @mkLine P L _ _\n mkPoint_ax := @mkLine_ax P L _ _ }", "start": [ 105, 1 ], "end": [ 108, 39 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasPoints.existsUnique_point", "code": "theorem HasPoints.existsUnique_point [HasPoints P L] (l₁ l₂ : L) (hl : l₁ ≠ l₂) :\n ∃! p, p ∈ l₁ ∧ p ∈ l₂", "start": [ 110, 1 ], "end": [ 113, 79 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines.existsUnique_line", "code": "theorem HasLines.existsUnique_line [HasLines P L] (p₁ p₂ : P) (hp : p₁ ≠ p₂) :\n ∃! l : L, p₁ ∈ l ∧ p₂ ∈ l", "start": [ 116, 1 ], "end": [ 118, 58 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.Nondegenerate.exists_injective_of_card_le", "code": "theorem Nondegenerate.exists_injective_of_card_le [Nondegenerate P L] [Fintype P] [Fintype L]\n (h : Fintype.card L ≤ Fintype.card P) : ∃ f : L → P, Function.Injective f ∧ ∀ l, f l ∉ l", "start": [ 123, 1 ], "end": [ 166, 55 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.lineCount", "code": "noncomputable def lineCount (p : P) : ℕ :=\n Nat.card { l : L // p ∈ l }", "start": [ 172, 1 ], "end": [ 174, 30 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.pointCount", "code": "noncomputable def pointCount (l : L) : ℕ :=\n Nat.card { p : P // p ∈ l }", "start": [ 179, 1 ], "end": [ 181, 30 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.sum_lineCount_eq_sum_pointCount", "code": "theorem sum_lineCount_eq_sum_pointCount [Fintype P] [Fintype L] :\n ∑ p : P, lineCount L p = ∑ l : L, pointCount P l", "start": [ 186, 1 ], "end": [ 195, 96 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines.pointCount_le_lineCount", "code": "theorem HasLines.pointCount_le_lineCount [HasLines P L] {p : P} {l : L} (h : p ∉ l)\n [Finite { l : L // p ∈ l }] : pointCount P l ≤ lineCount L p", "start": [ 200, 1 ], "end": [ 214, 74 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasPoints.lineCount_le_pointCount", "code": "theorem HasPoints.lineCount_le_pointCount [HasPoints P L] {p : P} {l : L} (h : p ∉ l)\n [hf : Finite { p : P // p ∈ l }] : lineCount L p ≤ pointCount P l", "start": [ 217, 1 ], "end": [ 219, 67 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines.card_le", "code": "theorem HasLines.card_le [HasLines P L] [Fintype P] [Fintype L] :\n Fintype.card P ≤ Fintype.card L", "start": [ 224, 1 ], "end": [ 245, 25 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasPoints.card_le", "code": "theorem HasPoints.card_le [HasPoints P L] [Fintype P] [Fintype L] :\n Fintype.card L ≤ Fintype.card P", "start": [ 248, 1 ], "end": [ 251, 46 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines.exists_bijective_of_card_eq", "code": "theorem HasLines.exists_bijective_of_card_eq [HasLines P L] [Fintype P] [Fintype L]\n (h : Fintype.card P = Fintype.card L) :\n ∃ f : L → P, Function.Bijective f ∧ ∀ l, pointCount P l = lineCount L (f l)", "start": [ 256, 1 ], "end": [ 263, 95 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines.lineCount_eq_pointCount", "code": "theorem HasLines.lineCount_eq_pointCount [HasLines P L] [Fintype P] [Fintype L]\n (hPL : Fintype.card P = Fintype.card L) {p : P} {l : L} (hpl : p ∉ l) :\n lineCount L p = pointCount P l", "start": [ 266, 1 ], "end": [ 290, 61 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasPoints.lineCount_eq_pointCount", "code": "theorem HasPoints.lineCount_eq_pointCount [HasPoints P L] [Fintype P] [Fintype L]\n (hPL : Fintype.card P = Fintype.card L) {p : P} {l : L} (hpl : p ∉ l) :\n lineCount L p = pointCount P l", "start": [ 293, 1 ], "end": [ 296, 86 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasLines.hasPoints", "code": "noncomputable def HasLines.hasPoints [HasLines P L] [Fintype P] [Fintype L]\n (h : Fintype.card P = Fintype.card L) : HasPoints P L :=\n let this : ∀ l₁ l₂ : L, l₁ ≠ l₂ → ∃ p : P, p ∈ l₁ ∧ p ∈ l₂ := fun l₁ l₂ hl => by\n classical\n obtain ⟨f, _, hf2⟩ := HasLines.exists_bijective_of_card_eq h\n haveI : Nontrivial L := ⟨⟨l₁, l₂, hl⟩⟩\n haveI := Fintype.one_lt_card_iff_nontrivial.mp ((congr_arg _ h).mpr Fintype.one_lt_card)\n have h₁ : ∀ p : P, 0 < lineCount L p := fun p =>\n Exists.elim (exists_ne p) fun q hq =>\n (congr_arg _ Nat.card_eq_fintype_card).mpr\n (Fintype.card_pos_iff.mpr ⟨⟨mkLine hq, (mkLine_ax hq).2⟩⟩)\n have h₂ : ∀ l : L, 0 < pointCount P l := fun l => (congr_arg _ (hf2 l)).mpr (h₁ (f l))\n obtain ⟨p, hl₁⟩ := Fintype.card_pos_iff.mp ((congr_arg _ Nat.card_eq_fintype_card).mp (h₂ l₁))\n by_cases hl₂ : p ∈ l₂\n · exact ⟨p, hl₁, hl₂⟩\n have key' : Fintype.card { q : P // q ∈ l₂ } = Fintype.card { l : L // p ∈ l } :=\n ((HasLines.lineCount_eq_pointCount h hl₂).trans Nat.card_eq_fintype_card).symm.trans\n Nat.card_eq_fintype_card\n have : ∀ q : { q // q ∈ l₂ }, p ≠ q := fun q hq => hl₂ ((congr_arg (· ∈ l₂) hq).mpr q.2)\n let f : { q : P // q ∈ l₂ } → { l : L // p ∈ l } := fun q =>\n ⟨mkLine (this q), (mkLine_ax (this q)).1⟩\n have hf : Function.Injective f := fun q₁ q₂ hq =>\n Subtype.ext\n ((eq_or_eq q₁.2 q₂.2 (mkLine_ax (this q₁)).2\n ((congr_arg _ (Subtype.ext_iff.mp hq)).mpr (mkLine_ax (this q₂)).2)).resolve_right\n fun h => (congr_arg (¬p ∈ ·) h).mp hl₂ (mkLine_ax (this q₁)).1)\n have key' := ((Fintype.bijective_iff_injective_and_card f).mpr ⟨hf, key'⟩).2\n obtain ⟨q, hq⟩ := key' ⟨l₁, hl₁⟩\n exact ⟨q, (congr_arg _ (Subtype.ext_iff.mp hq)).mp (mkLine_ax (this q)).2, q.2⟩\n { ‹HasLines P L› with\n mkPoint := fun {l₁ l₂} hl => Classical.choose (this l₁ l₂ hl)\n mkPoint_ax := fun {l₁ l₂} hl => Classical.choose_spec (this l₁ l₂ hl) }", "start": [ 299, 1 ], "end": [ 332, 76 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.HasPoints.hasLines", "code": "noncomputable def HasPoints.hasLines [HasPoints P L] [Fintype P] [Fintype L]\n (h : Fintype.card P = Fintype.card L) : HasLines P L :=\n let this := @HasLines.hasPoints (Dual L) (Dual P) _ _ _ _ h.symm\n { ‹HasPoints P L› with\n mkLine := @fun _ _ => this.mkPoint\n mkLine_ax := @fun _ _ => this.mkPoint_ax }", "start": [ 335, 1 ], "end": [ 342, 47 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane", "code": "class ProjectivePlane extends HasPoints P L, HasLines P L where\n exists_config :\n ∃ (p₁ p₂ p₃ : P) (l₁ l₂ l₃ : L),\n p₁ ∉ l₂ ∧ p₁ ∉ l₃ ∧ p₂ ∉ l₁ ∧ p₂ ∈ l₂ ∧ p₂ ∈ l₃ ∧ p₃ ∉ l₁ ∧ p₃ ∈ l₂ ∧ p₃ ∉ l₃", "start": [ 347, 1 ], "end": [ 353, 84 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.order", "code": "noncomputable def order : ℕ :=\n lineCount L (Classical.choose (@exists_config P L _ _)) - 1", "start": [ 366, 1 ], "end": [ 369, 62 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.card_points_eq_card_lines", "code": "theorem card_points_eq_card_lines [Fintype P] [Fintype L] : Fintype.card P = Fintype.card L", "start": [ 372, 1 ], "end": [ 373, 61 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.lineCount_eq_lineCount", "code": "theorem lineCount_eq_lineCount [Finite P] [Finite L] (p q : P) : lineCount L p = lineCount L q", "start": [ 378, 1 ], "end": [ 395, 54 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.pointCount_eq_pointCount", "code": "theorem pointCount_eq_pointCount [Finite P] [Finite L] (l m : L) :\n pointCount P l = pointCount P m", "start": [ 400, 1 ], "end": [ 402, 40 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.lineCount_eq_pointCount", "code": "theorem lineCount_eq_pointCount [Finite P] [Finite L] (p : P) (l : L) :\n lineCount L p = pointCount P l", "start": [ 407, 1 ], "end": [ 413, 80 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.Dual.order", "code": "theorem Dual.order [Finite P] [Finite L] : order (Dual L) (Dual P) = order P L", "start": [ 418, 1 ], "end": [ 419, 59 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.lineCount_eq", "code": "theorem lineCount_eq [Finite P] [Finite L] (p : P) : lineCount L p = order P L + 1", "start": [ 424, 1 ], "end": [ 430, 44 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.pointCount_eq", "code": "theorem pointCount_eq [Finite P] [Finite L] (l : L) : pointCount P l = order P L + 1", "start": [ 435, 1 ], "end": [ 436, 80 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.one_lt_order", "code": "theorem one_lt_order [Finite P] [Finite L] : 1 < order P L", "start": [ 441, 1 ], "end": [ 450, 66 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.two_lt_lineCount", "code": "theorem two_lt_lineCount [Finite P] [Finite L] (p : P) : 2 < lineCount L p", "start": [ 455, 1 ], "end": [ 456, 77 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.two_lt_pointCount", "code": "theorem two_lt_pointCount [Finite P] [Finite L] (l : L) : 2 < pointCount P l", "start": [ 461, 1 ], "end": [ 462, 78 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.card_points", "code": "theorem card_points [Fintype P] [Finite L] : Fintype.card P = order P L ^ 2 + order P L + 1", "start": [ 467, 1 ], "end": [ 493, 94 ], "kind": "commanddeclaration" }, { "full_name": "Configuration.ProjectivePlane.card_lines", "code": "theorem card_lines [Finite P] [Fintype L] : Fintype.card L = order P L ^ 2 + order P L + 1", "start": [ 496, 1 ], "end": [ 497, 94 ], "kind": "commanddeclaration" } ]

Mathlib/FieldTheory/Laurent.lean

[ "Mathlib/Algebra/Polynomial/Taylor.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/FieldTheory/RatFunc/AsPolynomial.lean" ]

[ { "full_name": "RatFunc.taylor_mem_nonZeroDivisors", "code": "theorem taylor_mem_nonZeroDivisors (hp : p ∈ R[X]⁰) : taylor r p ∈ R[X]⁰", "start": [ 39, 1 ], "end": [ 45, 60 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurentAux", "code": "def laurentAux : RatFunc R →+* RatFunc R :=\n RatFunc.mapRingHom\n ( { toFun := taylor r\n map_add' := map_add (taylor r)\n map_mul' := taylor_mul _\n map_zero' := map_zero (taylor r)\n map_one' := taylor_one r } : R[X] →+* R[X])\n (taylor_mem_nonZeroDivisors _)", "start": [ 48, 1 ], "end": [ 57, 35 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurentAux_ofFractionRing_mk", "code": "theorem laurentAux_ofFractionRing_mk (q : R[X]⁰) :\n laurentAux r (ofFractionRing (Localization.mk p q)) =\n ofFractionRing (.mk (taylor r p) ⟨taylor r q, taylor_mem_nonZeroDivisors r q q.prop⟩)", "start": [ 60, 1 ], "end": [ 63, 38 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurentAux_div", "code": "theorem laurentAux_div :\n laurentAux r (algebraMap _ _ p / algebraMap _ _ q) =\n algebraMap _ _ (taylor r p) / algebraMap _ _ (taylor r q)", "start": [ 66, 1 ], "end": [ 70, 62 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurentAux_algebraMap", "code": "@[simp]\ntheorem laurentAux_algebraMap : laurentAux r (algebraMap _ _ p) = algebraMap _ _ (taylor r p)", "start": [ 73, 1 ], "end": [ 75, 94 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent", "code": "def laurent : RatFunc R →ₐ[R] RatFunc R :=\n RatFunc.mapAlgHom (.ofLinearMap (taylor r) (taylor_one _) (taylor_mul _))\n (taylor_mem_nonZeroDivisors _)", "start": [ 78, 1 ], "end": [ 81, 35 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_div", "code": "theorem laurent_div :\n laurent r (algebraMap _ _ p / algebraMap _ _ q) =\n algebraMap _ _ (taylor r p) / algebraMap _ _ (taylor r q)", "start": [ 84, 1 ], "end": [ 87, 23 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_algebraMap", "code": "@[simp]\ntheorem laurent_algebraMap : laurent r (algebraMap _ _ p) = algebraMap _ _ (taylor r p)", "start": [ 90, 1 ], "end": [ 92, 28 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_X", "code": "@[simp]\ntheorem laurent_X : laurent r X = X + C r", "start": [ 95, 1 ], "end": [ 97, 82 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_C", "code": "@[simp]\ntheorem laurent_C (x : R) : laurent r (C x) = C x", "start": [ 101, 1 ], "end": [ 103, 52 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_at_zero", "code": "@[simp]\ntheorem laurent_at_zero : laurent 0 f = f", "start": [ 107, 1 ], "end": [ 108, 93 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_laurent", "code": "theorem laurent_laurent : laurent r (laurent s f) = laurent (r + s) f", "start": [ 111, 1 ], "end": [ 113, 39 ], "kind": "commanddeclaration" }, { "full_name": "RatFunc.laurent_injective", "code": "theorem laurent_injective : Function.Injective (laurent r)", "start": [ 116, 1 ], "end": [ 117, 59 ], "kind": "commanddeclaration" } ]

Mathlib/LinearAlgebra/Matrix/Dual.lean

[ "Mathlib/LinearAlgebra/Dual.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/LinearAlgebra/Matrix/ToLin.lean" ]

[ { "full_name": "LinearMap.toMatrix_transpose", "code": "@[simp]\ntheorem LinearMap.toMatrix_transpose (u : V₁ →ₗ[K] V₂) :\n LinearMap.toMatrix B₂.dualBasis B₁.dualBasis (Module.Dual.transpose (R := K) u) =\n (LinearMap.toMatrix B₁ B₂ u)ᵀ", "start": [ 31, 1 ], "end": [ 37, 70 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.toLin_transpose", "code": "@[simp]\ntheorem Matrix.toLin_transpose (M : Matrix ι₁ ι₂ K) : Matrix.toLin B₁.dualBasis B₂.dualBasis Mᵀ =\n Module.Dual.transpose (R := K) (Matrix.toLin B₂ B₁ M)", "start": [ 40, 1 ], "end": [ 44, 88 ], "kind": "commanddeclaration" } ]

Mathlib/Geometry/Euclidean/Sphere/Ptolemy.lean

[ "Mathlib/Geometry/Euclidean/Sphere/Power.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Geometry/Euclidean/Triangle.lean" ]

[ { "full_name": "EuclideanGeometry.mul_dist_add_mul_dist_eq_mul_dist_of_cospherical", "code": "theorem mul_dist_add_mul_dist_eq_mul_dist_of_cospherical {a b c d p : P}\n (h : Cospherical ({a, b, c, d} : Set P)) (hapc : ∠ a p c = π) (hbpd : ∠ b p d = π) :\n dist a b * dist c d + dist b c * dist d a = dist a c * dist b d", "start": [ 52, 1 ], "end": [ 70, 51 ], "kind": "commanddeclaration" } ]

Mathlib/Topology/Order/Hom/Esakia.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Order/Hom/Bounded.lean", "Mathlib/Topology/Order/Hom/Basic.lean" ]

[ { "full_name": "PseudoEpimorphism", "code": "structure PseudoEpimorphism (α β : Type*) [Preorder α] [Preorder β] extends α →o β where\n exists_map_eq_of_map_le' ⦃a : α⦄ ⦃b : β⦄ : toFun a ≤ b → ∃ c, a ≤ c ∧ toFun c = b", "start": [ 40, 1 ], "end": [ 42, 84 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom", "code": "structure EsakiaHom (α β : Type*) [TopologicalSpace α] [Preorder α] [TopologicalSpace β]\n [Preorder β] extends α →Co β where\n exists_map_eq_of_map_le' ⦃a : α⦄ ⦃b : β⦄ : toFun a ≤ b → ∃ c, a ≤ c ∧ toFun c = b", "start": [ 45, 1 ], "end": [ 48, 84 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphismClass", "code": "class PseudoEpimorphismClass (F : Type*) (α β : outParam Type*)\n [Preorder α] [Preorder β] [FunLike F α β]\n extends RelHomClass F ((· ≤ ·) : α → α → Prop) ((· ≤ ·) : β → β → Prop) : Prop where\n exists_map_eq_of_map_le (f : F) ⦃a : α⦄ ⦃b : β⦄ : f a ≤ b → ∃ c, a ≤ c ∧ f c = b", "start": [ 53, 1 ], "end": [ 59, 83 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHomClass", "code": "class EsakiaHomClass (F : Type*) (α β : outParam Type*) [TopologicalSpace α] [Preorder α]\n [TopologicalSpace β] [Preorder β] [FunLike F α β]\n extends ContinuousOrderHomClass F α β : Prop where\n exists_map_eq_of_map_le (f : F) ⦃a : α⦄ ⦃b : β⦄ : f a ≤ b → ∃ c, a ≤ c ∧ f c = b", "start": [ 62, 1 ], "end": [ 68, 83 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphismClass.toTopHomClass", "code": "instance (priority := 100) PseudoEpimorphismClass.toTopHomClass [PartialOrder α] [OrderTop α]\n [Preorder β] [OrderTop β] [PseudoEpimorphismClass F α β] : TopHomClass F α β where\n map_top f := by\n let ⟨b, h⟩ := exists_map_eq_of_map_le f (@le_top _ _ _ <| f ⊤)\n rw [← top_le_iff.1 h.1, h.2]", "start": [ 80, 1 ], "end": [ 84, 33 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHomClass.toPseudoEpimorphismClass", "code": "instance (priority := 100) EsakiaHomClass.toPseudoEpimorphismClass [TopologicalSpace α] [Preorder α]\n [TopologicalSpace β] [Preorder β] [EsakiaHomClass F α β] : PseudoEpimorphismClass F α β :=\n { ‹EsakiaHomClass F α β› with\n map_rel := ContinuousOrderHomClass.map_monotone }", "start": [ 88, 1 ], "end": [ 91, 54 ], "kind": "commanddeclaration" }, { "full_name": "OrderIsoClass.toPseudoEpimorphismClass", "code": "instance (priority := 100) OrderIsoClass.toPseudoEpimorphismClass [Preorder α] [Preorder β]\n [EquivLike F α β] [OrderIsoClass F α β] : PseudoEpimorphismClass F α β where\n exists_map_eq_of_map_le f _a b h :=\n ⟨EquivLike.inv f b, (le_map_inv_iff f).2 h, EquivLike.right_inv _ _⟩", "start": [ 105, 1 ], "end": [ 108, 73 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.instFunLike", "code": "instance instFunLike : FunLike (PseudoEpimorphism α β) α β where\n coe f := f.toFun\n coe_injective' f g h := by\n obtain ⟨⟨_, _⟩, _⟩ := f\n obtain ⟨⟨_, _⟩, _⟩ := g\n congr", "start": [ 118, 1 ], "end": [ 123, 10 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.toOrderHom_eq_coe", "code": "@[simp]\ntheorem toOrderHom_eq_coe (f : PseudoEpimorphism α β) : ⇑f.toOrderHom = f", "start": [ 129, 1 ], "end": [ 130, 81 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.toFun_eq_coe", "code": "theorem toFun_eq_coe {f : PseudoEpimorphism α β} : f.toFun = (f : α → β)", "start": [ 132, 1 ], "end": [ 132, 80 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.ext", "code": "@[ext]\ntheorem ext {f g : PseudoEpimorphism α β} (h : ∀ a, f a = g a) : f = g", "start": [ 135, 1 ], "end": [ 137, 21 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.copy", "code": "protected def copy (f : PseudoEpimorphism α β) (f' : α → β) (h : f' = f) : PseudoEpimorphism α β :=\n ⟨f.toOrderHom.copy f' h, by simpa only [h.symm, toFun_eq_coe] using f.exists_map_eq_of_map_le'⟩", "start": [ 140, 1 ], "end": [ 143, 98 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.coe_copy", "code": "@[simp]\ntheorem coe_copy (f : PseudoEpimorphism α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f'", "start": [ 146, 1 ], "end": [ 147, 100 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.copy_eq", "code": "theorem copy_eq (f : PseudoEpimorphism α β) (f' : α → β) (h : f' = f) : f.copy f' h = f", "start": [ 150, 1 ], "end": [ 151, 18 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.id", "code": "protected def id : PseudoEpimorphism α α :=\n ⟨OrderHom.id, fun _ b h => ⟨b, h, rfl⟩⟩", "start": [ 156, 1 ], "end": [ 158, 42 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.coe_id", "code": "@[simp]\ntheorem coe_id : ⇑(PseudoEpimorphism.id α) = id", "start": [ 164, 1 ], "end": [ 165, 55 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.coe_id_orderHom", "code": "@[simp]\ntheorem coe_id_orderHom : (PseudoEpimorphism.id α : α →o α) = OrderHom.id", "start": [ 168, 1 ], "end": [ 169, 81 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.id_apply", "code": "@[simp]\ntheorem id_apply (a : α) : PseudoEpimorphism.id α a = a", "start": [ 174, 1 ], "end": [ 175, 63 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.comp", "code": "def comp (g : PseudoEpimorphism β γ) (f : PseudoEpimorphism α β) : PseudoEpimorphism α γ :=\n ⟨g.toOrderHom.comp f.toOrderHom, fun a b h₀ => by\n obtain ⟨b, h₁, rfl⟩ := g.exists_map_eq_of_map_le' h₀\n obtain ⟨b, h₂, rfl⟩ := f.exists_map_eq_of_map_le' h₁\n exact ⟨b, h₂, rfl⟩⟩", "start": [ 178, 1 ], "end": [ 183, 24 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.coe_comp", "code": "@[simp]\ntheorem coe_comp (g : PseudoEpimorphism β γ) (f : PseudoEpimorphism α β) :\n (g.comp f : α → γ) = g ∘ f", "start": [ 186, 1 ], "end": [ 188, 38 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.coe_comp_orderHom", "code": "@[simp]\ntheorem coe_comp_orderHom (g : PseudoEpimorphism β γ) (f : PseudoEpimorphism α β) :\n (g.comp f : α →o γ) = (g : β →o γ).comp f", "start": [ 191, 1 ], "end": [ 193, 53 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.comp_apply", "code": "@[simp]\ntheorem comp_apply (g : PseudoEpimorphism β γ) (f : PseudoEpimorphism α β) (a : α) :\n (g.comp f) a = g (f a)", "start": [ 196, 1 ], "end": [ 198, 34 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.comp_assoc", "code": "@[simp]\ntheorem comp_assoc (h : PseudoEpimorphism γ δ) (g : PseudoEpimorphism β γ)\n (f : PseudoEpimorphism α β) : (h.comp g).comp f = h.comp (g.comp f)", "start": [ 201, 1 ], "end": [ 203, 79 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.comp_id", "code": "@[simp]\ntheorem comp_id (f : PseudoEpimorphism α β) : f.comp (PseudoEpimorphism.id α) = f", "start": [ 206, 1 ], "end": [ 208, 19 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.id_comp", "code": "@[simp]\ntheorem id_comp (f : PseudoEpimorphism α β) : (PseudoEpimorphism.id β).comp f = f", "start": [ 211, 1 ], "end": [ 213, 19 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.cancel_right", "code": "@[simp]\ntheorem cancel_right {g₁ g₂ : PseudoEpimorphism β γ} {f : PseudoEpimorphism α β}\n (hf : Surjective f) : g₁.comp f = g₂.comp f ↔ g₁ = g₂", "start": [ 216, 1 ], "end": [ 219, 78 ], "kind": "commanddeclaration" }, { "full_name": "PseudoEpimorphism.cancel_left", "code": "@[simp]\ntheorem cancel_left {g : PseudoEpimorphism β γ} {f₁ f₂ : PseudoEpimorphism α β} (hg : Injective g) :\n g.comp f₁ = g.comp f₂ ↔ f₁ = f₂", "start": [ 222, 1 ], "end": [ 225, 81 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.toPseudoEpimorphism", "code": "def toPseudoEpimorphism (f : EsakiaHom α β) : PseudoEpimorphism α β :=\n { f with }", "start": [ 238, 1 ], "end": [ 239, 13 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.instFunLike", "code": "instance instFunLike : FunLike (EsakiaHom α β) α β where\n coe f := f.toFun\n coe_injective' f g h := by\n obtain ⟨⟨⟨_, _⟩, _⟩, _⟩ := f\n obtain ⟨⟨⟨_, _⟩, _⟩, _⟩ := g\n congr", "start": [ 242, 1 ], "end": [ 247, 10 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.toContinuousOrderHom_coe", "code": "@[simp]\ntheorem toContinuousOrderHom_coe {f : EsakiaHom α β} :\n f.toContinuousOrderHom = (f : α → β)", "start": [ 255, 1 ], "end": [ 257, 48 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.toFun_eq_coe", "code": "theorem toFun_eq_coe {f : EsakiaHom α β} : f.toFun = (f : α → β)", "start": [ 260, 1 ], "end": [ 260, 72 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.ext", "code": "@[ext]\ntheorem ext {f g : EsakiaHom α β} (h : ∀ a, f a = g a) : f = g", "start": [ 263, 1 ], "end": [ 265, 21 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.copy", "code": "protected def copy (f : EsakiaHom α β) (f' : α → β) (h : f' = f) : EsakiaHom α β :=\n ⟨f.toContinuousOrderHom.copy f' h, by\n simpa only [h.symm, toFun_eq_coe] using f.exists_map_eq_of_map_le'⟩", "start": [ 268, 1 ], "end": [ 272, 72 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_copy", "code": "@[simp]\ntheorem coe_copy (f : EsakiaHom α β) (f' : α → β) (h : f' = f) : ⇑(f.copy f' h) = f'", "start": [ 275, 1 ], "end": [ 276, 92 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.copy_eq", "code": "theorem copy_eq (f : EsakiaHom α β) (f' : α → β) (h : f' = f) : f.copy f' h = f", "start": [ 279, 1 ], "end": [ 280, 18 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.id", "code": "protected def id : EsakiaHom α α :=\n ⟨ContinuousOrderHom.id α, fun _ b h => ⟨b, h, rfl⟩⟩", "start": [ 285, 1 ], "end": [ 287, 54 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_id", "code": "@[simp]\ntheorem coe_id : ⇑(EsakiaHom.id α) = id", "start": [ 293, 1 ], "end": [ 294, 47 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_id_pseudoEpimorphism", "code": "@[simp]\ntheorem coe_id_pseudoEpimorphism :\n (EsakiaHom.id α : PseudoEpimorphism α α) = PseudoEpimorphism.id α", "start": [ 297, 1 ], "end": [ 299, 77 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.id_apply", "code": "@[simp]\ntheorem id_apply (a : α) : EsakiaHom.id α a = a", "start": [ 304, 1 ], "end": [ 305, 55 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_id_continuousOrderHom", "code": "@[simp]\ntheorem coe_id_continuousOrderHom : (EsakiaHom.id α : α →Co α) = ContinuousOrderHom.id α", "start": [ 308, 1 ], "end": [ 309, 96 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.comp", "code": "def comp (g : EsakiaHom β γ) (f : EsakiaHom α β) : EsakiaHom α γ :=\n ⟨g.toContinuousOrderHom.comp f.toContinuousOrderHom, fun a b h₀ => by\n obtain ⟨b, h₁, rfl⟩ := g.exists_map_eq_of_map_le' h₀\n obtain ⟨b, h₂, rfl⟩ := f.exists_map_eq_of_map_le' h₁\n exact ⟨b, h₂, rfl⟩⟩", "start": [ 312, 1 ], "end": [ 317, 24 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_comp_continuousOrderHom", "code": "@[simp]\ntheorem coe_comp_continuousOrderHom (g : EsakiaHom β γ) (f : EsakiaHom α β) :\n (g.comp f : α →Co γ) = (g: β →Co γ).comp f", "start": [ 320, 1 ], "end": [ 322, 54 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_comp_pseudoEpimorphism", "code": "@[simp]\ntheorem coe_comp_pseudoEpimorphism (g : EsakiaHom β γ) (f : EsakiaHom α β) :\n (g.comp f : PseudoEpimorphism α γ) = (g : PseudoEpimorphism β γ).comp f", "start": [ 325, 1 ], "end": [ 327, 83 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.coe_comp", "code": "@[simp]\ntheorem coe_comp (g : EsakiaHom β γ) (f : EsakiaHom α β) : (g.comp f : α → γ) = g ∘ f", "start": [ 330, 1 ], "end": [ 331, 93 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.comp_apply", "code": "@[simp]\ntheorem comp_apply (g : EsakiaHom β γ) (f : EsakiaHom α β) (a : α) : (g.comp f) a = g (f a)", "start": [ 334, 1 ], "end": [ 335, 99 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.comp_assoc", "code": "@[simp]\ntheorem comp_assoc (h : EsakiaHom γ δ) (g : EsakiaHom β γ) (f : EsakiaHom α β) :\n (h.comp g).comp f = h.comp (g.comp f)", "start": [ 338, 1 ], "end": [ 340, 49 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.comp_id", "code": "@[simp]\ntheorem comp_id (f : EsakiaHom α β) : f.comp (EsakiaHom.id α) = f", "start": [ 343, 1 ], "end": [ 345, 19 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.id_comp", "code": "@[simp]\ntheorem id_comp (f : EsakiaHom α β) : (EsakiaHom.id β).comp f = f", "start": [ 348, 1 ], "end": [ 350, 19 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.cancel_right", "code": "@[simp]\ntheorem cancel_right {g₁ g₂ : EsakiaHom β γ} {f : EsakiaHom α β} (hf : Surjective f) :\n g₁.comp f = g₂.comp f ↔ g₁ = g₂", "start": [ 353, 1 ], "end": [ 356, 78 ], "kind": "commanddeclaration" }, { "full_name": "EsakiaHom.cancel_left", "code": "@[simp]\ntheorem cancel_left {g : EsakiaHom β γ} {f₁ f₂ : EsakiaHom α β} (hg : Injective g) :\n g.comp f₁ = g.comp f₂ ↔ f₁ = f₂", "start": [ 359, 1 ], "end": [ 362, 81 ], "kind": "commanddeclaration" } ]

Mathlib/Analysis/Convex/EGauge.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/Seminorm.lean" ]

[ { "full_name": "egauge", "code": "noncomputable def egauge (𝕜 : Type*) [NNNorm 𝕜] {E : Type*} [SMul 𝕜 E] (s : Set E) (x : E) : ℝ≥0∞ :=\n ⨅ (c : 𝕜) (_ : x ∈ c • s), ‖c‖₊", "start": [ 32, 1 ], "end": [ 43, 34 ], "kind": "commanddeclaration" }, { "full_name": "egauge_anti", "code": "@[mono, gcongr]\nlemma egauge_anti (h : s ⊆ t) (x : E) : egauge 𝕜 t x ≤ egauge 𝕜 s x :=\n iInf_mono fun _c ↦ iInf_mono' fun hc ↦ ⟨smul_set_mono h hc, le_rfl⟩", "start": [ 47, 1 ], "end": [ 49, 70 ], "kind": "lemma" }, { "full_name": "egauge_empty", "code": "@[simp] lemma egauge_empty (x : E) : egauge 𝕜 ∅ x = ∞ := by simp [egauge]", "start": [ 51, 1 ], "end": [ 51, 74 ], "kind": "lemma" }, { "full_name": "egauge_le_of_mem_smul", "code": "lemma egauge_le_of_mem_smul (h : x ∈ c • s) : egauge 𝕜 s x ≤ ‖c‖₊ := iInf₂_le c h", "start": [ 55, 1 ], "end": [ 55, 82 ], "kind": "lemma" }, { "full_name": "le_egauge_iff", "code": "lemma le_egauge_iff : r ≤ egauge 𝕜 s x ↔ ∀ c : 𝕜, x ∈ c • s → r ≤ ‖c‖₊ := le_iInf₂_iff", "start": [ 57, 1 ], "end": [ 57, 87 ], "kind": "lemma" }, { "full_name": "egauge_eq_top", "code": "lemma egauge_eq_top : egauge 𝕜 s x = ∞ ↔ ∀ c : 𝕜, x ∉ c • s := by simp [egauge]", "start": [ 59, 1 ], "end": [ 59, 80 ], "kind": "lemma" }, { "full_name": "egauge_lt_iff", "code": "lemma egauge_lt_iff : egauge 𝕜 s x < r ↔ ∃ c : 𝕜, x ∈ c • s ∧ ‖c‖₊ < r := by\n simp [egauge, iInf_lt_iff]", "start": [ 61, 1 ], "end": [ 62, 29 ], "kind": "lemma" }, { "full_name": "egauge_zero_left_eq_top", "code": "@[simp] lemma egauge_zero_left_eq_top : egauge 𝕜 0 x = ∞ ↔ x ≠ 0 := by\n simp [egauge_eq_top]", "start": [ 71, 1 ], "end": [ 72, 23 ], "kind": "lemma" }, { "full_name": "egauge_le_of_smul_mem_of_ne", "code": "lemma egauge_le_of_smul_mem_of_ne (h : c • x ∈ s) (hc : c ≠ 0) :\n egauge 𝕜 s x ≤ ↑(‖c‖₊⁻¹ : ℝ≥0) := by\n rw [← nnnorm_inv]\n exact egauge_le_of_mem_smul <| (mem_inv_smul_set_iff₀ hc _ _).2 h", "start": [ 83, 1 ], "end": [ 89, 68 ], "kind": "lemma" }, { "full_name": "egauge_le_of_smul_mem", "code": "lemma egauge_le_of_smul_mem (h : c • x ∈ s) : egauge 𝕜 s x ≤ (‖c‖₊ : ℝ≥0∞)⁻¹ := by\n rcases eq_or_ne c 0 with rfl | hc\n · simp\n · exact (egauge_le_of_smul_mem_of_ne h hc).trans ENNReal.coe_inv_le", "start": [ 91, 1 ], "end": [ 97, 70 ], "kind": "lemma" }, { "full_name": "mem_of_egauge_lt_one", "code": "lemma mem_of_egauge_lt_one (hs : Balanced 𝕜 s) (hx : egauge 𝕜 s x < 1) : x ∈ s :=\n let ⟨c, hxc, hc⟩ := egauge_lt_iff.1 hx\n hs c (mod_cast hc.le) hxc", "start": [ 99, 1 ], "end": [ 101, 28 ], "kind": "lemma" }, { "full_name": "egauge_zero_right", "code": "@[simp]\nlemma egauge_zero_right (hs : s.Nonempty) : egauge 𝕜 s 0 = 0 := by\n have : 0 ∈ (0 : 𝕜) • s := by simp [zero_smul_set hs]\n simpa using egauge_le_of_mem_smul this", "start": [ 105, 1 ], "end": [ 108, 41 ], "kind": "lemma" }, { "full_name": "egauge_zero_zero", "code": "@[simp]\nlemma egauge_zero_zero : egauge 𝕜 (0 : Set E) 0 = 0 := egauge_zero_right _ ⟨0, rfl⟩", "start": [ 110, 1 ], "end": [ 111, 84 ], "kind": "lemma" }, { "full_name": "egauge_le_one", "code": "lemma egauge_le_one (h : x ∈ s) : egauge 𝕜 s x ≤ 1 := by\n rw [← one_smul 𝕜 s] at h\n simpa using egauge_le_of_mem_smul h", "start": [ 113, 1 ], "end": [ 115, 38 ], "kind": "lemma" }, { "full_name": "le_egauge_smul_left", "code": "lemma le_egauge_smul_left (c : 𝕜) (s : Set E) (x : E) :\n egauge 𝕜 s x / ‖c‖₊ ≤ egauge 𝕜 (c • s) x := by\n simp_rw [le_egauge_iff, smul_smul]\n rintro a ⟨x, hx, rfl⟩\n apply ENNReal.div_le_of_le_mul\n rw [← ENNReal.coe_mul, ← nnnorm_mul]\n exact egauge_le_of_mem_smul <| smul_mem_smul_set hx", "start": [ 119, 1 ], "end": [ 125, 54 ], "kind": "lemma" }, { "full_name": "egauge_smul_left", "code": "lemma egauge_smul_left (hc : c ≠ 0) (s : Set E) (x : E) :\n egauge 𝕜 (c • s) x = egauge 𝕜 s x / ‖c‖₊ := by\n refine le_antisymm ?_ (le_egauge_smul_left _ _ _)\n rw [ENNReal.le_div_iff_mul_le (by simp [*]) (by simp)]\n calc\n egauge 𝕜 (c • s) x * ‖c‖₊ = egauge 𝕜 (c • s) x / ‖c⁻¹‖₊ := by\n rw [nnnorm_inv, ENNReal.coe_inv (by simpa), div_eq_mul_inv, inv_inv]\n _ ≤ egauge 𝕜 (c⁻¹ • c • s) x := le_egauge_smul_left _ _ _\n _ = egauge 𝕜 s x := by rw [inv_smul_smul₀ hc]", "start": [ 127, 1 ], "end": [ 135, 50 ], "kind": "lemma" }, { "full_name": "le_egauge_smul_right", "code": "lemma le_egauge_smul_right (c : 𝕜) (s : Set E) (x : E) :\n ‖c‖₊ * egauge 𝕜 s x ≤ egauge 𝕜 s (c • x) := by\n rw [le_egauge_iff]\n rintro a ⟨y, hy, hxy⟩\n rcases eq_or_ne c 0 with rfl | hc\n · simp\n · refine ENNReal.mul_le_of_le_div' <| le_trans ?_ ENNReal.coe_div_le\n rw [div_eq_inv_mul, ← nnnorm_inv, ← nnnorm_mul]\n refine egauge_le_of_mem_smul ⟨y, hy, ?_⟩\n simp only [mul_smul, hxy, inv_smul_smul₀ hc]", "start": [ 137, 1 ], "end": [ 146, 49 ], "kind": "lemma" }, { "full_name": "egauge_smul_right", "code": "lemma egauge_smul_right (h : c = 0 → s.Nonempty) (x : E) :\n egauge 𝕜 s (c • x) = ‖c‖₊ * egauge 𝕜 s x := by\n refine le_antisymm ?_ (le_egauge_smul_right c s x)\n rcases eq_or_ne c 0 with rfl | hc\n · simp [egauge_zero_right _ (h rfl)]\n · rw [mul_comm, ← ENNReal.div_le_iff_le_mul (.inl <| by simpa) (.inl ENNReal.coe_ne_top),\n ENNReal.div_eq_inv_mul, ← ENNReal.coe_inv (by simpa), ← nnnorm_inv]\n refine (le_egauge_smul_right _ _ _).trans_eq ?_\n rw [inv_smul_smul₀ hc]", "start": [ 148, 1 ], "end": [ 156, 27 ], "kind": "lemma" }, { "full_name": "div_le_egauge_closedBall", "code": "lemma div_le_egauge_closedBall (r : ℝ≥0) (x : E) : ‖x‖₊ / r ≤ egauge 𝕜 (closedBall 0 r) x := by\n rw [le_egauge_iff]\n rintro c ⟨y, hy, rfl⟩\n rw [mem_closedBall_zero_iff, ← coe_nnnorm, NNReal.coe_le_coe] at hy\n simp only [nnnorm_smul, ENNReal.coe_mul]\n apply ENNReal.div_le_of_le_mul\n gcongr", "start": [ 165, 1 ], "end": [ 171, 9 ], "kind": "lemma" }, { "full_name": "le_egauge_closedBall_one", "code": "lemma le_egauge_closedBall_one (x : E) : ‖x‖₊ ≤ egauge 𝕜 (closedBall 0 1) x := by\n simpa using div_le_egauge_closedBall 𝕜 1 x", "start": [ 173, 1 ], "end": [ 174, 45 ], "kind": "lemma" }, { "full_name": "div_le_egauge_ball", "code": "lemma div_le_egauge_ball (r : ℝ≥0) (x : E) : ‖x‖₊ / r ≤ egauge 𝕜 (ball 0 r) x :=\n (div_le_egauge_closedBall 𝕜 r x).trans <| egauge_anti _ ball_subset_closedBall _", "start": [ 176, 1 ], "end": [ 177, 83 ], "kind": "lemma" }, { "full_name": "le_egauge_ball_one", "code": "lemma le_egauge_ball_one (x : E) : ‖x‖₊ ≤ egauge 𝕜 (ball 0 1) x := by\n simpa using div_le_egauge_ball 𝕜 1 x", "start": [ 179, 1 ], "end": [ 180, 39 ], "kind": "lemma" }, { "full_name": "egauge_ball_le_of_one_lt_norm", "code": "lemma egauge_ball_le_of_one_lt_norm (hc : 1 < ‖c‖) (h₀ : r ≠ 0 ∨ x ≠ 0) :\n egauge 𝕜 (ball 0 r) x ≤ ‖c‖₊ * ‖x‖₊ / r := by\n rcases (zero_le r).eq_or_lt with rfl | hr\n · rw [ENNReal.coe_zero, ENNReal.div_zero (mul_ne_zero _ _)]\n · apply le_top\n · simpa using one_pos.trans hc\n · simpa using h₀\n · rcases eq_or_ne x 0 with rfl | hx\n · rw [egauge_zero_right] <;> simp [*]\n rcases rescale_to_shell hc hr hx with ⟨a, ha₀, har, -, hainv⟩\n calc\n egauge 𝕜 (ball 0 r) x ≤ ↑(‖a‖₊⁻¹) := egauge_le_of_smul_mem_of_ne (mem_ball_zero_iff.2 har) ha₀\n _ ≤ ↑(‖c‖₊ * ‖x‖₊ / r) := by rwa [ENNReal.coe_le_coe, div_eq_inv_mul, ← mul_assoc]\n _ ≤ ‖c‖₊ * ‖x‖₊ / r := ENNReal.coe_div_le.trans <| by rw [ENNReal.coe_mul]", "start": [ 189, 1 ], "end": [ 202, 81 ], "kind": "lemma" }, { "full_name": "egauge_ball_one_le_of_one_lt_norm", "code": "lemma egauge_ball_one_le_of_one_lt_norm (hc : 1 < ‖c‖) (x : E) :\n egauge 𝕜 (ball 0 1) x ≤ ‖c‖₊ * ‖x‖₊ := by\n simpa using egauge_ball_le_of_one_lt_norm hc (.inl one_ne_zero)", "start": [ 204, 1 ], "end": [ 206, 66 ], "kind": "lemma" } ]

Mathlib/CategoryTheory/Localization/FiniteProducts.lean

[ "Mathlib/CategoryTheory/Localization/HasLocalization.lean", "Mathlib/CategoryTheory/Localization/Adjunction.lean", "Mathlib/CategoryTheory/MorphismProperty/Limits.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/CategoryTheory/Limits/Preserves/Finite.lean", "Mathlib/CategoryTheory/Limits/ConeCategory.lean", "Mathlib/CategoryTheory/Localization/Pi.lean" ]

[ { "full_name": "CategoryTheory.Localization.HasProductsOfShapeAux.inverts", "code": "lemma inverts :\n (W.functorCategory (Discrete J)).IsInvertedBy (lim ⋙ L) :=\n fun _ _ f hf => Localization.inverts L W _ (hW.lim_map f hf)", "start": [ 38, 1 ], "end": [ 40, 63 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Localization.HasProductsOfShapeAux.limitFunctor", "code": "noncomputable abbrev limitFunctor :\n (Discrete J ⥤ D) ⥤ D :=\n Localization.lift _ (inverts L hW)\n ((whiskeringRight (Discrete J) C D).obj L)", "start": [ 42, 1 ], "end": [ 47, 47 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Localization.HasProductsOfShapeAux.compLimitFunctorIso", "code": "noncomputable def compLimitFunctorIso :\n ((whiskeringRight (Discrete J) C D).obj L) ⋙ limitFunctor L hW ≅\n lim ⋙ L := by\n apply Localization.fac", "start": [ 49, 1 ], "end": [ 53, 25 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Localization.HasProductsOfShapeAux.adj", "code": "noncomputable def adj :\n Functor.const _ ⊣ limitFunctor L hW :=\n constLimAdj.localization L W ((whiskeringRight (Discrete J) C D).obj L)\n (W.functorCategory (Discrete J)) (Functor.const _) (limitFunctor L hW)", "start": [ 64, 1 ], "end": [ 69, 75 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Localization.HasProductsOfShapeAux.adj_counit_app", "code": "lemma adj_counit_app (F : Discrete J ⥤ C) :\n (adj L hW).counit.app (F ⋙ L) =\n (Functor.const (Discrete J)).map ((compLimitFunctorIso L hW).hom.app F) ≫\n (Functor.compConstIso (Discrete J) L).hom.app (lim.obj F) ≫\n whiskerRight (constLimAdj.counit.app F) L := by\n apply constLimAdj.localization_counit_app", "start": [ 71, 1 ], "end": [ 76, 44 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Localization.HasProductsOfShapeAux.isLimitMapCone", "code": "noncomputable def isLimitMapCone (F : Discrete J ⥤ C) :\n IsLimit (L.mapCone (limit.cone F)) :=\n IsLimit.ofIsoLimit (isLimitConeOfAdj (adj L hW) (F ⋙ L))\n (Cones.ext ((compLimitFunctorIso L hW).app F) (by simp [adj_counit_app, constLimAdj]))", "start": [ 78, 1 ], "end": [ 82, 91 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Localization.hasProductsOfShape", "code": "lemma hasProductsOfShape (J : Type) [Finite J] [HasProductsOfShape J C]\n (hW : W.IsStableUnderProductsOfShape J) :\n HasProductsOfShape J D :=\n hasLimitsOfShape_iff_isLeftAdjoint_const.2\n (HasProductsOfShapeAux.adj L hW).isLeftAdjoint", "start": [ 88, 1 ], "end": [ 92, 51 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Localization.preservesProductsOfShape", "code": "noncomputable def preservesProductsOfShape (J : Type) [Finite J]\n [HasProductsOfShape J C] (hW : W.IsStableUnderProductsOfShape J) :\n PreservesLimitsOfShape (Discrete J) L where\n preservesLimit {F} := preservesLimitOfPreservesLimitCone (limit.isLimit F)\n (HasProductsOfShapeAux.isLimitMapCone L hW F)", "start": [ 94, 1 ], "end": [ 101, 50 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Localization.hasFiniteProducts", "code": "lemma hasFiniteProducts : HasFiniteProducts D :=\n ⟨fun _ => hasProductsOfShape L W _\n (W.isStableUnderProductsOfShape_of_isStableUnderFiniteProducts _)⟩", "start": [ 105, 1 ], "end": [ 107, 71 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Localization.preservesFiniteProducts", "code": "noncomputable def preservesFiniteProducts :\n PreservesFiniteProducts L where\n preserves J _ := preservesProductsOfShape L W J\n (W.isStableUnderProductsOfShape_of_isStableUnderFiniteProducts _)", "start": [ 109, 1 ], "end": [ 115, 72 ], "kind": "commanddeclaration" } ]

Mathlib/Analysis/Fourier/RiemannLebesgueLemma.lean

[ "Mathlib/MeasureTheory/Function/ContinuousMapDense.lean", "Mathlib/MeasureTheory/Integral/SetIntegral.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/Fourier/FourierTransform.lean", "Mathlib/Analysis/InnerProductSpace/Dual.lean", "Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean", "Mathlib/Topology/EMetricSpace/Paracompact.lean", "Mathlib/MeasureTheory/Group/Integral.lean", "Mathlib/MeasureTheory/Measure/Haar/NormedSpace.lean", "Mathlib/MeasureTheory/Measure/Haar/Unique.lean" ]

[ { "full_name": "fourierIntegral_half_period_translate", "code": "theorem fourierIntegral_half_period_translate {w : V} (hw : w ≠ 0) :\n (∫ v : V, 𝐞 (-⟪v, w⟫) • f (v + i w)) = -∫ v : V, 𝐞 (-⟪v, w⟫) • f v", "start": [ 67, 1 ], "end": [ 92, 37 ], "kind": "commanddeclaration" }, { "full_name": "fourierIntegral_eq_half_sub_half_period_translate", "code": "theorem fourierIntegral_eq_half_sub_half_period_translate {w : V} (hw : w ≠ 0)\n (hf : Integrable f) :\n ∫ v : V, 𝐞 (-⟪v, w⟫) • f v = (1 / (2 : ℂ)) • ∫ v : V, 𝐞 (-⟪v, w⟫) • (f v - f (v + i w))", "start": [ 95, 1 ], "end": [ 104, 69 ], "kind": "commanddeclaration" }, { "full_name": "tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support", "code": "theorem tendsto_integral_exp_inner_smul_cocompact_of_continuous_compact_support (hf1 : Continuous f)\n (hf2 : HasCompactSupport f) :\n Tendsto (fun w : V => ∫ v : V, 𝐞 (-⟪v, w⟫) • f v) (cocompact V) (𝓝 0)", "start": [ 107, 1 ], "end": [ 194, 74 ], "kind": "commanddeclaration" }, { "full_name": "tendsto_integral_exp_inner_smul_cocompact", "code": "theorem tendsto_integral_exp_inner_smul_cocompact :\n Tendsto (fun w : V => ∫ v, 𝐞 (-⟪v, w⟫) • f v) (cocompact V) (𝓝 0)", "start": [ 199, 1 ], "end": [ 226, 39 ], "kind": "commanddeclaration" }, { "full_name": "Real.tendsto_integral_exp_smul_cocompact", "code": "theorem Real.tendsto_integral_exp_smul_cocompact (f : ℝ → E) :\n Tendsto (fun w : ℝ => ∫ v : ℝ, 𝐞 (-(v * w)) • f v) (cocompact ℝ) (𝓝 0)", "start": [ 229, 1 ], "end": [ 232, 46 ], "kind": "commanddeclaration" }, { "full_name": "Real.zero_at_infty_fourierIntegral", "code": "theorem Real.zero_at_infty_fourierIntegral (f : ℝ → E) : Tendsto (𝓕 f) (cocompact ℝ) (𝓝 0)", "start": [ 235, 1 ], "end": [ 237, 46 ], "kind": "commanddeclaration" }, { "full_name": "tendsto_integral_exp_smul_cocompact_of_inner_product", "code": "theorem tendsto_integral_exp_smul_cocompact_of_inner_product (μ : Measure V) [μ.IsAddHaarMeasure] :\n Tendsto (fun w : V →L[ℝ] ℝ => ∫ v, 𝐞 (-w v) • f v ∂μ) (cocompact (V →L[ℝ] ℝ)) (𝓝 0)", "start": [ 240, 1 ], "end": [ 256, 55 ], "kind": "commanddeclaration" }, { "full_name": "tendsto_integral_exp_smul_cocompact", "code": "theorem tendsto_integral_exp_smul_cocompact (μ : Measure V) [μ.IsAddHaarMeasure] :\n Tendsto (fun w : V →L[ℝ] ℝ => ∫ v, 𝐞 (-w v) • f v ∂μ) (cocompact (V →L[ℝ] ℝ)) (𝓝 0)", "start": [ 267, 1 ], "end": [ 320, 60 ], "kind": "commanddeclaration" }, { "full_name": "Real.zero_at_infty_vector_fourierIntegral", "code": "theorem Real.zero_at_infty_vector_fourierIntegral (μ : Measure V) [μ.IsAddHaarMeasure] :\n Tendsto (VectorFourier.fourierIntegral 𝐞 μ (topDualPairing ℝ V).flip f) (cocompact (V →L[ℝ] ℝ))\n (𝓝 0)", "start": [ 323, 1 ], "end": [ 329, 49 ], "kind": "commanddeclaration" } ]

Mathlib/Analysis/Calculus/InverseFunctionTheorem/FiniteDimensional.lean

[ "Mathlib/Analysis/Calculus/InverseFunctionTheorem/ApproximatesLinearOn.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/NormedSpace/FiniteDimension.lean" ]

[ { "full_name": "ApproximatesLinearOn.exists_homeomorph_extension", "code": "theorem exists_homeomorph_extension {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]\n {F : Type*} [NormedAddCommGroup F] [NormedSpace ℝ F] [FiniteDimensional ℝ F] {s : Set E}\n {f : E → F} {f' : E ≃L[ℝ] F} {c : ℝ≥0} (hf : ApproximatesLinearOn f (f' : E →L[ℝ] F) s c)\n (hc : Subsingleton E ∨ lipschitzExtensionConstant F * c < ‖(f'.symm : F →L[ℝ] E)‖₊⁻¹) :\n ∃ g : E ≃ₜ F, EqOn f g s", "start": [ 25, 1 ], "end": [ 47, 35 ], "kind": "commanddeclaration" } ]

Mathlib/Analysis/Convex/Radon.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/Convex/Combination.lean", "Mathlib/Tactic/Linarith.lean" ]

[ { "full_name": "radon_partition", "code": "theorem radon_partition (h : ¬ AffineIndependent 𝕜 f) :\n ∃ I, (convexHull 𝕜 (f '' I) ∩ convexHull 𝕜 (f '' Iᶜ)).Nonempty", "start": [ 24, 1 ], "end": [ 50, 60 ], "kind": "commanddeclaration" } ]

Mathlib/RepresentationTheory/Character.lean

[ "Mathlib/LinearAlgebra/Trace.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/RepresentationTheory/Invariants.lean", "Mathlib/RepresentationTheory/FdRep.lean" ]

[ { "full_name": "FdRep.character", "code": "def character (V : FdRep k G) (g : G) :=\n LinearMap.trace k V (V.ρ g)", "start": [ 48, 1 ], "end": [ 51, 30 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_mul_comm", "code": "theorem char_mul_comm (V : FdRep k G) (g : G) (h : G) :\n V.character (h * g) = V.character (g * h)", "start": [ 54, 1 ], "end": [ 55, 99 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_one", "code": "@[simp]\ntheorem char_one (V : FdRep k G) : V.character 1 = FiniteDimensional.finrank k V", "start": [ 58, 1 ], "end": [ 60, 44 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_tensor", "code": "theorem char_tensor (V W : FdRep k G) : (V ⊗ W).character = V.character * W.character", "start": [ 63, 1 ], "end": [ 65, 54 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_tensor'", "code": "@[simp]\ntheorem char_tensor' (V W : FdRep k G) :\n character (Action.FunctorCategoryEquivalence.inverse.obj\n (Action.FunctorCategoryEquivalence.functor.obj V ⊗\n Action.FunctorCategoryEquivalence.functor.obj W)) = V.character * W.character", "start": [ 69, 1 ], "end": [ 74, 23 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_iso", "code": "theorem char_iso {V W : FdRep k G} (i : V ≅ W) : V.character = W.character", "start": [ 76, 1 ], "end": [ 78, 87 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_conj", "code": "@[simp]\ntheorem char_conj (V : FdRep k G) (g : G) (h : G) : V.character (h * g * h⁻¹) = V.character g", "start": [ 87, 1 ], "end": [ 90, 42 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_dual", "code": "@[simp]\ntheorem char_dual (V : FdRep k G) (g : G) : (of (dual V.ρ)).character g = V.character g⁻¹", "start": [ 93, 1 ], "end": [ 95, 29 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_linHom", "code": "@[simp]\ntheorem char_linHom (V W : FdRep k G) (g : G) :\n (of (linHom V.ρ W.ρ)).character g = V.character g⁻¹ * W.character g", "start": [ 98, 1 ], "end": [ 101, 82 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.average_char_eq_finrank_invariants", "code": "theorem average_char_eq_finrank_invariants (V : FdRep k G) :\n ⅟ (Fintype.card G : k) • ∑ g : G, V.character g = finrank k (invariants V.ρ)", "start": [ 106, 1 ], "end": [ 109, 57 ], "kind": "commanddeclaration" }, { "full_name": "FdRep.char_orthonormal", "code": "theorem char_orthonormal (V W : FdRep k G) [Simple V] [Simple W] :\n ⅟ (Fintype.card G : k) • ∑ g : G, V.character g * W.character g⁻¹ =\n if Nonempty (V ≅ W) then ↑1 else ↑0", "start": [ 122, 1 ], "end": [ 142, 69 ], "kind": "commanddeclaration" } ]

Mathlib/Algebra/Homology/HomotopyCategory/SingleFunctors.lean

[ "Mathlib/CategoryTheory/Shift/SingleFunctors.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Algebra/Homology/HomotopyCategory/Shift.lean" ]

[ { "full_name": "CochainComplex.singleFunctors", "code": "noncomputable def singleFunctors : SingleFunctors C (CochainComplex C ℤ) ℤ where\n functor n := single _ _ n\n shiftIso n a a' ha' := NatIso.ofComponents\n (fun X => Hom.isoOfComponents\n (fun i => eqToIso (by\n obtain rfl : a' = a + n := by omega\n dsimp [CategoryTheory.shiftFunctor, shiftMonoidalFunctor, single]\n by_cases h : i = a\n · subst h\n simp only [ite_true]\n · rw [if_neg h, if_neg (fun h' => h (by omega))])) (by simp))\n (fun {X Y} f => by\n obtain rfl : a' = a + n := by omega\n ext\n simp [single])\n shiftIso_zero a := by\n ext\n dsimp\n simp only [single, shiftFunctorZero_eq, shiftFunctorZero'_hom_app_f,\n XIsoOfEq, eqToIso.hom]\n shiftIso_add n m a a' a'' ha' ha'' := by\n ext\n dsimp\n simp only [shiftFunctorAdd_eq, shiftFunctorAdd'_hom_app_f, XIsoOfEq,\n eqToIso.hom, eqToHom_trans, id_comp]", "start": [ 31, 1 ], "end": [ 58, 43 ], "kind": "commanddeclaration" }, { "full_name": "CochainComplex.singleFunctor", "code": "noncomputable abbrev singleFunctor (n : ℤ) := (singleFunctors C).functor n", "start": [ 64, 1 ], "end": [ 68, 75 ], "kind": "commanddeclaration" }, { "full_name": "HomotopyCategory.singleFunctors", "code": "noncomputable def singleFunctors : SingleFunctors C (HomotopyCategory C (ComplexShape.up ℤ)) ℤ :=\n (CochainComplex.singleFunctors C).postcomp (HomotopyCategory.quotient _ _)", "start": [ 74, 1 ], "end": [ 77, 77 ], "kind": "commanddeclaration" }, { "full_name": "HomotopyCategory.singleFunctor", "code": "noncomputable abbrev singleFunctor (n : ℤ) :\n C ⥤ HomotopyCategory C (ComplexShape.up ℤ) :=\n (singleFunctors C).functor n", "start": [ 79, 1 ], "end": [ 83, 31 ], "kind": "commanddeclaration" }, { "full_name": "HomotopyCategory.singleFunctorsPostcompQuotientIso", "code": "noncomputable def singleFunctorsPostcompQuotientIso :\n singleFunctors C ≅\n (CochainComplex.singleFunctors C).postcomp (HomotopyCategory.quotient _ _) :=\n Iso.refl _", "start": [ 89, 1 ], "end": [ 93, 13 ], "kind": "commanddeclaration" }, { "full_name": "HomotopyCategory.singleFunctorPostcompQuotientIso", "code": "noncomputable def singleFunctorPostcompQuotientIso (n : ℤ) :\n singleFunctor C n ≅ CochainComplex.singleFunctor C n ⋙ quotient _ _ :=\n (SingleFunctors.evaluation _ _ n).mapIso (singleFunctorsPostcompQuotientIso C)", "start": [ 95, 1 ], "end": [ 98, 81 ], "kind": "commanddeclaration" } ]

Mathlib/Algebra/Lie/CartanMatrix.lean

[ "Mathlib/Data/Matrix/Notation.lean", "Mathlib/Algebra/Lie/Quotient.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Algebra/Lie/Free.lean" ]

[ { "full_name": "CartanMatrix.Generators", "code": "inductive Generators\n | H : B → Generators\n | E : B → Generators\n | F : B → Generators", "start": [ 96, 1 ], "end": [ 101, 23 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.HH", "code": "def HH : B × B → FreeLieAlgebra R (Generators B) :=\n uncurry fun i j => ⁅H i, H j⁆", "start": [ 118, 1 ], "end": [ 120, 32 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.EF", "code": "def EF : B × B → FreeLieAlgebra R (Generators B) :=\n uncurry fun i j => if i = j then ⁅E i, F i⁆ - H i else ⁅E i, F j⁆", "start": [ 123, 1 ], "end": [ 125, 68 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.HE", "code": "def HE : B × B → FreeLieAlgebra R (Generators B) :=\n uncurry fun i j => ⁅H i, E j⁆ - A i j • E j", "start": [ 128, 1 ], "end": [ 130, 46 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.HF", "code": "def HF : B × B → FreeLieAlgebra R (Generators B) :=\n uncurry fun i j => ⁅H i, F j⁆ + A i j • F j", "start": [ 133, 1 ], "end": [ 135, 46 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.adE", "code": "def adE : B × B → FreeLieAlgebra R (Generators B) :=\n uncurry fun i j => ad (E i) ^ (-A i j).toNat <| ⁅E i, E j⁆", "start": [ 138, 1 ], "end": [ 144, 61 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.adF", "code": "def adF : B × B → FreeLieAlgebra R (Generators B) :=\n uncurry fun i j => ad (F i) ^ (-A i j).toNat <| ⁅F i, F j⁆", "start": [ 147, 1 ], "end": [ 151, 61 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.adE_of_eq_eq_zero", "code": "private theorem adE_of_eq_eq_zero (i : B) (h : A i i = 2) : adE R A ⟨i, i⟩ = 0", "start": [ 154, 1 ], "end": [ 156, 20 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.adF_of_eq_eq_zero", "code": "private theorem adF_of_eq_eq_zero (i : B) (h : A i i = 2) : adF R A ⟨i, i⟩ = 0", "start": [ 158, 1 ], "end": [ 160, 20 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.toSet", "code": "def toSet : Set (FreeLieAlgebra R (Generators B)) :=\n (Set.range <| HH R) ∪ (Set.range <| EF R) ∪ (Set.range <| HE R A) ∪ (Set.range <| HF R A) ∪\n (Set.range <| adE R A) ∪\n (Set.range <| adF R A)", "start": [ 162, 1 ], "end": [ 166, 27 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.Relations.toIdeal", "code": "def toIdeal : LieIdeal R (FreeLieAlgebra R (Generators B)) :=\n LieSubmodule.lieSpan R _ <| toSet R A", "start": [ 169, 1 ], "end": [ 171, 40 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.ToLieAlgebra", "code": "def Matrix.ToLieAlgebra :=\n FreeLieAlgebra R _ ⧸ CartanMatrix.Relations.toIdeal R A", "start": [ 178, 1 ], "end": [ 183, 58 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.ToLieAlgebra.instLieRing", "code": "instance Matrix.ToLieAlgebra.instLieRing : LieRing (Matrix.ToLieAlgebra R A) :=\n inferInstanceAs (LieRing (FreeLieAlgebra R _ ⧸ CartanMatrix.Relations.toIdeal R A))", "start": [ 187, 1 ], "end": [ 188, 86 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.ToLieAlgebra.instInhabited", "code": "instance Matrix.ToLieAlgebra.instInhabited : Inhabited (Matrix.ToLieAlgebra R A) :=\n inferInstanceAs (Inhabited (FreeLieAlgebra R _ ⧸ CartanMatrix.Relations.toIdeal R A))", "start": [ 191, 1 ], "end": [ 192, 88 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.ToLieAlgebra.instLieAlgebra", "code": "instance Matrix.ToLieAlgebra.instLieAlgebra : LieAlgebra R (Matrix.ToLieAlgebra R A) :=\n inferInstanceAs (LieAlgebra R (FreeLieAlgebra R _ ⧸ CartanMatrix.Relations.toIdeal R A))", "start": [ 195, 1 ], "end": [ 196, 91 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.E₆", "code": "def E₆ : Matrix (Fin 6) (Fin 6) ℤ :=\n !![2, 0, -1, 0, 0, 0;\n 0, 2, 0, -1, 0, 0;\n -1, 0, 2, -1, 0, 0;\n 0, -1, -1, 2, -1, 0;\n 0, 0, 0, -1, 2, -1;\n 0, 0, 0, 0, -1, 2]", "start": [ 201, 1 ], "end": [ 216, 23 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.E₇", "code": "def E₇ : Matrix (Fin 7) (Fin 7) ℤ :=\n !![2, 0, -1, 0, 0, 0, 0;\n 0, 2, 0, -1, 0, 0, 0;\n -1, 0, 2, -1, 0, 0, 0;\n 0, -1, -1, 2, -1, 0, 0;\n 0, 0, 0, -1, 2, -1, 0;\n 0, 0, 0, 0, -1, 2, -1;\n 0, 0, 0, 0, 0, -1, 2]", "start": [ 219, 1 ], "end": [ 235, 26 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.E₈", "code": "def E₈ : Matrix (Fin 8) (Fin 8) ℤ :=\n !![2, 0, -1, 0, 0, 0, 0, 0;\n 0, 2, 0, -1, 0, 0, 0, 0;\n -1, 0, 2, -1, 0, 0, 0, 0;\n 0, -1, -1, 2, -1, 0, 0, 0;\n 0, 0, 0, -1, 2, -1, 0, 0;\n 0, 0, 0, 0, -1, 2, -1, 0;\n 0, 0, 0, 0, 0, -1, 2, -1;\n 0, 0, 0, 0, 0, 0, -1, 2]", "start": [ 238, 1 ], "end": [ 255, 29 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.F₄", "code": "def F₄ : Matrix (Fin 4) (Fin 4) ℤ :=\n !![2, -1, 0, 0; -1, 2, -2, 0; 0, -1, 2, -1; 0, 0, -1, 2]", "start": [ 258, 1 ], "end": [ 266, 59 ], "kind": "commanddeclaration" }, { "full_name": "CartanMatrix.G₂", "code": "def G₂ : Matrix (Fin 2) (Fin 2) ℤ :=\n !![2, -3; -1, 2]", "start": [ 269, 1 ], "end": [ 278, 19 ], "kind": "commanddeclaration" }, { "full_name": "LieAlgebra.e₆", "code": "abbrev e₆ :=\n CartanMatrix.E₆.ToLieAlgebra R", "start": [ 285, 1 ], "end": [ 287, 33 ], "kind": "commanddeclaration" }, { "full_name": "LieAlgebra.e₇", "code": "abbrev e₇ :=\n CartanMatrix.E₇.ToLieAlgebra R", "start": [ 290, 1 ], "end": [ 292, 33 ], "kind": "commanddeclaration" }, { "full_name": "LieAlgebra.e₈", "code": "abbrev e₈ :=\n CartanMatrix.E₈.ToLieAlgebra R", "start": [ 295, 1 ], "end": [ 297, 33 ], "kind": "commanddeclaration" }, { "full_name": "LieAlgebra.f₄", "code": "abbrev f₄ :=\n CartanMatrix.F₄.ToLieAlgebra R", "start": [ 300, 1 ], "end": [ 302, 33 ], "kind": "commanddeclaration" }, { "full_name": "LieAlgebra.g₂", "code": "abbrev g₂ :=\n CartanMatrix.G₂.ToLieAlgebra R", "start": [ 305, 1 ], "end": [ 307, 33 ], "kind": "commanddeclaration" } ]

Mathlib/SetTheory/ZFC/Ordinal.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/SetTheory/ZFC/Basic.lean" ]

[ { "full_name": "ZFSet.IsTransitive", "code": "def IsTransitive (x : ZFSet) : Prop :=\n ∀ y ∈ x, y ⊆ x", "start": [ 39, 1 ], "end": [ 41, 17 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.empty_isTransitive", "code": "@[simp]\ntheorem empty_isTransitive : IsTransitive ∅", "start": [ 44, 1 ], "end": [ 45, 85 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.IsTransitive.subset_of_mem", "code": "theorem IsTransitive.subset_of_mem (h : x.IsTransitive) : y ∈ x → y ⊆ x", "start": [ 48, 1 ], "end": [ 49, 6 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.isTransitive_iff_mem_trans", "code": "theorem isTransitive_iff_mem_trans : z.IsTransitive ↔ ∀ {x y : ZFSet}, x ∈ y → y ∈ z → x ∈ z", "start": [ 52, 1 ], "end": [ 53, 73 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.IsTransitive.inter", "code": "protected theorem IsTransitive.inter (hx : x.IsTransitive) (hy : y.IsTransitive) :\n (x ∩ y).IsTransitive", "start": [ 59, 1 ], "end": [ 62, 53 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.IsTransitive.sUnion", "code": "protected theorem IsTransitive.sUnion (h : x.IsTransitive) :\n (⋃₀ x : ZFSet).IsTransitive", "start": [ 65, 1 ], "end": [ 68, 50 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.IsTransitive.sUnion'", "code": "theorem IsTransitive.sUnion' (H : ∀ y ∈ x, IsTransitive y) :\n (⋃₀ x : ZFSet).IsTransitive", "start": [ 71, 1 ], "end": [ 74, 57 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.IsTransitive.union", "code": "protected theorem IsTransitive.union (hx : x.IsTransitive) (hy : y.IsTransitive) :\n (x ∪ y).IsTransitive", "start": [ 77, 1 ], "end": [ 84, 14 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.IsTransitive.powerset", "code": "protected theorem IsTransitive.powerset (h : x.IsTransitive) : (powerset x).IsTransitive", "start": [ 87, 1 ], "end": [ 90, 32 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.isTransitive_iff_sUnion_subset", "code": "theorem isTransitive_iff_sUnion_subset : x.IsTransitive ↔ (⋃₀ x : ZFSet) ⊆ x", "start": [ 93, 1 ], "end": [ 96, 79 ], "kind": "commanddeclaration" }, { "full_name": "ZFSet.isTransitive_iff_subset_powerset", "code": "theorem isTransitive_iff_subset_powerset : x.IsTransitive ↔ x ⊆ powerset x", "start": [ 102, 1 ], "end": [ 103, 100 ], "kind": "commanddeclaration" } ]

Mathlib/Analysis/InnerProductSpace/LaxMilgram.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/InnerProductSpace/Dual.lean" ]

[ { "full_name": "IsCoercive.bounded_below", "code": "theorem bounded_below (coercive : IsCoercive B) : ∃ C, 0 < C ∧ ∀ v, C * ‖v‖ ≤ ‖B♯ v‖", "start": [ 51, 1 ], "end": [ 62, 16 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.antilipschitz", "code": "theorem antilipschitz (coercive : IsCoercive B) : ∃ C : ℝ≥0, 0 < C ∧ AntilipschitzWith C B♯", "start": [ 65, 1 ], "end": [ 71, 26 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.ker_eq_bot", "code": "theorem ker_eq_bot (coercive : IsCoercive B) : ker B♯ = ⊥", "start": [ 74, 1 ], "end": [ 77, 32 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.isClosed_range", "code": "theorem isClosed_range (coercive : IsCoercive B) : IsClosed (range B♯ : Set V)", "start": [ 80, 1 ], "end": [ 82, 58 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.range_eq_top", "code": "theorem range_eq_top (coercive : IsCoercive B) : range B♯ = ⊤", "start": [ 87, 1 ], "end": [ 102, 26 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.continuousLinearEquivOfBilin", "code": "def continuousLinearEquivOfBilin (coercive : IsCoercive B) : V ≃L[ℝ] V :=\n ContinuousLinearEquiv.ofBijective B♯ coercive.ker_eq_bot coercive.range_eq_top", "start": [ 105, 1 ], "end": [ 111, 81 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.continuousLinearEquivOfBilin_apply", "code": "@[simp]\ntheorem continuousLinearEquivOfBilin_apply (coercive : IsCoercive B) (v w : V) :\n ⟪coercive.continuousLinearEquivOfBilin v, w⟫_ℝ = B v w", "start": [ 114, 1 ], "end": [ 117, 41 ], "kind": "commanddeclaration" }, { "full_name": "IsCoercive.unique_continuousLinearEquivOfBilin", "code": "theorem unique_continuousLinearEquivOfBilin (coercive : IsCoercive B) {v f : V}\n (is_lax_milgram : ∀ w, ⟪f, w⟫_ℝ = B v w) : f = coercive.continuousLinearEquivOfBilin v", "start": [ 120, 1 ], "end": [ 122, 53 ], "kind": "commanddeclaration" } ]

Mathlib/Data/Buffer/Basic.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Init/Align.lean" ]

[]

Mathlib/NumberTheory/SiegelsLemma.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Tactic/Rify.lean", "Mathlib/Analysis/Matrix.lean", "Mathlib/Data/Pi/Interval.lean" ]

[ { "full_name": "Int.Matrix.image_T_subset_S", "code": "private lemma image_T_subset_S (v) (hv : v ∈ T) : A *ᵥ v ∈ S := by\n rw [mem_Icc] at hv ⊢\n have mulVec_def : A.mulVec v =\n fun i ↦ Finset.sum univ fun j : Fin n ↦ A i j * v j := rfl\n rw [mulVec_def]\n refine ⟨fun i ↦ ?_, fun i ↦ ?_⟩\n all_goals\n simp only [mul_neg]\n gcongr ∑ _ : Fin n, ?_ with j _ rw [← mul_comm (v j)] rcases le_total 0 (A i j) with hsign | hsign· rw [negPart_eq_zero.2 hsign]\n exact mul_nonneg (hv.1 j) hsign\n · rw [negPart_eq_neg.2 hsign]\n simp only [mul_neg, neg_neg]\n exact mul_le_mul_of_nonpos_right (hv.2 j) hsign\n · rw [posPart_eq_self.2 hsign]\n exact mul_le_mul_of_nonneg_right (hv.2 j) hsign\n · rw [posPart_eq_zero.2 hsign]\n exact mul_nonpos_of_nonneg_of_nonpos (hv.1 j) hsign", "start": [ 68, 1 ], "end": [ 87, 56 ], "kind": "lemma" }, { "full_name": "Int.Matrix.card_T_eq", "code": "private lemma card_T_eq : (T).card = (B + 1) ^ n := by\n rw [Pi.card_Icc 0 B']\n simp only [Pi.zero_apply, Int.card_Icc, sub_zero, Int.toNat_ofNat_add_one, prod_const, card_fin]", "start": [ 91, 1 ], "end": [ 93, 99 ], "kind": "lemma" }, { "full_name": "Int.Matrix.N_le_P_add_one", "code": "private lemma N_le_P_add_one (i : Fin m) : N i ≤ P i + 1 := by\n calc N i\n _ ≤ 0 := by\n apply Finset.sum_nonpos\n intro j _\n simp only [mul_neg, Left.neg_nonpos_iff]\n exact mul_nonneg (Nat.cast_nonneg B) (negPart_nonneg (A i j))\n _ ≤ P i + 1 := by\n apply le_trans (Finset.sum_nonneg _) (Int.le_add_one (le_refl P i))\n intro j _\n exact mul_nonneg (Nat.cast_nonneg B) (posPart_nonneg (A i j))", "start": [ 96, 1 ], "end": [ 106, 66 ], "kind": "lemma" }, { "full_name": "Int.Matrix.card_S_eq", "code": "private lemma card_S_eq : (Finset.Icc N P).card = ∏ i : Fin m, (P i - N i + 1) := by\n rw [Pi.card_Icc N P, Nat.cast_prod]\n congr\n ext i\n rw [Int.card_Icc_of_le (N i) (P i) (N_le_P_add_one m n A i)]\n exact add_sub_right_comm (P i) 1 (N i)", "start": [ 108, 1 ], "end": [ 113, 41 ], "kind": "lemma" }, { "full_name": "Int.Matrix.one_le_norm_A_of_ne_zero", "code": "lemma one_le_norm_A_of_ne_zero : 1 ≤ ‖A‖ := by\n by_contra! h\n apply hA\n ext i j\n simp only [zero_apply]\n rw [norm_lt_iff Real.zero_lt_one] at h\n specialize h i j\n rw [Int.norm_eq_abs] at h\n norm_cast at h\n exact Int.abs_lt_one_iff.1 h", "start": [ 117, 1 ], "end": [ 127, 31 ], "kind": "lemma" }, { "full_name": "Int.Matrix.card_S_lt_card_T", "code": "private lemma card_S_lt_card_T : (S).card < (T).card := by\n zify rw [card_T_eq, card_S_eq]\n rify calc\n ∏ x : Fin m, (∑ x_1 : Fin n, ↑B * ↑(A x x_1)⁺ - ∑ x_1 : Fin n, ↑B * -↑(A x x_1)⁻ + 1)\n ≤ (n * ‖A‖ * B + 1) ^ m := by\n rw [← Fin.prod_const m (n * ‖A‖ * B + 1)] refine Finset.prod_le_prod (fun i _ ↦ ?_) (fun i _ ↦ ?_)\n · have h := N_le_P_add_one m n A i\n rify at h\n linarith only [h]\n · simp only [mul_neg, sum_neg_distrib, sub_neg_eq_add, add_le_add_iff_right]\n have h1 : n * ‖A‖ * B = ∑ _ : Fin n, ‖A‖ * B := by\n simp only [sum_const, card_univ, Fintype.card_fin, nsmul_eq_mul, mul_assoc ↑n ‖A‖ ↑B]\n simp_rw [h1, ← Finset.sum_add_distrib, ← mul_add, mul_comm ‖A‖, ← Int.cast_add]\n gcongr with j _\n rw [posPart_add_negPart (A i j), Int.cast_abs]\n exact norm_entry_le_entrywise_sup_norm A\n _ ≤ (n * ‖A‖) ^ m * (B + 1) ^ m := by\n rw [← mul_pow, mul_add, mul_one]\n gcongr\n have H : 1 ≤ (n : ℝ) := mod_cast (hm.trans hn)\n exact one_le_mul_of_one_le_of_one_le H <| one_le_norm_A_of_ne_zero m n A hA\n _ = ((n * ‖A‖) ^ (m / ((n : ℝ) - m))) ^ ((n : ℝ) - m) * (B + 1) ^ m := by\n congr 1\n rw [← rpow_mul (mul_nonneg n.cast_nonneg (norm_nonneg A)), ← Real.rpow_natCast,\n div_mul_cancel₀]\n exact sub_ne_zero_of_ne (mod_cast hn.ne')\n _ < (B + 1) ^ ((n : ℝ) - m) * (B + 1) ^ m := by\n gcongr\n · exact sub_pos.mpr (mod_cast hn)\n · exact Nat.lt_floor_add_one ((n * ‖A‖) ^ e)\n _ = (B + 1) ^ n := by\n rw [← rpow_natCast, ← rpow_add (Nat.cast_add_one_pos B), ← rpow_natCast, sub_add_cancel]", "start": [ 133, 1 ], "end": [ 167, 97 ], "kind": "lemma" }, { "full_name": "Int.Matrix.exists_ne_zero_int_vec_norm_le", "code": "theorem exists_ne_zero_int_vec_norm_le (hA_nezero : A ≠ 0) : ∃ t : Fin n → ℤ, t ≠ 0 ∧\n A *ᵥ t = 0 ∧ ‖t‖ ≤ (n * ‖A‖) ^ ((m : ℝ) / (n - m))", "start": [ 171, 1 ], "end": [ 199, 18 ], "kind": "commanddeclaration" } ]

Mathlib/Data/ZMod/Coprime.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/RingTheory/PrincipalIdealDomain.lean", "Mathlib/Data/ZMod/Basic.lean", "Mathlib/RingTheory/Int/Basic.lean" ]

[ { "full_name": "ZMod.eq_zero_iff_gcd_ne_one", "code": "theorem eq_zero_iff_gcd_ne_one {a : ℤ} {p : ℕ} [pp : Fact p.Prime] :\n (a : ZMod p) = 0 ↔ a.gcd p ≠ 1", "start": [ 22, 1 ], "end": [ 28, 34 ], "kind": "commanddeclaration" }, { "full_name": "ZMod.ne_zero_of_gcd_eq_one", "code": "theorem ne_zero_of_gcd_eq_one {a : ℤ} {p : ℕ} (pp : p.Prime) (h : a.gcd p = 1) : (a : ZMod p) ≠ 0", "start": [ 31, 1 ], "end": [ 33, 69 ], "kind": "commanddeclaration" }, { "full_name": "ZMod.eq_zero_of_gcd_ne_one", "code": "theorem eq_zero_of_gcd_ne_one {a : ℤ} {p : ℕ} (pp : p.Prime) (h : a.gcd p ≠ 1) : (a : ZMod p) = 0", "start": [ 36, 1 ], "end": [ 38, 43 ], "kind": "commanddeclaration" } ]

Mathlib/Data/Finset/Functor.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Data/Finset/NAry.lean", "Mathlib/Data/Finset/Lattice.lean", "Mathlib/Data/Multiset/Functor.lean" ]

[ { "full_name": "Finset.functor", "code": "protected instance functor : Functor Finset where map f s := s.image f", "start": [ 37, 1 ], "end": [ 39, 71 ], "kind": "commanddeclaration" }, { "full_name": "Finset.lawfulFunctor", "code": "instance lawfulFunctor : LawfulFunctor Finset where\n id_map s := image_id\n comp_map f g s := image_image.symm\n map_const {α} {β} := by simp only [Functor.mapConst, Functor.map]", "start": [ 41, 1 ], "end": [ 44, 68 ], "kind": "commanddeclaration" }, { "full_name": "Finset.fmap_def", "code": "@[simp]\ntheorem fmap_def {s : Finset α} (f : α → β) : f <$> s = s.image f", "start": [ 46, 1 ], "end": [ 47, 73 ], "kind": "commanddeclaration" }, { "full_name": "Finset.pure", "code": "protected instance pure : Pure Finset :=\n ⟨fun x => {x}⟩", "start": [ 55, 1 ], "end": [ 56, 17 ], "kind": "commanddeclaration" }, { "full_name": "Finset.pure_def", "code": "@[simp]\ntheorem pure_def {α} : (pure : α → Finset α) = singleton", "start": [ 58, 1 ], "end": [ 59, 64 ], "kind": "commanddeclaration" }, { "full_name": "Finset.applicative", "code": "protected instance applicative : Applicative Finset :=\n { Finset.functor, Finset.pure with\n seq := fun t s => t.sup fun f => (s ()).image f\n seqLeft := fun s t => if t () = ∅ then ∅ else s\n seqRight := fun s t => if s = ∅ then ∅ else t () }", "start": [ 69, 1 ], "end": [ 73, 55 ], "kind": "commanddeclaration" }, { "full_name": "Finset.seq_def", "code": "@[simp]\ntheorem seq_def (s : Finset α) (t : Finset (α → β)) : t <*> s = t.sup fun f => s.image f", "start": [ 75, 1 ], "end": [ 77, 6 ], "kind": "commanddeclaration" }, { "full_name": "Finset.seqLeft_def", "code": "@[simp]\ntheorem seqLeft_def (s : Finset α) (t : Finset β) : s <* t = if t = ∅ then ∅ else s", "start": [ 80, 1 ], "end": [ 82, 6 ], "kind": "commanddeclaration" }, { "full_name": "Finset.seqRight_def", "code": "@[simp]\ntheorem seqRight_def (s : Finset α) (t : Finset β) : s *> t = if s = ∅ then ∅ else t", "start": [ 85, 1 ], "end": [ 87, 6 ], "kind": "commanddeclaration" }, { "full_name": "Finset.image₂_def", "code": "theorem image₂_def {α β γ : Type u} (f : α → β → γ) (s : Finset α) (t : Finset β) :\n image₂ f s t = f <$> s <*> t", "start": [ 90, 1 ], "end": [ 95, 17 ], "kind": "commanddeclaration" }, { "full_name": "Finset.lawfulApplicative", "code": "instance lawfulApplicative : LawfulApplicative Finset :=\n { Finset.lawfulFunctor with\n seqLeft_eq := fun s t => by\n rw [seq_def, fmap_def, seqLeft_def]\n obtain rfl | ht := t.eq_empty_or_nonempty\n · simp_rw [image_empty, if_true]\n exact (sup_bot _).symm\n · ext a\n rw [if_neg ht.ne_empty, mem_sup]\n refine ⟨fun ha => ⟨const _ a, mem_image_of_mem _ ha, mem_image_const_self.2 ht⟩, ?_⟩\n rintro ⟨f, hf, ha⟩\n rw [mem_image] at hf ha\n obtain ⟨b, hb, rfl⟩ := hf\n obtain ⟨_, _, rfl⟩ := ha\n exact hb\n seqRight_eq := fun s t => by\n rw [seq_def, fmap_def, seqRight_def]\n obtain rfl | hs := s.eq_empty_or_nonempty\n · rw [if_pos rfl, image_empty, sup_empty, bot_eq_empty]\n · ext a\n rw [if_neg hs.ne_empty, mem_sup]\n refine ⟨fun ha => ⟨id, mem_image_const_self.2 hs, by rwa [image_id]⟩, ?_⟩\n rintro ⟨f, hf, ha⟩\n rw [mem_image] at hf ha\n obtain ⟨b, hb, rfl⟩ := ha\n obtain ⟨_, _, rfl⟩ := hf\n exact hb\n pure_seq := fun f s => by simp only [pure_def, seq_def, sup_singleton, fmap_def]\n map_pure := fun f a => image_singleton _ _\n seq_pure := fun s a => sup_singleton'' _ _\n seq_assoc := fun s t u => by\n ext a\n simp_rw [seq_def, fmap_def]\n simp only [exists_prop, mem_sup, mem_image]\n constructor\n · rintro ⟨g, hg, b, ⟨f, hf, a, ha, rfl⟩, rfl⟩\n exact ⟨g ∘ f, ⟨comp g, ⟨g, hg, rfl⟩, f, hf, rfl⟩, a, ha, rfl⟩\n · rintro ⟨c, ⟨_, ⟨g, hg, rfl⟩, f, hf, rfl⟩, a, ha, rfl⟩\n exact ⟨g, hg, f a, ⟨f, hf, a, ha, rfl⟩, rfl⟩ }", "start": [ 98, 1 ], "end": [ 136, 55 ], "kind": "commanddeclaration" }, { "full_name": "Finset.commApplicative", "code": "instance commApplicative : CommApplicative Finset :=\n { Finset.lawfulApplicative with\n commutative_prod := fun s t => by\n simp_rw [seq_def, fmap_def, sup_image, sup_eq_biUnion]\n change (s.biUnion fun a => t.image fun b => (a, b))\n = t.biUnion fun b => s.image fun a => (a, b)\n trans s ×ˢ t <;> [rw [product_eq_biUnion]; rw [product_eq_biUnion_right]] }", "start": [ 138, 1 ], "end": [ 144, 82 ], "kind": "commanddeclaration" }, { "full_name": "Finset.bind_def", "code": "@[simp]\ntheorem bind_def {α β} : (· >>= ·) = sup (α := Finset α) (β := β)", "start": [ 158, 1 ], "end": [ 160, 6 ], "kind": "commanddeclaration" }, { "full_name": "Finset.traverse", "code": "def traverse [DecidableEq β] (f : α → F β) (s : Finset α) : F (Finset β) :=\n Multiset.toFinset <$> Multiset.traverse f s.1", "start": [ 194, 1 ], "end": [ 196, 48 ], "kind": "commanddeclaration" }, { "full_name": "Finset.id_traverse", "code": "@[simp]\ntheorem id_traverse [DecidableEq α] (s : Finset α) : traverse (pure : α → Id α) s = s", "start": [ 199, 1 ], "end": [ 202, 23 ], "kind": "commanddeclaration" }, { "full_name": "Finset.map_comp_coe", "code": "@[simp]\ntheorem map_comp_coe (h : α → β) :\n Functor.map h ∘ Multiset.toFinset = Multiset.toFinset ∘ Functor.map h", "start": [ 207, 1 ], "end": [ 210, 33 ], "kind": "commanddeclaration" }, { "full_name": "Finset.map_traverse", "code": "theorem map_traverse (g : α → G β) (h : β → γ) (s : Finset α) :\n Functor.map h <$> traverse g s = traverse (Functor.map h ∘ g) s", "start": [ 213, 1 ], "end": [ 217, 53 ], "kind": "commanddeclaration" } ]

Mathlib/Data/UInt.lean

[ "Mathlib/Data/ZMod/Defs.lean", ".lake/packages/lean4/src/lean/Init.lean" ]

[ { "full_name": "neZero", "code": "instance neZero : NeZero size := ⟨by decide⟩", "start": [ 31, 7 ], "end": [ 31, 51 ], "kind": "commanddeclaration" }, { "full_name": "neg_def", "code": "lemma neg_def (a : $typeName) : -a = ⟨-a.val⟩ := rfl", "start": [ 45, 7 ], "end": [ 45, 59 ], "kind": "lemma" }, { "full_name": "pow_def", "code": "lemma pow_def (a : $typeName) (n : ℕ) : a ^ n = ⟨a.val ^ n⟩ := rfl", "start": [ 47, 7 ], "end": [ 47, 73 ], "kind": "lemma" }, { "full_name": "nsmul_def", "code": "lemma nsmul_def (n : ℕ) (a : $typeName) : n • a = ⟨n • a.val⟩ := rfl", "start": [ 49, 7 ], "end": [ 49, 75 ], "kind": "lemma" }, { "full_name": "zsmul_def", "code": "lemma zsmul_def (z : ℤ) (a : $typeName) : z • a = ⟨z • a.val⟩ := rfl", "start": [ 51, 7 ], "end": [ 51, 75 ], "kind": "lemma" }, { "full_name": "val_injective", "code": "lemma val_injective : Function.Injective val := @eq_of_val_eq", "start": [ 54, 7 ], "end": [ 54, 68 ], "kind": "lemma" }, { "full_name": "instCommMonoid", "code": "instance instCommMonoid : CommMonoid $typeName :=\n Function.Injective.commMonoid val val_injective\n rfl (fun _ _ => rfl) (fun _ _ => rfl)", "start": [ 56, 7 ], "end": [ 58, 48 ], "kind": "commanddeclaration" }, { "full_name": "instNonUnitalCommRing", "code": "instance instNonUnitalCommRing : NonUnitalCommRing $typeName :=\n Function.Injective.nonUnitalCommRing val val_injective\n rfl (fun _ _ => rfl) (fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl)\n (fun _ _ => rfl) (fun _ _ => rfl)", "start": [ 60, 7 ], "end": [ 63, 44 ], "kind": "commanddeclaration" }, { "full_name": "instNatCast", "code": "local instance instNatCast : NatCast $typeName where\n natCast n := mk n", "start": [ 65, 7 ], "end": [ 66, 26 ], "kind": "commanddeclaration" }, { "full_name": "instIntCast", "code": "local instance instIntCast : IntCast $typeName where\n intCast z := mk z", "start": [ 68, 7 ], "end": [ 69, 26 ], "kind": "commanddeclaration" }, { "full_name": "natCast_def", "code": "lemma natCast_def (n : ℕ) : (n : $typeName) = ⟨n⟩ := rfl", "start": [ 71, 7 ], "end": [ 71, 63 ], "kind": "lemma" }, { "full_name": "intCast_def", "code": "lemma intCast_def (z : ℤ) : (z : $typeName) = ⟨z⟩ := rfl", "start": [ 73, 7 ], "end": [ 73, 63 ], "kind": "lemma" }, { "full_name": "instCommRing", "code": "local instance instCommRing : CommRing $typeName :=\n Function.Injective.commRing val val_injective\n rfl rfl (fun _ _ => rfl) (fun _ _ => rfl) (fun _ => rfl) (fun _ _ => rfl)\n (fun _ _ => rfl) (fun _ _ => rfl) (fun _ _ => rfl) (fun _ => rfl) (fun _ => rfl)", "start": [ 75, 7 ], "end": [ 78, 91 ], "kind": "commanddeclaration" }, { "full_name": "UInt8.isASCIIUpper", "code": "def isASCIIUpper (c : UInt8) : Bool :=\n c ≥ 65 && c ≤ 90", "start": [ 96, 1 ], "end": [ 98, 19 ], "kind": "commanddeclaration" }, { "full_name": "UInt8.isASCIILower", "code": "def isASCIILower (c : UInt8) : Bool :=\n c ≥ 97 && c ≤ 122", "start": [ 100, 1 ], "end": [ 102, 20 ], "kind": "commanddeclaration" }, { "full_name": "UInt8.isASCIIAlpha", "code": "def isASCIIAlpha (c : UInt8) : Bool :=\n c.isASCIIUpper || c.isASCIILower", "start": [ 104, 1 ], "end": [ 106, 35 ], "kind": "commanddeclaration" }, { "full_name": "UInt8.isASCIIDigit", "code": "def isASCIIDigit (c : UInt8) : Bool :=\n c ≥ 48 && c ≤ 57", "start": [ 108, 1 ], "end": [ 110, 19 ], "kind": "commanddeclaration" }, { "full_name": "UInt8.isASCIIAlphanum", "code": "def isASCIIAlphanum (c : UInt8) : Bool :=\n c.isASCIIAlpha || c.isASCIIDigit", "start": [ 112, 1 ], "end": [ 114, 35 ], "kind": "commanddeclaration" }, { "full_name": "UInt8.toChar", "code": "def toChar (n : UInt8) : Char := ⟨n.toUInt32, .inl (n.1.2.trans (by decide))⟩", "start": [ 122, 1 ], "end": [ 123, 78 ], "kind": "commanddeclaration" } ]

Mathlib/Order/Category/OmegaCompletePartialOrder.lean

[ "Mathlib/CategoryTheory/Limits/Shapes/Products.lean", "Mathlib/CategoryTheory/Limits/Constructions/LimitsOfProductsAndEqualizers.lean", "Mathlib/Order/OmegaCompletePartialOrder.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/CategoryTheory/Limits/Shapes/Equalizers.lean", "Mathlib/CategoryTheory/ConcreteCategory/BundledHom.lean" ]

[ { "full_name": "ωCPO", "code": "def ωCPO : Type (u + 1) :=\n Bundled OmegaCompletePartialOrder", "start": [ 35, 1 ], "end": [ 37, 36 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.of", "code": "def of (α : Type*) [OmegaCompletePartialOrder α] : ωCPO :=\n Bundled.of α", "start": [ 57, 1 ], "end": [ 59, 15 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.coe_of", "code": "@[simp]\ntheorem coe_of (α : Type*) [OmegaCompletePartialOrder α] : ↥(of α) = α", "start": [ 62, 1 ], "end": [ 64, 6 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.HasProducts.product", "code": "def product {J : Type v} (f : J → ωCPO.{v}) : Fan f :=\n Fan.mk (of (∀ j, f j)) fun j => .mk (Pi.evalOrderHom j) fun _ => rfl", "start": [ 79, 1 ], "end": [ 81, 71 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.HasProducts.isProduct", "code": "def isProduct (J : Type v) (f : J → ωCPO) : IsLimit (product f) where\n lift s :=\n ⟨⟨fun t j => (s.π.app ⟨j⟩).toFun t, fun x y h j => (s.π.app ⟨j⟩).monotone h⟩,\n fun x => funext fun j => (s.π.app ⟨j⟩).continuous x⟩\n uniq s m w := by\n ext t; funext j change m.toFun t j = (s.π.app ⟨j⟩).toFun t\n rw [← w ⟨j⟩]\n rfl\n fac s j := rfl", "start": [ 84, 1 ], "end": [ 95, 17 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.omegaCompletePartialOrderEqualizer", "code": "instance omegaCompletePartialOrderEqualizer {α β : Type*} [OmegaCompletePartialOrder α]\n [OmegaCompletePartialOrder β] (f g : α →𝒄 β) :\n OmegaCompletePartialOrder { a : α // f a = g a } :=\n OmegaCompletePartialOrder.subtype _ fun c hc => by\n rw [f.continuous, g.continuous]\n congr 1\n apply OrderHom.ext; funext x apply hc _ ⟨_, rfl⟩", "start": [ 103, 1 ], "end": [ 110, 24 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.HasEqualizers.equalizerι", "code": "def equalizerι {α β : Type*} [OmegaCompletePartialOrder α] [OmegaCompletePartialOrder β]\n (f g : α →𝒄 β) : { a : α // f a = g a } →𝒄 α :=\n .mk (OrderHom.Subtype.val _) fun _ => rfl", "start": [ 115, 1 ], "end": [ 118, 44 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.HasEqualizers.equalizer", "code": "def equalizer {X Y : ωCPO.{v}} (f g : X ⟶ Y) : Fork f g :=\n Fork.ofι (P := ωCPO.of { a // f.toFun a = g.toFun a }) (equalizerι f g)\n (ContinuousHom.ext _ _ fun x => x.2)", "start": [ 121, 1 ], "end": [ 125, 41 ], "kind": "commanddeclaration" }, { "full_name": "ωCPO.HasEqualizers.isEqualizer", "code": "def isEqualizer {X Y : ωCPO.{v}} (f g : X ⟶ Y) : IsLimit (equalizer f g) :=\n Fork.IsLimit.mk' _ fun s =>\n ⟨{ toFun := fun x => ⟨s.ι.toFun x, by apply ContinuousHom.congr_fun s.condition⟩\n monotone' := fun x y h => s.ι.monotone h\n cont := fun x => Subtype.ext (s.ι.continuous x) }, by ext; rfl, fun hm => by\n apply ContinuousHom.ext _ _ fun x => Subtype.ext ?_ apply ContinuousHom.congr_fun hm⟩", "start": [ 128, 1 ], "end": [ 136, 40 ], "kind": "commanddeclaration" } ]

Mathlib/Analysis/Calculus/Rademacher.lean

[ "Mathlib/MeasureTheory/Measure/Lebesgue/EqHaar.lean", "Mathlib/MeasureTheory/Measure/Haar/Disintegration.lean", "Mathlib/Analysis/BoundedVariation.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/NormedSpace/FiniteDimension.lean", "Mathlib/MeasureTheory/Group/Integral.lean", "Mathlib/Analysis/Distribution/AEEqOfIntegralContDiff.lean", "Mathlib/Analysis/Calculus/LineDeriv/Measurable.lean" ]

[ { "full_name": "LipschitzWith.ae_lineDifferentiableAt", "code": "theorem ae_lineDifferentiableAt (hf : LipschitzWith C f) (v : E) :\n ∀ᵐ p ∂μ, LineDifferentiableAt ℝ f p v", "start": [ 63, 1 ], "end": [ 77, 77 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.memℒp_lineDeriv", "code": "theorem memℒp_lineDeriv (hf : LipschitzWith C f) (v : E) :\n Memℒp (fun x ↦ lineDeriv ℝ f x v) ∞ μ", "start": [ 79, 1 ], "end": [ 82, 84 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.locallyIntegrable_lineDeriv", "code": "theorem locallyIntegrable_lineDeriv (hf : LipschitzWith C f) (v : E) :\n LocallyIntegrable (fun x ↦ lineDeriv ℝ f x v) μ", "start": [ 84, 1 ], "end": [ 86, 50 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul", "code": "theorem integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul\n (hf : LipschitzWith C f) (hg : Integrable g μ) (v : E) :\n Tendsto (fun (t : ℝ) ↦ ∫ x, (t⁻¹ • (f (x + t • v) - f x)) * g x ∂μ) (𝓝[>] 0)\n (𝓝 (∫ x, lineDeriv ℝ f x v * g x ∂μ))", "start": [ 97, 1 ], "end": [ 117, 76 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul'", "code": "theorem integral_inv_smul_sub_mul_tendsto_integral_lineDeriv_mul'\n (hf : LipschitzWith C f) (h'f : HasCompactSupport f) (hg : Continuous g) (v : E) :\n Tendsto (fun (t : ℝ) ↦ ∫ x, (t⁻¹ • (f (x + t • v) - f x)) * g x ∂μ) (𝓝[>] 0)\n (𝓝 (∫ x, lineDeriv ℝ f x v * g x ∂μ))", "start": [ 119, 1 ], "end": [ 160, 76 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.integral_lineDeriv_mul_eq", "code": "theorem integral_lineDeriv_mul_eq\n (hf : LipschitzWith C f) (hg : LipschitzWith D g) (h'g : HasCompactSupport g) (v : E) :\n ∫ x, lineDeriv ℝ f x v * g x ∂μ = ∫ x, lineDeriv ℝ g x (-v) * f x ∂μ", "start": [ 162, 1 ], "end": [ 195, 89 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.ae_lineDeriv_sum_eq", "code": "theorem ae_lineDeriv_sum_eq\n (hf : LipschitzWith C f) {ι : Type*} (s : Finset ι) (a : ι → ℝ) (v : ι → E) :\n ∀ᵐ x ∂μ, lineDeriv ℝ f x (∑ i ∈ s, a i • v i) = ∑ i ∈ s, a i • lineDeriv ℝ f x (v i)", "start": [ 197, 1 ], "end": [ 233, 54 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.ae_exists_fderiv_of_countable", "code": "theorem ae_exists_fderiv_of_countable\n (hf : LipschitzWith C f) {s : Set E} (hs : s.Countable) :\n ∀ᵐ x ∂μ, ∃ (L : E →L[ℝ] ℝ), ∀ v ∈ s, HasLineDerivAt ℝ f (L v) x v", "start": [ 239, 1 ], "end": [ 253, 44 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.hasFderivAt_of_hasLineDerivAt_of_closure", "code": "theorem hasFderivAt_of_hasLineDerivAt_of_closure {f : E → F}\n (hf : LipschitzWith C f) {s : Set E} (hs : sphere 0 1 ⊆ closure s)\n {L : E →L[ℝ] F} {x : E} (hL : ∀ v ∈ s, HasLineDerivAt ℝ f (L v) x v) :\n HasFDerivAt f L x", "start": [ 255, 1 ], "end": [ 307, 34 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.ae_differentiableAt_of_real", "code": "theorem ae_differentiableAt_of_real (hf : LipschitzWith C f) :\n ∀ᵐ x ∂μ, DifferentiableAt ℝ f x", "start": [ 309, 1 ], "end": [ 320, 77 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzOnWith.ae_differentiableWithinAt_of_mem_of_real", "code": "theorem ae_differentiableWithinAt_of_mem_of_real (hf : LipschitzOnWith C f s) :\n ∀ᵐ x ∂μ, x ∈ s → DifferentiableWithinAt ℝ f s x", "start": [ 328, 1 ], "end": [ 336, 51 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzOnWith.ae_differentiableWithinAt_of_mem_pi", "code": "theorem ae_differentiableWithinAt_of_mem_pi\n {ι : Type*} [Fintype ι] {f : E → ι → ℝ} {s : Set E}\n (hf : LipschitzOnWith C f s) : ∀ᵐ x ∂μ, x ∈ s → DifferentiableWithinAt ℝ f s x", "start": [ 338, 1 ], "end": [ 350, 54 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzOnWith.ae_differentiableWithinAt_of_mem", "code": "theorem ae_differentiableWithinAt_of_mem {f : E → F} (hf : LipschitzOnWith C f s) :\n ∀ᵐ x ∂μ, x ∈ s → DifferentiableWithinAt ℝ f s x", "start": [ 352, 1 ], "end": [ 364, 44 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzOnWith.ae_differentiableWithinAt", "code": "theorem ae_differentiableWithinAt {f : E → F} (hf : LipschitzOnWith C f s)\n (hs : MeasurableSet s) :\n ∀ᵐ x ∂(μ.restrict s), DifferentiableWithinAt ℝ f s x", "start": [ 366, 1 ], "end": [ 372, 44 ], "kind": "commanddeclaration" }, { "full_name": "LipschitzWith.ae_differentiableAt", "code": "theorem LipschitzWith.ae_differentiableAt {f : E → F} (h : LipschitzWith C f) :\n ∀ᵐ x ∂μ, DifferentiableAt ℝ f x", "start": [ 376, 1 ], "end": [ 381, 79 ], "kind": "commanddeclaration" } ]

Mathlib/Analysis/Complex/UnitDisc/Basic.lean

[ "Mathlib/Analysis/Complex/Circle.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Analysis/NormedSpace/BallAction.lean" ]

[ { "full_name": "Complex.UnitDisc", "code": "def UnitDisc : Type :=\n ball (0 : ℂ) 1 deriving TopologicalSpace", "start": [ 27, 1 ], "end": [ 29, 43 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instCommSemigroup", "code": "instance instCommSemigroup : CommSemigroup UnitDisc := by unfold UnitDisc; infer_instance", "start": [ 37, 1 ], "end": [ 37, 90 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instHasDistribNeg", "code": "instance instHasDistribNeg : HasDistribNeg UnitDisc := by unfold UnitDisc; infer_instance", "start": [ 38, 1 ], "end": [ 38, 90 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instCoe", "code": "instance instCoe : Coe UnitDisc ℂ := ⟨Subtype.val⟩", "start": [ 39, 1 ], "end": [ 39, 51 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_injective", "code": "theorem coe_injective : Injective ((↑) : 𝔻 → ℂ)", "start": [ 41, 1 ], "end": [ 42, 24 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.abs_lt_one", "code": "theorem abs_lt_one (z : 𝔻) : abs (z : ℂ) < 1", "start": [ 45, 1 ], "end": [ 46, 26 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.abs_ne_one", "code": "theorem abs_ne_one (z : 𝔻) : abs (z : ℂ) ≠ 1", "start": [ 49, 1 ], "end": [ 50, 18 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.normSq_lt_one", "code": "theorem normSq_lt_one (z : 𝔻) : normSq z < 1", "start": [ 53, 1 ], "end": [ 55, 25 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_ne_one", "code": "theorem coe_ne_one (z : 𝔻) : (z : ℂ) ≠ 1", "start": [ 58, 1 ], "end": [ 59, 58 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_ne_neg_one", "code": "theorem coe_ne_neg_one (z : 𝔻) : (z : ℂ) ≠ -1", "start": [ 62, 1 ], "end": [ 65, 23 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.one_add_coe_ne_zero", "code": "theorem one_add_coe_ne_zero (z : 𝔻) : (1 + z : ℂ) ≠ 0", "start": [ 68, 1 ], "end": [ 69, 52 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_mul", "code": "@[simp, norm_cast]\ntheorem coe_mul (z w : 𝔻) : ↑(z * w) = (z * w : ℂ)", "start": [ 72, 1 ], "end": [ 74, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.mk", "code": "def mk (z : ℂ) (hz : abs z < 1) : 𝔻 :=\n ⟨z, mem_ball_zero_iff.2 hz⟩", "start": [ 77, 1 ], "end": [ 80, 30 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_mk", "code": "@[simp]\ntheorem coe_mk (z : ℂ) (hz : abs z < 1) : (mk z hz : ℂ) = z", "start": [ 83, 1 ], "end": [ 85, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.mk_coe", "code": "@[simp]\ntheorem mk_coe (z : 𝔻) (hz : abs (z : ℂ) < 1 := z.abs_lt_one) : mk z hz = z", "start": [ 88, 1 ], "end": [ 90, 18 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.mk_neg", "code": "@[simp]\ntheorem mk_neg (z : ℂ) (hz : abs (-z) < 1) : mk (-z) hz = -mk z (abs.map_neg z ▸ hz)", "start": [ 93, 1 ], "end": [ 95, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_zero", "code": "@[simp]\ntheorem coe_zero : ((0 : 𝔻) : ℂ) = 0", "start": [ 104, 1 ], "end": [ 106, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_eq_zero", "code": "@[simp]\ntheorem coe_eq_zero {z : 𝔻} : (z : ℂ) = 0 ↔ z = 0", "start": [ 109, 1 ], "end": [ 111, 33 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.circleAction", "code": "instance circleAction : MulAction circle 𝔻 :=\n mulActionSphereBall", "start": [ 117, 1 ], "end": [ 118, 22 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.isScalarTower_circle_circle", "code": "instance isScalarTower_circle_circle : IsScalarTower circle circle 𝔻 :=\n isScalarTower_sphere_sphere_ball", "start": [ 121, 1 ], "end": [ 122, 35 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.isScalarTower_circle", "code": "instance isScalarTower_circle : IsScalarTower circle 𝔻 𝔻 :=\n isScalarTower_sphere_ball_ball", "start": [ 125, 1 ], "end": [ 126, 33 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instSMulCommClass_circle", "code": "instance instSMulCommClass_circle : SMulCommClass circle 𝔻 𝔻 :=\n instSMulCommClass_sphere_ball_ball", "start": [ 129, 1 ], "end": [ 130, 37 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instSMulCommClass_circle'", "code": "instance instSMulCommClass_circle' : SMulCommClass 𝔻 circle 𝔻 :=\n SMulCommClass.symm _ _ _", "start": [ 133, 1 ], "end": [ 134, 27 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_smul_circle", "code": "@[simp, norm_cast]\ntheorem coe_smul_circle (z : circle) (w : 𝔻) : ↑(z • w) = (z * w : ℂ)", "start": [ 137, 1 ], "end": [ 139, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.closedBallAction", "code": "instance closedBallAction : MulAction (closedBall (0 : ℂ) 1) 𝔻 :=\n mulActionClosedBallBall", "start": [ 142, 1 ], "end": [ 143, 26 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.isScalarTower_closedBall_closedBall", "code": "instance isScalarTower_closedBall_closedBall :\n IsScalarTower (closedBall (0 : ℂ) 1) (closedBall (0 : ℂ) 1) 𝔻 :=\n isScalarTower_closedBall_closedBall_ball", "start": [ 146, 1 ], "end": [ 148, 43 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.isScalarTower_closedBall", "code": "instance isScalarTower_closedBall : IsScalarTower (closedBall (0 : ℂ) 1) 𝔻 𝔻 :=\n isScalarTower_closedBall_ball_ball", "start": [ 151, 1 ], "end": [ 152, 37 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instSMulCommClass_closedBall", "code": "instance instSMulCommClass_closedBall : SMulCommClass (closedBall (0 : ℂ) 1) 𝔻 𝔻 :=\n ⟨fun _ _ _ => Subtype.ext <| mul_left_comm _ _ _⟩", "start": [ 155, 1 ], "end": [ 156, 52 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instSMulCommClass_closedBall'", "code": "instance instSMulCommClass_closedBall' : SMulCommClass 𝔻 (closedBall (0 : ℂ) 1) 𝔻 :=\n SMulCommClass.symm _ _ _", "start": [ 159, 1 ], "end": [ 160, 27 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instSMulCommClass_circle_closedBall", "code": "instance instSMulCommClass_circle_closedBall : SMulCommClass circle (closedBall (0 : ℂ) 1) 𝔻 :=\n instSMulCommClass_sphere_closedBall_ball", "start": [ 163, 1 ], "end": [ 164, 43 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.instSMulCommClass_closedBall_circle", "code": "instance instSMulCommClass_closedBall_circle : SMulCommClass (closedBall (0 : ℂ) 1) circle 𝔻 :=\n SMulCommClass.symm _ _ _", "start": [ 167, 1 ], "end": [ 168, 27 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_smul_closedBall", "code": "@[simp, norm_cast]\ntheorem coe_smul_closedBall (z : closedBall (0 : ℂ) 1) (w : 𝔻) : ↑(z • w) = (z * w : ℂ)", "start": [ 171, 1 ], "end": [ 173, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.re", "code": "def re (z : 𝔻) : ℝ :=\n Complex.re z", "start": [ 176, 1 ], "end": [ 178, 15 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.im", "code": "def im (z : 𝔻) : ℝ :=\n Complex.im z", "start": [ 181, 1 ], "end": [ 183, 15 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.re_coe", "code": "@[simp, norm_cast]\ntheorem re_coe (z : 𝔻) : (z : ℂ).re = z.re", "start": [ 186, 1 ], "end": [ 188, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.im_coe", "code": "@[simp, norm_cast]\ntheorem im_coe (z : 𝔻) : (z : ℂ).im = z.im", "start": [ 191, 1 ], "end": [ 193, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.re_neg", "code": "@[simp]\ntheorem re_neg (z : 𝔻) : (-z).re = -z.re", "start": [ 196, 1 ], "end": [ 198, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.im_neg", "code": "@[simp]\ntheorem im_neg (z : 𝔻) : (-z).im = -z.im", "start": [ 201, 1 ], "end": [ 203, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.conj", "code": "def conj (z : 𝔻) : 𝔻 :=\n mk (conj' ↑z) <| (abs_conj z).symm ▸ z.abs_lt_one", "start": [ 206, 1 ], "end": [ 208, 52 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.coe_conj", "code": "@[simp]\ntheorem coe_conj (z : 𝔻) : (z.conj : ℂ) = conj' ↑z", "start": [ 213, 1 ], "end": [ 215, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.conj_zero", "code": "@[simp]\ntheorem conj_zero : conj 0 = 0", "start": [ 218, 1 ], "end": [ 220, 33 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.conj_conj", "code": "@[simp]\ntheorem conj_conj (z : 𝔻) : conj (conj z) = z", "start": [ 223, 1 ], "end": [ 225, 45 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.conj_neg", "code": "@[simp]\ntheorem conj_neg (z : 𝔻) : (-z).conj = -z.conj", "start": [ 228, 1 ], "end": [ 230, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.re_conj", "code": "@[simp]\ntheorem re_conj (z : 𝔻) : z.conj.re = z.re", "start": [ 233, 1 ], "end": [ 235, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.im_conj", "code": "@[simp]\ntheorem im_conj (z : 𝔻) : z.conj.im = -z.im", "start": [ 238, 1 ], "end": [ 240, 6 ], "kind": "commanddeclaration" }, { "full_name": "Complex.UnitDisc.conj_mul", "code": "@[simp]\ntheorem conj_mul (z w : 𝔻) : (z * w).conj = z.conj * w.conj", "start": [ 243, 1 ], "end": [ 245, 31 ], "kind": "commanddeclaration" } ]

Mathlib/Algebra/Order/Group/Bounds.lean

[ "Mathlib/Algebra/Order/Group/Defs.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Order/Bounds/Basic.lean" ]

[ { "full_name": "IsGLB.exists_between_self_add", "code": "theorem IsGLB.exists_between_self_add (h : IsGLB s a) (hε : 0 < ε) : ∃ b ∈ s, a ≤ b ∧ b < a + ε", "start": [ 19, 1 ], "end": [ 20, 47 ], "kind": "commanddeclaration" }, { "full_name": "IsGLB.exists_between_self_add'", "code": "theorem IsGLB.exists_between_self_add' (h : IsGLB s a) (h₂ : a ∉ s) (hε : 0 < ε) :\n ∃ b ∈ s, a < b ∧ b < a + ε", "start": [ 23, 1 ], "end": [ 25, 51 ], "kind": "commanddeclaration" }, { "full_name": "IsLUB.exists_between_sub_self", "code": "theorem IsLUB.exists_between_sub_self (h : IsLUB s a) (hε : 0 < ε) : ∃ b ∈ s, a - ε < b ∧ b ≤ a", "start": [ 28, 1 ], "end": [ 29, 39 ], "kind": "commanddeclaration" }, { "full_name": "IsLUB.exists_between_sub_self'", "code": "theorem IsLUB.exists_between_sub_self' (h : IsLUB s a) (h₂ : a ∉ s) (hε : 0 < ε) :\n ∃ b ∈ s, a - ε < b ∧ b < a", "start": [ 32, 1 ], "end": [ 34, 43 ], "kind": "commanddeclaration" } ]

Mathlib/Lean/Expr.lean

[ "Mathlib/Lean/Expr/Basic.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Lean/Expr/ReplaceRec.lean" ]

[]

Mathlib/CategoryTheory/Limits/EpiMono.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/CategoryTheory/Limits/Shapes/CommSq.lean" ]

[ { "full_name": "CategoryTheory.mono_iff_fst_eq_snd", "code": "lemma mono_iff_fst_eq_snd : Mono f ↔ c.fst = c.snd := by\n constructor\n · intro hf\n simpa only [← cancel_mono f] using c.condition\n · intro hf\n constructor\n intro Z g g' h\n obtain ⟨φ, rfl, rfl⟩ := PullbackCone.IsLimit.lift' hc g g' h\n rw [hf]", "start": [ 38, 1 ], "end": [ 46, 12 ], "kind": "lemma" }, { "full_name": "CategoryTheory.mono_iff_isIso_fst", "code": "lemma mono_iff_isIso_fst : Mono f ↔ IsIso c.fst := by\n rw [mono_iff_fst_eq_snd hc]\n constructor\n · intro h\n obtain ⟨φ, hφ₁, hφ₂⟩ := PullbackCone.IsLimit.lift' hc (𝟙 X) (𝟙 X) (by simp)\n refine ⟨φ, PullbackCone.IsLimit.hom_ext hc ?_ ?_, hφ₁⟩\n · dsimp\n simp only [assoc, hφ₁, id_comp, comp_id]\n · dsimp\n simp only [assoc, hφ₂, id_comp, comp_id, h]\n · intro\n obtain ⟨φ, hφ₁, hφ₂⟩ := PullbackCone.IsLimit.lift' hc (𝟙 X) (𝟙 X) (by simp)\n have : IsSplitEpi φ := IsSplitEpi.mk ⟨SplitEpi.mk c.fst (by\n rw [← cancel_mono c.fst, assoc, id_comp, hφ₁, comp_id])⟩\n rw [← cancel_epi φ, hφ₁, hφ₂]", "start": [ 48, 1 ], "end": [ 62, 34 ], "kind": "lemma" }, { "full_name": "CategoryTheory.mono_iff_isIso_snd", "code": "lemma mono_iff_isIso_snd : Mono f ↔ IsIso c.snd :=\n mono_iff_isIso_fst (PullbackCone.flipIsLimit hc)", "start": [ 64, 1 ], "end": [ 65, 51 ], "kind": "lemma" }, { "full_name": "CategoryTheory.mono_iff_isPullback", "code": "lemma mono_iff_isPullback : Mono f ↔ IsPullback (𝟙 X) (𝟙 X) f f := by\n constructor\n · intro\n exact IsPullback.of_isLimit (PullbackCone.isLimitMkIdId f)\n · intro hf\n exact (mono_iff_fst_eq_snd hf.isLimit).2 rfl", "start": [ 69, 1 ], "end": [ 74, 49 ], "kind": "lemma" }, { "full_name": "CategoryTheory.epi_iff_inl_eq_inr", "code": "lemma epi_iff_inl_eq_inr : Epi f ↔ c.inl = c.inr := by\n constructor\n · intro hf\n simpa only [← cancel_epi f] using c.condition\n · intro hf\n constructor\n intro Z g g' h\n obtain ⟨φ, rfl, rfl⟩ := PushoutCocone.IsColimit.desc' hc g g' h\n rw [hf]", "start": [ 82, 1 ], "end": [ 90, 12 ], "kind": "lemma" }, { "full_name": "CategoryTheory.epi_iff_isIso_inl", "code": "lemma epi_iff_isIso_inl : Epi f ↔ IsIso c.inl := by\n rw [epi_iff_inl_eq_inr hc]\n constructor\n · intro h\n obtain ⟨φ, hφ₁, hφ₂⟩ := PushoutCocone.IsColimit.desc' hc (𝟙 Y) (𝟙 Y) (by simp)\n refine ⟨φ, hφ₁, PushoutCocone.IsColimit.hom_ext hc ?_ ?_⟩\n · dsimp\n simp only [comp_id, reassoc_of% hφ₁]\n · dsimp\n simp only [comp_id, h, reassoc_of% hφ₂]\n · intro\n obtain ⟨φ, hφ₁, hφ₂⟩ := PushoutCocone.IsColimit.desc' hc (𝟙 Y) (𝟙 Y) (by simp)\n have : IsSplitMono φ := IsSplitMono.mk ⟨SplitMono.mk c.inl (by\n rw [← cancel_epi c.inl, reassoc_of% hφ₁, comp_id])⟩\n rw [← cancel_mono φ, hφ₁, hφ₂]", "start": [ 92, 1 ], "end": [ 106, 35 ], "kind": "lemma" }, { "full_name": "CategoryTheory.epi_iff_isIso_inr", "code": "lemma epi_iff_isIso_inr : Epi f ↔ IsIso c.inr :=\n epi_iff_isIso_inl (PushoutCocone.flipIsColimit hc)", "start": [ 108, 1 ], "end": [ 109, 53 ], "kind": "lemma" }, { "full_name": "CategoryTheory.epi_iff_isPushout", "code": "lemma epi_iff_isPushout : Epi f ↔ IsPushout f f (𝟙 Y) (𝟙 Y) := by\n constructor\n · intro\n exact IsPushout.of_isColimit (PushoutCocone.isColimitMkIdId f)\n · intro hf\n exact (epi_iff_inl_eq_inr hf.isColimit).2 rfl", "start": [ 113, 1 ], "end": [ 118, 50 ], "kind": "lemma" } ]

Mathlib/Data/Vector/Mem.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Data/Vector/Basic.lean" ]

[ { "full_name": "Vector.get_mem", "code": "@[simp]\ntheorem get_mem (i : Fin n) (v : Vector α n) : v.get i ∈ v.toList", "start": [ 25, 1 ], "end": [ 28, 27 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_iff_get", "code": "theorem mem_iff_get (v : Vector α n) : a ∈ v.toList ↔ ∃ i, v.get i = a", "start": [ 31, 1 ], "end": [ 35, 38 ], "kind": "commanddeclaration" }, { "full_name": "Vector.not_mem_nil", "code": "theorem not_mem_nil : a ∉ (Vector.nil : Vector α 0).toList", "start": [ 38, 1 ], "end": [ 41, 7 ], "kind": "commanddeclaration" }, { "full_name": "Vector.not_mem_zero", "code": "theorem not_mem_zero (v : Vector α 0) : a ∉ v.toList", "start": [ 44, 1 ], "end": [ 45, 41 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_cons_iff", "code": "theorem mem_cons_iff (v : Vector α n) : a' ∈ (a ::ᵥ v).toList ↔ a' = a ∨ a' ∈ v.toList", "start": [ 48, 1 ], "end": [ 49, 41 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_succ_iff", "code": "theorem mem_succ_iff (v : Vector α (n + 1)) : a ∈ v.toList ↔ a = v.head ∨ a ∈ v.tail.toList", "start": [ 52, 1 ], "end": [ 54, 71 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_cons_self", "code": "theorem mem_cons_self (v : Vector α n) : a ∈ (a ::ᵥ v).toList", "start": [ 57, 1 ], "end": [ 58, 67 ], "kind": "commanddeclaration" }, { "full_name": "Vector.head_mem", "code": "@[simp]\ntheorem head_mem (v : Vector α (n + 1)) : v.head ∈ v.toList", "start": [ 61, 1 ], "end": [ 63, 57 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_cons_of_mem", "code": "theorem mem_cons_of_mem (v : Vector α n) (ha' : a' ∈ v.toList) : a' ∈ (a ::ᵥ v).toList", "start": [ 66, 1 ], "end": [ 67, 46 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_of_mem_tail", "code": "theorem mem_of_mem_tail (v : Vector α n) (ha : a ∈ v.tail.toList) : a ∈ v.toList", "start": [ 70, 1 ], "end": [ 73, 43 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_map_iff", "code": "theorem mem_map_iff (b : β) (v : Vector α n) (f : α → β) :\n b ∈ (v.map f).toList ↔ ∃ a : α, a ∈ v.toList ∧ f a = b", "start": [ 76, 1 ], "end": [ 78, 39 ], "kind": "commanddeclaration" }, { "full_name": "Vector.not_mem_map_zero", "code": "theorem not_mem_map_zero (b : β) (v : Vector α 0) (f : α → β) : b ∉ (v.map f).toList", "start": [ 81, 1 ], "end": [ 82, 91 ], "kind": "commanddeclaration" }, { "full_name": "Vector.mem_map_succ_iff", "code": "theorem mem_map_succ_iff (b : β) (v : Vector α (n + 1)) (f : α → β) :\n b ∈ (v.map f).toList ↔ f v.head = b ∨ ∃ a : α, a ∈ v.tail.toList ∧ f a = b", "start": [ 85, 1 ], "end": [ 87, 67 ], "kind": "commanddeclaration" } ]

Mathlib/CategoryTheory/Functor/Derived/RightDerived.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/CategoryTheory/Localization/Predicate.lean", "Mathlib/CategoryTheory/Functor/KanExtension/Basic.lean" ]

[ { "full_name": "CategoryTheory.Functor.IsRightDerivedFunctor", "code": "class IsRightDerivedFunctor [L.IsLocalization W] : Prop where\n isLeftKanExtension' : RF.IsLeftKanExtension α", "start": [ 47, 1 ], "end": [ 52, 48 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.IsRightDerivedFunctor.isLeftKanExtension", "code": "lemma IsRightDerivedFunctor.isLeftKanExtension\n [L.IsLocalization W] [RF.IsRightDerivedFunctor α W] :\n RF.IsLeftKanExtension α :=\n IsRightDerivedFunctor.isLeftKanExtension' W", "start": [ 54, 1 ], "end": [ 57, 46 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.isRightDerivedFunctor_iff_isLeftKanExtension", "code": "lemma isRightDerivedFunctor_iff_isLeftKanExtension [L.IsLocalization W] :\n RF.IsRightDerivedFunctor α W ↔ RF.IsLeftKanExtension α := by\n constructor\n · exact fun _ => IsRightDerivedFunctor.isLeftKanExtension RF α W\n · exact fun h => ⟨h⟩", "start": [ 59, 1 ], "end": [ 63, 23 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.isRightDerivedFunctor_iff_of_iso", "code": "lemma isRightDerivedFunctor_iff_of_iso (α' : F ⟶ L ⋙ RF') (W : MorphismProperty C)\n [L.IsLocalization W] (e : RF ≅ RF') (comm : α ≫ whiskerLeft L e.hom = α') :\n RF.IsRightDerivedFunctor α W ↔ RF'.IsRightDerivedFunctor α' W := by\n simp only [isRightDerivedFunctor_iff_isLeftKanExtension]\n exact isLeftKanExtension_iff_of_iso e _ _ comm", "start": [ 66, 1 ], "end": [ 70, 49 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerivedDesc", "code": "noncomputable def rightDerivedDesc (G : D ⥤ H) (β : F ⟶ L ⋙ G) : RF ⟶ G :=\n have := IsRightDerivedFunctor.isLeftKanExtension RF α W\n RF.descOfIsLeftKanExtension α G β", "start": [ 77, 1 ], "end": [ 80, 36 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.rightDerived_fac", "code": "@[reassoc (attr := simp)]\nlemma rightDerived_fac (G : D ⥤ H) (β : F ⟶ L ⋙ G) :\n α ≫ whiskerLeft L (RF.rightDerivedDesc α W G β) = β :=\n have := IsRightDerivedFunctor.isLeftKanExtension RF α W\n RF.descOfIsLeftKanExtension_fac α G β", "start": [ 82, 1 ], "end": [ 86, 40 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerived_fac_app", "code": "@[reassoc (attr := simp)]\nlemma rightDerived_fac_app (G : D ⥤ H) (β : F ⟶ L ⋙ G) (X : C):\n α.app X ≫ (RF.rightDerivedDesc α W G β).app (L.obj X) = β.app X :=\n have := IsRightDerivedFunctor.isLeftKanExtension RF α W\n RF.descOfIsLeftKanExtension_fac_app α G β X", "start": [ 88, 1 ], "end": [ 92, 46 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerived_ext", "code": "lemma rightDerived_ext (G : D ⥤ H) (γ₁ γ₂ : RF ⟶ G)\n (hγ : α ≫ whiskerLeft L γ₁ = α ≫ whiskerLeft L γ₂) : γ₁ = γ₂ :=\n have := IsRightDerivedFunctor.isLeftKanExtension RF α W\n RF.hom_ext_of_isLeftKanExtension α γ₁ γ₂ hγ", "start": [ 94, 1 ], "end": [ 97, 46 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerivedNatTrans", "code": "noncomputable def rightDerivedNatTrans (τ : F ⟶ F') : RF ⟶ RF' :=\n RF.rightDerivedDesc α W RF' (τ ≫ α')", "start": [ 99, 1 ], "end": [ 102, 39 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.rightDerivedNatTrans_fac", "code": "@[reassoc (attr := simp)]\nlemma rightDerivedNatTrans_fac (τ : F ⟶ F') :\n α ≫ whiskerLeft L (rightDerivedNatTrans RF RF' α α' W τ) = τ ≫ α' := by\n dsimp only [rightDerivedNatTrans]\n simp", "start": [ 104, 1 ], "end": [ 108, 7 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerivedNatTrans_app", "code": "@[reassoc (attr := simp)]\nlemma rightDerivedNatTrans_app (τ : F ⟶ F') (X : C) :\n α.app X ≫ (rightDerivedNatTrans RF RF' α α' W τ).app (L.obj X) =\n τ.app X ≫ α'.app X := by\n dsimp only [rightDerivedNatTrans]\n simp", "start": [ 110, 1 ], "end": [ 115, 7 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerivedNatTrans_id", "code": "@[simp]\nlemma rightDerivedNatTrans_id :\n rightDerivedNatTrans RF RF α α W (𝟙 F) = 𝟙 RF :=\n rightDerived_ext RF α W _ _ _ (by aesop_cat)", "start": [ 117, 1 ], "end": [ 120, 47 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerivedNatTrans_comp", "code": "@[reassoc (attr:= simp)]\nlemma rightDerivedNatTrans_comp (τ : F ⟶ F') (τ' : F' ⟶ F'') :\n rightDerivedNatTrans RF RF' α α' W τ ≫ rightDerivedNatTrans RF' RF'' α' α'' W τ' =\n rightDerivedNatTrans RF RF'' α α'' W (τ ≫ τ') :=\n rightDerived_ext RF α W _ _ _ (by aesop_cat)", "start": [ 122, 1 ], "end": [ 126, 47 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.rightDerivedNatIso", "code": "@[simps]\nnoncomputable def rightDerivedNatIso (τ : F ≅ F') :\n RF ≅ RF' where\n hom := rightDerivedNatTrans RF RF' α α' W τ.hom\n inv := rightDerivedNatTrans RF' RF α' α W τ.inv", "start": [ 128, 1 ], "end": [ 134, 50 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.rightDerivedUnique", "code": "noncomputable abbrev rightDerivedUnique [RF'.IsRightDerivedFunctor α'₂ W] : RF ≅ RF' :=\n rightDerivedNatIso RF RF' α α'₂ W (Iso.refl F)", "start": [ 136, 1 ], "end": [ 138, 49 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.isRightDerivedFunctor_iff_isIso_rightDerivedDesc", "code": "lemma isRightDerivedFunctor_iff_isIso_rightDerivedDesc (G : D ⥤ H) (β : F ⟶ L ⋙ G) :\n G.IsRightDerivedFunctor β W ↔ IsIso (RF.rightDerivedDesc α W G β) := by\n rw [isRightDerivedFunctor_iff_isLeftKanExtension]\n have := IsRightDerivedFunctor.isLeftKanExtension _ α W\n exact isLeftKanExtension_iff_isIso _ α _ (by simp)", "start": [ 140, 1 ], "end": [ 144, 53 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.HasRightDerivedFunctor", "code": "class HasRightDerivedFunctor : Prop where\n hasLeftKanExtension' : HasLeftKanExtension W.Q F", "start": [ 150, 1 ], "end": [ 155, 51 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.hasRightDerivedFunctor_iff", "code": "lemma hasRightDerivedFunctor_iff :\n F.HasRightDerivedFunctor W ↔ HasLeftKanExtension L F := by\n have : HasRightDerivedFunctor F W ↔ HasLeftKanExtension W.Q F :=\n ⟨fun h => h.hasLeftKanExtension', fun h => ⟨h⟩⟩\n rw [this, hasLeftExtension_iff_postcomp₁ (Localization.compUniqFunctor W.Q L W) F]", "start": [ 160, 1 ], "end": [ 164, 85 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.hasRightDerivedFunctor_iff_of_iso", "code": "lemma hasRightDerivedFunctor_iff_of_iso :\n HasRightDerivedFunctor F W ↔ HasRightDerivedFunctor F' W := by\n rw [hasRightDerivedFunctor_iff F W.Q W, hasRightDerivedFunctor_iff F' W.Q W,\n hasLeftExtension_iff_of_iso₂ W.Q e]", "start": [ 168, 1 ], "end": [ 171, 40 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.HasRightDerivedFunctor.hasLeftKanExtension", "code": "lemma HasRightDerivedFunctor.hasLeftKanExtension [HasRightDerivedFunctor F W] :\n HasLeftKanExtension L F := by\n simpa only [← hasRightDerivedFunctor_iff F L W]", "start": [ 175, 1 ], "end": [ 177, 50 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.HasRightDerivedFunctor.mk'", "code": "lemma HasRightDerivedFunctor.mk' [RF.IsRightDerivedFunctor α W] :\n HasRightDerivedFunctor F W := by\n have := IsRightDerivedFunctor.isLeftKanExtension RF α W\n simpa only [hasRightDerivedFunctor_iff F L W] using HasLeftKanExtension.mk RF α", "start": [ 181, 1 ], "end": [ 184, 82 ], "kind": "lemma" }, { "full_name": "CategoryTheory.Functor.totalRightDerived", "code": "noncomputable def totalRightDerived : D ⥤ H :=\n have := HasRightDerivedFunctor.hasLeftKanExtension F L W\n leftKanExtension L F", "start": [ 190, 1 ], "end": [ 195, 23 ], "kind": "commanddeclaration" }, { "full_name": "CategoryTheory.Functor.totalRightDerivedUnit", "code": "noncomputable def totalRightDerivedUnit : F ⟶ L ⋙ F.totalRightDerived L W :=\n have := HasRightDerivedFunctor.hasLeftKanExtension F L W\n leftKanExtensionUnit L F", "start": [ 197, 1 ], "end": [ 200, 27 ], "kind": "commanddeclaration" } ]

Mathlib/NumberTheory/Modular.lean

[ "Mathlib/LinearAlgebra/Matrix/GeneralLinearGroup.lean", "Mathlib/Analysis/Complex/UpperHalfPlane/Basic.lean", "Mathlib/Topology/Algebra/Module/FiniteDimension.lean", "Mathlib/LinearAlgebra/GeneralLinearGroup.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Topology/Instances/Matrix.lean" ]

[ { "full_name": "ModularGroup.bottom_row_coprime", "code": "theorem bottom_row_coprime {R : Type*} [CommRing R] (g : SL(2, R)) :\n IsCoprime ((↑g : Matrix (Fin 2) (Fin 2) R) 1 0) ((↑g : Matrix (Fin 2) (Fin 2) R) 1 1)", "start": [ 84, 1 ], "end": [ 89, 18 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.bottom_row_surj", "code": "theorem bottom_row_surj {R : Type*} [CommRing R] :\n Set.SurjOn (fun g : SL(2, R) => (↑g : Matrix (Fin 2) (Fin 2) R) 1) Set.univ\n {cd | IsCoprime (cd 0) (cd 1)}", "start": [ 92, 1 ], "end": [ 104, 16 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.tendsto_normSq_coprime_pair", "code": "theorem tendsto_normSq_coprime_pair :\n Filter.Tendsto (fun p : Fin 2 → ℤ => normSq ((p 0 : ℂ) * z + p 1)) cofinite atTop", "start": [ 115, 1 ], "end": [ 161, 76 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.lcRow0", "code": "def lcRow0 (p : Fin 2 → ℤ) : Matrix (Fin 2) (Fin 2) ℝ →ₗ[ℝ] ℝ :=\n ((p 0 : ℝ) • LinearMap.proj (0 : Fin 2) +\n (p 1 : ℝ) • LinearMap.proj (1 : Fin 2) : (Fin 2 → ℝ) →ₗ[ℝ] ℝ).comp\n (LinearMap.proj 0)", "start": [ 164, 1 ], "end": [ 170, 23 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.lcRow0_apply", "code": "@[simp]\ntheorem lcRow0_apply (p : Fin 2 → ℤ) (g : Matrix (Fin 2) (Fin 2) ℝ) :\n lcRow0 p g = p 0 * g 0 0 + p 1 * g 0 1", "start": [ 173, 1 ], "end": [ 176, 6 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.lcRow0Extend", "code": "@[simps!]\ndef lcRow0Extend {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :\n Matrix (Fin 2) (Fin 2) ℝ ≃ₗ[ℝ] Matrix (Fin 2) (Fin 2) ℝ :=\n LinearEquiv.piCongrRight\n ![by\n refine\n LinearMap.GeneralLinearGroup.generalLinearEquiv ℝ (Fin 2 → ℝ)\n (GeneralLinearGroup.toLinear (planeConformalMatrix (cd 0 : ℝ) (-(cd 1 : ℝ)) ?_))\n norm_cast\n rw [neg_sq]\n exact hcd.sq_add_sq_ne_zero, LinearEquiv.refl ℝ (Fin 2 → ℝ)]", "start": [ 179, 1 ], "end": [ 191, 67 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.tendsto_lcRow0", "code": "theorem tendsto_lcRow0 {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :\n Tendsto (fun g : { g : SL(2, ℤ) // (↑ₘg) 1 = cd } => lcRow0 cd ↑(↑g : SL(2, ℝ))) cofinite\n (cocompact ℝ)", "start": [ 197, 1 ], "end": [ 236, 8 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.smul_eq_lcRow0_add", "code": "theorem smul_eq_lcRow0_add {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) (hg : (↑ₘg) 1 = p) :\n ↑(g • z) =\n (lcRow0 p ↑(g : SL(2, ℝ)) : ℂ) / ((p 0 : ℂ) ^ 2 + (p 1 : ℂ) ^ 2) +\n ((p 1 : ℂ) * z - p 0) / (((p 0 : ℂ) ^ 2 + (p 1 : ℂ) ^ 2) * (p 0 * z + p 1))", "start": [ 239, 1 ], "end": [ 255, 7 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.tendsto_abs_re_smul", "code": "theorem tendsto_abs_re_smul {p : Fin 2 → ℤ} (hp : IsCoprime (p 0) (p 1)) :\n Tendsto\n (fun g : { g : SL(2, ℤ) // (↑ₘg) 1 = p } => |((g : SL(2, ℤ)) • z).re|) cofinite atTop", "start": [ 258, 1 ], "end": [ 276, 68 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.exists_max_im", "code": "theorem exists_max_im : ∃ g : SL(2, ℤ), ∀ g' : SL(2, ℤ), (g' • z).im ≤ (g • z).im", "start": [ 287, 1 ], "end": [ 301, 31 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.exists_row_one_eq_and_min_re", "code": "theorem exists_row_one_eq_and_min_re {cd : Fin 2 → ℤ} (hcd : IsCoprime (cd 0) (cd 1)) :\n ∃ g : SL(2, ℤ), (↑ₘg) 1 = cd ∧ ∀ g' : SL(2, ℤ), (↑ₘg) 1 = (↑ₘg') 1 →\n |(g • z).re| ≤ |(g' • z).re|", "start": [ 304, 1 ], "end": [ 318, 22 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.coe_T_zpow_smul_eq", "code": "theorem coe_T_zpow_smul_eq {n : ℤ} : (↑(T ^ n • z) : ℂ) = z + n", "start": [ 321, 1 ], "end": [ 323, 43 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.re_T_zpow_smul", "code": "theorem re_T_zpow_smul (n : ℤ) : (T ^ n • z).re = z.re + n", "start": [ 326, 1 ], "end": [ 327, 64 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.im_T_zpow_smul", "code": "theorem im_T_zpow_smul (n : ℤ) : (T ^ n • z).im = z.im", "start": [ 330, 1 ], "end": [ 331, 74 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.re_T_smul", "code": "theorem re_T_smul : (T • z).re = z.re + 1", "start": [ 334, 1 ], "end": [ 334, 79 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.im_T_smul", "code": "theorem im_T_smul : (T • z).im = z.im", "start": [ 337, 1 ], "end": [ 337, 75 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.re_T_inv_smul", "code": "theorem re_T_inv_smul : (T⁻¹ • z).re = z.re - 1", "start": [ 340, 1 ], "end": [ 340, 88 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.im_T_inv_smul", "code": "theorem im_T_inv_smul : (T⁻¹ • z).im = z.im", "start": [ 343, 1 ], "end": [ 343, 84 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.exists_eq_T_zpow_of_c_eq_zero", "code": "theorem exists_eq_T_zpow_of_c_eq_zero (hc : (↑ₘg) 1 0 = 0) :\n ∃ n : ℤ, ∀ z : ℍ, g • z = T ^ n • z", "start": [ 349, 1 ], "end": [ 361, 83 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.g_eq_of_c_eq_one", "code": "theorem g_eq_of_c_eq_one (hc : (↑ₘg) 1 0 = 1) : g = T ^ (↑ₘg) 0 0 * S * T ^ (↑ₘg) 1 1", "start": [ 365, 1 ], "end": [ 372, 37 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.normSq_S_smul_lt_one", "code": "theorem normSq_S_smul_lt_one (h : 1 < normSq z) : normSq ↑(S • z) < 1", "start": [ 375, 1 ], "end": [ 377, 78 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.im_lt_im_S_smul", "code": "theorem im_lt_im_S_smul (h : normSq z < 1) : z.im < (S • z).im", "start": [ 380, 1 ], "end": [ 388, 22 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.fd", "code": "def fd : Set ℍ :=\n {z | 1 ≤ normSq (z : ℂ) ∧ |z.re| ≤ (1 : ℝ) / 2}", "start": [ 391, 1 ], "end": [ 393, 50 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.fdo", "code": "def fdo : Set ℍ :=\n {z | 1 < normSq (z : ℂ) ∧ |z.re| < (1 : ℝ) / 2}", "start": [ 396, 1 ], "end": [ 398, 50 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.abs_two_mul_re_lt_one_of_mem_fdo", "code": "theorem abs_two_mul_re_lt_one_of_mem_fdo (h : z ∈ 𝒟ᵒ) : |2 * z.re| < 1", "start": [ 409, 1 ], "end": [ 411, 12 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.three_lt_four_mul_im_sq_of_mem_fdo", "code": "theorem three_lt_four_mul_im_sq_of_mem_fdo (h : z ∈ 𝒟ᵒ) : 3 < 4 * z.im ^ 2", "start": [ 414, 1 ], "end": [ 417, 37 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.one_lt_normSq_T_zpow_smul", "code": "theorem one_lt_normSq_T_zpow_smul (hz : z ∈ 𝒟ᵒ) (n : ℤ) : 1 < normSq (T ^ n • z : ℍ)", "start": [ 420, 1 ], "end": [ 425, 52 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.eq_zero_of_mem_fdo_of_T_zpow_mem_fdo", "code": "theorem eq_zero_of_mem_fdo_of_T_zpow_mem_fdo {n : ℤ} (hz : z ∈ 𝒟ᵒ) (hg : T ^ n • z ∈ 𝒟ᵒ) :\n n = 0", "start": [ 428, 1 ], "end": [ 438, 26 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.exists_smul_mem_fd", "code": "theorem exists_smul_mem_fd (z : ℍ) : ∃ g : SL(2, ℤ), g • z ∈ 𝒟", "start": [ 441, 1 ], "end": [ 472, 83 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.abs_c_le_one", "code": "theorem abs_c_le_one (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : |(↑ₘg) 1 0| ≤ 1", "start": [ 477, 1 ], "end": [ 509, 42 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.c_eq_zero", "code": "theorem c_eq_zero (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : (↑ₘg) 1 0 = 0", "start": [ 512, 1 ], "end": [ 531, 71 ], "kind": "commanddeclaration" }, { "full_name": "ModularGroup.eq_smul_self_of_mem_fdo_mem_fdo", "code": "theorem eq_smul_self_of_mem_fdo_mem_fdo (hz : z ∈ 𝒟ᵒ) (hg : g • z ∈ 𝒟ᵒ) : z = g • z", "start": [ 534, 1 ], "end": [ 539, 62 ], "kind": "commanddeclaration" } ]

Mathlib/Topology/ContinuousFunction/Sigma.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Topology/CompactOpen.lean" ]

[ { "full_name": "ContinuousMap.embedding_sigmaMk_comp", "code": "theorem embedding_sigmaMk_comp [Nonempty X] :\n Embedding (fun g : Σ i, C(X, Y i) ↦ (sigmaMk g.1).comp g.2) where", "start": [ 44, 1 ], "end": [ 54, 21 ], "kind": "commanddeclaration" }, { "full_name": "ContinuousMap.exists_lift_sigma", "code": "theorem exists_lift_sigma (f : C(X, Σ i, Y i)) : ∃ i g, f = (sigmaMk i).comp g", "start": [ 60, 1 ], "end": [ 67, 34 ], "kind": "commanddeclaration" }, { "full_name": "ContinuousMap.sigmaCodHomeomorph", "code": "@[simps! symm_apply]\ndef sigmaCodHomeomorph : C(X, Σ i, Y i) ≃ₜ Σ i, C(X, Y i) :=\n .symm <| Equiv.toHomeomorphOfInducing\n (.ofBijective _ ⟨embedding_sigmaMk_comp.inj, fun f ↦\n let ⟨i, g, hg⟩ := f.exists_lift_sigma; ⟨⟨i, g⟩, hg.symm⟩⟩)\n embedding_sigmaMk_comp.toInducing", "start": [ 71, 1 ], "end": [ 81, 38 ], "kind": "commanddeclaration" } ]

Mathlib/Data/Finset/NatDivisors.lean

[ "Mathlib/Data/Nat/Order/Lemmas.lean", "Mathlib/Data/Finset/Pointwise.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/NumberTheory/Divisors.lean" ]

[ { "full_name": "Nat.divisors_mul", "code": "lemma Nat.divisors_mul (m n : ℕ) : divisors (m * n) = divisors m * divisors n := by\n ext k\n simp_rw [mem_mul, mem_divisors, dvd_mul, mul_ne_zero_iff, ← exists_and_left, ← exists_and_right]\n simp only [and_assoc, and_comm, and_left_comm]", "start": [ 20, 1 ], "end": [ 25, 49 ], "kind": "lemma" }, { "full_name": "Nat.divisorsHom", "code": "@[simps]\ndef Nat.divisorsHom : ℕ →* Finset ℕ where\n toFun := Nat.divisors\n map_mul' := divisors_mul\n map_one' := divisors_one", "start": [ 27, 1 ], "end": [ 32, 27 ], "kind": "commanddeclaration" }, { "full_name": "Nat.Prime.divisors_sq", "code": "lemma Nat.Prime.divisors_sq {p : ℕ} (hp : p.Prime) : (p ^ 2).divisors = {p ^ 2, p, 1} := by\n simp [divisors_prime_pow hp, range_succ]", "start": [ 34, 1 ], "end": [ 35, 43 ], "kind": "lemma" }, { "full_name": "List.nat_divisors_prod", "code": "lemma List.nat_divisors_prod (l : List ℕ) : divisors l.prod = (l.map divisors).prod :=\n map_list_prod Nat.divisorsHom l", "start": [ 37, 1 ], "end": [ 38, 34 ], "kind": "lemma" }, { "full_name": "Multiset.nat_divisors_prod", "code": "lemma Multiset.nat_divisors_prod (s : Multiset ℕ) : divisors s.prod = (s.map divisors).prod :=\n map_multiset_prod Nat.divisorsHom s", "start": [ 40, 1 ], "end": [ 41, 38 ], "kind": "lemma" }, { "full_name": "Finset.nat_divisors_prod", "code": "lemma Finset.nat_divisors_prod {ι : Type*} (s : Finset ι) (f : ι → ℕ) :\n divisors (∏ i ∈ s, f i) = ∏ i ∈ s, divisors (f i) :=\n map_prod Nat.divisorsHom f s", "start": [ 43, 1 ], "end": [ 45, 31 ], "kind": "lemma" } ]

Mathlib/GroupTheory/GroupAction/Sum.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/Algebra/Group/Action/Defs.lean" ]

[ { "full_name": "Sum.smul_def", "code": "@[to_additive]\ntheorem smul_def : a • x = x.map (a • ·) (a • ·)", "start": [ 37, 1 ], "end": [ 39, 6 ], "kind": "commanddeclaration" }, { "full_name": "Sum.smul_inl", "code": "@[to_additive (attr := simp)]\ntheorem smul_inl : a • (inl b : Sum α β) = inl (a • b)", "start": [ 43, 1 ], "end": [ 45, 6 ], "kind": "commanddeclaration" }, { "full_name": "Sum.smul_inr", "code": "@[to_additive (attr := simp)]\ntheorem smul_inr : a • (inr c : Sum α β) = inr (a • c)", "start": [ 49, 1 ], "end": [ 51, 6 ], "kind": "commanddeclaration" }, { "full_name": "Sum.smul_swap", "code": "@[to_additive (attr := simp)]\ntheorem smul_swap : (a • x).swap = a • x.swap", "start": [ 55, 1 ], "end": [ 56, 68 ], "kind": "commanddeclaration" }, { "full_name": "Sum.FaithfulSMulLeft", "code": "@[to_additive]\ninstance FaithfulSMulLeft [FaithfulSMul M α] : FaithfulSMul M (Sum α β) :=\n ⟨fun h => eq_of_smul_eq_smul fun a : α => by injection h (inl a)⟩", "start": [ 78, 1 ], "end": [ 80, 68 ], "kind": "commanddeclaration" }, { "full_name": "Sum.FaithfulSMulRight", "code": "@[to_additive]\ninstance FaithfulSMulRight [FaithfulSMul M β] : FaithfulSMul M (Sum α β) :=\n ⟨fun h => eq_of_smul_eq_smul fun b : β => by injection h (inr b)⟩", "start": [ 84, 1 ], "end": [ 86, 68 ], "kind": "commanddeclaration" } ]

Mathlib/Init/Data/Int/Lemmas.lean

[ "Mathlib/Mathport/Rename.lean", ".lake/packages/lean4/src/lean/Init.lean" ]

[]

Mathlib/NumberTheory/PrimesCongruentOne.lean

[ ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/RingTheory/Polynomial/Cyclotomic/Eval.lean" ]

[ { "full_name": "Nat.exists_prime_gt_modEq_one", "code": "theorem exists_prime_gt_modEq_one {k : ℕ} (n : ℕ) (hk0 : k ≠ 0) :\n ∃ p : ℕ, Nat.Prime p ∧ n < p ∧ p ≡ 1 [MOD k]", "start": [ 24, 1 ], "end": [ 57, 54 ], "kind": "commanddeclaration" }, { "full_name": "Nat.frequently_atTop_modEq_one", "code": "theorem frequently_atTop_modEq_one {k : ℕ} (hk0 : k ≠ 0) :\n ∃ᶠ p in atTop, Nat.Prime p ∧ p ≡ 1 [MOD k]", "start": [ 60, 1 ], "end": [ 64, 39 ], "kind": "commanddeclaration" }, { "full_name": "Nat.infinite_setOf_prime_modEq_one", "code": "theorem infinite_setOf_prime_modEq_one {k : ℕ} (hk0 : k ≠ 0) :\n Set.Infinite {p : ℕ | Nat.Prime p ∧ p ≡ 1 [MOD k]}", "start": [ 67, 1 ], "end": [ 70, 67 ], "kind": "commanddeclaration" } ]

Mathlib/LinearAlgebra/TensorProduct/Matrix.lean

[ "Mathlib/LinearAlgebra/TensorProduct/Basis.lean", ".lake/packages/lean4/src/lean/Init.lean", "Mathlib/LinearAlgebra/Matrix/ToLin.lean", "Mathlib/Data/Matrix/Kronecker.lean" ]

[ { "full_name": "TensorProduct.toMatrix_map", "code": "theorem TensorProduct.toMatrix_map (f : M →ₗ[R] M') (g : N →ₗ[R] N') :\n toMatrix (bM.tensorProduct bN) (bM'.tensorProduct bN') (TensorProduct.map f g) =\n toMatrix bM bM' f ⊗ₖ toMatrix bN bN' g", "start": [ 37, 1 ], "end": [ 44, 65 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.toLin_kronecker", "code": "theorem Matrix.toLin_kronecker (A : Matrix ι' ι R) (B : Matrix κ' κ R) :\n toLin (bM.tensorProduct bN) (bM'.tensorProduct bN') (A ⊗ₖ B) =\n TensorProduct.map (toLin bM bM' A) (toLin bN bN' B)", "start": [ 47, 1 ], "end": [ 53, 20 ], "kind": "commanddeclaration" }, { "full_name": "TensorProduct.toMatrix_comm", "code": "theorem TensorProduct.toMatrix_comm :\n toMatrix (bM.tensorProduct bN) (bN.tensorProduct bM) (TensorProduct.comm R M N) =\n (1 : Matrix (ι × κ) (ι × κ) R).submatrix Prod.swap _root_.id", "start": [ 56, 1 ], "end": [ 64, 75 ], "kind": "commanddeclaration" }, { "full_name": "TensorProduct.toMatrix_assoc", "code": "theorem TensorProduct.toMatrix_assoc :\n toMatrix ((bM.tensorProduct bN).tensorProduct bP) (bM.tensorProduct (bN.tensorProduct bP))\n (TensorProduct.assoc R M N P) =\n (1 : Matrix (ι × κ × τ) (ι × κ × τ) R).submatrix _root_.id (Equiv.prodAssoc _ _ _)", "start": [ 67, 1 ], "end": [ 78, 21 ], "kind": "commanddeclaration" } ]

.lake/packages/lean4/src/lean/Lean/Compiler/IR/LLVMBindings.lean

[ ".lake/packages/lean4/src/lean/Init/System/IO.lean" ]

[ { "full_name": "LLVM.CodegenFileType", "code": "structure CodegenFileType where\n private mk :: val : UInt64", "start": [ 20, 1 ], "end": [ 21, 29 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.CodegenFileType.AssemblyFile", "code": "def CodegenFileType.AssemblyFile : CodegenFileType := { val := 0 }", "start": [ 23, 1 ], "end": [ 23, 67 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.CodegenFileType.ObjectFile", "code": "def CodegenFileType.ObjectFile : CodegenFileType := { val := 1 }", "start": [ 24, 1 ], "end": [ 24, 65 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.IntPredicate", "code": "structure IntPredicate where\n private mk :: val : UInt64", "start": [ 27, 1 ], "end": [ 28, 29 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.IntPredicate.EQ", "code": "def IntPredicate.EQ : IntPredicate := { val := 32 }", "start": [ 30, 1 ], "end": [ 30, 52 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.IntPredicate.NE", "code": "def IntPredicate.NE : IntPredicate := { val := IntPredicate.EQ.val + 1 }", "start": [ 31, 1 ], "end": [ 31, 73 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.IntPredicate.UGT", "code": "def IntPredicate.UGT : IntPredicate := { val := IntPredicate.NE.val + 1 }", "start": [ 32, 1 ], "end": [ 32, 74 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.AttributeIndex", "code": "structure AttributeIndex where\n private mk :: val : UInt64", "start": [ 35, 1 ], "end": [ 36, 29 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.AttributeIndex.AttributeReturnIndex", "code": "def AttributeIndex.AttributeReturnIndex : AttributeIndex := { val := 0 }", "start": [ 38, 1 ], "end": [ 38, 73 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.AttributeIndex.AttributeFunctionIndex", "code": "def AttributeIndex.AttributeFunctionIndex : AttributeIndex := { val := 18446744073709551615 }", "start": [ 40, 1 ], "end": [ 40, 94 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.BasicBlock", "code": "structure BasicBlock (ctx : Context) where\n private mk :: ptr : USize", "start": [ 42, 1 ], "end": [ 43, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Builder", "code": "structure Builder (ctx : Context) where\n private mk :: ptr : USize", "start": [ 46, 1 ], "end": [ 47, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Context", "code": "structure Context where\n private mk :: ptr : USize", "start": [ 50, 1 ], "end": [ 51, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.LLVMType", "code": "structure LLVMType (ctx : Context) where\n private mk :: ptr : USize", "start": [ 54, 1 ], "end": [ 55, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.MemoryBuffer", "code": "structure MemoryBuffer (ctx : Context) where\n private mk :: ptr : USize", "start": [ 58, 1 ], "end": [ 59, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Module", "code": "structure Module (ctx : Context) where\n private mk :: ptr : USize", "start": [ 62, 1 ], "end": [ 63, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.PassManager", "code": "structure PassManager (ctx : Context) where\n private mk :: ptr : USize", "start": [ 66, 1 ], "end": [ 67, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.PassManagerBuilder", "code": "structure PassManagerBuilder (ctx : Context) where\n private mk :: ptr : USize", "start": [ 70, 1 ], "end": [ 71, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Target", "code": "structure Target (ctx : Context) where\n private mk :: ptr : USize", "start": [ 74, 1 ], "end": [ 75, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.TargetMachine", "code": "structure TargetMachine (ctx : Context) where\n private mk :: ptr : USize", "start": [ 78, 1 ], "end": [ 79, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Value", "code": "structure Value (ctx : Context) where\n private mk :: ptr : USize", "start": [ 82, 1 ], "end": [ 83, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Value.isNull", "code": "def Value.isNull (v : Value ctx) : Bool := v.ptr == 0", "start": [ 86, 1 ], "end": [ 87, 54 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Value.getName", "code": "@[extern \"lean_llvm_get_value_name2\"]\nopaque Value.getName {ctx : Context} (value : Value ctx) : BaseIO String", "start": [ 89, 1 ], "end": [ 90, 73 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Attribute", "code": "structure Attribute (ctx : Context) where\n private mk :: ptr : USize", "start": [ 92, 1 ], "end": [ 93, 28 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.llvmInitializeTargetInfo", "code": "@[extern \"lean_llvm_initialize_target_info\"]\nopaque llvmInitializeTargetInfo : BaseIO (Unit)", "start": [ 96, 1 ], "end": [ 97, 48 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createContext", "code": "@[extern \"lean_llvm_create_context\"]\nopaque createContext : BaseIO (Context)", "start": [ 99, 1 ], "end": [ 100, 40 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createModule", "code": "@[extern \"lean_llvm_create_module\"]\nopaque createModule (ctx : Context) (name : @&String) : BaseIO (Module ctx)", "start": [ 102, 1 ], "end": [ 103, 76 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.moduleToString", "code": "@[extern \"lean_llvm_module_to_string\"]\nopaque moduleToString (m : Module ctx) : BaseIO String", "start": [ 105, 1 ], "end": [ 106, 55 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.writeBitcodeToFile", "code": "@[extern \"lean_llvm_write_bitcode_to_file\"]\nopaque writeBitcodeToFile (m : Module ctx) (path : @&String) : BaseIO Unit", "start": [ 108, 1 ], "end": [ 109, 75 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.addFunction", "code": "@[extern \"lean_llvm_add_function\"]\nopaque addFunction (m : Module ctx) (name : @&String) (type : LLVMType ctx) : BaseIO (Value ctx)", "start": [ 111, 1 ], "end": [ 112, 97 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getFirstFunction", "code": "@[extern \"lean_llvm_get_first_function\"]\nopaque getFirstFunction (m : Module ctx) : BaseIO (Value ctx)", "start": [ 114, 1 ], "end": [ 115, 62 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getNextFunction", "code": "@[extern \"lean_llvm_get_next_function\"]\nopaque getNextFunction (glbl : Value ctx) : BaseIO (Value ctx)", "start": [ 117, 1 ], "end": [ 118, 63 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getNamedFunction", "code": "@[extern \"lean_llvm_get_named_function\"]\nopaque getNamedFunction (m : Module ctx) (name : @&String) : BaseIO (Option (Value ctx))", "start": [ 120, 1 ], "end": [ 121, 89 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.addGlobal", "code": "@[extern \"lean_llvm_add_global\"]\nopaque addGlobal (m : Module ctx) (name : @&String) (type : LLVMType ctx) : BaseIO (Value ctx)", "start": [ 123, 1 ], "end": [ 124, 95 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getNamedGlobal", "code": "@[extern \"lean_llvm_get_named_global\"]\nopaque getNamedGlobal (m : Module ctx) (name : @&String) : BaseIO (Option (Value ctx))", "start": [ 126, 1 ], "end": [ 127, 87 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getFirstGlobal", "code": "@[extern \"lean_llvm_get_first_global\"]\nopaque getFirstGlobal (m : Module ctx) : BaseIO (Value ctx)", "start": [ 129, 1 ], "end": [ 130, 60 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getNextGlobal", "code": "@[extern \"lean_llvm_get_next_global\"]\nopaque getNextGlobal (glbl : Value ctx) : BaseIO (Value ctx)", "start": [ 132, 1 ], "end": [ 133, 61 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildGlobalString", "code": "@[extern \"lean_llvm_build_global_string\"]\nopaque buildGlobalString (builder : Builder ctx) (value : @&String) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 135, 1 ], "end": [ 136, 113 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.isDeclaration", "code": "@[extern \"llvm_is_declaration\"]\nopaque isDeclaration (global : Value ctx) : BaseIO Bool", "start": [ 138, 1 ], "end": [ 139, 56 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.setInitializer", "code": "@[extern \"lean_llvm_set_initializer\"]\nopaque setInitializer (glbl : Value ctx) (val : Value ctx) : BaseIO Unit", "start": [ 141, 1 ], "end": [ 142, 73 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.functionType", "code": "@[extern \"lean_llvm_function_type\"]\nopaque functionType (retty : LLVMType ctx) (args : @&Array (LLVMType ctx)) (isVarArg : Bool := false) : BaseIO (LLVMType ctx)", "start": [ 144, 1 ], "end": [ 145, 126 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.voidType", "code": "@[extern \"lean_llvm_void_type_in_context\"]\nopaque voidType (ctx : Context) : BaseIO (LLVMType ctx)", "start": [ 147, 1 ], "end": [ 148, 56 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.intTypeInContext", "code": "@[extern \"lean_llvm_int_type_in_context\"]\nopaque intTypeInContext (ctx : Context) (width : UInt64) : BaseIO (LLVMType ctx)", "start": [ 150, 1 ], "end": [ 151, 81 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.opaquePointerTypeInContext", "code": "@[extern \"lean_llvm_opaque_pointer_type_in_context\"]\nopaque opaquePointerTypeInContext (ctx : Context) (addrspace: UInt64 := 0) : BaseIO (LLVMType ctx)", "start": [ 153, 1 ], "end": [ 154, 99 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.floatTypeInContext", "code": "@[extern \"lean_llvm_float_type_in_context\"]\nopaque floatTypeInContext (ctx : Context) : BaseIO (LLVMType ctx)", "start": [ 156, 1 ], "end": [ 157, 66 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.doubleTypeInContext", "code": "@[extern \"lean_llvm_double_type_in_context\"]\nopaque doubleTypeInContext (ctx : Context) : BaseIO (LLVMType ctx)", "start": [ 159, 1 ], "end": [ 160, 67 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.pointerType", "code": "@[extern \"lean_llvm_pointer_type\"]\nopaque pointerType (elemty : LLVMType ctx) : BaseIO (LLVMType ctx)", "start": [ 162, 1 ], "end": [ 163, 67 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.arrayType", "code": "@[extern \"lean_llvm_array_type\"]\nopaque arrayType (elemty : LLVMType ctx) (nelem : UInt64) : BaseIO (LLVMType ctx)", "start": [ 165, 1 ], "end": [ 166, 82 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constArray", "code": "@[extern \"lean_llvm_const_array\"]\nopaque constArray (elemty : LLVMType ctx) (vals : @&Array (Value ctx)) : BaseIO (LLVMType ctx)", "start": [ 168, 1 ], "end": [ 169, 95 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constString", "code": "@[extern \"lean_llvm_const_string\"]\nopaque constString (ctx : Context) (str : @&String) : BaseIO (Value ctx)", "start": [ 172, 1 ], "end": [ 173, 73 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constPointerNull", "code": "@[extern \"lean_llvm_const_pointer_null\"]\nopaque constPointerNull (elemty : LLVMType ctx) : BaseIO (Value ctx)", "start": [ 175, 1 ], "end": [ 176, 69 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getUndef", "code": "@[extern \"lean_llvm_get_undef\"]\nopaque getUndef (elemty : LLVMType ctx) : BaseIO (Value ctx)", "start": [ 178, 1 ], "end": [ 179, 61 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createBuilderInContext", "code": "@[extern \"lean_llvm_create_builder_in_context\"]\nopaque createBuilderInContext (ctx : Context) : BaseIO (Builder ctx)", "start": [ 181, 1 ], "end": [ 182, 69 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.appendBasicBlockInContext", "code": "@[extern \"lean_llvm_append_basic_block_in_context\"]\nopaque appendBasicBlockInContext (ctx : Context) (fn : Value ctx) (name : @&String) : BaseIO (BasicBlock ctx)", "start": [ 184, 1 ], "end": [ 185, 112 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.countBasicBlocks", "code": "@[extern \"lean_llvm_count_basic_blocks\"]\nopaque countBasicBlocks (fn : Value ctx) : BaseIO UInt64", "start": [ 187, 1 ], "end": [ 188, 57 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getEntryBasicBlock", "code": "@[extern \"lean_llvm_get_entry_basic_block\"]\nopaque getEntryBasicBlock (fn : Value ctx) : BaseIO (BasicBlock ctx)", "start": [ 190, 1 ], "end": [ 191, 69 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getFirstInstruction", "code": "@[extern \"lean_llvm_get_first_instruction\"]\nopaque getFirstInstruction (bb : BasicBlock ctx) : BaseIO (Option (Value ctx))", "start": [ 193, 1 ], "end": [ 194, 79 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.positionBuilderBefore", "code": "@[extern \"lean_llvm_position_builder_before\"]\nopaque positionBuilderBefore (builder : Builder ctx) (instr : Value ctx) : BaseIO Unit", "start": [ 196, 1 ], "end": [ 197, 87 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.positionBuilderAtEnd", "code": "@[extern \"lean_llvm_position_builder_at_end\"]\nopaque positionBuilderAtEnd (builder : Builder ctx) (bb : BasicBlock ctx) : BaseIO Unit", "start": [ 199, 1 ], "end": [ 200, 89 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildCall2", "code": "@[extern \"lean_llvm_build_call2\"]\nopaque buildCall2 (builder : Builder ctx) (ty: LLVMType ctx) (fn : Value ctx) (args : @&Array (Value ctx)) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 202, 1 ], "end": [ 203, 153 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.setTailCall", "code": "@[extern \"lean_llvm_set_tail_call\"]\nopaque setTailCall (fn : Value ctx) (istail : Bool) : BaseIO Unit", "start": [ 205, 1 ], "end": [ 206, 66 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildCondBr", "code": "@[extern \"lean_llvm_build_cond_br\"]\nopaque buildCondBr (builder : Builder ctx) (if_ : Value ctx) (thenbb : BasicBlock ctx) (elsebb : BasicBlock ctx) : BaseIO (Value ctx)", "start": [ 208, 1 ], "end": [ 209, 134 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildBr", "code": "@[extern \"lean_llvm_build_br\"]\nopaque buildBr (builder : Builder ctx) (bb : BasicBlock ctx) : BaseIO (Value ctx)", "start": [ 211, 1 ], "end": [ 212, 82 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildAlloca", "code": "@[extern \"lean_llvm_build_alloca\"]\nopaque buildAlloca (builder : Builder ctx) (ty : LLVMType ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 214, 1 ], "end": [ 215, 108 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildLoad2", "code": "@[extern \"lean_llvm_build_load2\"]\nopaque buildLoad2 (builder : Builder ctx) (ty: LLVMType ctx) (val : Value ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 217, 1 ], "end": [ 218, 124 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildStore", "code": "@[extern \"lean_llvm_build_store\"]\nopaque buildStore (builder : Builder ctx) (val : Value ctx) (store_loc_ptr : Value ctx) : BaseIO Unit", "start": [ 220, 1 ], "end": [ 221, 102 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildRet", "code": "@[extern \"lean_llvm_build_ret\"]\nopaque buildRet (builder : Builder ctx) (val : Value ctx) : BaseIO (Value ctx)", "start": [ 223, 1 ], "end": [ 224, 79 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildUnreachable", "code": "@[extern \"lean_llvm_build_unreachable\"]\nopaque buildUnreachable (builder : Builder ctx) : BaseIO (Value ctx)", "start": [ 226, 1 ], "end": [ 227, 69 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildGEP2", "code": "@[extern \"lean_llvm_build_gep2\"]\nopaque buildGEP2 (builder : Builder ctx) (ty: LLVMType ctx) (base : Value ctx) (ixs : @&Array (Value ctx)) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 229, 1 ], "end": [ 230, 152 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildInBoundsGEP2", "code": "@[extern \"lean_llvm_build_inbounds_gep2\"]\nopaque buildInBoundsGEP2 (builder : Builder ctx) (ty: LLVMType ctx) (base : Value ctx) (ixs : @&Array (Value ctx)) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 232, 1 ], "end": [ 233, 160 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildSext", "code": "@[extern \"lean_llvm_build_sext\"]\nopaque buildSext (builder : Builder ctx) (val : Value ctx) (destTy : LLVMType ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 235, 1 ], "end": [ 236, 128 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildZext", "code": "@[extern \"lean_llvm_build_zext\"]\nopaque buildZext (builder : Builder ctx) (val : Value ctx) (destTy : LLVMType ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 238, 1 ], "end": [ 239, 128 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildSextOrTrunc", "code": "@[extern \"lean_llvm_build_sext_or_trunc\"]\nopaque buildSextOrTrunc (builder : Builder ctx) (val : Value ctx) (destTy : LLVMType ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 241, 1 ], "end": [ 242, 135 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildSwitch", "code": "@[extern \"lean_llvm_build_switch\"]\nopaque buildSwitch (builder : Builder ctx) (val : Value ctx) (elseBB : BasicBlock ctx) (numCasesHint : UInt64) : BaseIO (Value ctx)", "start": [ 244, 1 ], "end": [ 245, 132 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildPtrToInt", "code": "@[extern \"lean_llvm_build_ptr_to_int\"]\nopaque buildPtrToInt (builder : Builder ctx) (ptr : Value ctx) (destTy : LLVMType ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 247, 1 ], "end": [ 248, 132 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildMul", "code": "@[extern \"lean_llvm_build_mul\"]\nopaque buildMul (builder : Builder ctx) (x y : Value ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 250, 1 ], "end": [ 251, 103 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildAdd", "code": "@[extern \"lean_llvm_build_add\"]\nopaque buildAdd (builder : Builder ctx) (x y : Value ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 253, 1 ], "end": [ 254, 103 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildSub", "code": "@[extern \"lean_llvm_build_sub\"]\nopaque buildSub (builder : Builder ctx) (x y : Value ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 256, 1 ], "end": [ 257, 103 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildNot", "code": "@[extern \"lean_llvm_build_not\"]\nopaque buildNot (builder : Builder ctx) (x : Value ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 259, 1 ], "end": [ 260, 101 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.buildICmp", "code": "@[extern \"lean_llvm_build_icmp\"]\nopaque buildICmp (builder : Builder ctx) (predicate : IntPredicate) (x y : Value ctx) (name : @&String := \"\") : BaseIO (Value ctx)", "start": [ 262, 1 ], "end": [ 263, 131 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.addCase", "code": "@[extern \"lean_llvm_add_case\"]\nopaque addCase (switch onVal : Value ctx) (destBB : BasicBlock ctx) : BaseIO Unit", "start": [ 265, 1 ], "end": [ 266, 82 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getInsertBlock", "code": "@[extern \"lean_llvm_get_insert_block\"]\nopaque getInsertBlock (builder : Builder ctx) : BaseIO (BasicBlock ctx)", "start": [ 268, 1 ], "end": [ 269, 72 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.clearInsertionPosition", "code": "@[extern \"lean_llvm_clear_insertion_position\"]\nopaque clearInsertionPosition (builder : Builder ctx) : BaseIO Unit", "start": [ 271, 1 ], "end": [ 272, 68 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getBasicBlockParent", "code": "@[extern \"lean_llvm_get_basic_block_parent\"]\nopaque getBasicBlockParent (bb : BasicBlock ctx) : BaseIO (Value ctx)", "start": [ 274, 1 ], "end": [ 275, 70 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.typeOf", "code": "@[extern \"lean_llvm_type_of\"]\nopaque typeOf (val : Value ctx) : BaseIO (LLVMType ctx)", "start": [ 277, 1 ], "end": [ 278, 56 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constInt", "code": "@[extern \"lean_llvm_const_int\"]\nopaque constInt (intty : LLVMType ctx) (value : UInt64) (signExtend : @Bool := false) : BaseIO (Value ctx)", "start": [ 280, 1 ], "end": [ 281, 107 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.printModuletoString", "code": "@[extern \"lean_llvm_print_module_to_string\"]\nopaque printModuletoString (mod : Module ctx) : BaseIO (String)", "start": [ 283, 1 ], "end": [ 284, 64 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.printModuletoFile", "code": "@[extern \"lean_llvm_print_module_to_file\"]\nopaque printModuletoFile (mod : Module ctx) (file : @&String) : BaseIO Unit", "start": [ 286, 1 ], "end": [ 287, 76 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.countParams", "code": "@[extern \"llvm_count_params\"]\nopaque countParams (fn : Value ctx) : BaseIO UInt64", "start": [ 289, 1 ], "end": [ 290, 52 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getParam", "code": "@[extern \"llvm_get_param\"]\nopaque getParam (fn : Value ctx) (ix : UInt64) : BaseIO (Value ctx)", "start": [ 292, 1 ], "end": [ 293, 68 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createMemoryBufferWithContentsOfFile", "code": "@[extern \"lean_llvm_create_memory_buffer_with_contents_of_file\"]\nopaque createMemoryBufferWithContentsOfFile (path : @&String) : BaseIO (MemoryBuffer ctx)", "start": [ 295, 1 ], "end": [ 296, 90 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.parseBitcode", "code": "@[extern \"lean_llvm_parse_bitcode\"]\nopaque parseBitcode (ctx : Context) (membuf : MemoryBuffer ctx) : BaseIO (Module ctx)", "start": [ 298, 1 ], "end": [ 299, 86 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.linkModules", "code": "@[extern \"lean_llvm_link_modules\"]\nopaque linkModules (dest : Module ctx) (src : Module ctx) : BaseIO Unit", "start": [ 301, 1 ], "end": [ 302, 72 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getDefaultTargetTriple", "code": "@[extern \"lean_llvm_get_default_target_triple\"]\nopaque getDefaultTargetTriple : BaseIO String", "start": [ 304, 1 ], "end": [ 305, 46 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.getTargetFromTriple", "code": "@[extern \"lean_llvm_get_target_from_triple\"]\nopaque getTargetFromTriple (triple : @&String) : BaseIO (Target ctx)", "start": [ 307, 1 ], "end": [ 308, 69 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createTargetMachine", "code": "@[extern \"lean_llvm_create_target_machine\"]\nopaque createTargetMachine (target : Target ctx) (tripleStr : @&String) (cpu : @&String) (features : @&String) : BaseIO (TargetMachine ctx)", "start": [ 310, 1 ], "end": [ 311, 140 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.targetMachineEmitToFile", "code": "@[extern \"lean_llvm_target_machine_emit_to_file\"]\nopaque targetMachineEmitToFile (targetMachine : TargetMachine ctx) (module : Module ctx) (filepath : @&String) (codegenType : LLVM.CodegenFileType) : BaseIO Unit", "start": [ 313, 1 ], "end": [ 314, 162 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createPassManager", "code": "@[extern \"lean_llvm_create_pass_manager\"]\nopaque createPassManager : BaseIO (PassManager ctx)", "start": [ 316, 1 ], "end": [ 317, 52 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.disposePassManager", "code": "@[extern \"lean_llvm_dispose_pass_manager\"]\nopaque disposePassManager (pm : PassManager ctx) : BaseIO Unit", "start": [ 319, 1 ], "end": [ 320, 63 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.runPassManager", "code": "@[extern \"lean_llvm_run_pass_manager\"]\nopaque runPassManager (pm : PassManager ctx) (mod : Module ctx): BaseIO Unit", "start": [ 322, 1 ], "end": [ 323, 77 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createPassManagerBuilder", "code": "@[extern \"lean_llvm_create_pass_manager_builder\"]\nopaque createPassManagerBuilder : BaseIO (PassManagerBuilder ctx)", "start": [ 325, 1 ], "end": [ 326, 66 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.disposePassManagerBuilder", "code": "@[extern \"lean_llvm_dispose_pass_manager_builder\"]\nopaque disposePassManagerBuilder (pmb : PassManagerBuilder ctx) : BaseIO Unit", "start": [ 328, 1 ], "end": [ 329, 78 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.PassManagerBuilder.setOptLevel", "code": "@[extern \"lean_llvm_pass_manager_builder_set_opt_level\"]\nopaque PassManagerBuilder.setOptLevel (pmb : PassManagerBuilder ctx) (optLevel : unsigned) : BaseIO Unit", "start": [ 331, 1 ], "end": [ 332, 105 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.PassManagerBuilder.populateModulePassManager", "code": "@[extern \"lean_llvm_pass_manager_builder_populate_module_pass_manager\"]\nopaque PassManagerBuilder.populateModulePassManager (pmb : PassManagerBuilder ctx) (pm : PassManager ctx): BaseIO Unit", "start": [ 334, 1 ], "end": [ 335, 119 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.disposeTargetMachine", "code": "@[extern \"lean_llvm_dispose_target_machine\"]\nopaque disposeTargetMachine (tm : TargetMachine ctx) : BaseIO Unit", "start": [ 337, 1 ], "end": [ 338, 67 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.disposeModule", "code": "@[extern \"lean_llvm_dispose_module\"]\nopaque disposeModule (m : Module ctx) : BaseIO Unit", "start": [ 340, 1 ], "end": [ 341, 52 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.verifyModule", "code": "@[extern \"lean_llvm_verify_module\"]\nopaque verifyModule (m : Module ctx) : BaseIO (Option String)", "start": [ 343, 1 ], "end": [ 344, 62 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.createStringAttribute", "code": "@[extern \"lean_llvm_create_string_attribute\"]\nopaque createStringAttribute (key : String) (value : String) : BaseIO (Attribute ctx)", "start": [ 346, 1 ], "end": [ 347, 86 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.addAttributeAtIndex", "code": "@[extern \"lean_llvm_add_attribute_at_index\"]\nopaque addAttributeAtIndex (fn : Value ctx) (idx: AttributeIndex) (attr: Attribute ctx) : BaseIO Unit", "start": [ 349, 1 ], "end": [ 350, 102 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Visibility", "code": "structure Visibility where\n private mk :: val : UInt64", "start": [ 354, 1 ], "end": [ 355, 29 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Visibility.default", "code": "def Visibility.default : Visibility := { val := 0 }", "start": [ 357, 1 ], "end": [ 357, 54 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Visibility.hidden", "code": "def Visibility.hidden : Visibility := { val := 1 }", "start": [ 358, 1 ], "end": [ 358, 54 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Visibility.protected", "code": "def Visibility.protected : Visibility := { val := 2 }", "start": [ 359, 1 ], "end": [ 359, 54 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.setVisibility", "code": "@[extern \"lean_llvm_set_visibility\"]\nopaque setVisibility {ctx : Context} (value : Value ctx) (visibility : Visibility) : BaseIO Unit", "start": [ 361, 1 ], "end": [ 362, 97 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.DLLStorageClass", "code": "structure DLLStorageClass where\n private mk :: val : UInt64", "start": [ 365, 1 ], "end": [ 366, 29 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.DLLStorageClass.default", "code": "def DLLStorageClass.default : DLLStorageClass := { val := 0 }", "start": [ 368, 1 ], "end": [ 368, 62 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.DLLStorageClass.import", "code": "def DLLStorageClass.import : DLLStorageClass := { val := 1 }", "start": [ 369, 1 ], "end": [ 369, 62 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.DLLStorageClass.export", "code": "def DLLStorageClass.export : DLLStorageClass := { val := 2 }", "start": [ 370, 1 ], "end": [ 370, 62 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.setDLLStorageClass", "code": "@[extern \"lean_llvm_set_dll_storage_class\"]\nopaque setDLLStorageClass {ctx : Context} (value : Value ctx) (dllStorageClass : DLLStorageClass) : BaseIO Unit", "start": [ 372, 1 ], "end": [ 373, 112 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage", "code": "structure Linkage where\n private mk :: val : UInt64", "start": [ 376, 1 ], "end": [ 377, 29 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.external", "code": "def Linkage.external : Linkage := { val := 0 }", "start": [ 379, 1 ], "end": [ 380, 47 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.availableExternally", "code": "def Linkage.availableExternally : Linkage := { val := 1 }", "start": [ 381, 1 ], "end": [ 381, 58 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.linkOnceAny", "code": "def Linkage.linkOnceAny : Linkage := { val := 2 }", "start": [ 382, 1 ], "end": [ 383, 50 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.linkOnceODR", "code": "def Linkage.linkOnceODR : Linkage := { val := 3 }", "start": [ 384, 1 ], "end": [ 385, 50 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.linkOnceODRAutoHide", "code": "def Linkage.linkOnceODRAutoHide : Linkage := { val := 4 }", "start": [ 386, 1 ], "end": [ 387, 58 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.weakAny", "code": "def Linkage.weakAny : Linkage := { val := 5 }", "start": [ 388, 1 ], "end": [ 389, 46 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.weakODR", "code": "def Linkage.weakODR : Linkage := { val := 6 }", "start": [ 390, 1 ], "end": [ 391, 46 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.appending", "code": "def Linkage.appending : Linkage := { val := 7 }", "start": [ 392, 1 ], "end": [ 393, 48 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.internal", "code": "def Linkage.internal : Linkage := { val := 8 }", "start": [ 394, 1 ], "end": [ 395, 47 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.private", "code": "def Linkage.private : Linkage := { val := 9 }", "start": [ 396, 1 ], "end": [ 397, 46 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.dllImport", "code": "def Linkage.dllImport : Linkage := { val := 10 }", "start": [ 398, 1 ], "end": [ 399, 49 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.dllExport", "code": "def Linkage.dllExport : Linkage := { val := 11 }", "start": [ 400, 1 ], "end": [ 401, 49 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.externalWeak", "code": "def Linkage.externalWeak : Linkage := { val := 12 }", "start": [ 402, 1 ], "end": [ 403, 52 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.ghost", "code": "def Linkage.ghost : Linkage := { val := 13 }", "start": [ 404, 1 ], "end": [ 405, 45 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.common", "code": "def Linkage.common : Linkage := { val := 14 }", "start": [ 406, 1 ], "end": [ 407, 46 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.linkerPrivate", "code": "def Linkage.linkerPrivate : Linkage := { val := 15 }", "start": [ 408, 1 ], "end": [ 409, 53 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.Linkage.linkerPrivateWeak", "code": "def Linkage.linkerPrivateWeak : Linkage := { val := 16 }", "start": [ 410, 1 ], "end": [ 411, 57 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.setLinkage", "code": "@[extern \"lean_llvm_set_linkage\"]\nopaque setLinkage {ctx : Context} (value : Value ctx) (linkage : Linkage) : BaseIO Unit", "start": [ 413, 1 ], "end": [ 414, 88 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.i1Type", "code": "def i1Type (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n LLVM.intTypeInContext ctx 1", "start": [ 417, 1 ], "end": [ 418, 30 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.i8Type", "code": "def i8Type (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n LLVM.intTypeInContext ctx 8", "start": [ 420, 1 ], "end": [ 421, 30 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.i16Type", "code": "def i16Type (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n LLVM.intTypeInContext ctx 16", "start": [ 423, 1 ], "end": [ 424, 31 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.i32Type", "code": "def i32Type (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n LLVM.intTypeInContext ctx 32", "start": [ 426, 1 ], "end": [ 427, 31 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.i64Type", "code": "def i64Type (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n LLVM.intTypeInContext ctx 64", "start": [ 429, 1 ], "end": [ 430, 31 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.voidPtrType", "code": "def voidPtrType (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n do LLVM.pointerType (← LLVM.intTypeInContext ctx 8)", "start": [ 432, 1 ], "end": [ 433, 54 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.i8PtrType", "code": "def i8PtrType (ctx : LLVM.Context) : BaseIO (LLVM.LLVMType ctx) :=\n voidPtrType ctx", "start": [ 435, 1 ], "end": [ 436, 18 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constTrue", "code": "def constTrue (ctx : Context) : BaseIO (Value ctx) :=\n do constInt (← i1Type ctx) 1 (signExtend := false)", "start": [ 438, 1 ], "end": [ 439, 53 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constFalse", "code": "def constFalse (ctx : Context) : BaseIO (Value ctx) :=\n do constInt (← i1Type ctx) 0 (signExtend := false)", "start": [ 441, 1 ], "end": [ 442, 53 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constInt'", "code": "def constInt' (ctx : Context) (width : UInt64) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n do constInt (← LLVM.intTypeInContext ctx width) value signExtend", "start": [ 444, 1 ], "end": [ 445, 66 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constInt1", "code": "def constInt1 (ctx : Context) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n constInt' ctx 1 value signExtend", "start": [ 447, 1 ], "end": [ 448, 35 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constInt8", "code": "def constInt8 (ctx : Context) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n constInt' ctx 8 value signExtend", "start": [ 450, 1 ], "end": [ 451, 35 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constInt32", "code": "def constInt32 (ctx : Context) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n constInt' ctx 32 value signExtend", "start": [ 453, 1 ], "end": [ 454, 36 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constInt64", "code": "def constInt64 (ctx : Context) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n constInt' ctx 64 value signExtend", "start": [ 456, 1 ], "end": [ 457, 36 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constIntSizeT", "code": "def constIntSizeT (ctx : Context) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n constInt' ctx 64 value signExtend", "start": [ 459, 1 ], "end": [ 461, 36 ], "kind": "commanddeclaration" }, { "full_name": "LLVM.constIntUnsigned", "code": "def constIntUnsigned (ctx : Context) (value : UInt64) (signExtend : Bool := false) : BaseIO (Value ctx) :=\n constInt' ctx 32 value signExtend", "start": [ 463, 1 ], "end": [ 465, 36 ], "kind": "commanddeclaration" } ]

.lake/packages/lean4/src/lean/lake/Lake.lean

[ ".lake/packages/lean4/src/lean/lake/Lake/Config.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/lean4/src/lean/lake/Lake/Toml.lean", ".lake/packages/lean4/src/lean/lake/Lake/DSL.lean", ".lake/packages/lean4/src/lean/lake/Lake/Version.lean", ".lake/packages/lean4/src/lean/lake/Lake/Build.lean", ".lake/packages/lean4/src/lean/lake/Lake/CLI/Actions.lean" ]

[]

.lake/packages/lean4/src/lean/lake/Lake/CLI.lean

[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/lean4/src/lean/lake/Lake/CLI/Main.lean" ]

[]

Mathlib.lean

[ "Mathlib/Data/Finset/Union.lean", "Mathlib/LinearAlgebra/TensorProduct/Matrix.lean", "Mathlib/NumberTheory/PrimesCongruentOne.lean", "Mathlib/Init/Data/Int/Lemmas.lean", "Mathlib/Topology/Homotopy/Equiv.lean", "Mathlib/CategoryTheory/Functor/Functorial.lean", "Mathlib/GroupTheory/GroupAction/Sum.lean", "Mathlib/Analysis/InnerProductSpace/Calculus.lean", "Mathlib/Data/Rat/Cast/Lemmas.lean", "Mathlib/Algebra/Category/ModuleCat/Presheaf/Sheafification.lean", "Mathlib/Topology/Connected/LocallyConnected.lean", "Mathlib/ModelTheory/Encoding.lean", "Mathlib/Tactic/Linarith/Oracle/SimplexAlgorithm/SimplexAlgorithm.lean", "Mathlib/LinearAlgebra/FreeModule/StrongRankCondition.lean", "Mathlib/RingTheory/Ideal/Basic.lean", "Mathlib/Data/Finset/NatDivisors.lean", "Mathlib/NumberTheory/LegendreSymbol/QuadraticReciprocity.lean", "Mathlib/Tactic/CC/Datatypes.lean", "Mathlib/Topology/ContinuousFunction/Sigma.lean", "Mathlib/Tactic/PPWithUniv.lean", "Mathlib/RingTheory/Polynomial/Eisenstein/Basic.lean", "Mathlib/MeasureTheory/Integral/ExpDecay.lean", "Mathlib/Analysis/InnerProductSpace/NormPow.lean", "Mathlib/ModelTheory/Skolem.lean", "Mathlib/Analysis/LocallyConvex/Basic.lean", "Mathlib/NumberTheory/Modular.lean", "Mathlib/Algebra/GroupWithZero/Hom.lean", "Mathlib/Topology/Algebra/Module/Multilinear/Basic.lean", "Mathlib/Order/CompactlyGenerated/Basic.lean", "Mathlib/AlgebraicTopology/DoldKan/Homotopies.lean", "Mathlib/Data/Multiset/NatAntidiagonal.lean", "Mathlib/Analysis/Distribution/AEEqOfIntegralContDiff.lean", "Mathlib/Algebra/Order/BigOperators/Group/Multiset.lean", "Mathlib/RingTheory/FiniteStability.lean", "Mathlib/Control/Fix.lean", "Mathlib/Topology/ContinuousFunction/Algebra.lean", "Mathlib/CategoryTheory/Sites/Coherent/ExtensiveSheaves.lean", "Mathlib/CategoryTheory/Functor/Derived/RightDerived.lean", "Mathlib/Deprecated/Group.lean", "Mathlib/LinearAlgebra/TensorAlgebra/Basic.lean", "Mathlib/Topology/Order/Hom/Basic.lean", "Mathlib/Data/Sign.lean", "Mathlib/ModelTheory/Satisfiability.lean", "Mathlib/Data/Vector/Mem.lean", "Mathlib/Topology/MetricSpace/Dilation.lean", "Mathlib/Topology/Order/IntermediateValue.lean", "Mathlib/Analysis/Convex/Between.lean", "Mathlib/Topology/Algebra/Group/Basic.lean", "Mathlib/Topology/Sheaves/Limits.lean", "Mathlib/Logic/IsEmpty.lean", "Mathlib/Algebra/GroupWithZero/Divisibility.lean", "Mathlib/CategoryTheory/Limits/EpiMono.lean", "Mathlib/CategoryTheory/Limits/Shapes/Biproducts.lean", "Mathlib/CategoryTheory/Shift/CommShift.lean", "Mathlib/Tactic/Choose.lean", "Mathlib/Control/Basic.lean", "Mathlib/Tactic/Sat/FromLRAT.lean", "Mathlib/GroupTheory/Transfer.lean", "Mathlib/LinearAlgebra/DirectSum/Finsupp.lean", "Mathlib/Algebra/Category/Grp/Basic.lean", "Mathlib/RingTheory/Polynomial/Cyclotomic/Eval.lean", "Mathlib/Topology/Order/T5.lean", "Mathlib/Algebra/MvPolynomial/Cardinal.lean", "Mathlib/Lean/Expr.lean", "Mathlib/Algebra/Group/Semiconj/Units.lean", "Mathlib/Data/List/TFAE.lean", "Mathlib/Order/Filter/ENNReal.lean", "Mathlib/Order/Filter/CountableSeparatingOn.lean", "Mathlib/Algebra/Category/FGModuleCat/Basic.lean", "Mathlib/Data/Matroid/Basic.lean", "Mathlib/LinearAlgebra/Dimension/Finrank.lean", "Mathlib/Algebra/Order/Group/Bounds.lean", "Mathlib/Data/Fin/Tuple/Sort.lean", "Mathlib/Tactic/Positivity.lean", "Mathlib/Topology/MetricSpace/Thickening.lean", "Mathlib/Analysis/Complex/UnitDisc/Basic.lean", "Mathlib/Analysis/Calculus/Rademacher.lean", "Mathlib/Order/Category/OmegaCompletePartialOrder.lean", "Mathlib/Logic/Pairwise.lean", "Mathlib/Analysis/PSeriesComplex.lean", "Mathlib/CategoryTheory/LiftingProperties/Adjunction.lean", "Mathlib/CategoryTheory/Sites/Coherent/Basic.lean", "Mathlib/Combinatorics/SimpleGraph/Hasse.lean", "Mathlib/Computability/PartrecCode.lean", "Mathlib/Control/Monad/Basic.lean", "Mathlib/Algebra/Category/Ring/Constructions.lean", 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"Mathlib/Data/Sigma/Interval.lean", "Mathlib/CategoryTheory/Limits/Shapes/Kernels.lean", "Mathlib/Dynamics/BirkhoffSum/NormedSpace.lean", "Mathlib/RingTheory/DedekindDomain/Factorization.lean", "Mathlib/Algebra/Polynomial/GroupRingAction.lean", "Mathlib/CategoryTheory/Localization/Triangulated.lean", "Mathlib/MeasureTheory/Group/Action.lean", "Mathlib/MeasureTheory/SetAlgebra.lean", "Mathlib/RingTheory/NonUnitalSubsemiring/Basic.lean", "Mathlib/Algebra/MvPolynomial/Variables.lean", "Mathlib/Tactic/Hint.lean", "Mathlib/Algebra/Order/Interval/Set/Instances.lean", "Mathlib/Data/PFunctor/Multivariate/W.lean", "Mathlib/Algebra/Quotient.lean", "Mathlib/Algebra/Homology/HomotopyCategory/HomologicalFunctor.lean", "Mathlib/Combinatorics/SimpleGraph/Turan.lean", "Mathlib/Analysis/Convex/Topology.lean", "Mathlib/Dynamics/FixedPoints/Basic.lean", "Mathlib/Algebra/BigOperators/Module.lean", "Mathlib/NumberTheory/PellMatiyasevic.lean", "Mathlib/Data/Bool/Count.lean", "Mathlib/NumberTheory/Cyclotomic/Embeddings.lean", "Mathlib/Tactic/Linarith/Oracle/SimplexAlgorithm/Datatypes.lean", "Mathlib/Algebra/GCDMonoid/Nat.lean", "Mathlib/Algebra/GroupWithZero/Commute.lean", "Mathlib/CategoryTheory/Monoidal/OfChosenFiniteProducts/Basic.lean", "Mathlib/CategoryTheory/Limits/Shapes/Terminal.lean", "Mathlib/Combinatorics/SimpleGraph/Subgraph.lean", "Mathlib/Algebra/Algebra/Unitization.lean", "Mathlib/MeasureTheory/Function/ConvergenceInMeasure.lean", "Mathlib/Analysis/Convex/Body.lean", "Mathlib/Topology/Algebra/Group/OpenMapping.lean", "Mathlib/GroupTheory/Exponent.lean", "Mathlib/MeasureTheory/Integral/DivergenceTheorem.lean", "Mathlib/Algebra/Homology/DerivedCategory/Basic.lean", "Mathlib/Algebra/Polynomial/Smeval.lean", "Mathlib/MeasureTheory/Measure/OpenPos.lean", "Mathlib/Algebra/Algebra/Subalgebra/Tower.lean", "Mathlib/MeasureTheory/Measure/Restrict.lean", "Mathlib/Analysis/SpecialFunctions/Pow/Complex.lean", "Mathlib/NumberTheory/EllipticDivisibilitySequence.lean", "Mathlib/Combinatorics/Enumerative/DoubleCounting.lean", "Mathlib/Tactic/FunProp/ToBatteries.lean", "Mathlib/RingTheory/Polynomial/ScaleRoots.lean", "Mathlib/CategoryTheory/Limits/Opposites.lean", "Mathlib/Geometry/Euclidean/Sphere/Basic.lean", "Mathlib/Topology/Category/TopCat/Limits/Pullbacks.lean", "Mathlib/Data/Vector/Basic.lean", "Mathlib/RingTheory/OreLocalization/Ring.lean", "Mathlib/CategoryTheory/EqToHom.lean", "Mathlib/Algebra/Group/Aut.lean", "Mathlib/Init/Order/Defs.lean", "Mathlib/Tactic/ProdAssoc.lean", "Mathlib/Data/Holor.lean", "Mathlib/Algebra/Homology/ShortComplex/QuasiIso.lean", "Mathlib/Data/Matroid/Init.lean", "Mathlib/ModelTheory/Substructures.lean", "Mathlib/Data/Real/Sqrt.lean", "Mathlib/Algebra/Category/ModuleCat/Presheaf/Abelian.lean", "Mathlib/Geometry/Manifold/Algebra/Monoid.lean", "Mathlib/LinearAlgebra/Matrix/Permutation.lean", "Mathlib/Data/List/Defs.lean", "Mathlib/Analysis/Complex/UpperHalfPlane/Basic.lean", "Mathlib/Data/Nat/PrimeNormNum.lean", "Mathlib/Topology/Algebra/Valuation.lean", "Mathlib/Data/Set/Pointwise/Support.lean", "Mathlib/Analysis/Calculus/Deriv/Shift.lean", "Mathlib/Analysis/NormedSpace/Spectrum.lean", "Mathlib/Algebra/Group/Indicator.lean", "Mathlib/RepresentationTheory/GroupCohomology/Basic.lean", "Mathlib/Analysis/InnerProductSpace/MeanErgodic.lean", "Mathlib/Order/OrdContinuous.lean", "Mathlib/Testing/SlimCheck/Gen.lean", "Mathlib/Topology/MetricSpace/GromovHausdorff.lean", "Mathlib/Topology/MetricSpace/GromovHausdorffRealized.lean", "Mathlib/Analysis/NormedSpace/MatrixExponential.lean", "Mathlib/Topology/Algebra/Nonarchimedean/AdicTopology.lean", "Mathlib/Analysis/SpecialFunctions/Trigonometric/Bounds.lean", "Mathlib/Data/Nat/Factorization/PrimePow.lean", "Mathlib/Probability/Kernel/CondDistrib.lean", "Mathlib/Tactic/SuccessIfFailWithMsg.lean", "Mathlib/Data/String/Basic.lean", "Mathlib/NumberTheory/Cyclotomic/Discriminant.lean", "Mathlib/LinearAlgebra/Matrix/DotProduct.lean", "Mathlib/Algebra/GroupWithZero/InjSurj.lean", "Mathlib/Data/Fintype/Fin.lean", "Mathlib/Tactic/ExtractLets.lean", "Mathlib/Data/Sym/Sym2.lean", "Mathlib/Topology/UniformSpace/Compact.lean", "Mathlib/Topology/UniformSpace/UniformConvergenceTopology.lean", "Mathlib/MeasureTheory/Function/Jacobian.lean", "Mathlib/Algebra/RingQuot.lean", "Mathlib/Analysis/InnerProductSpace/EuclideanDist.lean", "Mathlib/Algebra/Homology/Augment.lean", "Mathlib/CategoryTheory/Limits/IsConnected.lean", "Mathlib/RingTheory/Filtration.lean", "Mathlib/Analysis/Complex/Convex.lean", "Mathlib/Geometry/Manifold/InteriorBoundary.lean", "Mathlib/Algebra/Homology/Factorizations/Basic.lean" ]

[]

.lake/packages/proofwidgets/ProofWidgets/Demos/Conv.lean

[ ".lake/packages/lean4/src/lean/Lean/Meta/ExprLens.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/MakeEditLink.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/Basic.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/OfRpcMethod.lean", ".lake/packages/proofwidgets/ProofWidgets/Data/Html.lean" ]

[ { "full_name": "NewCursorPos", "code": "structure NewCursorPos where\n newCursorPos? : Option Lsp.Position\n uri? : Option String\n deriving ToJson, FromJson", "start": [ 17, 1 ], "end": [ 20, 28 ], "kind": "commanddeclaration" }, { "full_name": "SolveReturn", "code": "private structure SolveReturn where\n expr : Expr\n val? : Option String\n listRest : List Nat", "start": [ 22, 1 ], "end": [ 25, 22 ], "kind": "commanddeclaration" }, { "full_name": "solveLevel", "code": "private def solveLevel (expr : Expr) (path : List Nat) : MetaM SolveReturn := match expr with\n | Expr.app _ _ => do\n let mut descExp := expr\n let mut count := 0\n let mut explicitList := []\n\n while descExp.isApp do\n if (←Lean.Meta.inferType descExp.appFn!).bindingInfo!.isExplicit then\n explicitList := true::explicitList\n count := count + 1\n else\n explicitList := false::explicitList\n descExp := descExp.appFn!\n\n let mut mutablePath := path\n let mut length := count\n explicitList := List.reverse explicitList\n while !mutablePath.isEmpty && mutablePath.head! == 0 do\n if explicitList.head! == true then\n count := count - 1\n explicitList := explicitList.tail!\n mutablePath := mutablePath.tail!\n\n let mut nextExp := expr\n while length > count do\n nextExp := nextExp.appFn!\n length := length - 1\n nextExp := nextExp.appArg!\n\n let pathRest := if mutablePath.isEmpty then [] else mutablePath.tail!\n\n return { expr := nextExp, val? := toString count , listRest := pathRest }\n\n | Expr.lam n _ b _ => do\n let name := match n with\n | Name.str _ s => s\n | _ => panic! \"no name found\"\n return { expr := b, val? := name, listRest := path.tail! }\n\n | Expr.forallE n _ b _ => do\n let name := match n with\n | Name.str _ s => s\n | _ => panic! \"no name found\"\n return { expr := b, val? := name, listRest := path.tail! }\n\n | Expr.mdata _ b => do\n match b with\n | Expr.mdata _ _ => return { expr := b, val? := none, listRest := path }\n | _ => return { expr := b.appFn!.appArg!, val? := none, listRest := path.tail!.tail! }\n\n | _ => do\n return { expr := ←(Lean.Core.viewSubexpr path.head! expr), val? := toString (path.head! + 1), listRest := path.tail! }", "start": [ 27, 1 ], "end": [ 81, 123 ], "kind": "commanddeclaration" }, { "full_name": "reprint!", "code": "def reprint! (stx : Syntax) : String :=\n match stx.reprint with\n | some x => x\n | none => panic! \"Could not reprint syntax\"", "start": [ 84, 1 ], "end": [ 87, 49 ], "kind": "commanddeclaration" }, { "full_name": "LocateReturn", "code": "structure LocateReturn where\n pathBeforeConv : List Nat\n pathAfterConv : List Nat\n deriving Inhabited", "start": [ 89, 1 ], "end": [ 92, 21 ], "kind": "commanddeclaration" }, { "full_name": "locate", "code": "private def locate (stx : Syntax) (pos : String.Pos) : LocateReturn := Id.run do\n let mut t := Syntax.Traverser.fromSyntax stx\n let mut path := []\n let mut rangeList := []\n\n while !t.cur.getArgs.isEmpty do\n let mut args := t.cur.getArgs\n let mut i := 0\n let mut newT := t\n let mut found := false\n rangeList := []\n for arg in args do\n let mut range := match arg.getRange? with\n | some x => x\n | none => { start := 0, stop := 0 }\n rangeList := range::rangeList\n if range.start < pos && pos <= range.stop then do\n newT := t.down i\n path := i::path\n found := true\n i := i + 1\n if !found then break\n t := newT\n\n let mut pathAfterConv := []\n while !(t.cur.getKind == `Lean.Parser.Tactic.Conv.conv\n || t.cur.getKind == `Lean.Parser.Tactic.Conv.convConvSeq\n || t.cur.getKind == `Lean.Widget.conv!)\n && path.length > 0 do\n t := t.up\n pathAfterConv := path.head!::pathAfterConv\n path := path.tail!\n\n if pathAfterConv == [] || pathAfterConv.length == 1 then\n pathAfterConv := [t.cur.getArgs.size - 2]\n\n else if pathAfterConv.length == 3 then\n let mut rangeList' := rangeList.reverse\n let mut ctr := 0\n while rangeList'.head!.stop < pos do\n ctr := ctr + 1\n rangeList' := rangeList'.tail!\n pathAfterConv := List.append pathAfterConv ((ctr-2)::[0])\n\n return {pathBeforeConv := path.reverse, pathAfterConv := pathAfterConv }", "start": [ 94, 1 ], "end": [ 142, 75 ], "kind": "commanddeclaration" }, { "full_name": "extractIndentation", "code": "private partial def extractIndentation (input : String) : String := match \" \".isPrefixOf input with\n | true => \" \" ++ extractIndentation (input.drop 2)\n | false => \"\"", "start": [ 144, 1 ], "end": [ 146, 16 ], "kind": "commanddeclaration" }, { "full_name": "InsertReturn", "code": "private structure InsertReturn where\n stx : Syntax\n newPath : List Nat\n newCursorPos : Lsp.Position", "start": [ 148, 1 ], "end": [ 151, 30 ], "kind": "commanddeclaration" }, { "full_name": "insertAfterArrow", "code": "private def insertAfterArrow (stx : Syntax) (pathBeforeConvParam : List Nat) (pathAfterConvParam : List Nat) (value : String) (text : FileMap) : InsertReturn := Id.run do\n let mut t := Syntax.Traverser.fromSyntax stx\n let mut pathBeforeConv := pathBeforeConvParam\n while pathBeforeConv.length > 0 do\n t := t.down pathBeforeConv.head!\n pathBeforeConv := pathBeforeConv.tail!\n let mut pathAfterConv := pathAfterConvParam\n\nlet mut pathBeforeConv' := pathBeforeConvParam.reverse\n let mut returnPath := []\n for _ in [:4] do\n t := t.up\n returnPath := pathBeforeConv'.head!::returnPath\n pathBeforeConv' := pathBeforeConv'.tail!\n t := t.up\n\n let argNr := pathBeforeConv'.head! - 1\n let prevArg := reprint! t.cur.getArgs[argNr]!\n let mut previousIndentation := extractIndentation (prevArg.splitOn \"\\n\").reverse.head!\n\n t := t.down pathBeforeConv'.head!\n while returnPath.length > 0 do\n t := t.down returnPath.head!\n returnPath := returnPath.tail!\n\n let arrow := reprint! t.cur.getArgs[pathAfterConv.head!]!\n let mut arrowIndentation := extractIndentation (arrow.splitOn \"\\n\").reverse.head!\n let mut newCursorPos := match t.cur.getArgs[pathAfterConv.head!]!.getRange? with\n | some range => text.utf8PosToLspPos range.stop\n | none => text.utf8PosToLspPos 0\n\n let mut newNode := Syntax.missing\n if reprint! t.cur.getArgs[pathAfterConv.head! + 1]! == \"\" || previousIndentation == arrowIndentation then\n let newArrow := Syntax.atom (SourceInfo.original \"\".toSubstring 0 \"\".toSubstring 0) \"=>\\n\"\n t := t.setCur (t.cur.setArgs (List.append (t.cur.getArgs.toList.take pathAfterConv.head!) (newArrow::t.cur.getArgs.toList.drop (pathAfterConv.head! + 1))).toArray)\n newNode := Syntax.atom (SourceInfo.original \"\".toSubstring 0 \"\".toSubstring 0) (\" \" ++ previousIndentation ++ value ++ \"\\n\" ++ arrowIndentation)\n newCursorPos := { line := newCursorPos.line + 1, character := 2 + previousIndentation.length + value.length }\n else\n newNode := Syntax.atom (SourceInfo.original \"\".toSubstring 0 \"\".toSubstring 0) (value ++ \"\\n\" ++ arrowIndentation)\n newCursorPos := { line := newCursorPos.line + 1, character := arrowIndentation.length + value.length }\n\n t := t.down (pathAfterConv.head! + 1)\n t := t.down 0\n t := t.down 0\n\n let newArgList := newNode::t.cur.getArgs.toList\n t := t.setCur (t.cur.setArgs newArgList.toArray)\n while t.parents.size > 0 do\n t := t.up\n\n let newPath := pathBeforeConvParam ++ (pathAfterConv.head! + 1)::0::0::[0]\n\n return { stx := t.cur, newPath := newPath, newCursorPos }", "start": [ 153, 1 ], "end": [ 212, 60 ], "kind": "commanddeclaration" }, { "full_name": "insertAnywhereElse", "code": "private def insertAnywhereElse (stx : Syntax) (pathBeforeConvParam : List Nat) (pathAfterConvParam : List Nat) (value : String) (text : FileMap): InsertReturn := Id.run do\n let mut t := Syntax.Traverser.fromSyntax stx\n let mut pathBeforeConv := pathBeforeConvParam\n while pathBeforeConv.length > 0 do\n t := t.down pathBeforeConv.head!\n pathBeforeConv := pathBeforeConv.tail!\n let mut pathAfterConv := pathAfterConvParam\n\nlet nothingAfterConv := t.up.cur.getArgs.size - 1 == pathBeforeConvParam.reverse.head!\n\n for _ in [:3] do\n t := t.down pathAfterConv.head!\n pathAfterConv := pathAfterConv.tail!\n\n let argAsString := reprint! t.cur.getArgs[pathAfterConv.head!]!\n let mut newval := value\n let mut entersMerged := false\n if toString t.cur.getArgs[pathAfterConv.head!]!.getKind == \"Lean.Parser.Tactic.Conv.«convEnter[__]»\" then\n let mut additionalArgs := (argAsString.splitOn \"\\n\").head!\n additionalArgs := (additionalArgs.drop \"enter [\".length).dropRight 1\n\n let left := value.take \"enter [\".length\n let right := value.drop \"enter [\".length\n newval := left ++ additionalArgs ++ \", \" ++ right\n entersMerged := true\n\n let mut newCursorPos := match t.cur.getArgs[pathAfterConv.head!]!.getRange? with\n | some range => text.utf8PosToLspPos range.stop\n | none => text.utf8PosToLspPos 0\n\n let mut argNr := pathAfterConv.head!\n let mut indentation := \"\"\n if argNr == 0 then\n indentation := extractIndentation ((reprint! t.up.up.up.cur).splitOn \"\\n\").tail!.head!\n else\n argNr := argNr - 2\n let mut prevArg := reprint! t.cur.getArgs[argNr]!\n let mut split := prevArg.splitOn \"\\n\"\n while split.length == 1 do\n argNr := argNr + 2\n prevArg := reprint! t.cur.getArgs[argNr]!\n split := prevArg.splitOn \"\\n\"\n\n let mut indentationLine := split.reverse.head!\n indentation := extractIndentation indentationLine\n\n newCursorPos := match entersMerged with\n | true => { line := newCursorPos.line, character := indentation.length + newval.length }\n | false => { line := newCursorPos.line + 1, character := indentation.length + newval.length }\n\n let mut frontIndentation := \"\"\n if pathAfterConv.head! == t.cur.getArgs.size - 1 then\n let lastArg := reprint! t.cur.getArgs[ t.cur.getArgs.size - 1]!\n let mut lastArgIndentation := extractIndentation (lastArg.splitOn \"\\n\").reverse.head!\n let numOfWhitespace := indentation.length - lastArgIndentation.length\n for _ in [:numOfWhitespace] do\n frontIndentation := frontIndentation ++ \" \"\n indentation := indentation.drop numOfWhitespace\n\n let mut argList := []\n if nothingAfterConv then\n let mut adjustedLastLine := reprint! t.cur.getArgs[t.cur.getArgs.size - 1]!\n while adjustedLastLine.takeRight 1 == \"\\n\" do\n adjustedLastLine := adjustedLastLine.dropRight 1\n adjustedLastLine := adjustedLastLine ++ \"\\n\"\n let adjustedLastNode := Syntax.atom (SourceInfo.original \"\".toSubstring 0 \"\".toSubstring 0) adjustedLastLine\n argList := (adjustedLastNode::t.cur.getArgs.toList.reverse.tail!).reverse\n else\n argList := t.cur.getArgs.toList\n\n let newNode := match entersMerged with\n | true => Syntax.atom (SourceInfo.original \"\".toSubstring 0 \"\".toSubstring 0) (newval ++ \"\\n\" ++ indentation)\n | false => Syntax.atom (SourceInfo.original \"\".toSubstring 0 \"\".toSubstring 0) (frontIndentation ++ newval ++ \"\\n\" ++ indentation)\n let newArgList := match entersMerged with\n | true => List.append (argList.take (pathAfterConv.head!) ) (newNode::(argList.drop (pathAfterConv.head! + 1)))\n | false => List.append (argList.take (pathAfterConv.head! + 1) ) (newNode::(argList.drop (pathAfterConv.head! + 1)))\n let newPath := match entersMerged with\n | true => pathBeforeConvParam ++ (pathAfterConvParam.take 4)\n | false => pathBeforeConvParam ++ (pathAfterConvParam.take 3) ++ [(pathAfterConvParam.get! 3) + 2]\n\n t := t.setCur (t.cur.setArgs newArgList.toArray)\n while t.parents.size > 0 do\n t := t.up\n\n return { stx := t.cur, newPath := newPath, newCursorPos := newCursorPos }", "start": [ 214, 1 ], "end": [ 309, 76 ], "kind": "commanddeclaration" }, { "full_name": "syntaxInsert", "code": "private def syntaxInsert (stx : Syntax) (pathBeforeConvParam : List Nat) (pathAfterConvParam : List Nat) (value : String) (text : FileMap): InsertReturn := Id.run do\n if value == \"\" then return { stx := stx, newPath := pathBeforeConvParam ++ pathAfterConvParam, newCursorPos := {line := 0, character := 0} }\n if pathAfterConvParam.length == 1 then\n return insertAfterArrow stx pathBeforeConvParam pathAfterConvParam value text\n else\n return insertAnywhereElse stx pathBeforeConvParam pathAfterConvParam value text", "start": [ 311, 1 ], "end": [ 316, 84 ], "kind": "commanddeclaration" }, { "full_name": "InsertEnterResponse", "code": "structure InsertEnterResponse where\n \n label : String\n edit : Lsp.TextDocumentEdit\n \n newCursorPos : Lsp.Position\n deriving FromJson, ToJson", "start": [ 318, 1 ], "end": [ 324, 28 ], "kind": "commanddeclaration" }, { "full_name": "insertEnter", "code": "def insertEnter (subexprPos : SubExpr.Pos) (goalType : Expr) (cmdStx : Syntax)\n (cursorPos : String.Pos) (doc : Lean.Server.FileWorker.EditableDocument) : MetaM InsertEnterResponse := do\n let mut list := (SubExpr.Pos.toArray subexprPos).toList\n let mut expr := goalType\n let mut retList := []\n while !list.isEmpty do\n let res ← solveLevel expr list\n expr := res.expr\n retList := match res.val? with\n | none => retList\n | some val => val::retList\n list := res.listRest\n\n retList := List.reverse retList\n let mut enterval := \"enter \" ++ toString retList\n if enterval.contains '0' then enterval := \"Error: Not a valid conv target\"\n if retList.isEmpty then enterval := \"\"\n\n let range := match cmdStx.getRange? with\n | some x => x\n | none => panic! \"could not get range\"\n\n let text := doc.meta.text\n\n let located := locate cmdStx { byteIdx := (min cursorPos.byteIdx range.stop.byteIdx) }\n let inserted := syntaxInsert cmdStx located.pathBeforeConv located.pathAfterConv enterval text\n let mut newSyntax := reprint! inserted.stx\n\n let mut syntaxAsList := newSyntax.data.reverse\n while syntaxAsList.head! == '\\n' || syntaxAsList.head! == ' ' do\n newSyntax := newSyntax.dropRight 1\n syntaxAsList := syntaxAsList.tail!\n\n let textEdit : Lsp.TextEdit := { range := { start := text.utf8PosToLspPos range.start, «end» := text.utf8PosToLspPos { byteIdx := range.stop.byteIdx } }, newText := newSyntax }\n let edit : Lsp.TextDocumentEdit := { textDocument := { uri := doc.meta.uri, version? := doc.meta.version }, edits := [textEdit].toArray }\n\n return { label := enterval, edit, newCursorPos := inserted.newCursorPos }", "start": [ 326, 1 ], "end": [ 367, 76 ], "kind": "commanddeclaration" }, { "full_name": "ConvButtonProps", "code": "structure ConvButtonProps where\n pos : Lsp.Position\n goal : Widget.InteractiveGoal\n loc : SubExpr.GoalLocation\n deriving RpcEncodable", "start": [ 373, 1 ], "end": [ 377, 24 ], "kind": "commanddeclaration" }, { "full_name": "ConvButton.rpc", "code": "@[server_rpc_method]\ndef ConvButton.rpc (props : ConvButtonProps) : RequestM (RequestTask Html) :=\n RequestM.withWaitFindSnapAtPos props.pos fun snap => do\n if props.goal.goalPrefix != \"| \" then\n throw $ .invalidParams s!\"The current goal is not a conv goal.\"\n let .target subexprPos := props.loc\n | throw $ .invalidParams s!\"Select something in the target type.\"\n let doc ← RequestM.readDoc\n let cursorPos := doc.meta.text.lspPosToUtf8Pos props.pos\n props.goal.ctx.val.runMetaM {} do\n let md ← props.goal.mvarId.getDecl\n let lctx := md.lctx |>.sanitizeNames.run' {options := (← getOptions)}\n Meta.withLCtx lctx md.localInstances do\n let resp ← insertEnter subexprPos md.type snap.stx cursorPos doc\n return <div><MakeEditLink\n edit={resp.edit}\n newSelection?={some ⟨resp.newCursorPos, resp.newCursorPos⟩}\n title?={resp.label}\n >\n {.text resp.label}\n </MakeEditLink></div>", "start": [ 380, 1 ], "end": [ 400, 32 ], "kind": "commanddeclaration" }, { "full_name": "ConvButton", "code": "@[widget_module]\ndef ConvButton : Component ConvButtonProps :=\n mk_rpc_widget% ConvButton.rpc", "start": [ 402, 1 ], "end": [ 404, 32 ], "kind": "commanddeclaration" }, { "full_name": "findGoalForLocation", "code": "def findGoalForLocation (goals : Array Widget.InteractiveGoal) (loc : SubExpr.GoalsLocation) :\n Option Widget.InteractiveGoal :=\n goals.find? (·.mvarId == loc.mvarId)", "start": [ 406, 1 ], "end": [ 408, 39 ], "kind": "commanddeclaration" }, { "full_name": "ConvPanel.rpc", "code": "@[server_rpc_method]\ndef ConvPanel.rpc (props : PanelWidgetProps) : RequestM (RequestTask Html) :=\n RequestM.asTask do\n let inner : Html ← (do\n if props.selectedLocations.isEmpty then\n return <span>No actions available. You can use shift-click to select an expression in the goal state.</span>\n let buttons : Array Html ← props.selectedLocations.mapM fun loc => do\n let some g := findGoalForLocation props.goals loc\n | throw $ .invalidParams s!\"could not find goal for location {toJson loc}\"\n return <ConvButton pos={props.pos} goal={g} loc={loc.loc} />\n return Html.element \"div\" #[] buttons)\n return <details «open»={true}>\n <summary className=\"mv2 pointer\">Conv 🔍</summary>\n <div className=\"ml1\">{inner}</div>\n </details>", "start": [ 411, 1 ], "end": [ 425, 17 ], "kind": "commanddeclaration" }, { "full_name": "ConvPanel", "code": "@[widget_module]\ndef ConvPanel : Component PanelWidgetProps :=\n mk_rpc_widget% ConvPanel.rpc", "start": [ 427, 1 ], "end": [ 429, 31 ], "kind": "commanddeclaration" }, { "full_name": "test_sorry", "code": "axiom test_sorry {α} : α", "start": [ 434, 1 ], "end": [ 434, 25 ], "kind": "commanddeclaration" } ]

.lake/packages/proofwidgets/ProofWidgets/Demos/SelectInsertConv.lean

[ ".lake/packages/lean4/src/lean/Lean/Meta/ExprLens.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/MakeEditLink.lean", ".lake/packages/batteries/Batteries/Lean/Position.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/Basic.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/OfRpcMethod.lean", ".lake/packages/proofwidgets/ProofWidgets/Data/Html.lean" ]

[ { "full_name": "SolveReturn", "code": "private structure SolveReturn where\n expr : Expr\n val? : Option String\n listRest : List Nat", "start": [ 23, 1 ], "end": [ 26, 22 ], "kind": "commanddeclaration" }, { "full_name": "solveLevel", "code": "private def solveLevel (expr : Expr) (path : List Nat) : MetaM SolveReturn := match expr with\n | Expr.app _ _ => do\n let mut descExp := expr\n let mut count := 0\n let mut explicitList := []\n\n while descExp.isApp do\n if (←Lean.Meta.inferType descExp.appFn!).bindingInfo!.isExplicit then\n explicitList := true::explicitList\n count := count + 1\n else\n explicitList := false::explicitList\n descExp := descExp.appFn!\n\n let mut mutablePath := path\n let mut length := count\n explicitList := List.reverse explicitList\n while !mutablePath.isEmpty && mutablePath.head! == 0 do\n if explicitList.head! == true then\n count := count - 1\n explicitList := explicitList.tail!\n mutablePath := mutablePath.tail!\n\n let mut nextExp := expr\n while length > count do\n nextExp := nextExp.appFn!\n length := length - 1\n nextExp := nextExp.appArg!\n\n let pathRest := if mutablePath.isEmpty then [] else mutablePath.tail!\n\n return { expr := nextExp, val? := toString count , listRest := pathRest }\n\n | Expr.lam n _ b _ => do\n let name := match n with\n | Name.str _ s => s\n | _ => panic! \"no name found\"\n return { expr := b, val? := name, listRest := path.tail! }\n\n | Expr.forallE n _ b _ => do\n let name := match n with\n | Name.str _ s => s\n | _ => panic! \"no name found\"\n return { expr := b, val? := name, listRest := path.tail! }\n\n | Expr.mdata _ b => do\n match b with\n | Expr.mdata _ _ => return { expr := b, val? := none, listRest := path }\n | _ => return { expr := b.appFn!.appArg!, val? := none, listRest := path.tail!.tail! }\n\n | _ => do\n return {\n expr := ←(Lean.Core.viewSubexpr path.head! expr)\n val? := toString (path.head! + 1)\n listRest := path.tail!\n }", "start": [ 28, 1 ], "end": [ 86, 6 ], "kind": "commanddeclaration" }, { "full_name": "insertEnter", "code": "def insertEnter (locations : Array Lean.SubExpr.GoalsLocation) (goalType : Expr) : MetaM String := do\n let some pos := locations[0]? | throwError \"You must select something.\"\n let ⟨_, .target subexprPos⟩ := pos | throwError \"You must select something in the goal.\"\n let mut list := (SubExpr.Pos.toArray subexprPos).toList\n let mut expr := goalType\n let mut retList := []\n while !list.isEmpty do\n let res ← solveLevel expr list\n expr := res.expr\n retList := match res.val? with\n | none => retList\n | some val => val::retList\n list := res.listRest\n\n retList := List.reverse retList\n let mut enterval := \"conv => enter \" ++ toString retList\n if enterval.contains '0' then enterval := \"Error: Not a valid conv target\"\n if retList.isEmpty then enterval := \"\"\n return enterval", "start": [ 89, 1 ], "end": [ 109, 18 ], "kind": "commanddeclaration" }, { "full_name": "findGoalForLocation", "code": "def findGoalForLocation (goals : Array Widget.InteractiveGoal) (loc : SubExpr.GoalsLocation) :\n Option Widget.InteractiveGoal :=\n goals.find? (·.mvarId == loc.mvarId)", "start": [ 111, 1 ], "end": [ 113, 39 ], "kind": "commanddeclaration" }, { "full_name": "ConvSelectionPanelProps", "code": "structure ConvSelectionPanelProps extends PanelWidgetProps where\n \n replaceRange : Lsp.Range\n deriving RpcEncodable", "start": [ 115, 1 ], "end": [ 118, 24 ], "kind": "commanddeclaration" }, { "full_name": "ConvSelectionPanel.rpc", "code": "@[server_rpc_method]\ndef ConvSelectionPanel.rpc (props : ConvSelectionPanelProps) : RequestM (RequestTask Html) :=\n RequestM.asTask do\n let doc ← RequestM.readDoc\n let inner : Html ← (do\n if props.selectedLocations.isEmpty then\n return <span>Use shift-click to select one sub-expression in the goal that you want to zoom on.</span>\n let some selectedLoc := props.selectedLocations[0]? | unreachable!\n\n let some g := findGoalForLocation props.goals selectedLoc\n | throw $ .invalidParams\n s!\"could not find goal for location {toJson selectedLoc}\"\n g.ctx.val.runMetaM {} do\n let md ← g.mvarId.getDecl\n let lctx := md.lctx |>.sanitizeNames.run' {options := (← getOptions)}\n Meta.withLCtx lctx md.localInstances do\n let newCode ← insertEnter props.selectedLocations md.type\n return .ofComponent\n MakeEditLink\n (.ofReplaceRange doc.meta props.replaceRange newCode)\n #[ .text newCode ])\n return <details «open»={true}>\n <summary className=\"mv2 pointer\">Conv 🔍</summary>\n <div className=\"ml1\">{inner}</div>\n </details>", "start": [ 121, 1 ], "end": [ 145, 17 ], "kind": "commanddeclaration" }, { "full_name": "ConvSelectionPanel", "code": "@[widget_module]\ndef ConvSelectionPanel : Component ConvSelectionPanelProps :=\n mk_rpc_widget% ConvSelectionPanel.rpc", "start": [ 147, 1 ], "end": [ 149, 40 ], "kind": "commanddeclaration" }, { "full_name": "test_sorry", "code": "axiom test_sorry {α} : α", "start": [ 158, 1 ], "end": [ 158, 25 ], "kind": "commanddeclaration" } ]

.lake/packages/proofwidgets/ProofWidgets/Demos/Plot.lean

[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Recharts.lean" ]

[ { "full_name": "fn", "code": "def fn (t : Float) (x : Float): Float :=\n 50 * (x - 0.25) * (x - 0.5) * (x - 0.7) + 0.1 * (x * 40 - t * 2 * 3.141).sin", "start": [ 6, 1 ], "end": [ 7, 80 ], "kind": "commanddeclaration" }, { "full_name": "Plot", "code": "def Plot (fn : Float → Float) (steps := 100) : Html :=\n let jsonData : Array Json :=\n Nat.fold (flip Array.push) (steps + 1) #[]\n |> Array.map (fun (x : Nat) => let x : Float := x.toFloat / steps.toFloat; (x, fn x))\n |> Array.map (fun (x,y) => json% {x: $(toJson x) , y: $(toJson y)});\n <LineChart width={400} height={400} data={jsonData}>\n <XAxis domain?={#[toJson 0, toJson 1]} dataKey?=\"x\" />\n <YAxis domain?={#[toJson (-1), toJson 1]} allowDataOverflow={Bool.false} />\n <Line type={.monotone} dataKey=\"y\" stroke=\"#8884d8\" dot?={Bool.false} />\n </LineChart>", "start": [ 10, 1 ], "end": [ 19, 15 ], "kind": "commanddeclaration" }, { "full_name": "mkFrames", "code": "def mkFrames (fn : Float → Float → Float) (steps := 100) : Array Html:=\n List.range (steps + 1) |>.toArray |>.map (fun t => Plot (fn (t.toFloat / steps.toFloat)))", "start": [ 30, 1 ], "end": [ 31, 92 ], "kind": "commanddeclaration" }, { "full_name": "AnimatedHtmlProps", "code": "structure AnimatedHtmlProps where\n frames : Array Html\n framesPerSecond? : Option Nat := none\n deriving Server.RpcEncodable", "start": [ 33, 1 ], "end": [ 36, 31 ], "kind": "commanddeclaration" }, { "full_name": "AnimatedHtml", "code": "@[widget_module]\ndef AnimatedHtml : Component AnimatedHtmlProps where\n javascript := include_str \"..\" / \"..\" / \".lake\" / \"build\" / \"js\" / \"animatedHtml.js\"", "start": [ 38, 1 ], "end": [ 40, 87 ], "kind": "commanddeclaration" } ]

.lake/packages/proofwidgets/ProofWidgets/Demos/InteractiveSvg.lean

[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/InteractiveSvg.lean" ]

[ { "full_name": "State", "code": "abbrev State := Array (Float × Float)", "start": [ 7, 1 ], "end": [ 7, 38 ], "kind": "commanddeclaration" }, { "full_name": "isvg", "code": "def isvg : InteractiveSvg State where\n init := #[(-0.5, -0.5), (0.5, -0.5), (0.5, 0.5), (-0.5, 0.5)]\n\n frame :=\n { xmin := -1\n ymin := -1\n xSize := 2\n width := 400\n height := 400 }\n\n update _time _Δt _action _mouseStart mouseEnd _selected getData state :=\n match getData Nat, mouseEnd with\n | some id, some p => state.set! id p.toAbsolute\n | _, _ => state\n\n render _time mouseStart mouseEnd state :=\n {\n elements :=\n let mousePointer :=\n match mouseStart, mouseEnd with\n | some s, some e =>\n #[\n Svg.circle e (.px 5) |>.setFill (1.,1.,1.),\n Svg.line s e |>.setStroke (1.,1.,1.) (.px 2)\n ]\n | _, _ => #[]\n let circles := (state.mapIdx fun idx (p : Float × Float) =>\n Svg.circle p (.abs 0.2) |>.setFill (0.7,0.7,0.7) |>.setId s!\"circle{idx}\" |>.setData idx.1\n )\n mousePointer.append circles\n }", "start": [ 9, 1 ], "end": [ 39, 6 ], "kind": "commanddeclaration" }, { "full_name": "updateSvg", "code": "@[server_rpc_method]\ndef updateSvg (params : UpdateParams State) : RequestM (RequestTask (UpdateResult State)) := isvg.serverRpcMethod params", "start": [ 42, 1 ], "end": [ 43, 121 ], "kind": "commanddeclaration" }, { "full_name": "SvgWidget", "code": "@[widget_module]\ndef SvgWidget : Component (UpdateResult State) where\n javascript := include_str \"..\" / \"..\" / \".lake\" / \"build\" / \"js\" / \"interactiveSvg.js\"", "start": [ 45, 1 ], "end": [ 47, 89 ], "kind": "commanddeclaration" }, { "full_name": "init", "code": "def init : UpdateResult State := {\n html := <div>Init!!!</div>,\n state := { state := isvg.init\n time := 0\n selected := none\n mousePos := none\n idToData := isvg.render 0 none none isvg.init |>.idToDataList}\n}", "start": [ 49, 1 ], "end": [ 56, 2 ], "kind": "commanddeclaration" } ]

.lake/packages/proofwidgets/ProofWidgets/Demos/Venn.lean

[ ".lake/packages/proofwidgets/ProofWidgets/Component/PenroseDiagram.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean", ".lake/packages/lean4/src/lean/Lean/Data/HashMap.lean", ".lake/packages/lean4/src/lean/Lean/Elab/Tactic.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/Basic.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/OfRpcMethod.lean" ]

[ { "full_name": "Set", "code": "def Set (α : Type u) := α → Prop", "start": [ 12, 1 ], "end": [ 12, 33 ], "kind": "commanddeclaration" }, { "full_name": "Set.Mem", "code": "protected def Mem (a : α) (s : Set α) : Prop :=\n s a", "start": [ 16, 1 ], "end": [ 18, 6 ], "kind": "commanddeclaration" }, { "full_name": "Set.ext", "code": "theorem ext {a b : Set α} (h : ∀ (x : α), x ∈ a ↔ x ∈ b) : a = b", "start": [ 23, 1 ], "end": [ 24, 33 ], "kind": "commanddeclaration" }, { "full_name": "Set.Subset", "code": "protected def Subset (s₁ s₂ : Set α) :=\n ∀ ⦃a⦄, a ∈ s₁ → a ∈ s₂", "start": [ 26, 1 ], "end": [ 27, 25 ], "kind": "commanddeclaration" }, { "full_name": "isSubsetPred?", "code": "def isSubsetPred? (e : Expr) : Option (Expr × Expr) := do\n let some (_, _, S, T) := e.app4? ``HasSubset.Subset | none\n return (S, T)", "start": [ 41, 1 ], "end": [ 44, 16 ], "kind": "commanddeclaration" }, { "full_name": "ExprEmbeds", "code": "abbrev ExprEmbeds := Array (String × Expr)", "start": [ 46, 1 ], "end": [ 47, 43 ], "kind": "commanddeclaration" }, { "full_name": "mkSetDiag", "code": "def mkSetDiag (sub : String) (embeds : ExprEmbeds) : MetaM Html := do\n let embeds ← embeds.mapM fun (s, h) =>\n return (s, <InteractiveCode fmt={← Widget.ppExprTagged h} />)\n return <PenroseDiagram\n embeds={embeds}\n dsl={include_str \"..\"/\"..\"/\"widget\"/\"penrose\"/\"setTheory.dsl\"}\n sty={include_str \"..\"/\"..\"/\"widget\"/\"penrose\"/\"venn.sty\"}\n sub={sub} />", "start": [ 50, 1 ], "end": [ 57, 19 ], "kind": "commanddeclaration" }, { "full_name": "isSetGoal?", "code": "def isSetGoal? (hyps : Array LocalDecl) : MetaM (Option Html) := do\n let mut sub := \"AutoLabel All\\n\"\n let mut sets : HashMap String Expr := .empty\n for assm in hyps do\n let tp ← instantiateMVars assm.type\n if let some (S, T) := isSubsetPred? tp then\n let sS ← toString <$> Lean.Meta.ppExpr S\n let sT ← toString <$> Lean.Meta.ppExpr T\n let (sets', cS) := sets.insert' sS S\n let (sets', cT) := sets'.insert' sT T\n sets := sets'\n if !cS then\n sub := sub ++ s!\"Set {sS}\\n\"\n if !cT then\n sub := sub ++ s!\"Set {sT}\\n\"\n sub := sub ++ s!\"IsSubset({sS}, {sT})\\n\"\n if sets.isEmpty then return none\n some <$> mkSetDiag sub sets.toArray", "start": [ 59, 1 ], "end": [ 76, 38 ], "kind": "commanddeclaration" }, { "full_name": "findGoalForLocation", "code": "def findGoalForLocation (goals : Array Widget.InteractiveGoal) (loc : SubExpr.GoalsLocation) :\n Option Widget.InteractiveGoal :=\n goals.find? (·.mvarId == loc.mvarId)", "start": [ 80, 1 ], "end": [ 82, 39 ], "kind": "commanddeclaration" }, { "full_name": "VennDisplay.rpc", "code": "@[server_rpc_method]\ndef VennDisplay.rpc (props : PanelWidgetProps) : RequestM (RequestTask Html) :=\n RequestM.asTask do\n let inner : Html ← (do\n if props.selectedLocations.isEmpty then\n return <span>Use shift-click to select hypotheses to include in the diagram.</span>\n let some selectedLoc := props.selectedLocations[0]? | unreachable!\n\n let some g := findGoalForLocation props.goals selectedLoc\n | throw $ .invalidParams\n s!\"could not find goal for location {toJson selectedLoc}\"\n g.ctx.val.runMetaM {} do\n let md ← g.mvarId.getDecl\n let lctx := md.lctx |>.sanitizeNames.run' {options := (← getOptions)}\n Meta.withLCtx lctx md.localInstances do\n let locs : Array LocalDecl ← props.selectedLocations.filterMapM fun\n | ⟨mv, .hyp fv⟩ | ⟨mv, .hypType fv _⟩ =>\n if mv == g.mvarId then return some (← fv.getDecl) else return none\n | _ => return none\n match ← isSetGoal? locs with\n | some html => return html\n | none => return <span>No set goal.</span>)\n return <details «open»={true}>\n <summary className=\"mv2 pointer\">Venn diagram</summary>\n <div className=\"ml1\">{inner}</div>\n </details>", "start": [ 85, 1 ], "end": [ 110, 17 ], "kind": "commanddeclaration" }, { "full_name": "VennDisplay", "code": "@[widget_module]\ndef VennDisplay : Component PanelWidgetProps :=\n mk_rpc_widget% VennDisplay.rpc", "start": [ 112, 1 ], "end": [ 114, 33 ], "kind": "commanddeclaration" } ]

.lake/packages/proofwidgets/ProofWidgets/Demos/Euclidean.lean

[ ".lake/packages/proofwidgets/ProofWidgets/Component/PenroseDiagram.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/MakeEditLink.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean", ".lake/packages/lean4/src/lean/Lean/Data/HashMap.lean", ".lake/packages/lean4/src/lean/Lean/Elab/Tactic.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/Basic.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/OfRpcMethod.lean" ]

[ { "full_name": "IncidenceGeometry", "code": "class IncidenceGeometry where\n Point : Type u₁\n Line : Type u₂\n Circle : Type u₃\n\n between : Point → Point → Point → Prop onLine : Point → Line → Prop\n onCircle : Point → Circle → Prop\n inCircle : Point → Circle → Prop\n centerCircle : Point → Circle → Prop\n circlesInter : Circle → Circle → Prop\n\n ne_23_of_between : ∀ {a b c : Point}, between a b c → b ≠ c\n line_unique_of_pts : ∀ {a b : Point}, ∀ {L M : Line},\n a ≠ b → onLine a L → onLine b L → onLine a M → onLine b M → L = M\n onLine_2_of_between : ∀ {a b c : Point}, ∀ {L : Line},\n between a b c → onLine a L → onLine c L → onLine b L\n line_of_pts : ∀ a b, ∃ L, onLine a L ∧ onLine b L\n circle_of_ne : ∀ a b, a ≠ b → ∃ C, centerCircle a C ∧ onCircle b C\n circlesInter_of_onCircle_inCircle :\n ∀ {a b α β}, onCircle b α → onCircle a β → inCircle a α →\n inCircle b β → circlesInter α β\n pts_of_circlesInter : ∀ {α β}, circlesInter α β →\n ∃ a b, a ≠ b ∧ onCircle a α ∧ onCircle a β ∧ onCircle b α ∧ onCircle b β\n inCircle_of_centerCircle : ∀ {a α}, centerCircle a α → inCircle a α", "start": [ 25, 1 ], "end": [ 49, 70 ], "kind": "commanddeclaration" }, { "full_name": "isBetweenPred?", "code": "def isBetweenPred? (e : Expr) : Option (Expr × Expr × Expr) := do\n let some (_, a, b, c) := e.app4? ``between | none\n return (a, b, c)", "start": [ 55, 1 ], "end": [ 58, 19 ], "kind": "commanddeclaration" }, { "full_name": "isOnLinePred?", "code": "def isOnLinePred? (e : Expr) : Option (Expr × Expr) := do\n let some (_, a, L) := e.app3? ``onLine | none\n return (a, L)", "start": [ 60, 1 ], "end": [ 63, 16 ], "kind": "commanddeclaration" }, { "full_name": "isOnCirclePred?", "code": "def isOnCirclePred? (e : Expr) : Option (Expr × Expr) := do\n let some (_, a, C) := e.app3? ``onCircle | none\n return (a, C)", "start": [ 65, 1 ], "end": [ 68, 16 ], "kind": "commanddeclaration" }, { "full_name": "isInCirclePred?", "code": "def isInCirclePred? (e : Expr) : Option (Expr × Expr) := do\n let some (_, a, C) := e.app3? ``inCircle | none\n return (a, C)", "start": [ 70, 1 ], "end": [ 73, 16 ], "kind": "commanddeclaration" }, { "full_name": "isCenterCirclePred?", "code": "def isCenterCirclePred? (e : Expr) : Option (Expr × Expr) := do\n let some (_, a, C) := e.app3? ``centerCircle | none\n return (a, C)", "start": [ 75, 1 ], "end": [ 78, 16 ], "kind": "commanddeclaration" }, { "full_name": "isCirclesInterPred?", "code": "def isCirclesInterPred? (e : Expr) : Option (Expr × Expr) := do\n let some (_, a, C) := e.app3? ``circlesInter | none\n return (a, C)", "start": [ 80, 1 ], "end": [ 83, 16 ], "kind": "commanddeclaration" }, { "full_name": "isPoint?", "code": "def isPoint? (e : Expr) : Bool :=\n e.isAppOf ``Point", "start": [ 85, 1 ], "end": [ 86, 20 ], "kind": "commanddeclaration" }, { "full_name": "isLine?", "code": "def isLine? (e : Expr) : Bool :=\n e.isAppOf ``Line", "start": [ 88, 1 ], "end": [ 89, 19 ], "kind": "commanddeclaration" }, { "full_name": "addHypotheses", "code": "def addHypotheses (hyps : Array LocalDecl) : DiagramBuilderM Unit := do\n for h in hyps do\n let tp ← instantiateMVars h.type\n if isPoint? tp then\n discard $ addExpr \"Point\" h.toExpr\n if isLine? tp then\n discard $ addExpr \"Line\" h.toExpr\n if let some (a, b, c) := isBetweenPred? tp then\n let sa ← addExpr \"Point\" a\n let sb ← addExpr \"Point\" b\n let sc ← addExpr \"Point\" c\n addInstruction s!\"Between({sa}, {sb}, {sc})\"\n if let some (a, L) := isOnLinePred? tp then\n let sa ← addExpr \"Point\" a\n let sL ← addExpr \"Line\" L\n addInstruction s!\"OnLine({sa}, {sL})\"\n if let some (a, C) := isOnCirclePred? tp then\n let sa ← addExpr \"Point\" a\n let sC ← addExpr \"Circle\" C\n addInstruction s!\"OnCircle({sa}, {sC})\"\n if let some (a, C) := isInCirclePred? tp then\n let sa ← addExpr \"Point\" a\n let sC ← addExpr \"Circle\" C\n addInstruction s!\"InCircle({sa}, {sC})\"\n if let some (a, C) := isCenterCirclePred? tp then\n let sa ← addExpr \"Point\" a\n let sC ← addExpr \"Circle\" C\n addInstruction s!\"CenterCircle({sa}, {sC})\"\n if let some (C, D) := isCirclesInterPred? tp then\n let sC ← addExpr \"Circle\" C\n let sD ← addExpr \"Circle\" D\n addInstruction s!\"CirclesInter({sC}, {sD})\"", "start": [ 94, 1 ], "end": [ 125, 50 ], "kind": "commanddeclaration" }, { "full_name": "EuclideanDisplay.dsl", "code": "def EuclideanDisplay.dsl :=\n include_str \"..\"/\"..\"/\"widget\"/\"penrose\"/\"euclidean.dsl\"", "start": [ 129, 1 ], "end": [ 130, 59 ], "kind": "commanddeclaration" }, { "full_name": "EuclideanDisplay.sty", "code": "def EuclideanDisplay.sty :=\n include_str \"..\"/\"..\"/\"widget\"/\"penrose\"/\"euclidean.sty\"", "start": [ 132, 1 ], "end": [ 133, 59 ], "kind": "commanddeclaration" }, { "full_name": "EuclideanDisplay.rpc", "code": "@[server_rpc_method]\ndef EuclideanDisplay.rpc (props : PanelWidgetProps) : RequestM (RequestTask Html) :=\n RequestM.asTask do\n let inner : Html ← (do\n if props.goals.isEmpty then\n return <span>No goals.</span>\n let some g := props.goals[0]? | unreachable!\n\n g.ctx.val.runMetaM {} do\n let md ← g.mvarId.getDecl\n let lctx := md.lctx |>.sanitizeNames.run' {options := (← getOptions)}\n Meta.withLCtx lctx md.localInstances do\n let mut hiddenLocs : HashSet FVarId := mkHashSet props.selectedLocations.size\n for l in props.selectedLocations do\n match l with\n | ⟨mv, .hyp fv⟩ | ⟨mv, .hypType fv _⟩ =>\n if mv == g.mvarId then\n hiddenLocs := hiddenLocs.insert fv\n | _ => continue\n let locs := (← getLCtx).decls.toArray.filterMap (fun d? =>\n if let some d := d? then\n if !hiddenLocs.contains d.fvarId then some d else none\n else\n none)\n DiagramBuilderM.run do\n addHypotheses locs\n match ← DiagramBuilderM.buildDiagram dsl sty with\n | some html => return html\n | none => return <span>No Euclidean goal.</span>)\n\n return <details «open»={true}>\n <summary className=\"mv2 pointer\">Euclidean diagram</summary>\n <div className=\"ml1\">{inner}</div>\n </details>", "start": [ 136, 1 ], "end": [ 175, 17 ], "kind": "commanddeclaration" }, { "full_name": "EuclideanDisplay", "code": "@[widget_module]\ndef EuclideanDisplay : Component PanelWidgetProps :=\n mk_rpc_widget% EuclideanDisplay.rpc", "start": [ 177, 1 ], "end": [ 179, 38 ], "kind": "commanddeclaration" }, { "full_name": "constructLines", "code": "def constructLines (hyps : Array LocalDecl) (meta : Server.DocumentMeta) (cursorPos : Lsp.Position)\n : DiagramBuilderM Unit := do\n let mut points : Array LocalDecl := {}\n let mut circleInters : Array (LocalDecl × LocalDecl × LocalDecl) := {}\n for h in hyps do\n let tp ← instantiateMVars h.type\n if isPoint? tp then\n points := points.push h\n if let some (.fvar C, .fvar D) := isCirclesInterPred? tp then\n circleInters := circleInters.push (h, ← C.getDecl, ← D.getDecl)\n\n let addConstruction (nm tp ctr : String) : DiagramBuilderM Unit := do\n addEmbed nm tp (\n <span>\n <b>{.text nm}</b> ({\n .ofComponent MakeEditLink\n (MakeEditLinkProps.ofReplaceRange meta ⟨cursorPos, cursorPos⟩ ctr)\n #[.text \"insert\"]\n })\n </span>)\n addInstruction s!\"Emphasize({nm})\"\n\n for hi : i in [0:points.size] do\n let p := points[i]\n let sp ← addExpr \"Point\" p.toExpr\n for hj : j in [i+1:points.size] do\n let q := points[j]\n let sq ← addExpr \"Point\" q.toExpr\n\n let nm := s!\"{sp}{sq}\"\n addConstruction nm \"Line\" s!\"let ⟨{nm}, _, _⟩ := line_of_pts {sp} {sq}\"\n addInstruction s!\"OnLine({sp}, {nm})\"\n addInstruction s!\"OnLine({sq}, {nm})\"\n\n let nm := s!\"C{sp}{sq}\"\n addConstruction nm \"Circle\" s!\"let ⟨{nm}, _, _⟩ := circle_of_ne {sp} {sq} (by assumption)\"\n addInstruction s!\"CenterCircle({sp}, {nm})\"\n addInstruction s!\"OnCircle({sq}, {nm})\"\n\n let nm := s!\"C{sq}{sp}\"\n addConstruction nm \"Circle\" s!\"let ⟨{nm}, _, _⟩ := circle_of_ne {sq} {sp} (by assumption)\"\n addInstruction s!\"CenterCircle({sq}, {nm})\"\n addInstruction s!\"OnCircle({sp}, {nm})\"\n\n for hi : i in [0:circleInters.size] do\n let (h, C, D) := circleInters[i]\n let sC ← addExpr \"Circle\" C.toExpr\n let sD ← addExpr \"Circle\" D.toExpr\n let nm := s!\"{sC}{sD}\"\n let nm' := s!\"{sD}{sC}\"\n addConstruction nm \"Point\" s!\"let ⟨{nm}, {nm'}, _, _, _, _, _⟩ := pts_of_circlesInter {h.userName}\"\n addEmbed nm' \"Point\" <b>{.text nm'}</b>\n addInstruction s!\"OnCircle({nm'}, {sC})\"\n addInstruction s!\"OnCircle({nm}, {sD})\"\n addInstruction s!\"OnCircle({nm}, {sC})\"\n addInstruction s!\"OnCircle({nm'}, {sD})\"", "start": [ 197, 1 ], "end": [ 261, 45 ], "kind": "commanddeclaration" }, { "full_name": "EuclideanConstructions.rpc", "code": "@[server_rpc_method]\ndef EuclideanConstructions.rpc (props : PanelWidgetProps) : RequestM (RequestTask Html) :=\n RequestM.asTask do\n let doc ← RequestM.readDoc\n let inner : Html ← (do\n if props.goals.isEmpty then\n return <span>No goals.</span>\n let some g := props.goals[0]? | unreachable!\n\n g.ctx.val.runMetaM {} do\n let md ← g.mvarId.getDecl\n let lctx := md.lctx |>.sanitizeNames.run' {options := (← getOptions)}\n Meta.withLCtx lctx md.localInstances do\n\n let allHyps := (← getLCtx).decls.toArray.filterMap id\n\n let selectedHyps ← props.selectedLocations.filterMapM fun\n | ⟨mv, .hyp fv⟩ | ⟨mv, .hypType fv _⟩ =>\n if mv == g.mvarId then return some (← fv.getDecl) else return none\n | _ =>\n return none\n\n DiagramBuilderM.run do\n addHypotheses allHyps\n constructLines selectedHyps doc.meta props.pos\n match ← DiagramBuilderM.buildDiagram EuclideanDisplay.dsl EuclideanDisplay.sty 1500 with\n | some html => return html\n | none => return <span>No Euclidean goal.</span>)\n\n return <details «open»={true}>\n <summary className=\"mv2 pointer\">Euclidean constructions</summary>\n <div className=\"ml1\">{inner}</div>\n </details>", "start": [ 264, 1 ], "end": [ 302, 17 ], "kind": "commanddeclaration" }, { "full_name": "EuclideanConstructions", "code": "@[widget_module]\ndef EuclideanConstructions : Component PanelWidgetProps :=\n mk_rpc_widget% EuclideanConstructions.rpc", "start": [ 304, 1 ], "end": [ 306, 44 ], "kind": "commanddeclaration" }, { "full_name": "test_sorry", "code": "axiom test_sorry {α} : α", "start": [ 308, 1 ], "end": [ 308, 25 ], "kind": "commanddeclaration" } ]

.lake/packages/proofwidgets/ProofWidgets/Demos/Rubiks.lean

[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean" ]

[ { "full_name": "RubiksProps", "code": "structure RubiksProps where\n seq : Array String := #[]\n deriving ToJson, FromJson, Inhabited", "start": [ 6, 1 ], "end": [ 8, 39 ], "kind": "commanddeclaration" }, { "full_name": "Rubiks", "code": "@[widget_module]\ndef Rubiks : Component RubiksProps where\n javascript := include_str \"..\" / \"..\" / \".lake\" / \"build\" / \"js\" / \"rubiks.js\"", "start": [ 10, 1 ], "end": [ 12, 81 ], "kind": "commanddeclaration" }, { "full_name": "eg", "code": "def eg := #[\"L\", \"L\", \"D⁻¹\", \"U⁻¹\", \"L\", \"D\", \"D\", \"L\", \"U⁻¹\", \"R\", \"D\", \"F\", \"F\", \"D\"]", "start": [ 14, 1 ], "end": [ 14, 88 ], "kind": "commanddeclaration" } ]

.lake/packages/proofwidgets/ProofWidgets/Demos/Macro.lean

[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean" ]

[ { "full_name": "Lean.SourceInfo.mkCanonical", "code": "def Lean.SourceInfo.mkCanonical : SourceInfo → SourceInfo\n | .synthetic s e _ => .synthetic s e true\n | si => si", "start": [ 13, 1 ], "end": [ 15, 13 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Syntax.mkInfoCanonical", "code": "def Lean.Syntax.mkInfoCanonical : Syntax → Syntax\n | .missing => .missing\n | .node i k a => .node i.mkCanonical k a\n | .atom i v => .atom i.mkCanonical v\n | .ident i r v p => .ident i.mkCanonical r v p", "start": [ 17, 1 ], "end": [ 21, 49 ], "kind": "commanddeclaration" }, { "full_name": "Lean.TSyntax.mkInfoCanonical", "code": "def Lean.TSyntax.mkInfoCanonical : TSyntax k → TSyntax k :=\n (.mk ·.raw.mkInfoCanonical)", "start": [ 23, 1 ], "end": [ 24, 30 ], "kind": "commanddeclaration" } ]

.lake/packages/proofwidgets/ProofWidgets/Demos/Jsx.lean

[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean" ]

[ { "full_name": "htmlLetters", "code": "def htmlLetters : Array ProofWidgets.Html := #[\n <span style={json% {color: \"red\"}}>H</span>,\n <span style={json% {color: \"yellow\"}}>T</span>,\n <span style={json% {color: \"green\"}}>M</span>,\n <span style={json% {color: \"blue\"}}>L</span>\n ]", "start": [ 13, 1 ], "end": [ 18, 4 ], "kind": "commanddeclaration" }, { "full_name": "x", "code": "def x := <b>You can use {...htmlLetters} in Lean {.text s!\"{1 + 3}\"}! <hr/> </b>", "start": [ 21, 1 ], "end": [ 21, 81 ], "kind": "commanddeclaration" } ]

.lake/packages/proofwidgets/ProofWidgets/Demos/LazyComputation.lean

[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Basic.lean" ]

[ { "full_name": "MetaMStringCont", "code": "structure MetaMStringCont where\n ci : Elab.ContextInfo\n lctx : LocalContext\n k : MetaM String\n deriving TypeName", "start": [ 6, 1 ], "end": [ 12, 20 ], "kind": "commanddeclaration" }, { "full_name": "RunnerWidgetProps", "code": "structure RunnerWidgetProps where\n \n k : WithRpcRef MetaMStringCont\n deriving RpcEncodable", "start": [ 14, 1 ], "end": [ 18, 24 ], "kind": "commanddeclaration" }, { "full_name": "runMetaMStringCont", "code": "@[server_rpc_method]\ndef runMetaMStringCont : RunnerWidgetProps → RequestM (RequestTask String)\n | {k := ⟨{ci, lctx, k}⟩} => RequestM.asTask do\n ci.runMetaM lctx k", "start": [ 20, 1 ], "end": [ 23, 23 ], "kind": "commanddeclaration" }, { "full_name": "runnerWidget", "code": "@[widget_module]\ndef runnerWidget : Component RunnerWidgetProps where\n javascript := \"\n import { RpcContext, mapRpcError } from '@leanprover/infoview'\n import * as React from 'react';\n const e = React.createElement;\n\n export default function(props) {\n const [contents, setContents] = React.useState('Run!')\n const rs = React.useContext(RpcContext)\n return e('button', { onClick: () => {\n setContents('Running..')\n rs.call('runMetaMStringCont', props)\n .then(setContents)\n .catch(e => { setContents(mapRpcError(e).message) })\n }}, contents)\n }\n \"", "start": [ 25, 1 ], "end": [ 42, 4 ], "kind": "commanddeclaration" }, { "full_name": "makeRunner", "code": "@[tactic makeRunnerTac] def makeRunner : Tactic\n | `(tactic| make_runner%$tk) => do\n let x : MetaM String := do\n return \"Hello, world!\"\n let props : RunnerWidgetProps := {\n k := ⟨{\n ci := { ← CommandContextInfo.save with }\n lctx := (← getLCtx)\n k := x\n }⟩}\n Widget.savePanelWidgetInfo runnerWidget.javascriptHash (rpcEncode props) tk\n | _ => throwUnsupportedSyntax", "start": [ 46, 1 ], "end": [ 59, 32 ], "kind": "commanddeclaration" } ]

.lake/packages/proofwidgets/ProofWidgets/Demos/Dynkin.lean

[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean" ]

[ { "full_name": "List.product", "code": "def List.product : List α → List β → List (α × β)\n | [], _ => []\n | a::as, bs => bs.map ((a, ·)) ++ as.product bs", "start": [ 6, 1 ], "end": [ 8, 50 ], "kind": "commanddeclaration" }, { "full_name": "Matrix", "code": "def Matrix (n m α : Type) := n → m → α", "start": [ 10, 1 ], "end": [ 10, 39 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.nat_index", "code": "def nat_index (i j : Nat) : Int :=\n if h : i < n ∧ j < n then A ⟨i, h.1⟩ ⟨j, h.2⟩ else 999", "start": [ 19, 1 ], "end": [ 20, 57 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_node_pos_E", "code": "def get_node_pos_E : Nat → Nat × Nat\n | 0 => ⟨0, 0⟩\n | 1 => ⟨2, 1⟩\n | (i+1) => ⟨i, 0⟩", "start": [ 22, 1 ], "end": [ 26, 20 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_node_pos", "code": "def get_node_pos (n : Nat) : Nat → Nat × Nat := if n < 6 then ((·, 0)) else get_node_pos_E", "start": [ 28, 1 ], "end": [ 29, 91 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_node_cx", "code": "def get_node_cx (n i : Nat) : Int := 20 + (get_node_pos n i).1 * 40", "start": [ 31, 1 ], "end": [ 31, 68 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_node_cy", "code": "def get_node_cy (n i : Nat) : Int := 20 + (get_node_pos n i).2 * 40", "start": [ 33, 1 ], "end": [ 33, 68 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_node_html", "code": "def get_node_html (n i : Nat) : Html :=\n <circle\n cx={toString <| get_node_cx n i}\n cy={toString <| get_node_cy n i}\n r=\"10\"\n fill=\"white\"\n stroke=\"black\" />", "start": [ 35, 1 ], "end": [ 41, 22 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_edge_html", "code": "def get_edge_html : Nat × Nat → List Html\n | (i, j) => if A.nat_index i j = 0 then [] else\n [<line\n x1={toString <| get_node_cx n i}\n y1={toString <| get_node_cy n i}\n x2={toString <| get_node_cx n j}\n y2={toString <| get_node_cy n j}\n fill=\"black\"\n stroke=\"black\" />]", "start": [ 43, 1 ], "end": [ 56, 24 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_nodes_html", "code": "def get_nodes_html (n : Nat) : List Html :=\n (List.range n).map (get_node_html n)", "start": [ 58, 1 ], "end": [ 59, 39 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.get_edges_html", "code": "def get_edges_html : List Html := Id.run do\n let mut out := []\n for j in [:n] do\n for i in [:j] do\n out := A.get_edge_html (i, j) ++ out\n return out", "start": [ 61, 1 ], "end": [ 66, 13 ], "kind": "commanddeclaration" }, { "full_name": "Matrix.toHtml", "code": "def toHtml (M : Matrix (Fin n) (Fin n) Int) : Html :=\n <div style={json% { height: \"100px\", width: \"300px\", background: \"grey\" }}>\n {Html.element \"svg\" #[] (M.get_edges_html ++ Matrix.get_nodes_html n).toArray}\n </div>", "start": [ 68, 1 ], "end": [ 71, 9 ], "kind": "commanddeclaration" }, { "full_name": "cartanMatrix.E₈", "code": "def cartanMatrix.E₈ : Matrix (Fin 8) (Fin 8) Int :=\n fun i j =>\n [[ 2, 0, -1, 0, 0, 0, 0, 0],\n [ 0, 2, 0, -1, 0, 0, 0, 0],\n [-1, 0, 2, -1, 0, 0, 0, 0],\n [ 0, -1, -1, 2, -1, 0, 0, 0],\n [ 0, 0, 0, -1, 2, -1, 0, 0],\n [ 0, 0, 0, 0, -1, 2, -1, 0],\n [ 0, 0, 0, 0, 0, -1, 2, -1],\n [ 0, 0, 0, 0, 0, 0, -1, 2]].get! i |>.get! j", "start": [ 75, 1 ], "end": [ 84, 56 ], "kind": "commanddeclaration" } ]

.lake/packages/proofwidgets/ProofWidgets/Demos/ExprPresentation.lean

[ ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/SelectionPanel.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/GoalTypePanel.lean" ]

[ { "full_name": "presenter", "code": "@[expr_presenter]\ndef presenter : ExprPresenter where\n userName := \"With octopodes\"\n layoutKind := .inline\n present e :=\n return <span>\n {.text \"🐙 \"}<InteractiveCode fmt={← Lean.Widget.ppExprTagged e} />{.text \" 🐙\"}\n </span>", "start": [ 6, 1 ], "end": [ 13, 14 ], "kind": "commanddeclaration" } ]

.lake/packages/proofwidgets/ProofWidgets/Demos/RbTree.lean

[ ".lake/packages/proofwidgets/ProofWidgets/Component/Panel/SelectionPanel.lean", ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Presentation/Expr.lean" ]

[ { "full_name": "RBColour", "code": "inductive RBColour where\n | red | black", "start": [ 7, 1 ], "end": [ 8, 16 ], "kind": "commanddeclaration" }, { "full_name": "RBTree", "code": "inductive RBTree (α : Type u) where\n | empty : RBTree α\n | node (color : RBColour) (l : RBTree α) (a : α) (r : RBTree α) : RBTree α", "start": [ 10, 1 ], "end": [ 12, 77 ], "kind": "commanddeclaration" }, { "full_name": "RBTree.contains", "code": "def contains [Ord α] (a : α) : RBTree α → Bool\n | empty => false\n | node _ l b r => match compare a b with\n | .lt => l.contains a\n | .eq => true\n | .gt => r.contains a", "start": [ 16, 1 ], "end": [ 21, 26 ], "kind": "commanddeclaration" }, { "full_name": "RBTree.balance", "code": "def balance : RBColour → RBTree α → α → RBTree α → RBTree α\n | .black, (node .red (node .red a x b) y c), z, d\n | .black, (node .red a x (node .red b y c)), z, d\n | .black, a, x, (node .red (node .red b y c) z d)\n | .black, a, x, (node .red b y (node .red c z d)) =>\n node .red (node .black a x b) y (node .black c z d)\n | color, a, x, b => node color a x b", "start": [ 23, 1 ], "end": [ 29, 39 ], "kind": "commanddeclaration" }, { "full_name": "RBTree.insert", "code": "def insert [Ord α] (a : α) (s : RBTree α) : RBTree α :=\n makeBlack (ins s)\nwhere\n ins : RBTree α → RBTree α\n | empty => node .red empty a empty\n | node c l b r => match compare a b with\n | .lt => balance c (ins l) b r\n | .eq => node c l b r\n | .gt => balance c l b (ins r)\n makeBlack : RBTree α → RBTree α\n | empty => empty\n | node _ l b r => node .black l b r", "start": [ 31, 1 ], "end": [ 42, 40 ], "kind": "commanddeclaration" }, { "full_name": "empty?", "code": "def empty? (e : Expr) : Bool :=\n e.app1? ``RBTree.empty matches some _", "start": [ 50, 1 ], "end": [ 51, 40 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Expr.app5?", "code": "@[inline] def Lean.Expr.app5? (e : Expr) (fName : Name) : Option (Expr × Expr × Expr × Expr × Expr) :=\n if e.isAppOfArity fName 5 then\n some (\n e.appFn!.appFn!.appFn!.appFn!.appArg!,\n e.appFn!.appFn!.appFn!.appArg!,\n e.appFn!.appFn!.appArg!,\n e.appFn!.appArg!,\n e.appArg!)\n else\n none", "start": [ 53, 1 ], "end": [ 62, 9 ], "kind": "commanddeclaration" }, { "full_name": "node?", "code": "def node? (e : Expr) : Option (Expr × Expr × Expr × Expr) := do\n let some (_, color, l, a, r) := e.app5? ``RBTree.node | none\n return (color, l, a, r)", "start": [ 64, 1 ], "end": [ 66, 26 ], "kind": "commanddeclaration" }, { "full_name": "evalColourUnsafe", "code": "unsafe def evalColourUnsafe (e : Expr) : MetaM RBColour :=\n Lean.Meta.evalExpr' RBColour ``RBColour e", "start": [ 68, 1 ], "end": [ 69, 44 ], "kind": "commanddeclaration" }, { "full_name": "evalColour", "code": "@[implemented_by evalColourUnsafe]\nopaque evalColour (e : Expr) : MetaM RBColour", "start": [ 71, 1 ], "end": [ 72, 46 ], "kind": "commanddeclaration" }, { "full_name": "RBTreeVarsColour", "code": "inductive RBTreeVarsColour where\n | red | black | blue\n deriving FromJson, ToJson", "start": [ 74, 1 ], "end": [ 77, 28 ], "kind": "commanddeclaration" }, { "full_name": "RBTreeVars", "code": "inductive RBTreeVars where\n | empty : RBTreeVars\n | var : CodeWithInfos → RBTreeVars\n | node (color : RBTreeVarsColour) (l : RBTreeVars) (a : CodeWithInfos) (r : RBTreeVars) : RBTreeVars\n deriving Server.RpcEncodable", "start": [ 80, 1 ], "end": [ 89, 31 ], "kind": "commanddeclaration" }, { "full_name": "RBDisplayProps", "code": "structure RBDisplayProps where\n tree : RBTreeVars\n deriving Server.RpcEncodable", "start": [ 93, 1 ], "end": [ 95, 31 ], "kind": "commanddeclaration" }, { "full_name": "RBDisplay", "code": "@[widget_module]\ndef RBDisplay : Component RBDisplayProps where\n javascript := include_str \"..\" / \"..\" / \".lake\" / \"build\" / \"js\" / \"rbTree.js\"", "start": [ 99, 1 ], "end": [ 101, 81 ], "kind": "commanddeclaration" }, { "full_name": "drawTree?", "code": "partial def drawTree? (e : Expr) : MetaM (Option Html) := do\n if let some _ := node? e then\n return some <RBDisplay tree={← go e}/>\n else if empty? e then\n return some <RBDisplay tree={← go e}/>\n else\n return none\nwhere go (e : Expr) : MetaM RBTreeVars := do\n if let some (color, l, a, r) := node? e then\n let color ← try\n match ← evalColour color with\n | .red => pure .red\n | .black => pure .black\n catch _ => pure .blue\n return .node color (← go l) (← Widget.ppExprTagged a) (← go r)\n else if empty? e then\n return .empty\n else\n return .var (← Widget.ppExprTagged e)", "start": [ 104, 1 ], "end": [ 122, 42 ], "kind": "commanddeclaration" }, { "full_name": "RBTree.presenter", "code": "@[expr_presenter]\ndef RBTree.presenter : ExprPresenter where\n userName := \"Red-black tree\"\n present e := do\n let some t ← drawTree? e\n | throwError \"not a tree :(\"\n return t", "start": [ 124, 1 ], "end": [ 130, 13 ], "kind": "commanddeclaration" } ]

.lake/packages/proofwidgets/ProofWidgets/Demos/Svg.lean

[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/proofwidgets/ProofWidgets/Component/HtmlDisplay.lean", ".lake/packages/proofwidgets/ProofWidgets/Data/Svg.lean" ]

[ { "full_name": "frame", "code": "private def frame : Frame where\n xmin := -2\n ymin := -2\n xSize := 4\n width := 400\n height := 400", "start": [ 6, 1 ], "end": [ 11, 16 ], "kind": "commanddeclaration" }, { "full_name": "svg", "code": "private def svg : Svg frame :=\n { elements :=\n #[line (0.,0.) (1.,0.) |>.setStroke (1.,0.,0.) (.px 2),\n line (1.,0.) (0.,1.) |>.setStroke (0.,1.,0.) (.px 2),\n line (0.,1.) (0.,0.) |>.setStroke (0.,0.,1.) (.px 2),\n circle (0.,0.) (.abs 0.1) |>.setStroke (0.,0.,0.) (.px 2) |>.setFill (0.,1.,1.) |>.setId \"point1\",\n circle (1.,0.) (.abs 0.1) |>.setStroke (0.,0.,0.) (.px 2) |>.setFill (1.,0.,1.) |>.setId \"point2\",\n circle (0.,1.) (.abs 0.1) |>.setStroke (0.,0.,0.) (.px 2) |>.setFill (1.,1.,0.) |>.setId \"point3\"] }", "start": [ 13, 1 ], "end": [ 20, 109 ], "kind": "commanddeclaration" } ]

.lake/packages/lean4/src/lean/Lean/Compiler/IR/EmitLLVM.lean

[ ".lake/packages/lean4/src/lean/Lean/Compiler/ExportAttr.lean", ".lake/packages/lean4/src/lean/Lean/Runtime.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/EmitUtil.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/ResetReuse.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/Boxing.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/SimpCase.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/NameMangling.lean", ".lake/packages/lean4/src/lean/Lean/Data/HashMap.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/InitAttr.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/NormIds.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/CompilerM.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/IR/LLVMBindings.lean" ]

[ { "full_name": "Lean.IR.leanMainFn", "code": "def leanMainFn := \"_lean_main\"", "start": [ 24, 1 ], "end": [ 24, 31 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.LLVM.size_tType", "code": "def size_tType (llvmctx : LLVM.Context) : BaseIO (LLVM.LLVMType llvmctx) :=\n LLVM.i64Type llvmctx", "start": [ 28, 1 ], "end": [ 29, 23 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.LLVM.unsignedType", "code": "def unsignedType (llvmctx : LLVM.Context) : BaseIO (LLVM.LLVMType llvmctx) :=\n LLVM.i32Type llvmctx", "start": [ 32, 1 ], "end": [ 33, 23 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.LLVM.getOrAddFunction", "code": "def getOrAddFunction (m : LLVM.Module ctx) (name : String) (type : LLVM.LLVMType ctx) : BaseIO (LLVM.Value ctx) := do\n match (← LLVM.getNamedFunction m name) with\n | some fn => return fn\n | none =>\n \n let fn ← LLVM.addFunction m name type\n let attr ← LLVM.createStringAttribute \"probe-stack\" \"inline-asm\"\n LLVM.addAttributeAtIndex fn LLVM.AttributeIndex.AttributeFunctionIndex attr\n return fn", "start": [ 36, 1 ], "end": [ 48, 14 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.LLVM.getOrAddGlobal", "code": "def getOrAddGlobal (m : LLVM.Module ctx) (name : String) (type : LLVM.LLVMType ctx) : BaseIO (LLVM.Value ctx) := do\n match (← LLVM.getNamedGlobal m name) with\n | .some fn => return fn\n | .none => LLVM.addGlobal m name type", "start": [ 50, 1 ], "end": [ 53, 40 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.Context", "code": "structure Context (llvmctx : LLVM.Context) where\n env : Environment\n modName : Name\n jpMap : JPParamsMap := {}\n mainFn : FunId := default\n mainParams : Array Param := #[]\n llvmmodule : LLVM.Module llvmctx", "start": [ 59, 1 ], "end": [ 65, 35 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.State", "code": "structure State (llvmctx : LLVM.Context) where\n var2val : HashMap VarId (LLVM.LLVMType llvmctx × LLVM.Value llvmctx)\n jp2bb : HashMap JoinPointId (LLVM.BasicBlock llvmctx)", "start": [ 67, 1 ], "end": [ 69, 58 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.Error", "code": "abbrev Error := String", "start": [ 71, 1 ], "end": [ 71, 23 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.M", "code": "abbrev M (llvmctx : LLVM.Context) :=\n StateRefT (State llvmctx) (ReaderT (Context llvmctx) (ExceptT Error IO))", "start": [ 73, 1 ], "end": [ 74, 75 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.addVartoState", "code": "def addVartoState (x : VarId) (v : LLVM.Value llvmctx) (ty : LLVM.LLVMType llvmctx) : M llvmctx Unit := do\n modify (fun s => { s with var2val := s.var2val.insert x (ty, v) })", "start": [ 79, 1 ], "end": [ 80, 69 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.addJpTostate", "code": "def addJpTostate (jp : JoinPointId) (bb : LLVM.BasicBlock llvmctx) : M llvmctx Unit :=\n modify (fun s => { s with jp2bb := s.jp2bb.insert jp bb })", "start": [ 82, 1 ], "end": [ 83, 61 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitJp", "code": "def emitJp (jp : JoinPointId) : M llvmctx (LLVM.BasicBlock llvmctx) := do\n let state ← get\n match state.jp2bb.find? jp with\n | .some bb => return bb\n | .none => throw s!\"unable to find join point {jp}\"", "start": [ 85, 1 ], "end": [ 89, 54 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getLLVMModule", "code": "def getLLVMModule : M llvmctx (LLVM.Module llvmctx) := Context.llvmmodule <$> read", "start": [ 91, 1 ], "end": [ 91, 83 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getEnv", "code": "def getEnv : M llvmctx Environment := Context.env <$> read", "start": [ 93, 1 ], "end": [ 93, 59 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getModName", "code": "def getModName : M llvmctx Name := Context.modName <$> read", "start": [ 95, 1 ], "end": [ 95, 61 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getDecl", "code": "def getDecl (n : Name) : M llvmctx Decl := do\n let env ← getEnv\n match findEnvDecl env n with\n | some d => pure d\n | none => throw s!\"unknown declaration {n}\"", "start": [ 97, 1 ], "end": [ 101, 48 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.constInt8", "code": "def constInt8 (n : Nat) : M llvmctx (LLVM.Value llvmctx) := do\n LLVM.constInt8 llvmctx (UInt64.ofNat n)", "start": [ 103, 1 ], "end": [ 104, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.constInt64", "code": "def constInt64 (n : Nat) : M llvmctx (LLVM.Value llvmctx) := do\n LLVM.constInt64 llvmctx (UInt64.ofNat n)", "start": [ 106, 1 ], "end": [ 107, 45 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.constIntSizeT", "code": "def constIntSizeT (n : Nat) : M llvmctx (LLVM.Value llvmctx) := do\n LLVM.constIntSizeT llvmctx (UInt64.ofNat n)", "start": [ 109, 1 ], "end": [ 110, 48 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.constIntUnsigned", "code": "def constIntUnsigned (n : Nat) : M llvmctx (LLVM.Value llvmctx) := do\n LLVM.constIntUnsigned llvmctx (UInt64.ofNat n)", "start": [ 112, 1 ], "end": [ 113, 51 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getOrCreateFunctionPrototype", "code": "def getOrCreateFunctionPrototype (mod : LLVM.Module llvmctx)\n (retty : LLVM.LLVMType llvmctx) (name : String) (args : Array (LLVM.LLVMType llvmctx)) : M llvmctx (LLVM.Value llvmctx) := do\n LLVM.getOrAddFunction mod name $ ← LLVM.functionType retty args (isVarArg := false)", "start": [ 115, 1 ], "end": [ 117, 86 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanBox", "code": "def callLeanBox (builder : LLVM.Builder llvmctx)\n (arg : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_box\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[ ← LLVM.size_tType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[arg] name", "start": [ 119, 1 ], "end": [ 126, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanMarkPersistentFn", "code": "def callLeanMarkPersistentFn (builder : LLVM.Builder llvmctx) (arg : LLVM.Value llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_mark_persistent\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[arg]", "start": [ 128, 1 ], "end": [ 134, 52 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.RefcountKind", "code": "inductive RefcountKind where\n | inc | dec", "start": [ 137, 1 ], "end": [ 138, 14 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanRefcountFn", "code": "def callLeanRefcountFn (builder : LLVM.Builder llvmctx)\n (kind : RefcountKind) (checkRef? : Bool) (arg : LLVM.Value llvmctx)\n (delta : Option (LLVM.Value llvmctx) := Option.none) : M llvmctx Unit := do\n let fnName := s!\"lean_{kind}{if checkRef? then \"\" else \"_ref\"}{if delta.isNone then \"\" else \"_n\"}\"\n let retty ← LLVM.voidType llvmctx\n let argtys ← if delta.isNone then pure #[← LLVM.voidPtrType llvmctx] else pure #[← LLVM.voidPtrType llvmctx, ← LLVM.size_tType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n match delta with\n | .none => do\n let _ ← LLVM.buildCall2 builder fnty fn #[arg]\n | .some n => do\n let _ ← LLVM.buildCall2 builder fnty fn #[arg, n]", "start": [ 145, 1 ], "end": [ 158, 54 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanDecRef", "code": "def callLeanDecRef (builder : LLVM.Builder llvmctx) (res : LLVM.Value llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_dec_ref\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.i8PtrType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[res]", "start": [ 163, 1 ], "end": [ 169, 50 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanUnsignedToNatFn", "code": "def callLeanUnsignedToNatFn (builder : LLVM.Builder llvmctx)\n (n : Nat) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let mod ← getLLVMModule\n let argtys := #[← LLVM.i32Type llvmctx]\n let retty ← LLVM.voidPtrType llvmctx\n let f ← getOrCreateFunctionPrototype mod retty \"lean_unsigned_to_nat\" argtys\n let fnty ← LLVM.functionType retty argtys\n let nv ← constIntUnsigned n\n LLVM.buildCall2 builder fnty f #[nv] name", "start": [ 171, 1 ], "end": [ 179, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanMkStringUncheckedFn", "code": "def callLeanMkStringUncheckedFn (builder : LLVM.Builder llvmctx)\n (strPtr nBytes nChars : LLVM.Value llvmctx) (name : String) : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_mk_string_unchecked\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[← LLVM.voidPtrType llvmctx, ← LLVM.size_tType llvmctx, ← LLVM.size_tType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[strPtr, nBytes, nChars] name", "start": [ 181, 1 ], "end": [ 188, 65 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanMkString", "code": "def callLeanMkString (builder : LLVM.Builder llvmctx)\n (strPtr : LLVM.Value llvmctx) (name : String) : M llvmctx (LLVM.Value llvmctx) := do\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty \"lean_mk_string\" argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[strPtr] name", "start": [ 190, 1 ], "end": [ 196, 49 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanCStrToNatFn", "code": "def callLeanCStrToNatFn (builder : LLVM.Builder llvmctx)\n (n : Nat) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_cstr_to_nat\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let s ← LLVM.buildGlobalString builder (value := toString n)\n LLVM.buildCall2 builder fnty fn #[s] name", "start": [ 198, 1 ], "end": [ 206, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOMkWorld", "code": "def callLeanIOMkWorld (builder : LLVM.Builder llvmctx) : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_io_mk_world\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[] \"mk_io_out\"", "start": [ 208, 1 ], "end": [ 214, 50 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOResultIsError", "code": "def callLeanIOResultIsError (builder : LLVM.Builder llvmctx)\n (arg : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_io_result_is_error\"\n let retty ← LLVM.i1Type llvmctx\n let argtys := #[← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[arg] name", "start": [ 216, 1 ], "end": [ 223, 46 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanAllocCtor", "code": "def callLeanAllocCtor (builder : LLVM.Builder llvmctx)\n (tag num_objs scalar_sz : Nat) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_alloc_ctor\"\n let retty ← LLVM.voidPtrType llvmctx\n let i32 ← LLVM.i32Type llvmctx\n let argtys := #[i32, i32, i32]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n\n let tag ← constIntUnsigned tag\n let num_objs ← constIntUnsigned num_objs\n let scalar_sz ← constIntUnsigned scalar_sz\n LLVM.buildCall2 builder fnty fn #[tag, num_objs, scalar_sz] name", "start": [ 225, 1 ], "end": [ 237, 67 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanCtorSet", "code": "def callLeanCtorSet (builder : LLVM.Builder llvmctx)\n (o i v : LLVM.Value llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_ctor_set\"\n let retty ← LLVM.voidType llvmctx\n let voidptr ← LLVM.voidPtrType llvmctx\n let unsigned ← LLVM.unsignedType llvmctx\n let argtys := #[voidptr, unsigned, voidptr]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n _ <- LLVM.buildCall2 builder fnty fn #[o, i, v]", "start": [ 239, 1 ], "end": [ 248, 51 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOResultMKOk", "code": "def callLeanIOResultMKOk (builder : LLVM.Builder llvmctx)\n (v : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_io_result_mk_ok\"\n let voidptr ← LLVM.voidPtrType llvmctx\n let retty := voidptr\n let argtys := #[voidptr]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[v] name", "start": [ 250, 1 ], "end": [ 258, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanAllocClosureFn", "code": "def callLeanAllocClosureFn (builder : LLVM.Builder llvmctx)\n (f arity nys : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_alloc_closure\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx, ← LLVM.unsignedType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[f, arity, nys] retName", "start": [ 260, 1 ], "end": [ 267, 60 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanClosureSetFn", "code": "def callLeanClosureSetFn (builder : LLVM.Builder llvmctx)\n (closure ix arg : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx Unit := do\n let fnName := \"lean_closure_set\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx, ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[closure, ix, arg] retName", "start": [ 269, 1 ], "end": [ 276, 71 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanObjTag", "code": "def callLeanObjTag (builder : LLVM.Builder llvmctx)\n (closure : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_obj_tag\"\n let retty ← LLVM.i32Type llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let out ← LLVM.buildCall2 builder fnty fn #[closure] retName\n LLVM.buildSextOrTrunc builder out (← LLVM.i64Type llvmctx)", "start": [ 278, 1 ], "end": [ 286, 61 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOResultGetValue", "code": "def callLeanIOResultGetValue (builder : LLVM.Builder llvmctx)\n (v : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_io_result_get_value\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[v] name", "start": [ 288, 1 ], "end": [ 295, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanCtorRelease", "code": "def callLeanCtorRelease (builder : LLVM.Builder llvmctx)\n (closure i : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx Unit := do\n let fnName := \"lean_ctor_release\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[closure, i] retName", "start": [ 297, 1 ], "end": [ 304, 65 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanCtorSetTag", "code": "def callLeanCtorSetTag (builder : LLVM.Builder llvmctx)\n (closure i : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx Unit := do\n let fnName := \"lean_ctor_set_tag\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.i8Type llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[closure, i] retName", "start": [ 306, 1 ], "end": [ 313, 65 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.toLLVMType", "code": "def toLLVMType (t : IRType) : M llvmctx (LLVM.LLVMType llvmctx) := do\n match t with\n | IRType.float => LLVM.doubleTypeInContext llvmctx\n | IRType.uint8 => LLVM.intTypeInContext llvmctx 8\n | IRType.uint16 => LLVM.intTypeInContext llvmctx 16\n | IRType.uint32 => LLVM.intTypeInContext llvmctx 32\n | IRType.uint64 => LLVM.intTypeInContext llvmctx 64\n | IRType.usize => LLVM.size_tType llvmctx\n | IRType.object => do LLVM.pointerType (← LLVM.i8Type llvmctx)\n | IRType.tobject => do LLVM.pointerType (← LLVM.i8Type llvmctx)\n | IRType.irrelevant => do LLVM.pointerType (← LLVM.i8Type llvmctx)\n | IRType.struct _ _ => panic! \"not implemented yet\"\n | IRType.union _ _ => panic! \"not implemented yet\"", "start": [ 315, 1 ], "end": [ 328, 54 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.throwInvalidExportName", "code": "def throwInvalidExportName {α : Type} (n : Name) : M llvmctx α := do\n throw s!\"invalid export name {n.toString}\"", "start": [ 330, 1 ], "end": [ 331, 45 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.toCName", "code": "def toCName (n : Name) : M llvmctx String := do\n match getExportNameFor? (← getEnv) n with\n | some (.str .anonymous s) => pure s\n | some _ => throwInvalidExportName n\n | none => if n == `main then pure leanMainFn else pure n.mangle", "start": [ 333, 1 ], "end": [ 337, 86 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.toCInitName", "code": "def toCInitName (n : Name) : M llvmctx String := do\n match getExportNameFor? (← getEnv) n with\n | some (.str .anonymous s) => return \"_init_\" ++ s\n | some _ => throwInvalidExportName n\n | none => pure (\"_init_\" ++ n.mangle)", "start": [ 339, 1 ], "end": [ 343, 60 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.ShouldForwardControlFlow", "code": "inductive ShouldForwardControlFlow where\n| yes | no", "start": [ 345, 1 ], "end": [ 352, 11 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.builderGetInsertionFn", "code": "def builderGetInsertionFn (builder : LLVM.Builder llvmctx) : M llvmctx (LLVM.Value llvmctx) := do\n let builderBB ← LLVM.getInsertBlock builder\n LLVM.getBasicBlockParent builderBB", "start": [ 355, 1 ], "end": [ 357, 37 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.builderAppendBasicBlock", "code": "def builderAppendBasicBlock (builder : LLVM.Builder llvmctx) (name : String) : M llvmctx (LLVM.BasicBlock llvmctx) := do\n let fn ← builderGetInsertionFn builder\n LLVM.appendBasicBlockInContext llvmctx fn name", "start": [ 359, 1 ], "end": [ 361, 49 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.buildPrologueAlloca", "code": "def buildPrologueAlloca (builder : LLVM.Builder llvmctx) (ty : LLVM.LLVMType llvmctx) (name : @&String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let origBB ← LLVM.getInsertBlock builder\n\n let fn ← builderGetInsertionFn builder\n if (← LLVM.countBasicBlocks fn) == 0 then\n throw \"Attempt to obtain first BB of function without BBs\"\n\n let entryBB ← LLVM.getEntryBasicBlock fn\n match ← LLVM.getFirstInstruction entryBB with\n | some instr => LLVM.positionBuilderBefore builder instr\n | none => LLVM.positionBuilderAtEnd builder entryBB\n\n let alloca ← LLVM.buildAlloca builder ty name\n LLVM.positionBuilderAtEnd builder origBB\n return alloca", "start": [ 363, 1 ], "end": [ 385, 16 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.buildWhile_", "code": "def buildWhile_ (builder : LLVM.Builder llvmctx) (name : String)\n (condcodegen : LLVM.Builder llvmctx → M llvmctx (LLVM.Value llvmctx))\n (bodycodegen : LLVM.Builder llvmctx → M llvmctx Unit) : M llvmctx Unit := do\n let fn ← builderGetInsertionFn builder\n\n let nameHeader := name ++ \"header\"\n let nameBody := name ++ \"body\"\n let nameMerge := name ++ \"merge\"\n\n let headerbb ← LLVM.appendBasicBlockInContext llvmctx fn nameHeader\n let _ ← LLVM.buildBr builder headerbb\n\n let bodybb ← LLVM.appendBasicBlockInContext llvmctx fn nameBody\n let mergebb ← LLVM.appendBasicBlockInContext llvmctx fn nameMerge\n\n LLVM.positionBuilderAtEnd builder headerbb\n let cond ← condcodegen builder\n let _ ← LLVM.buildCondBr builder cond bodybb mergebb\n\n LLVM.positionBuilderAtEnd builder bodybb\n bodycodegen builder\n let _ ← LLVM.buildBr builder headerbb\n\n LLVM.positionBuilderAtEnd builder mergebb", "start": [ 388, 1 ], "end": [ 415, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.buildIfThen_", "code": "def buildIfThen_ (builder : LLVM.Builder llvmctx) (name : String) (brval : LLVM.Value llvmctx)\n (thencodegen : LLVM.Builder llvmctx → M llvmctx ShouldForwardControlFlow) : M llvmctx Unit := do\n let fn ← builderGetInsertionFn builder\n\n let nameThen := name ++ \"Then\"\n let nameElse := name ++ \"Else\"\n let nameMerge := name ++ \"Merge\"\n\n let thenbb ← LLVM.appendBasicBlockInContext llvmctx fn nameThen\n let elsebb ← LLVM.appendBasicBlockInContext llvmctx fn nameElse\n let mergebb ← LLVM.appendBasicBlockInContext llvmctx fn nameMerge\n let _ ← LLVM.buildCondBr builder brval thenbb elsebb\n LLVM.positionBuilderAtEnd builder thenbb\n let fwd? ← thencodegen builder\n match fwd? with\n | .yes => let _ ← LLVM.buildBr builder mergebb\n | .no => pure ()\n LLVM.positionBuilderAtEnd builder elsebb\n let _ ← LLVM.buildBr builder mergebb\n LLVM.positionBuilderAtEnd builder mergebb", "start": [ 419, 1 ], "end": [ 441, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.buildIfThenElse_", "code": "def buildIfThenElse_ (builder : LLVM.Builder llvmctx) (name : String) (brval : LLVM.Value llvmctx)\n (thencodegen : LLVM.Builder llvmctx → M llvmctx ShouldForwardControlFlow)\n (elsecodegen : LLVM.Builder llvmctx → M llvmctx ShouldForwardControlFlow) : M llvmctx Unit := do\n let fn ← LLVM.getBasicBlockParent (← LLVM.getInsertBlock builder)\n let thenbb ← LLVM.appendBasicBlockInContext llvmctx fn (name ++ \"Then\")\n let elsebb ← LLVM.appendBasicBlockInContext llvmctx fn (name ++ \"Else\")\n let mergebb ← LLVM.appendBasicBlockInContext llvmctx fn (name ++ \"Merge\")\n let _ ← LLVM.buildCondBr builder brval thenbb elsebb\n LLVM.positionBuilderAtEnd builder thenbb\n let fwd? ← thencodegen builder\n match fwd? with\n | .yes => let _ ← LLVM.buildBr builder mergebb\n | .no => pure ()\n LLVM.positionBuilderAtEnd builder elsebb\n let fwd? ← elsecodegen builder\n match fwd? with\n | .yes => let _ ← LLVM.buildBr builder mergebb\n | .no => pure ()\n LLVM.positionBuilderAtEnd builder mergebb", "start": [ 443, 1 ], "end": [ 464, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.buildLeanBoolTrue?", "code": "def buildLeanBoolTrue? (builder : LLVM.Builder llvmctx)\n (b : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n LLVM.buildICmp builder LLVM.IntPredicate.NE b (← constInt8 0) name", "start": [ 467, 1 ], "end": [ 469, 69 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFnDeclAux", "code": "def emitFnDeclAux (mod : LLVM.Module llvmctx)\n (decl : Decl) (cppBaseName : String) (isExternal : Bool) : M llvmctx (LLVM.Value llvmctx) := do\n let ps := decl.params\n let env ← getEnv\n let global ←\n if ps.isEmpty then\n let retty ← (toLLVMType decl.resultType)\n let global ← LLVM.getOrAddGlobal mod cppBaseName retty\n if !isExternal then\n LLVM.setInitializer global (← LLVM.getUndef retty)\n pure global\n else\n let retty ← (toLLVMType decl.resultType)\n let mut argtys := #[]\n for p in ps do\n if !(isExternC env decl.name) || !p.ty.isIrrelevant then\n argtys := argtys.push (← toLLVMType p.ty)\n if argtys.size > closureMaxArgs && isBoxedName decl.name then\n argtys := #[← LLVM.pointerType (← LLVM.voidPtrType llvmctx)]\n let fnty ← LLVM.functionType retty argtys (isVarArg := false)\n LLVM.getOrAddFunction mod cppBaseName fnty\n if ps.isEmpty then\n if isClosedTermName env decl.name then LLVM.setVisibility global LLVM.Visibility.hidden else if isExternal then pure () else LLVM.setDLLStorageClass global LLVM.DLLStorageClass.export else if !isExternal\n then LLVM.setDLLStorageClass global LLVM.DLLStorageClass.export\n return global", "start": [ 471, 1 ], "end": [ 507, 16 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFnDecl", "code": "def emitFnDecl (decl : Decl) (isExternal : Bool) : M llvmctx Unit := do\n let cppBaseName ← toCName decl.name\n let _ ← emitFnDeclAux (← getLLVMModule) decl cppBaseName isExternal", "start": [ 510, 1 ], "end": [ 512, 70 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitExternDeclAux", "code": "def emitExternDeclAux (decl : Decl) (cNameStr : String) : M llvmctx Unit := do\n let env ← getEnv\n let extC := isExternC env decl.name\n let _ ← emitFnDeclAux (← getLLVMModule) decl cNameStr extC", "start": [ 514, 1 ], "end": [ 517, 61 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFnDecls", "code": "def emitFnDecls : M llvmctx Unit := do\n let env ← getEnv\n let decls := getDecls env\n let modDecls : NameSet := decls.foldl (fun s d => s.insert d.name) {}\n let usedDecls : NameSet := decls.foldl (fun s d => collectUsedDecls env d (s.insert d.name)) {}\n let usedDecls := usedDecls.toList\n for n in usedDecls do\n let decl ← getDecl n\n match getExternNameFor env `c decl.name with\n | some cName => emitExternDeclAux decl cName\n | none => emitFnDecl decl (!modDecls.contains n)\n return ()", "start": [ 519, 1 ], "end": [ 530, 12 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitLhsSlot_", "code": "def emitLhsSlot_ (x : VarId) : M llvmctx (LLVM.LLVMType llvmctx × LLVM.Value llvmctx) := do\n let state ← get\n match state.var2val.find? x with\n | .some v => return v\n | .none => throw s!\"unable to find variable {x}\"", "start": [ 532, 1 ], "end": [ 536, 51 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitLhsVal", "code": "def emitLhsVal (builder : LLVM.Builder llvmctx)\n (x : VarId) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let (xty, xslot) ← emitLhsSlot_ x\n LLVM.buildLoad2 builder xty xslot name", "start": [ 538, 1 ], "end": [ 541, 41 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitLhsSlotStore", "code": "def emitLhsSlotStore (builder : LLVM.Builder llvmctx)\n (x : VarId) (v : LLVM.Value llvmctx) : M llvmctx Unit := do\n let (_, slot) ← emitLhsSlot_ x\n LLVM.buildStore builder v slot", "start": [ 543, 1 ], "end": [ 546, 33 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitArgSlot_", "code": "def emitArgSlot_ (builder : LLVM.Builder llvmctx)\n (x : Arg) : M llvmctx (LLVM.LLVMType llvmctx × LLVM.Value llvmctx) := do\n match x with\n | Arg.var x => emitLhsSlot_ x\n | _ => do\n let slotty ← LLVM.voidPtrType llvmctx\n let slot ← buildPrologueAlloca builder slotty \"irrelevant_slot\"\n let v ← callLeanBox builder (← constIntSizeT 0) \"irrelevant_val\"\n let _ ← LLVM.buildStore builder v slot\n return (slotty, slot)", "start": [ 548, 1 ], "end": [ 557, 26 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitArgVal", "code": "def emitArgVal (builder : LLVM.Builder llvmctx)\n (x : Arg) (name : String := \"\") : M llvmctx (LLVM.LLVMType llvmctx × LLVM.Value llvmctx) := do\n let (xty, xslot) ← emitArgSlot_ builder x\n let xval ← LLVM.buildLoad2 builder xty xslot name\n return (xty, xval)", "start": [ 559, 1 ], "end": [ 563, 21 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitAllocCtor", "code": "def emitAllocCtor (builder : LLVM.Builder llvmctx)\n (c : CtorInfo) : M llvmctx (LLVM.Value llvmctx) := do\n let hackSizeofVoidPtr := 8\n let scalarSize := hackSizeofVoidPtr * c.usize + c.ssize\n callLeanAllocCtor builder c.cidx c.size scalarSize \"lean_alloc_ctor_out\"", "start": [ 565, 1 ], "end": [ 570, 75 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitCtorSetArgs", "code": "def emitCtorSetArgs (builder : LLVM.Builder llvmctx)\n (z : VarId) (ys : Array Arg) : M llvmctx Unit := do\n ys.size.forM fun i => do\n let zv ← emitLhsVal builder z\n let (_yty, yv) ← emitArgVal builder ys[i]!\n let iv ← constIntUnsigned i\n callLeanCtorSet builder zv iv yv\n emitLhsSlotStore builder z zv\n pure ()", "start": [ 572, 1 ], "end": [ 580, 12 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitCtor", "code": "def emitCtor (builder : LLVM.Builder llvmctx)\n (z : VarId) (c : CtorInfo) (ys : Array Arg) : M llvmctx Unit := do\n let (_llvmty, slot) ← emitLhsSlot_ z\n if c.size == 0 && c.usize == 0 && c.ssize == 0 then do\n let v ← callLeanBox builder (← constIntSizeT c.cidx) \"lean_box_outv\"\n let _ ← LLVM.buildStore builder v slot\n else do\n let v ← emitAllocCtor builder c\n let _ ← LLVM.buildStore builder v slot\n emitCtorSetArgs builder z ys", "start": [ 582, 1 ], "end": [ 591, 33 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitInc", "code": "def emitInc (builder : LLVM.Builder llvmctx)\n (x : VarId) (n : Nat) (checkRef? : Bool) : M llvmctx Unit := do\n let xv ← emitLhsVal builder x\n if n != 1\n then do\n let nv ← constIntSizeT n\n callLeanRefcountFn builder (kind := RefcountKind.inc) (checkRef? := checkRef?) (delta := nv) xv\n else callLeanRefcountFn builder (kind := RefcountKind.inc) (checkRef? := checkRef?) xv", "start": [ 593, 1 ], "end": [ 600, 89 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitDec", "code": "def emitDec (builder : LLVM.Builder llvmctx)\n (x : VarId) (n : Nat) (checkRef? : Bool) : M llvmctx Unit := do\n let xv ← emitLhsVal builder x\n if n != 1\n then throw \"expected n = 1 for emitDec\"\n else callLeanRefcountFn builder (kind := RefcountKind.dec) (checkRef? := checkRef?) xv", "start": [ 602, 1 ], "end": [ 607, 89 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitNumLit", "code": "def emitNumLit (builder : LLVM.Builder llvmctx)\n (t : IRType) (v : Nat) : M llvmctx (LLVM.Value llvmctx) := do\n if t.isObj then\n if v < UInt32.size then\n callLeanUnsignedToNatFn builder v\n else\n callLeanCStrToNatFn builder v\n else\n LLVM.constInt (← toLLVMType t) (UInt64.ofNat v)", "start": [ 609, 1 ], "end": [ 617, 52 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.toHexDigit", "code": "def toHexDigit (c : Nat) : String :=\n String.singleton c.digitChar", "start": [ 619, 1 ], "end": [ 620, 31 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.quoteString", "code": "def quoteString (s : String) : String :=\n let q := \"\\\"\";\n let q := s.foldl\n (fun q c => q ++\n if c == '\\n' then \"\\\\n\"\n else if c == '\\r' then \"\\\\r\"\n else if c == '\\t' then \"\\\\t\"\n else if c == '\\\\' then \"\\\\\\\\\"\n else if c == '\\\"' then \"\\\\\\\"\"\n else if c.toNat <= 31 then\n \"\\\\x\" ++ toHexDigit (c.toNat / 16) ++ toHexDigit (c.toNat % 16)\n else String.singleton c)\n q;\n q ++ \"\\\"\"", "start": [ 623, 1 ], "end": [ 637, 12 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitSimpleExternalCall", "code": "def emitSimpleExternalCall (builder : LLVM.Builder llvmctx)\n (f : String)\n (ps : Array Param)\n (ys : Array Arg)\n (retty : IRType)\n (name : String) : M llvmctx (LLVM.Value llvmctx) := do\n let mut args := #[]\n let mut argTys := #[]\n for (p, y) in ps.zip ys do\n if !p.ty.isIrrelevant then\n let (_yty, yv) ← emitArgVal builder y \"\"\n argTys := argTys.push (← toLLVMType p.ty)\n args := args.push yv\n let fnty ← LLVM.functionType (← toLLVMType retty) argTys\n let fn ← LLVM.getOrAddFunction (← getLLVMModule) f fnty\n LLVM.buildCall2 builder fnty fn args name", "start": [ 639, 1 ], "end": [ 654, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitExternCall", "code": "def emitExternCall (builder : LLVM.Builder llvmctx)\n (f : FunId)\n (ps : Array Param)\n (extData : ExternAttrData)\n (ys : Array Arg) (retty : IRType)\n (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) :=\n match getExternEntryFor extData `c with\n | some (ExternEntry.standard _ extFn) => emitSimpleExternalCall builder extFn ps ys retty name\n | some (ExternEntry.inline `llvm _pat) => throw \"Unimplemented codegen of inline LLVM\"\n | some (ExternEntry.inline _ pat) => throw s!\"Cannot codegen non-LLVM inline code '{pat}'.\"\n | some (ExternEntry.foreign _ extFn) => emitSimpleExternalCall builder extFn ps ys retty name\n | _ => throw s!\"Failed to emit extern application '{f}'.\"", "start": [ 658, 1 ], "end": [ 669, 60 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getFunIdTy", "code": "def getFunIdTy (f : FunId) : M llvmctx (LLVM.LLVMType llvmctx) := do\n let decl ← getDecl f\n let retty ← toLLVMType decl.resultType\n let argtys ← decl.params.mapM (fun p => do toLLVMType p.ty)\n LLVM.functionType retty argtys", "start": [ 671, 1 ], "end": [ 675, 33 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.getOrAddFunIdValue", "code": "def getOrAddFunIdValue (builder : LLVM.Builder llvmctx) (f : FunId) : M llvmctx (LLVM.Value llvmctx) := do\n let decl ← getDecl f\n let fcname ← toCName f\n let retty ← toLLVMType decl.resultType\n if decl.params.isEmpty then\n let gslot ← LLVM.getOrAddGlobal (← getLLVMModule) fcname retty\n LLVM.buildLoad2 builder retty gslot\n else\n let argtys ← decl.params.mapM (fun p => do toLLVMType p.ty)\n let fnty ← LLVM.functionType retty argtys\n LLVM.getOrAddFunction (← getLLVMModule) fcname fnty", "start": [ 677, 1 ], "end": [ 694, 56 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitPartialApp", "code": "def emitPartialApp (builder : LLVM.Builder llvmctx) (z : VarId) (f : FunId) (ys : Array Arg) : M llvmctx Unit := do\n let decl ← getDecl f\n let fv ← getOrAddFunIdValue builder f\n let arity := decl.params.size\n let (_zty, zslot) ← emitLhsSlot_ z\n let zval ← callLeanAllocClosureFn builder fv\n (← constIntUnsigned arity)\n (← constIntUnsigned ys.size)\n LLVM.buildStore builder zval zslot\n ys.size.forM fun i => do\n let (yty, yslot) ← emitArgSlot_ builder ys[i]!\n let yval ← LLVM.buildLoad2 builder yty yslot\n callLeanClosureSetFn builder zval (← constIntUnsigned i) yval", "start": [ 696, 1 ], "end": [ 708, 66 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitApp", "code": "def emitApp (builder : LLVM.Builder llvmctx) (z : VarId) (f : VarId) (ys : Array Arg) : M llvmctx Unit := do\n if ys.size > closureMaxArgs then do\n let aargs ← buildPrologueAlloca builder (← LLVM.arrayType (← LLVM.voidPtrType llvmctx) (UInt64.ofNat ys.size)) \"aargs\"\n for i in List.range ys.size do\n let (yty, yv) ← emitArgVal builder ys[i]!\n let aslot ← LLVM.buildInBoundsGEP2 builder yty aargs #[← constIntUnsigned 0, ← constIntUnsigned i] s!\"param_{i}_slot\"\n LLVM.buildStore builder yv aslot\n let fnName := s!\"lean_apply_m\"\n let retty ← LLVM.voidPtrType llvmctx\n let args := #[← emitLhsVal builder f, ← constIntUnsigned ys.size, aargs]\n let argtys := #[← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx, ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let zv ← LLVM.buildCall2 builder fnty fn args\n emitLhsSlotStore builder z zv\n else do\n\n let fnName := s!\"lean_apply_{ys.size}\"\n let retty ← LLVM.voidPtrType llvmctx\n let args : Array (LLVM.Value llvmctx) := #[← emitLhsVal builder f] ++ (← ys.mapM (fun y => Prod.snd <$> (emitArgVal builder y)))\n let argtys := (List.replicate (1 + ys.size) (← LLVM.voidPtrType llvmctx)).toArray\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let zv ← LLVM.buildCall2 builder fnty fn args\n emitLhsSlotStore builder z zv", "start": [ 710, 1 ], "end": [ 736, 34 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFullApp", "code": "def emitFullApp (builder : LLVM.Builder llvmctx)\n (z : VarId) (f : FunId) (ys : Array Arg) : M llvmctx Unit := do\n let (__zty, zslot) ← emitLhsSlot_ z\n let decl ← getDecl f\n match decl with\n | Decl.extern _ ps retty extData =>\n let zv ← emitExternCall builder f ps extData ys retty\n LLVM.buildStore builder zv zslot\n | Decl.fdecl .. =>\n if ys.size > 0 then\n let fv ← getOrAddFunIdValue builder f\n let ys ← ys.mapM (fun y => do\n let (yty, yslot) ← emitArgSlot_ builder y\n let yv ← LLVM.buildLoad2 builder yty yslot\n return yv)\n let zv ← LLVM.buildCall2 builder (← getFunIdTy f) fv ys\n LLVM.buildStore builder zv zslot\n else\n let zv ← getOrAddFunIdValue builder f\n LLVM.buildStore builder zv zslot", "start": [ 738, 1 ], "end": [ 757, 40 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitLit", "code": "def emitLit (builder : LLVM.Builder llvmctx)\n (z : VarId) (t : IRType) (v : LitVal) : M llvmctx (LLVM.Value llvmctx) := do\n let llvmty ← toLLVMType t\n let zslot ← buildPrologueAlloca builder llvmty\n addVartoState z zslot llvmty\n let zv ← match v with\n | LitVal.num v => emitNumLit builder t v\n | LitVal.str v =>\n let zero ← constIntUnsigned 0\n let str_global ← LLVM.buildGlobalString builder v\n let strPtr ← LLVM.buildInBoundsGEP2 builder\n (← LLVM.opaquePointerTypeInContext llvmctx)\n str_global #[zero] \"\"\n let nbytes ← constIntSizeT v.utf8ByteSize\n let nchars ← constIntSizeT v.length\n callLeanMkStringUncheckedFn builder strPtr nbytes nchars \"\"\n LLVM.buildStore builder zv zslot\n return zslot", "start": [ 760, 1 ], "end": [ 778, 15 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanCtorGet", "code": "def callLeanCtorGet (builder : LLVM.Builder llvmctx)\n (x i : LLVM.Value llvmctx) (retName : String) : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_ctor_get\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.i32Type llvmctx]\n let fnty ← LLVM.functionType retty argtys\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let i ← LLVM.buildSextOrTrunc builder i (← LLVM.i32Type llvmctx)\n LLVM.buildCall2 builder fnty fn #[x, i] retName", "start": [ 780, 1 ], "end": [ 788, 51 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitProj", "code": "def emitProj (builder : LLVM.Builder llvmctx) (z : VarId) (i : Nat) (x : VarId) : M llvmctx Unit := do\n let xval ← emitLhsVal builder x\n let zval ← callLeanCtorGet builder xval (← constIntUnsigned i) \"\"\n emitLhsSlotStore builder z zval", "start": [ 790, 1 ], "end": [ 793, 34 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanCtorGetUsize", "code": "def callLeanCtorGetUsize (builder : LLVM.Builder llvmctx)\n (x i : LLVM.Value llvmctx) (retName : String) : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_ctor_get_usize\"\n let retty ← LLVM.size_tType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx]\n let fnty ← LLVM.functionType retty argtys\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n LLVM.buildCall2 builder fnty fn #[x, i] retName", "start": [ 795, 1 ], "end": [ 802, 51 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitUProj", "code": "def emitUProj (builder : LLVM.Builder llvmctx) (z : VarId) (i : Nat) (x : VarId) : M llvmctx Unit := do\n let xval ← emitLhsVal builder x\n let zval ← callLeanCtorGetUsize builder xval (← constIntUnsigned i) \"\"\n emitLhsSlotStore builder z zval", "start": [ 804, 1 ], "end": [ 807, 34 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitOffset", "code": "def emitOffset (builder : LLVM.Builder llvmctx)\n (n : Nat) (offset : Nat) : M llvmctx (LLVM.Value llvmctx) := do\n let out ← constIntUnsigned 8\n let out ← LLVM.buildMul builder out (← constIntUnsigned n) \"\" LLVM.buildAdd builder out (← constIntUnsigned offset) \"\"", "start": [ 809, 1 ], "end": [ 814, 60 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitSProj", "code": "def emitSProj (builder : LLVM.Builder llvmctx)\n (z : VarId) (t : IRType) (n offset : Nat) (x : VarId) : M llvmctx Unit := do\n let (fnName, retty) ←\n match t with\n | IRType.float => pure (\"lean_ctor_get_float\", ← LLVM.doubleTypeInContext llvmctx)\n | IRType.uint8 => pure (\"lean_ctor_get_uint8\", ← LLVM.i8Type llvmctx)\n | IRType.uint16 => pure (\"lean_ctor_get_uint16\", ← LLVM.i16Type llvmctx)\n | IRType.uint32 => pure (\"lean_ctor_get_uint32\", ← LLVM.i32Type llvmctx)\n | IRType.uint64 => pure (\"lean_ctor_get_uint64\", ← LLVM.i64Type llvmctx)\n | _ => throw s!\"Invalid type for lean_ctor_get: '{t}'\"\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let xval ← emitLhsVal builder x\n let offset ← emitOffset builder n offset\n let fnty ← LLVM.functionType retty argtys\n let zval ← LLVM.buildCall2 builder fnty fn #[xval, offset]\n emitLhsSlotStore builder z zval", "start": [ 816, 1 ], "end": [ 832, 34 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIsExclusive", "code": "def callLeanIsExclusive (builder : LLVM.Builder llvmctx)\n (closure : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_is_exclusive\"\n let retty ← LLVM.i1Type llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let out ← LLVM.buildCall2 builder fnty fn #[closure] retName\n LLVM.buildSextOrTrunc builder out (← LLVM.i8Type llvmctx)", "start": [ 834, 1 ], "end": [ 842, 60 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIsScalar", "code": "def callLeanIsScalar (builder : LLVM.Builder llvmctx)\n (closure : LLVM.Value llvmctx) (retName : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_is_scalar\"\n let retty ← LLVM.i8Type llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[closure] retName", "start": [ 844, 1 ], "end": [ 851, 54 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitIsShared", "code": "def emitIsShared (builder : LLVM.Builder llvmctx) (z : VarId) (x : VarId) : M llvmctx Unit := do\n let xv ← emitLhsVal builder x\n let exclusive? ← callLeanIsExclusive builder xv\n let exclusive? ← LLVM.buildSextOrTrunc builder exclusive? (← LLVM.i1Type llvmctx)\n let shared? ← LLVM.buildNot builder exclusive?\n let shared? ← LLVM.buildSext builder shared? (← LLVM.i8Type llvmctx)\n emitLhsSlotStore builder z shared?", "start": [ 853, 1 ], "end": [ 859, 39 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitBox", "code": "def emitBox (builder : LLVM.Builder llvmctx) (z : VarId) (x : VarId) (xType : IRType) : M llvmctx Unit := do\n let xv ← emitLhsVal builder x\n let (fnName, argTy, xv) ←\n match xType with\n | IRType.usize => pure (\"lean_box_usize\", ← LLVM.size_tType llvmctx, xv)\n | IRType.uint32 => pure (\"lean_box_uint32\", ← LLVM.i32Type llvmctx, xv)\n | IRType.uint64 => pure (\"lean_box_uint64\", ← LLVM.size_tType llvmctx, xv)\n | IRType.float => pure (\"lean_box_float\", ← LLVM.doubleTypeInContext llvmctx, xv)\n | _ => do\n let xv ← LLVM.buildSext builder xv (← LLVM.size_tType llvmctx)\n pure (\"lean_box\", ← LLVM.size_tType llvmctx, xv)\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[argTy]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let zv ← LLVM.buildCall2 builder fnty fn #[xv]\n emitLhsSlotStore builder z zv", "start": [ 861, 1 ], "end": [ 878, 32 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.IRType.isIntegerType", "code": "def IRType.isIntegerType (t : IRType) : Bool :=\n match t with\n | .uint8 => true\n | .uint16 => true\n | .uint32 => true\n | .uint64 => true\n | .usize => true\n | _ => false", "start": [ 880, 1 ], "end": [ 887, 15 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callUnboxForType", "code": "def callUnboxForType (builder : LLVM.Builder llvmctx)\n (t : IRType)\n (v : LLVM.Value llvmctx)\n (retName : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let (fnName, retty) ←\n match t with\n | IRType.usize => pure (\"lean_unbox_usize\", ← toLLVMType t)\n | IRType.uint32 => pure (\"lean_unbox_uint32\", ← toLLVMType t)\n | IRType.uint64 => pure (\"lean_unbox_uint64\", ← toLLVMType t)\n | IRType.float => pure (\"lean_unbox_float\", ← toLLVMType t)\n | _ => pure (\"lean_unbox\", ← LLVM.size_tType llvmctx)\n let argtys := #[← LLVM.voidPtrType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[v] retName", "start": [ 889, 1 ], "end": [ 903, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitUnbox", "code": "def emitUnbox (builder : LLVM.Builder llvmctx)\n (z : VarId) (t : IRType) (x : VarId) (retName : String := \"\") : M llvmctx Unit := do\n let zval ← callUnboxForType builder t (← emitLhsVal builder x) retName\n let zval ←\n if IRType.isIntegerType t\n then LLVM.buildSextOrTrunc builder zval (← toLLVMType t)\n else pure zval\n emitLhsSlotStore builder z zval", "start": [ 907, 1 ], "end": [ 916, 34 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitReset", "code": "def emitReset (builder : LLVM.Builder llvmctx) (z : VarId) (n : Nat) (x : VarId) : M llvmctx Unit := do\n let xv ← emitLhsVal builder x\n let isExclusive ← callLeanIsExclusive builder xv\n let isExclusive ← buildLeanBoolTrue? builder isExclusive\n buildIfThenElse_ builder \"isExclusive\" isExclusive\n (fun builder => do\n let xv ← emitLhsVal builder x\n n.forM fun i => do\n callLeanCtorRelease builder xv (← constIntUnsigned i)\n emitLhsSlotStore builder z xv\n return ShouldForwardControlFlow.yes\n )\n (fun builder => do\n let xv ← emitLhsVal builder x\n callLeanDecRef builder xv\n let box0 ← callLeanBox builder (← constIntSizeT 0) \"box0\"\n emitLhsSlotStore builder z box0\n return ShouldForwardControlFlow.yes\n )", "start": [ 918, 1 ], "end": [ 936, 5 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitReuse", "code": "def emitReuse (builder : LLVM.Builder llvmctx)\n (z : VarId) (x : VarId) (c : CtorInfo) (updtHeader : Bool) (ys : Array Arg) : M llvmctx Unit := do\n let xv ← emitLhsVal builder x\n let isScalar ← callLeanIsScalar builder xv\n let isScalar ← buildLeanBoolTrue? builder isScalar\n buildIfThenElse_ builder \"isScalar\" isScalar\n (fun builder => do\n let cv ← emitAllocCtor builder c\n emitLhsSlotStore builder z cv\n return ShouldForwardControlFlow.yes\n )\n (fun builder => do\n let xv ← emitLhsVal builder x\n emitLhsSlotStore builder z xv\n if updtHeader then\n let zv ← emitLhsVal builder z\n callLeanCtorSetTag builder zv (← constInt8 c.cidx)\n return ShouldForwardControlFlow.yes\n )\n emitCtorSetArgs builder z ys", "start": [ 938, 1 ], "end": [ 957, 31 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitVDecl", "code": "def emitVDecl (builder : LLVM.Builder llvmctx) (z : VarId) (t : IRType) (v : Expr) : M llvmctx Unit := do\n match v with\n | Expr.ctor c ys => emitCtor builder z c ys\n | Expr.reset n x => emitReset builder z n x\n | Expr.reuse x c u ys => emitReuse builder z x c u ys\n | Expr.proj i x => emitProj builder z i x\n | Expr.uproj i x => emitUProj builder z i x\n | Expr.sproj n o x => emitSProj builder z t n o x\n | Expr.fap c ys => emitFullApp builder z c ys\n | Expr.pap c ys => emitPartialApp builder z c ys\n | Expr.ap x ys => emitApp builder z x ys\n | Expr.box t x => emitBox builder z x t\n | Expr.unbox x => emitUnbox builder z t x\n | Expr.isShared x => emitIsShared builder z x\n | Expr.lit v => let _ ← emitLit builder z t v", "start": [ 959, 1 ], "end": [ 973, 57 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.declareVar", "code": "def declareVar (builder : LLVM.Builder llvmctx) (x : VarId) (t : IRType) : M llvmctx Unit := do\n let llvmty ← toLLVMType t\n let alloca ← buildPrologueAlloca builder llvmty \"varx\"\n addVartoState x alloca llvmty", "start": [ 975, 1 ], "end": [ 978, 32 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.declareVars", "code": "partial def declareVars (builder : LLVM.Builder llvmctx) (f : FnBody) : M llvmctx Unit := do\n match f with\n | FnBody.vdecl x t _ b => do\n declareVar builder x t\n declareVars builder b\n | FnBody.jdecl _ xs _ b => do\n for param in xs do declareVar builder param.x param.ty\n declareVars builder b\n | e => do\n if e.isTerminal then pure () else declareVars builder e.body", "start": [ 980, 1 ], "end": [ 989, 67 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitTag", "code": "def emitTag (builder : LLVM.Builder llvmctx) (x : VarId) (xType : IRType) : M llvmctx (LLVM.Value llvmctx) := do\n if xType.isObj then do\n let xval ← emitLhsVal builder x\n callLeanObjTag builder xval\n else if xType.isScalar then do\n emitLhsVal builder x\n else\n throw \"Do not know how to `emitTag` in general.\"", "start": [ 991, 1 ], "end": [ 998, 53 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitSet", "code": "def emitSet (builder : LLVM.Builder llvmctx) (x : VarId) (i : Nat) (y : Arg) : M llvmctx Unit := do\n let fnName := \"lean_ctor_set\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx , ← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[← emitLhsVal builder x, ← constIntUnsigned i, (← emitArgVal builder y).2]", "start": [ 1000, 1 ], "end": [ 1006, 119 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitUSet", "code": "def emitUSet (builder : LLVM.Builder llvmctx) (x : VarId) (i : Nat) (y : VarId) : M llvmctx Unit := do\n let fnName := \"lean_ctor_set_usize\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx, ← LLVM.size_tType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[← emitLhsVal builder x, ← constIntUnsigned i, (← emitLhsVal builder y)]", "start": [ 1008, 1 ], "end": [ 1014, 117 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitTailCall", "code": "def emitTailCall (builder : LLVM.Builder llvmctx) (f : FunId) (v : Expr) : M llvmctx Unit := do\n match v with\n | Expr.fap _ ys => do\n let llvmctx ← read\n let ps := llvmctx.mainParams\n unless ps.size == ys.size do throw s!\"Invalid tail call. f:'{f}' v:'{v}'\"\n let args ← ys.mapM (fun y => Prod.snd <$> emitArgVal builder y)\n let fn ← builderGetInsertionFn builder\n let call ← LLVM.buildCall2 builder (← getFunIdTy f) fn args\n LLVM.setTailCall call true let _ ← LLVM.buildRet builder call\n | _ => throw s!\"EmitTailCall expects function application, found '{v}'\"", "start": [ 1016, 1 ], "end": [ 1028, 74 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitJmp", "code": "def emitJmp (builder : LLVM.Builder llvmctx) (jp : JoinPointId) (xs : Array Arg) : M llvmctx Unit := do\n let llvmctx ← read\n let ps ← match llvmctx.jpMap.find? jp with\n | some ps => pure ps\n | none => throw s!\"Unknown join point {jp}\"\n unless xs.size == ps.size do throw s!\"Invalid goto, mismatched sizes between arguments, formal parameters.\"\n for (p, x) in ps.zip xs do\n let (_xty, xv) ← emitArgVal builder x\n emitLhsSlotStore builder p.x xv\n let _ ← LLVM.buildBr builder (← emitJp jp)", "start": [ 1030, 1 ], "end": [ 1039, 45 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitSSet", "code": "def emitSSet (builder : LLVM.Builder llvmctx) (x : VarId) (n : Nat) (offset : Nat) (y : VarId) (t : IRType) : M llvmctx Unit := do\n let (fnName, setty) ←\n match t with\n | IRType.float => pure (\"lean_ctor_set_float\", ← LLVM.doubleTypeInContext llvmctx)\n | IRType.uint8 => pure (\"lean_ctor_set_uint8\", ← LLVM.i8Type llvmctx)\n | IRType.uint16 => pure (\"lean_ctor_set_uint16\", ← LLVM.i16Type llvmctx)\n | IRType.uint32 => pure (\"lean_ctor_set_uint32\", ← LLVM.i32Type llvmctx)\n | IRType.uint64 => pure (\"lean_ctor_set_uint64\", ← LLVM.i64Type llvmctx)\n | _ => throw s!\"invalid type for 'lean_ctor_set': '{t}'\"\n let argtys := #[ ← LLVM.voidPtrType llvmctx, ← LLVM.unsignedType llvmctx, setty]\n let retty ← LLVM.voidType llvmctx\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let xv ← emitLhsVal builder x\n let offset ← emitOffset builder n offset\n let yv ← emitLhsVal builder y\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[xv, offset, yv]", "start": [ 1041, 1 ], "end": [ 1057, 61 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitDel", "code": "def emitDel (builder : LLVM.Builder llvmctx) (x : VarId) : M llvmctx Unit := do\n let argtys := #[ ← LLVM.voidPtrType llvmctx]\n let retty ← LLVM.voidType llvmctx\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty \"lean_free_object\" argtys\n let xv ← emitLhsVal builder x\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[xv]", "start": [ 1059, 1 ], "end": [ 1065, 49 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitSetTag", "code": "def emitSetTag (builder : LLVM.Builder llvmctx) (x : VarId) (i : Nat) : M llvmctx Unit := do\n let argtys := #[← LLVM.voidPtrType llvmctx, ← LLVM.i8Type llvmctx]\n let retty ← LLVM.voidType llvmctx\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty \"lean_ctor_set_tag\" argtys\n let xv ← emitLhsVal builder x\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[xv, ← constInt8 i]", "start": [ 1067, 1 ], "end": [ 1073, 64 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.ensureHasDefault'", "code": "def ensureHasDefault' (alts : Array Alt) : Array Alt :=\n if alts.any Alt.isDefault then alts\n else\n let last := alts.back\n let alts := alts.pop\n alts.push (Alt.default last.body)", "start": [ 1075, 1 ], "end": [ 1080, 38 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitCase", "code": "partial def emitCase (builder : LLVM.Builder llvmctx)\n (x : VarId) (xType : IRType) (alts : Array Alt) : M llvmctx Unit := do\n let oldBB ← LLVM.getInsertBlock builder\n let tag ← emitTag builder x xType\n let tag ← LLVM.buildZext builder tag (← LLVM.i64Type llvmctx)\n let alts := ensureHasDefault' alts\n let defaultBB ← builderAppendBasicBlock builder s!\"case_{xType}_default\"\n let numCasesHint := alts.size\n let switch ← LLVM.buildSwitch builder tag defaultBB (UInt64.ofNat numCasesHint)\n alts.forM fun alt => do\n match alt with\n | Alt.ctor c b =>\n let destbb ← builderAppendBasicBlock builder s!\"case_{xType}_{c.name}_{c.cidx}\"\n LLVM.addCase switch (← constIntSizeT c.cidx) destbb\n LLVM.positionBuilderAtEnd builder destbb\n emitFnBody builder b\n | Alt.default b =>\n LLVM.positionBuilderAtEnd builder defaultBB\n emitFnBody builder b\n LLVM.clearInsertionPosition builder\n LLVM.positionBuilderAtEnd builder oldBB", "start": [ 1083, 1 ], "end": [ 1106, 42 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitJDecl", "code": "partial def emitJDecl (builder : LLVM.Builder llvmctx)\n (jp : JoinPointId) (_ps : Array Param) (b : FnBody) : M llvmctx Unit := do\n let oldBB ← LLVM.getInsertBlock builder\n let jpbb ← builderAppendBasicBlock builder s!\"jp_{jp.idx}\"\n addJpTostate jp jpbb\n LLVM.positionBuilderAtEnd builder jpbb\n declareVars builder b\n emitBlock builder b\n LLVM.positionBuilderAtEnd builder oldBB", "start": [ 1109, 1 ], "end": [ 1122, 42 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitUnreachable", "code": "partial def emitUnreachable (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let retty ← LLVM.voidType llvmctx\n let argtys := #[]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty \"lean_internal_panic_unreachable\" argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[]\n let _ ← LLVM.buildUnreachable builder", "start": [ 1124, 1 ], "end": [ 1130, 40 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitBlock", "code": "partial def emitBlock (builder : LLVM.Builder llvmctx) (b : FnBody) : M llvmctx Unit := do\n match b with\n | FnBody.jdecl j xs v b =>\n emitJDecl builder j xs v\n emitBlock builder b\n | d@(FnBody.vdecl x t v b) => do\n let llvmctx ← read\n if isTailCallTo llvmctx.mainFn d then\n emitTailCall builder llvmctx.mainFn v\n else\n emitVDecl builder x t v\n emitBlock builder b\n | FnBody.inc x n c p b =>\n unless p do emitInc builder x n c\n emitBlock builder b\n | FnBody.dec x n c p b =>\n unless p do emitDec builder x n c\n emitBlock builder b\n | FnBody.del x b => emitDel builder x; emitBlock builder b\n | FnBody.setTag x i b => emitSetTag builder x i; emitBlock builder b\n | FnBody.set x i y b => emitSet builder x i y; emitBlock builder b\n | FnBody.uset x i y b => emitUSet builder x i y; emitBlock builder b\n | FnBody.sset x i o y t b => emitSSet builder x i o y t; emitBlock builder b\n | FnBody.mdata _ b => emitBlock builder b\n | FnBody.ret x => do\n let (_xty, xv) ← emitArgVal builder x \"ret_val\"\n let _ ← LLVM.buildRet builder xv\n | FnBody.case _ x xType alts =>\n emitCase builder x xType alts\n | FnBody.jmp j xs =>\n emitJmp builder j xs\n | FnBody.unreachable => emitUnreachable builder", "start": [ 1132, 1 ], "end": [ 1163, 58 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFnBody", "code": "partial def emitFnBody (builder : LLVM.Builder llvmctx) (b : FnBody) : M llvmctx Unit := do\n declareVars builder b\n emitBlock builder b", "start": [ 1165, 1 ], "end": [ 1167, 22 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFnArgs", "code": "def emitFnArgs (builder : LLVM.Builder llvmctx)\n (needsPackedArgs? : Bool) (llvmfn : LLVM.Value llvmctx) (params : Array Param) : M llvmctx Unit := do\n if needsPackedArgs? then do\n let argsp ← LLVM.getParam llvmfn 0 for i in List.range params.size do\n let param := params[i]!\n let argsi ← LLVM.buildGEP2 builder (← LLVM.voidPtrType llvmctx) argsp #[← constIntUnsigned i] s!\"packed_arg_{i}_slot\"\n let llvmty ← toLLVMType param.ty\n let pv ← LLVM.buildLoad2 builder llvmty argsi\n let alloca ← buildPrologueAlloca builder llvmty s!\"arg_{i}\"\n LLVM.buildStore builder pv alloca\n addVartoState params[i]!.x alloca llvmty\n else\n let n ← LLVM.countParams llvmfn\n for i in (List.range n.toNat) do\n let llvmty ← toLLVMType params[i]!.ty\n let alloca ← buildPrologueAlloca builder llvmty s!\"arg_{i}\"\n let arg ← LLVM.getParam llvmfn (UInt64.ofNat i)\n let _ ← LLVM.buildStore builder arg alloca\n addVartoState params[i]!.x alloca llvmty", "start": [ 1171, 1 ], "end": [ 1193, 49 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitDeclAux", "code": "def emitDeclAux (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) (d : Decl) : M llvmctx Unit := do\n let env ← getEnv\n let (_, jpMap) := mkVarJPMaps d\n withReader (fun llvmctx => { llvmctx with jpMap := jpMap }) do\n unless hasInitAttr env d.name do\n match d with\n | .fdecl (f := f) (xs := xs) (type := t) (body := b) .. =>\n let baseName ← toCName f\n let name := if xs.size > 0 then baseName else \"_init_\" ++ baseName\n let retty ← toLLVMType t\n let mut argtys := #[]\n let needsPackedArgs? := xs.size > closureMaxArgs && isBoxedName d.name\n if needsPackedArgs? then\n argtys := #[← LLVM.pointerType (← LLVM.voidPtrType llvmctx)]\n else\n for x in xs do\n argtys := argtys.push (← toLLVMType x.ty)\n let fnty ← LLVM.functionType retty argtys (isVarArg := false)\n let llvmfn ← LLVM.getOrAddFunction mod name fnty\n if xs.size == 0 then\n LLVM.setVisibility llvmfn LLVM.Visibility.hidden else\n LLVM.setDLLStorageClass llvmfn LLVM.DLLStorageClass.export withReader (fun llvmctx => { llvmctx with mainFn := f, mainParams := xs }) do\n set { var2val := default, jp2bb := default : EmitLLVM.State llvmctx } let bb ← LLVM.appendBasicBlockInContext llvmctx llvmfn \"entry\"\n LLVM.positionBuilderAtEnd builder bb\n emitFnArgs builder needsPackedArgs? llvmfn xs\n emitFnBody builder b\n pure ()\n | _ => pure ()", "start": [ 1195, 1 ], "end": [ 1229, 19 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitDecl", "code": "def emitDecl (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) (d : Decl) : M llvmctx Unit := do\n let d := d.normalizeIds try\n emitDeclAux mod builder d\n return ()\n catch err =>\n throw (s!\"emitDecl:\\ncompiling:\\n{d}\\nerr:\\n{err}\\n\")", "start": [ 1231, 1 ], "end": [ 1237, 58 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitFns", "code": "def emitFns (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let env ← getEnv\n let decls := getDecls env\n decls.reverse.forM (emitDecl mod builder)", "start": [ 1239, 1 ], "end": [ 1242, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callIODeclInitFn", "code": "def callIODeclInitFn (builder : LLVM.Builder llvmctx)\n (initFnName : String)\n (world : LLVM.Value llvmctx): M llvmctx (LLVM.Value llvmctx) := do\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[← LLVM.voidPtrType llvmctx]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty initFnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[world]", "start": [ 1244, 1 ], "end": [ 1251, 43 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callPureDeclInitFn", "code": "def callPureDeclInitFn (builder : LLVM.Builder llvmctx)\n (initFnName : String)\n (retty : LLVM.LLVMType llvmctx): M llvmctx (LLVM.Value llvmctx) := do\n let argtys := #[]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty initFnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[]", "start": [ 1253, 1 ], "end": [ 1259, 38 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitDeclInit", "code": "def emitDeclInit (builder : LLVM.Builder llvmctx)\n (parentFn : LLVM.Value llvmctx) (d : Decl) : M llvmctx Unit := do\n let env ← getEnv\n if isIOUnitInitFn env d.name then do\n let world ← callLeanIOMkWorld builder\n let resv ← callIODeclInitFn builder (← toCName d.name) world\n let err? ← callLeanIOResultIsError builder resv \"is_error\"\n buildIfThen_ builder s!\"init_{d.name}_isError\" err?\n (fun builder => do\n let _ ← LLVM.buildRet builder resv\n pure ShouldForwardControlFlow.no)\n else if d.params.size == 0 then\n match getInitFnNameFor? env d.name with\n | some initFn =>\n let llvmty ← toLLVMType d.resultType\n let dslot ← LLVM.getOrAddGlobal (← getLLVMModule) (← toCName d.name) llvmty\n LLVM.setInitializer dslot (← LLVM.getUndef llvmty)\n let initBB ← builderAppendBasicBlock builder s!\"do_{d.name}_init\"\n let restBB ← builderAppendBasicBlock builder s!\"post_{d.name}_init\"\n let checkBuiltin? := getBuiltinInitFnNameFor? env d.name |>.isSome\n if checkBuiltin? then\n let builtinParam ← LLVM.getParam parentFn 0\n let cond ← buildLeanBoolTrue? builder builtinParam \"is_builtin_true\"\n let _ ← LLVM.buildCondBr builder cond initBB restBB\n else\n let _ ← LLVM.buildBr builder initBB\n LLVM.positionBuilderAtEnd builder initBB\n let world ← callLeanIOMkWorld builder\n let resv ← callIODeclInitFn builder (← toCName initFn) world\n let err? ← callLeanIOResultIsError builder resv s!\"{d.name}_is_error\"\n buildIfThen_ builder s!\"init_{d.name}_isError\" err?\n (fun builder => do\n let _ ← LLVM.buildRet builder resv\n pure ShouldForwardControlFlow.no)\n if d.resultType.isScalar then\n let dval ← callLeanIOResultGetValue builder resv s!\"{d.name}_res\"\n let dval ← callUnboxForType builder d.resultType dval\n LLVM.buildStore builder dval dslot\n else\n let dval ← callLeanIOResultGetValue builder resv s!\"{d.name}_res\"\n LLVM.buildStore builder dval dslot\n callLeanMarkPersistentFn builder dval\n let _ ← LLVM.buildBr builder restBB\n LLVM.positionBuilderAtEnd builder restBB\n | none => do\n let llvmty ← toLLVMType d.resultType\n let dslot ← LLVM.getOrAddGlobal (← getLLVMModule) (← toCName d.name) llvmty\n LLVM.setInitializer dslot (← LLVM.getUndef llvmty)\n let dval ← callPureDeclInitFn builder (← toCInitName d.name) (← toLLVMType d.resultType)\n LLVM.buildStore builder dval dslot\n if d.resultType.isObj then\n callLeanMarkPersistentFn builder dval", "start": [ 1261, 1 ], "end": [ 1315, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callModInitFn", "code": "def callModInitFn (builder : LLVM.Builder llvmctx)\n (modName : Name) (input world : LLVM.Value llvmctx) (retName : String): M llvmctx (LLVM.Value llvmctx) := do\n let fnName := mkModuleInitializationFunctionName modName\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[ (← LLVM.i8Type llvmctx), (← LLVM.voidPtrType llvmctx)]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[input, world] retName", "start": [ 1317, 1 ], "end": [ 1324, 58 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitInitFn", "code": "def emitInitFn (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let env ← getEnv\n let modName ← getModName\n\n let initFnTy ← LLVM.functionType (← LLVM.voidPtrType llvmctx) #[ (← LLVM.i8Type llvmctx), (← LLVM.voidPtrType llvmctx)] (isVarArg := false)\n let initFn ← LLVM.getOrAddFunction mod (mkModuleInitializationFunctionName modName) initFnTy\n LLVM.setDLLStorageClass initFn LLVM.DLLStorageClass.export let entryBB ← LLVM.appendBasicBlockInContext llvmctx initFn \"entry\"\n LLVM.positionBuilderAtEnd builder entryBB\n let ginit?ty := ← LLVM.i1Type llvmctx\n let ginit?slot ← LLVM.getOrAddGlobal mod (modName.mangle ++ \"_G_initialized\") ginit?ty\n LLVM.setVisibility ginit?slot LLVM.Visibility.hidden LLVM.setInitializer ginit?slot (← LLVM.constFalse llvmctx)\n let ginit?v ← LLVM.buildLoad2 builder ginit?ty ginit?slot \"init_v\"\n buildIfThen_ builder \"isGInitialized\" ginit?v\n (fun builder => do\n let box0 ← callLeanBox builder (← constIntSizeT 0) \"box0\"\n let out ← callLeanIOResultMKOk builder box0 \"retval\"\n let _ ← LLVM.buildRet builder out\n pure ShouldForwardControlFlow.no)\n LLVM.buildStore builder (← LLVM.constTrue llvmctx) ginit?slot\n\n env.imports.forM fun import_ => do\n let builtin ← LLVM.getParam initFn 0\n let world ← callLeanIOMkWorld builder\n let res ← callModInitFn builder import_.module builtin world (\"res_\" ++ import_.module.mangle)\n let err? ← callLeanIOResultIsError builder res (\"res_is_error_\" ++ import_.module.mangle)\n buildIfThen_ builder (\"IsError\" ++ import_.module.mangle) err?\n (fun builder => do\n let _ ← LLVM.buildRet builder res\n pure ShouldForwardControlFlow.no)\n callLeanDecRef builder res\n let decls := getDecls env\n decls.reverse.forM (emitDeclInit builder initFn)\n let box0 ← callLeanBox builder (← constIntSizeT 0) \"box0\"\n let out ← callLeanIOResultMKOk builder box0 \"retval\"\n let _ ← LLVM.buildRet builder out", "start": [ 1326, 1 ], "end": [ 1362, 36 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanInitialize", "code": "def callLeanInitialize (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_initialize\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[]\n let fnty ← LLVM.functionType retty argtys\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[]", "start": [ 1364, 1 ], "end": [ 1370, 46 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanInitializeRuntimeModule", "code": "def callLeanInitializeRuntimeModule (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_initialize_runtime_module\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[]\n let fnty ← LLVM.functionType retty argtys\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[]", "start": [ 1372, 1 ], "end": [ 1378, 46 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanSetPanicMessages", "code": "def callLeanSetPanicMessages (builder : LLVM.Builder llvmctx)\n (enable? : LLVM.Value llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_set_panic_messages\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.i1Type llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[enable?]", "start": [ 1380, 1 ], "end": [ 1387, 53 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOMarkEndInitialization", "code": "def callLeanIOMarkEndInitialization (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_io_mark_end_initialization\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[]", "start": [ 1389, 1 ], "end": [ 1395, 46 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOResultIsOk", "code": "def callLeanIOResultIsOk (builder : LLVM.Builder llvmctx)\n (arg : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_io_result_is_ok\"\n let retty ← LLVM.i1Type llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[arg] name", "start": [ 1397, 1 ], "end": [ 1404, 46 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanInitTaskManager", "code": "def callLeanInitTaskManager (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_init_task_manager\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[]", "start": [ 1406, 1 ], "end": [ 1412, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanFinalizeTaskManager", "code": "def callLeanFinalizeTaskManager (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let fnName := \"lean_finalize_task_manager\"\n let retty ← LLVM.voidPtrType llvmctx\n let argtys := #[]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[]", "start": [ 1414, 1 ], "end": [ 1420, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanUnboxUint32", "code": "def callLeanUnboxUint32 (builder : LLVM.Builder llvmctx)\n (v : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx (LLVM.Value llvmctx) := do\n let fnName := \"lean_unbox_uint32\"\n let retty ← LLVM.i32Type llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n LLVM.buildCall2 builder fnty fn #[v] name", "start": [ 1422, 1 ], "end": [ 1429, 45 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanIOResultShowError", "code": "def callLeanIOResultShowError (builder : LLVM.Builder llvmctx)\n (v : LLVM.Value llvmctx) (name : String := \"\") : M llvmctx Unit := do\n let fnName := \"lean_io_result_show_error\"\n let retty ← LLVM.voidType llvmctx\n let argtys := #[ ← LLVM.voidPtrType llvmctx ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty fnName argtys\n let fnty ← LLVM.functionType retty argtys\n let _ ← LLVM.buildCall2 builder fnty fn #[v] name", "start": [ 1431, 1 ], "end": [ 1438, 52 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.callLeanMainFn", "code": "def callLeanMainFn (builder : LLVM.Builder llvmctx)\n (argv? : Option (LLVM.Value llvmctx))\n (world : LLVM.Value llvmctx)\n (name : String) : M llvmctx (LLVM.Value llvmctx) := do\n let retty ← LLVM.voidPtrType llvmctx\n let voidptr ← LLVM.voidPtrType llvmctx\n let argtys := if argv?.isSome then #[ voidptr, voidptr ] else #[ voidptr ]\n let fn ← getOrCreateFunctionPrototype (← getLLVMModule) retty leanMainFn argtys\n let fnty ← LLVM.functionType retty argtys\n let args := match argv? with\n | .some argv => #[argv, world]\n | .none => #[world]\n LLVM.buildCall2 builder fnty fn args name", "start": [ 1440, 1 ], "end": [ 1452, 44 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitMainFn", "code": "def emitMainFn (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n let d ← getDecl `main\n let xs ← match d with\n | .fdecl (xs := xs) .. => pure xs\n | _ => throw \"Function declaration expected for 'main'\"\n\n unless xs.size == 2 || xs.size == 1 do throw s!\"Invalid main function, main expected to have '2' or '1' arguments, found '{xs.size}' arguments\"\n let env ← getEnv\n let usesLeanAPI := usesModuleFrom env `Lean\n let mainTy ← LLVM.functionType (← LLVM.i64Type llvmctx)\n #[(← LLVM.i64Type llvmctx), (← LLVM.pointerType (← LLVM.voidPtrType llvmctx))]\n let main ← LLVM.getOrAddFunction mod \"main\" mainTy\n let entry ← LLVM.appendBasicBlockInContext llvmctx main \"entry\"\n LLVM.positionBuilderAtEnd builder entry\n \n let inty ← LLVM.voidPtrType llvmctx\n let inslot ← buildPrologueAlloca builder (← LLVM.pointerType inty) \"in\"\n let resty ← LLVM.voidPtrType llvmctx\n let res ← buildPrologueAlloca builder (← LLVM.pointerType resty) \"res\"\n if usesLeanAPI then callLeanInitialize builder else callLeanInitializeRuntimeModule builder\n \n callLeanSetPanicMessages builder (← LLVM.constFalse llvmctx)\n let world ← callLeanIOMkWorld builder\n let resv ← callModInitFn builder (← getModName) (← constInt8 1) world ((← getModName).toString ++ \"_init_out\")\n let _ ← LLVM.buildStore builder resv res\n\n callLeanSetPanicMessages builder (← LLVM.constTrue llvmctx)\n callLeanIOMarkEndInitialization builder\n\n let resv ← LLVM.buildLoad2 builder resty res \"resv\"\n let res_is_ok ← callLeanIOResultIsOk builder resv \"res_is_ok\"\n buildIfThen_ builder \"resIsOkBranches\" res_is_ok\n (fun builder => do callLeanDecRef builder resv\n callLeanInitTaskManager builder\n if xs.size == 2 then\n let inv ← callLeanBox builder (← constIntSizeT 0) \"inv\"\n let _ ← LLVM.buildStore builder inv inslot\n let ity ← LLVM.size_tType llvmctx\n let islot ← buildPrologueAlloca builder ity \"islot\"\n let argcval ← LLVM.getParam main 0\n let argvval ← LLVM.getParam main 1\n LLVM.buildStore builder argcval islot\n buildWhile_ builder \"argv\"\n (condcodegen := fun builder => do\n let iv ← LLVM.buildLoad2 builder ity islot \"iv\"\n let i_gt_1 ← LLVM.buildICmp builder LLVM.IntPredicate.UGT iv (← constIntSizeT 1) \"i_gt_1\"\n return i_gt_1)\n (bodycodegen := fun builder => do\n let iv ← LLVM.buildLoad2 builder ity islot \"iv\"\n let iv_next ← LLVM.buildSub builder iv (← constIntSizeT 1) \"iv.next\"\n LLVM.buildStore builder iv_next islot\n let nv ← callLeanAllocCtor builder 1 2 0 \"nv\"\n let argv_i_next_slot ← LLVM.buildGEP2 builder (← LLVM.voidPtrType llvmctx) argvval #[iv_next] \"argv.i.next.slot\"\n let argv_i_next_val ← LLVM.buildLoad2 builder (← LLVM.voidPtrType llvmctx) argv_i_next_slot \"argv.i.next.val\"\n let argv_i_next_val_str ← callLeanMkString builder argv_i_next_val \"arg.i.next.val.str\"\n callLeanCtorSet builder nv (← constIntUnsigned 0) argv_i_next_val_str\n let inv ← LLVM.buildLoad2 builder inty inslot \"inv\"\n callLeanCtorSet builder nv (← constIntUnsigned 1) inv\n LLVM.buildStore builder nv inslot)\n let world ← callLeanIOMkWorld builder\n let inv ← LLVM.buildLoad2 builder inty inslot \"inv\"\n let resv ← callLeanMainFn builder (argv? := .some inv) (world := world) \"resv\"\n let _ ← LLVM.buildStore builder resv res\n pure ShouldForwardControlFlow.yes\n else\n let world ← callLeanIOMkWorld builder\n let resv ← callLeanMainFn builder (argv? := .none) (world := world) \"resv\"\n let _ ← LLVM.buildStore builder resv res\n pure ShouldForwardControlFlow.yes\n )\n\n let retTy := env.find? `main |>.get! |>.type |>.getForallBody\n let retTy := retTy.appArg!\n callLeanFinalizeTaskManager builder\n let resv ← LLVM.buildLoad2 builder resty res \"resv\"\n let res_is_ok ← callLeanIOResultIsOk builder resv \"res_is_ok\"\n buildIfThenElse_ builder \"res.is.ok\" res_is_ok\n (fun builder => if retTy.constName? == some ``UInt32 then do\n let resv ← LLVM.buildLoad2 builder resty res \"resv\"\n let retv ← callLeanUnboxUint32 builder (← callLeanIOResultGetValue builder resv \"io_val\") \"retv\"\n let retv ← LLVM.buildSext builder retv (← LLVM.i64Type llvmctx) \"retv_sext\"\n callLeanDecRef builder resv\n let _ ← LLVM.buildRet builder retv\n pure ShouldForwardControlFlow.no\n else do\n callLeanDecRef builder resv\n let _ ← LLVM.buildRet builder (← constInt64 0)\n pure ShouldForwardControlFlow.no\n\n )\n (fun builder => do let resv ← LLVM.buildLoad2 builder resty res \"resv\"\n callLeanIOResultShowError builder resv\n callLeanDecRef builder resv\n let _ ← LLVM.buildRet builder (← constInt64 1)\n pure ShouldForwardControlFlow.no)\n let _ ← LLVM.buildUnreachable builder", "start": [ 1454, 1 ], "end": [ 1562, 40 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.hasMainFn", "code": "def hasMainFn : M llvmctx Bool := do\n let env ← getEnv\n let decls := getDecls env\n return decls.any (fun d => d.name == `main)", "start": [ 1564, 1 ], "end": [ 1567, 46 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.emitMainFnIfNeeded", "code": "def emitMainFnIfNeeded (mod : LLVM.Module llvmctx) (builder : LLVM.Builder llvmctx) : M llvmctx Unit := do\n if (← hasMainFn) then emitMainFn mod builder", "start": [ 1569, 1 ], "end": [ 1570, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.EmitLLVM.main", "code": "def main : M llvmctx Unit := do\n emitFnDecls\n let builder ← LLVM.createBuilderInContext llvmctx\n emitFns (← getLLVMModule) builder\n emitInitFn (← getLLVMModule) builder\n emitMainFnIfNeeded (← getLLVMModule) builder", "start": [ 1572, 1 ], "end": [ 1577, 47 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.getLeanHBcPath", "code": "def getLeanHBcPath : IO System.FilePath := do\n return (← getLibDir (← getBuildDir)) / \"lean.h.bc\"", "start": [ 1580, 1 ], "end": [ 1581, 53 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.getModuleGlobals", "code": "partial def getModuleGlobals (mod : LLVM.Module llvmctx) : IO (Array (LLVM.Value llvmctx)) := do\n let rec go (v : LLVM.Value llvmctx) (acc : Array (LLVM.Value llvmctx)) : IO (Array (LLVM.Value llvmctx)) := do\n if v.isNull then return acc\n else go (← LLVM.getNextGlobal v) (acc.push v)\n go (← LLVM.getFirstGlobal mod) #[]", "start": [ 1583, 1 ], "end": [ 1588, 37 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.getModuleFunctions", "code": "partial def getModuleFunctions (mod : LLVM.Module llvmctx) : IO (Array (LLVM.Value llvmctx)) := do\n let rec go (v : LLVM.Value llvmctx) (acc : Array (LLVM.Value llvmctx)) : IO (Array (LLVM.Value llvmctx)) := do\n if v.isNull then return acc\n else go (← LLVM.getNextFunction v) (acc.push v)\n go (← LLVM.getFirstFunction mod) #[]", "start": [ 1590, 1 ], "end": [ 1595, 39 ], "kind": "commanddeclaration" }, { "full_name": "Lean.IR.emitLLVM", "code": "@[export lean_ir_emit_llvm]\ndef emitLLVM (env : Environment) (modName : Name) (filepath : String) : IO Unit := do\n LLVM.llvmInitializeTargetInfo\n let llvmctx ← LLVM.createContext\n let module ← LLVM.createModule llvmctx modName.toString\n let emitLLVMCtx : EmitLLVM.Context llvmctx := {env := env, modName := modName, llvmmodule := module}\n let initState := { var2val := default, jp2bb := default : EmitLLVM.State llvmctx}\n let out? ← ((EmitLLVM.main (llvmctx := llvmctx)).run initState).run emitLLVMCtx\n match out? with\n | .ok _ => do\n let membuf ← LLVM.createMemoryBufferWithContentsOfFile (← getLeanHBcPath).toString\n let modruntime ← LLVM.parseBitcode llvmctx membuf\n \n let runtimeGlobals ← (← getModuleGlobals modruntime).mapM (·.getName)\n let filter func := do\n if (← LLVM.isDeclaration func) then\n return none\n else\n return some (← func.getName)\n let runtimeFunctions ← (← getModuleFunctions modruntime).filterMapM filter\n LLVM.linkModules (dest := emitLLVMCtx.llvmmodule) (src := modruntime)\n for name in runtimeGlobals do\n let some global ← LLVM.getNamedGlobal emitLLVMCtx.llvmmodule name\n | throw <| IO.Error.userError s!\"ERROR: linked module must have global from runtime module: '{name}'\"\n LLVM.setLinkage global LLVM.Linkage.internal\n for name in runtimeFunctions do\n let some fn ← LLVM.getNamedFunction emitLLVMCtx.llvmmodule name\n | throw <| IO.Error.userError s!\"ERROR: linked module must have function from runtime module: '{name}'\"\n LLVM.setLinkage fn LLVM.Linkage.internal\n if let some err ← LLVM.verifyModule emitLLVMCtx.llvmmodule then\n throw <| .userError err\n LLVM.writeBitcodeToFile emitLLVMCtx.llvmmodule filepath\n LLVM.disposeModule emitLLVMCtx.llvmmodule\n | .error err => throw (IO.Error.userError err)", "start": [ 1597, 1 ], "end": [ 1638, 49 ], "kind": "commanddeclaration" } ]

.lake/packages/lean4/src/lean/lake/Lake/Main.lean

[ ".lake/packages/lean4/src/lean/Init.lean", ".lake/packages/lean4/src/lean/lake/Lake/CLI.lean", ".lake/packages/lean4/src/lean/lake/Lake.lean" ]

[ { "full_name": "main", "code": "def main (args : List String) : IO UInt32 := do\n Lake.cli args", "start": [ 9, 1 ], "end": [ 10, 16 ], "kind": "commanddeclaration" } ]

.lake/packages/lean4/src/lean/Lean/Compiler/LCNF/Probing.lean

[ ".lake/packages/lean4/src/lean/Lean/Compiler/LCNF/ForEachExpr.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/LCNF/CompilerM.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/LCNF/PassManager.lean", ".lake/packages/lean4/src/lean/Lean/Compiler/LCNF/PhaseExt.lean" ]

[ { "full_name": "Lean.Compiler.LCNF.Probe", "code": "abbrev Probe α β := Array α → CompilerM (Array β)", "start": [ 14, 1 ], "end": [ 14, 50 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.map", "code": "@[inline]\ndef map (f : α → CompilerM β) : Probe α β := fun data => data.mapM f", "start": [ 18, 1 ], "end": [ 19, 69 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filter", "code": "@[inline]\ndef filter (f : α → CompilerM Bool) : Probe α α := fun data => data.filterM f", "start": [ 21, 1 ], "end": [ 22, 78 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.sorted", "code": "@[inline]\ndef sorted [Inhabited α] [inst : LT α] [DecidableRel inst.lt] : Probe α α := fun data => return data.qsort (· < ·)", "start": [ 24, 1 ], "end": [ 25, 115 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.sortedBySize", "code": "@[inline]\ndef sortedBySize : Probe Decl (Nat × Decl) := fun decls =>\n let decls := decls.map fun decl => (decl.size, decl)\n return decls.qsort fun (sz₁, decl₁) (sz₂, decl₂) =>\n if sz₁ == sz₂ then Name.lt decl₁.name decl₂.name else sz₁ < sz₂", "start": [ 27, 1 ], "end": [ 31, 68 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.countUnique", "code": "def countUnique [ToString α] [BEq α] [Hashable α] : Probe α (α × Nat) := fun data => do\n let mut map := HashMap.empty\n for d in data do\n if let some count := map.find? d then\n map := map.insert d (count + 1)\n else\n map := map.insert d 1\n return map.toArray", "start": [ 33, 1 ], "end": [ 40, 21 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.countUniqueSorted", "code": "@[inline]\ndef countUniqueSorted [ToString α] [BEq α] [Hashable α] [Inhabited α] : Probe α (α × Nat) :=\n countUnique >=> fun data => return data.qsort (fun l r => l.snd < r.snd)", "start": [ 42, 1 ], "end": [ 44, 75 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.getLetValues", "code": "partial def getLetValues : Probe Decl LetValue := fun decls => do\n let (_, res) ← start decls |>.run #[]\n return res\nwhere\n go (c : Code) : StateRefT (Array LetValue) CompilerM Unit := do\n match c with\n | .let (decl : LetDecl) (k : Code) =>\n modify fun s => s.push decl.value\n go k\n | .fun decl k | .jp decl k =>\n go decl.value\n go k\n | .cases (cases : CasesCore Code) => cases.alts.forM (go ·.getCode)\n | .jmp .. | .return .. | .unreach .. => return ()\n start (decls : Array Decl) : StateRefT (Array LetValue) CompilerM Unit :=\n decls.forM (go ·.value)", "start": [ 46, 1 ], "end": [ 61, 28 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.getJps", "code": "partial def getJps : Probe Decl FunDecl := fun decls => do\n let (_, res) ← start decls |>.run #[]\n return res\nwhere\n go (code : Code) : StateRefT (Array FunDecl) CompilerM Unit := do\n match code with\n | .let _ k => go k\n | .fun decl k => go decl.value; go k\n | .jp decl k => modify (·.push decl); go decl.value; go k\n | .cases cs => cs.alts.forM (go ·.getCode)\n | .jmp .. | .return .. | .unreach .. => return ()\n\n start (decls : Array Decl) : StateRefT (Array FunDecl) CompilerM Unit :=\n decls.forM fun decl => go decl.value", "start": [ 63, 1 ], "end": [ 76, 41 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByLet", "code": "partial def filterByLet (f : LetDecl → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n | .let decl k => do if (← f decl) then return true else go k\n | .fun decl k | .jp decl k => go decl.value <||> go k\n | .cases cs => cs.alts.anyM (go ·.getCode)\n | .jmp .. | .return .. | .unreach .. => return false", "start": [ 78, 1 ], "end": [ 85, 55 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByFun", "code": "partial def filterByFun (f : FunDecl → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n | .let _ k | .jp _ k => go k\n | .fun decl k => do if (← f decl) then return true else go decl.value <||> go k\n | .cases cs => cs.alts.anyM (go ·.getCode)\n | .jmp .. | .return .. | .unreach .. => return false", "start": [ 87, 1 ], "end": [ 94, 55 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByJp", "code": "partial def filterByJp (f : FunDecl → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n | .let _ k => go k\n | .fun decl k => go decl.value <||> go k\n | .jp decl k => do if (← f decl) then return true else go decl.value <||> go k\n | .cases cs => cs.alts.anyM (go ·.getCode)\n | .jmp .. | .return .. | .unreach .. => return false", "start": [ 96, 1 ], "end": [ 104, 55 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByFunDecl", "code": "partial def filterByFunDecl (f : FunDecl → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n | .let _ k => go k\n | .fun decl k | .jp decl k => do if (← f decl) then return true else go decl.value <||> go k\n | .cases cs => cs.alts.anyM (go ·.getCode)\n | .jmp .. | .return .. | .unreach .. => return false", "start": [ 106, 1 ], "end": [ 113, 55 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByCases", "code": "partial def filterByCases (f : Cases → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n | .let _ k => go k\n | .fun decl k | .jp decl k => go decl.value <||> go k\n | .cases cs => do if (← f cs) then return true else cs.alts.anyM (go ·.getCode)\n | .jmp .. | .return .. | .unreach .. => return false", "start": [ 115, 1 ], "end": [ 122, 55 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByJmp", "code": "partial def filterByJmp (f : FVarId → Array Arg → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n | .let _ k => go k\n | .fun decl k | .jp decl k => go decl.value <||> go k\n | .cases cs => cs.alts.anyM (go ·.getCode)\n | .jmp fn var => f fn var\n | .return .. | .unreach .. => return false", "start": [ 124, 1 ], "end": [ 132, 45 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByReturn", "code": "partial def filterByReturn (f : FVarId → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n | .let _ k => go k\n | .fun decl k | .jp decl k => go decl.value <||> go k\n | .cases cs => cs.alts.anyM (go ·.getCode)\n | .jmp .. | .unreach .. => return false\n | .return var => f var", "start": [ 134, 1 ], "end": [ 142, 26 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.filterByUnreach", "code": "partial def filterByUnreach (f : Expr → CompilerM Bool) : Probe Decl Decl :=\n filter (fun decl => go decl.value)\nwhere\n go : Code → CompilerM Bool\n | .let _ k => go k\n | .fun decl k | .jp decl k => go decl.value <||> go k\n | .cases cs => cs.alts.anyM (go ·.getCode)\n | .jmp .. | .return .. => return false\n | .unreach typ => f typ", "start": [ 144, 1 ], "end": [ 152, 27 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.declNames", "code": "@[inline]\ndef declNames : Probe Decl Name :=\n Probe.map (fun decl => return decl.name)", "start": [ 154, 1 ], "end": [ 156, 43 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.toString", "code": "@[inline]\ndef toString [ToString α] : Probe α String :=\n Probe.map (return ToString.toString ·)", "start": [ 158, 1 ], "end": [ 160, 41 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.count", "code": "@[inline]\ndef count : Probe α Nat := fun data => return #[data.size]", "start": [ 162, 1 ], "end": [ 163, 59 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.sum", "code": "@[inline]\ndef sum : Probe Nat Nat := fun data => return #[data.foldl (init := 0) (·+·)]", "start": [ 165, 1 ], "end": [ 166, 78 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.tail", "code": "@[inline]\ndef tail (n : Nat) : Probe α α := fun data => return data[data.size - n:]", "start": [ 168, 1 ], "end": [ 169, 74 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.head", "code": "@[inline]\ndef head (n : Nat) : Probe α α := fun data => return data[:n]", "start": [ 171, 1 ], "end": [ 172, 62 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.runOnModule", "code": "def runOnModule (moduleName : Name) (probe : Probe Decl β) (phase : Phase := Phase.base): CoreM (Array β) := do\n let ext := getExt phase\n let env ← getEnv\n let some modIdx := env.getModuleIdx? moduleName | throwError \"module `{moduleName}` not found\"\n let decls := ext.getModuleEntries env modIdx\n probe decls |>.run (phase := phase)", "start": [ 174, 1 ], "end": [ 179, 38 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.runGlobally", "code": "def runGlobally (probe : Probe Decl β) (phase : Phase := Phase.base) : CoreM (Array β) := do\n let ext := getExt phase\n let env ← getEnv\n let mut decls := #[]\n for modIdx in [:env.allImportedModuleNames.size] do\n decls := decls.append <| ext.getModuleEntries env modIdx\n probe decls |>.run (phase := phase)", "start": [ 181, 1 ], "end": [ 187, 38 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Compiler.LCNF.Probe.toPass", "code": "def toPass [ToString β] (probe : Probe Decl β) (phase : Phase) : Pass where\n phase := phase\n name := `probe\n run := fun decls => do\n let res ← probe decls\n trace[Compiler.probe] s!\"{res}\"\n return decls", "start": [ 189, 1 ], "end": [ 195, 17 ], "kind": "commanddeclaration" } ]

.lake/packages/lean4/src/lean/Lean/Meta/Match/MatcherApp.lean

[ ".lake/packages/lean4/src/lean/Lean/Meta/Match/MatcherApp/Basic.lean", ".lake/packages/lean4/src/lean/Lean/Meta/Match/MatcherApp/Transform.lean" ]

[]

.lake/packages/lean4/src/lean/Lean/Meta/Match/MVarRenaming.lean

[ ".lake/packages/lean4/src/lean/Lean/Util/ReplaceExpr.lean" ]

[ { "full_name": "Lean.Meta.MVarRenaming", "code": "structure MVarRenaming where\n map : MVarIdMap MVarId := {}", "start": [ 11, 1 ], "end": [ 13, 31 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Meta.MVarRenaming.isEmpty", "code": "def MVarRenaming.isEmpty (s : MVarRenaming) : Bool :=\n s.map.isEmpty", "start": [ 15, 1 ], "end": [ 16, 16 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Meta.MVarRenaming.find?", "code": "def MVarRenaming.find? (s : MVarRenaming) (mvarId : MVarId) : Option MVarId :=\n s.map.find? mvarId", "start": [ 18, 1 ], "end": [ 19, 21 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Meta.MVarRenaming.find!", "code": "def MVarRenaming.find! (s : MVarRenaming) (mvarId : MVarId) : MVarId :=\n (s.find? mvarId).get!", "start": [ 21, 1 ], "end": [ 22, 24 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Meta.MVarRenaming.insert", "code": "def MVarRenaming.insert (s : MVarRenaming) (mvarId mvarId' : MVarId) : MVarRenaming :=\n { s with map := s.map.insert mvarId mvarId' }", "start": [ 24, 1 ], "end": [ 25, 48 ], "kind": "commanddeclaration" }, { "full_name": "Lean.Meta.MVarRenaming.apply", "code": "def MVarRenaming.apply (s : MVarRenaming) (e : Expr) : Expr :=\n if !e.hasMVar then e\n else if s.map.isEmpty then e\n else e.replace fun e => match e with\n | Expr.mvar mvarId => match s.map.find? mvarId with\n | none => e\n | some newMVarId => mkMVar newMVarId\n | _ => none", "start": [ 27, 1 ], "end": [ 34, 16 ], "kind": "commanddeclaration" } ]

.lake/packages/lean4/src/lean/Lean/Data/Lsp/Window.lean

[ ".lake/packages/lean4/src/lean/Lean/Data/Json.lean" ]

[ { "full_name": "MessageType", "code": "inductive MessageType where\n | error\n | warning\n | info\n | log", "start": [ 11, 1 ], "end": [ 15, 8 ], "kind": "commanddeclaration" }, { "full_name": "ShowMessageParams", "code": "structure ShowMessageParams where\n type : MessageType\n message : String\n deriving FromJson, ToJson", "start": [ 32, 1 ], "end": [ 35, 28 ], "kind": "commanddeclaration" }, { "full_name": "MessageActionItem", "code": "structure MessageActionItem where\n title : String\n deriving FromJson, ToJson", "start": [ 37, 1 ], "end": [ 39, 28 ], "kind": "commanddeclaration" }, { "full_name": "ShowMessageRequestParams", "code": "structure ShowMessageRequestParams where\n type : MessageType\n message : String\n actions? : Option (Array MessageActionItem)\n deriving FromJson, ToJson", "start": [ 41, 1 ], "end": [ 45, 28 ], "kind": "commanddeclaration" }, { "full_name": "ShowMessageResponse", "code": "def ShowMessageResponse := Option MessageActionItem\n deriving FromJson, ToJson", "start": [ 47, 1 ], "end": [ 48, 28 ], "kind": "commanddeclaration" } ]

.lake/packages/lean4/src/lean/Std.lean

[ ".lake/packages/lean4/src/lean/Init.lean" ]

[]