module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Control.LawfulFix | {
"line": 188,
"column": 4
} | {
"line": 188,
"column": 80
} | [
{
"pp": "α : Type u_1\nβ : α → Type u_2\nf : Part α → Part α\nhc : ωScottContinuous f\n⊢ Part.fix ⇑(toUnitMono { toFun := f, monotone' := ⋯ }) () = f (Fix.fix f)",
"usedConstants": [
"Part",
"Eq.mpr",
"Unit.unit",
"Pi.preorder",
"congrArg",
"Fix.fix",
"PartialOrder.... | rw [Part.fix_eq_of_ωScottContinuous (ωScottContinuous_toUnitMono f hc)]; rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Control.Monad.Cont | {
"line": 225,
"column": 4
} | {
"line": 225,
"column": 57
} | [
{
"pp": "m : Type u → Type v\ninst✝² : Monad m\ninst✝¹ : MonadCont m\ninst✝ : LawfulMonadCont m\nα✝ ω✝ γ✝ : Type u\nx✝¹ : OptionT m α✝\nx✝ : Label ω✝ (OptionT m) γ✝ → α✝ → OptionT m ω✝\n⊢ (callCC fun f ↦ x✝¹ >>= x✝ f).run =\n (do\n let x ← x✝¹\n callCC fun f ↦ x✝ f x).run",
"usedConstants":... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.TypeVec | {
"line": 668,
"column": 2
} | {
"line": 669,
"column": 56
} | [
{
"pp": "case a.h\nn : ℕ\nα : TypeVec.{u_1} n\nr : α ⊗ α ⟹ «repeat» n Prop\ni : Fin2 n\nx : Subtype_ r i\n⊢ (toSubtype' r ⊚ ofSubtype' r) i x = id i x",
"usedConstants": [
"Fin2.rec",
"TypeVec.ofRepeat",
"TypeVec.prod.mk",
"Subtype",
"TypeVec.toSubtype'",
"TypeVec.comp",
... | induction i
<;> dsimp only [id, toSubtype', comp, ofSubtype'] at * | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.Analysis.Filter | {
"line": 69,
"column": 34
} | {
"line": 69,
"column": 45
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\ninst✝ : PartialOrder α\nF : CFilter α σ\nE : σ ≃ τ\nf : σ → α\np : σ\ng : σ → σ → σ\nh₁ : ∀ (a b : σ), f (g a b) ≤ f a\nh₂ : ∀ (a b : σ), f (g a b) ≤ f b\na b : τ\n⊢ f (E.symm (E (g (E.symm a) (E.symm b)))) ≤ f (E.symm a)",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Filter | {
"line": 70,
"column": 35
} | {
"line": 70,
"column": 46
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\ninst✝ : PartialOrder α\nF : CFilter α σ\nE : σ ≃ τ\nf : σ → α\np : σ\ng : σ → σ → σ\nh₁ : ∀ (a b : σ), f (g a b) ≤ f a\nh₂ : ∀ (a b : σ), f (g a b) ≤ f b\na b : τ\n⊢ f (E.symm (E (g (E.symm a) (E.symm b)))) ≤ f (E.symm b)",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 71,
"column": 28
} | {
"line": 71,
"column": 39
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\nF : Ctop α σ\nE : σ ≃ τ\nf : σ → Set α\nT : α → σ\nh₁ : ∀ (x : α), x ∈ f (T x)\nI : (a b : σ) → (x : α) → x ∈ f a ∩ f b → σ\nh₂ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), x ∈ f (I a b x h)\nh₃ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), f (I a b x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Filter | {
"line": 129,
"column": 34
} | {
"line": 129,
"column": 45
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\nf : Filter α\nF : f.Realizer\nE : F.σ ≃ τ\nx✝¹ : Set α\nx✝ : x✝¹ ∈ (CFilter.ofEquiv E F.F).toFilter.sets\ns : τ\nh : (CFilter.ofEquiv E F.F).f s ⊆ x✝¹\n⊢ F.F.f (E.symm s) ⊆ x✝¹",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 73,
"column": 36
} | {
"line": 73,
"column": 47
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\nF : Ctop α σ\nE : σ ≃ τ\nf : σ → Set α\nT : α → σ\nh₁ : ∀ (x : α), x ∈ f (T x)\nI : (a b : σ) → (x : α) → x ∈ f a ∩ f b → σ\nh₂ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), x ∈ f (I a b x h)\nh₃ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), f (I a b x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 74,
"column": 36
} | {
"line": 74,
"column": 47
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\nF : Ctop α σ\nE : σ ≃ τ\nf : σ → Set α\nT : α → σ\nh₁ : ∀ (x : α), x ∈ f (T x)\nI : (a b : σ) → (x : α) → x ∈ f a ∩ f b → σ\nh₂ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), x ∈ f (I a b x h)\nh₃ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), f (I a b x ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 146,
"column": 33
} | {
"line": 146,
"column": 44
} | [
{
"pp": "α : Type u_1\ninst✝ : TopologicalSpace α\nF : Realizer α\ns : F.σ\na : α\nm : a ∈ F.F.f s\n⊢ 𝓝 a ≤ 𝓟 (F.F.f s)",
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership.mem",
"nhds",
"id",
"Ctop.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 178,
"column": 31
} | {
"line": 178,
"column": 42
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\ninst✝ : TopologicalSpace α\nF : Realizer α\nE : F.σ ≃ τ\na : α\ns✝ : Set α\nx✝ : ∃ b, a ∈ F.F.f b ∧ F.F.f b ⊆ s✝\ns : F.σ\nh : a ∈ F.F.f s ∧ F.F.f s ⊆ s✝\n⊢ a ∈ (Ctop.ofEquiv E F.F).f (E s) ∧ (Ctop.ofEquiv E F.F).f (E s) ⊆ s✝",
"usedConstants"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 178,
"column": 74
} | {
"line": 178,
"column": 85
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\ninst✝ : TopologicalSpace α\nF : Realizer α\nE : F.σ ≃ τ\na : α\ns : Set α\nx✝ : ∃ b, a ∈ (Ctop.ofEquiv E F.F).f b ∧ (Ctop.ofEquiv E F.F).f b ⊆ s\nt : τ\nh : a ∈ (Ctop.ofEquiv E F.F).f t ∧ (Ctop.ofEquiv E F.F).f t ⊆ s\n⊢ a ∈ F.F.f (E.symm t) ∧ F.F.... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Erased | {
"line": 63,
"column": 71
} | {
"line": 63,
"column": 82
} | [
{
"pp": "α : Sort u_1\na b : Erased α\nh : a.out = b.out\n⊢ a = b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Semiquot | {
"line": 186,
"column": 20
} | {
"line": 186,
"column": 31
} | [
{
"pp": "α : Type u_1\nq : Semiquot α\np : q.IsPure\na : α\n⊢ a ∈ q ↔ a ∈ pure (q.get p)",
"usedConstants": [
"Pure.pure",
"Semiquot.instMonad",
"Eq.mpr",
"congrArg",
"Monad.toApplicative",
"Membership.mem",
"id",
"Applicative.toPure",
"Iff",
"Semi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Condensed.Light.Sequence | {
"line": 326,
"column": 19
} | {
"line": 326,
"column": 30
} | [
{
"pp": "R : Type\ninst✝ : CommRing R\nX Y : LightCondMod R\np : X ⟶ Y\nhp : Epi p\nS : LightProfinite\nf : (free R).obj (S ⊗ ℕ∪{∞}).toCondensed ⟶ Y\nT : LightProfinite\nπ : T ⟶ S ⊗ ℕ∪{∞}\ng : (free R).obj T.toCondensed ⟶ X\nhπ : Epi π\ncomm : (lightProfiniteToLightCondSet ⋙ free R).map π ≫ f = g ≫ p\nS' T' : L... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Semiquot | {
"line": 203,
"column": 43
} | {
"line": 203,
"column": 54
} | [
{
"pp": "α : Type u_1\ns t : Semiquot α\nh : t.IsPure\nst : s ≤ t\n⊢ pure (t.get h) ≤ pure (s.get ⋯)",
"usedConstants": [
"Pure.pure",
"Semiquot.instMonad",
"Semiquot.pure_le._simp_1",
"Eq.mpr",
"Monad.toApplicative",
"PartialOrder.toPreorder",
"Preorder.toLE",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 28,
"column": 2
} | {
"line": 28,
"column": 13
} | [
{
"pp": "m n : ℕ\nf : Fin m → Fin n\nhf : Function.Injective f\n⊢ m ≤ n",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 35,
"column": 2
} | {
"line": 35,
"column": 13
} | [
{
"pp": "m n : ℕ\nf : Fin m ↪ Fin n\n⊢ m ≤ n",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 44,
"column": 2
} | {
"line": 44,
"column": 13
} | [
{
"pp": "m n : ℕ\nf : Fin m → Fin n\nhf : Function.Injective f\nb : Fin n\nhb : b ∉ Set.range f\n⊢ m < n",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 51,
"column": 2
} | {
"line": 51,
"column": 13
} | [
{
"pp": "m n : ℕ\nf : Fin m → Fin n\nhf : Function.Surjective f\n⊢ n ≤ m",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 59,
"column": 2
} | {
"line": 59,
"column": 13
} | [
{
"pp": "m : ℕ\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf : Fin m → α\n⊢ Fintype.card ↑(Set.range f) ≤ m",
"usedConstants": [
"Eq.mpr",
"Fintype.card_ofFinset",
"Finset.univ",
"Finset.univ_filter_exists",
"Iff.of_eq",
"congrArg",
"Finset",
"Me... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.FlagRange | {
"line": 42,
"column": 27
} | {
"line": 42,
"column": 46
} | [
{
"pp": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : BoundedOrder α\nn : ℕ\nf : Fin (n + 1) → α\nh0 : f 0 = ⊥\nhlast : f (Fin.last n) = ⊤\nhcovBy : ∀ (k : Fin n), f k.castSucc ⩿ f k.succ\nhmono : Monotone f\nt : Set α\nhtc : IsChain (fun x1 x2 ↦ x1 ≤ x2) t\nhbt : range f ⊆ t\nx : α\nhx : x ∈ t\nh : ∀ (y : Fi... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.FlagRange | {
"line": 45,
"column": 12
} | {
"line": 45,
"column": 47
} | [
{
"pp": "case zero\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : BoundedOrder α\nn : ℕ\nf : Fin (n + 1) → α\nh0 : f 0 = ⊥\nhlast : f (Fin.last n) = ⊤\nhcovBy : ∀ (k : Fin n), f k.castSucc ⩿ f k.succ\nhmono : Monotone f\nt : Set α\nhtc : IsChain (fun x1 x2 ↦ x1 ≤ x2) t\nhbt : range f ⊆ t\nx : α\nhx : x ∈ t\nh ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.FP.Basic | {
"line": 87,
"column": 10
} | {
"line": 87,
"column": 24
} | [
{
"pp": "C : FloatCfg\nthis : prec ≤ 2 * emax\n⊢ emin + ↑prec - 1 ≤ ↑emax",
"usedConstants": [
"HMul.hMul",
"FP.prec",
"congrArg",
"FP.emax",
"Eq.mp",
"instMulNat",
"instOfNatNat",
"Int",
"LE.le",
"instLENat",
"Nat.cast",
"Nat",
"... | ← Int.ofNat_le | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Condensed.Light.Sequence | {
"line": 360,
"column": 70
} | {
"line": 360,
"column": 81
} | [
{
"pp": "R : Type\ninst✝ : CommRing R\nX Y : LightCondMod R\np : X ⟶ Y\nhp : Epi p\nS : LightProfinite\nf : (free R).obj (S ⊗ ℕ∪{∞}).toCondensed ⟶ Y\nT : LightProfinite\nπ : T ⟶ S ⊗ ℕ∪{∞}\ng : (free R).obj T.toCondensed ⟶ X\nhπ : Epi π\ncomm : (lightProfiniteToLightCondSet ⋙ free R).map π ≫ f = g ≫ p\nS' T' : L... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 83,
"column": 6
} | {
"line": 83,
"column": 22
} | [
{
"pp": "case none\nα : Type u_1\nβ : Type u_2\nf : α → Option α\ng : α → β\nh : ∀ (a b : α), b ∈ f a → g a = g b\na : α\nl : List α\nh' : f a = none\n⊢ map g (lookmap f (a :: l)) = map g (a :: l)",
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.map",
"List.lookmap",
"id",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.FinEnum | {
"line": 83,
"column": 39
} | {
"line": 83,
"column": 50
} | [
{
"pp": "α : Type u\nβ✝ : α → Type v\nβ : Type ?u.2416\nf : β → α\ninst✝¹ : DecidableEq α\ninst✝ : FinEnum β\nh : Surjective f\nx✝ : α\n⊢ x✝ ∈ List.map f (toList β)",
"usedConstants": [
"Eq.mpr",
"FinEnum.toList",
"congrArg",
"List.map",
"Membership.mem",
"Exists",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 101,
"column": 6
} | {
"line": 101,
"column": 21
} | [
{
"pp": "case cons.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na : α\nl₁✝ l₂✝ : List α\np : l₁✝ ~ l₂✝\nIH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) l₁✝ → lookmap f l₁✝ ~ lookmap f l₂✝\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finite.Perm | {
"line": 49,
"column": 2
} | {
"line": 49,
"column": 25
} | [
{
"pp": "α : Type u_1\ninst✝ : Finite α\nhα : Nat.card α ≤ 2\n⊢ Nat.card (Perm α) ∣ 2",
"usedConstants": [
"Eq.mpr",
"Dvd.dvd",
"congrArg",
"Nat.card_perm",
"id",
"Nat.card",
"instOfNatNat",
"Nat.instDvd",
"Nat.factorial",
"Equiv.Perm",
"Nat"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finite.Perm | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 46
} | [
{
"pp": "α : Type u_1\ninst✝ : Finite α\na b c : α\nleft✝² : a ∈ _root_.Set.univ\nleft✝¹ : b ∈ _root_.Set.univ\nleft✝ : c ∈ _root_.Set.univ\nhab : a ≠ b\nhac : a ≠ c\nhbc : b ≠ c\nh : ∀ (a b : Perm α) (x : α), (a * b) x = (b * a) x\n⊢ b = c",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 105,
"column": 6
} | {
"line": 105,
"column": 26
} | [
{
"pp": "case swap.none.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nh₁ : f a = none\nh₂ : f b = none\n⊢ lookmap f (b :: a :: l) ~ lookmap f (a :: b :: l)",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 106,
"column": 6
} | {
"line": 106,
"column": 48
} | [
{
"pp": "case swap.none.some\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nh₁ : f a = none\nd : α\nh₂ : f b = some d\n⊢ lookmap f (b :: a :: l) ~ lookmap f (a :: b :: l)",
"usedConstants":... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 107,
"column": 6
} | {
"line": 107,
"column": 48
} | [
{
"pp": "case swap.some.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nc : α\nh₁ : f a = some c\nh₂ : f b = none\n⊢ lookmap f (b :: a :: l) ~ lookmap f (a :: b :: l)",
"usedConstants":... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.FinEnum | {
"line": 328,
"column": 24
} | {
"line": 328,
"column": 45
} | [
{
"pp": "α : Type u_1\ninst✝¹ : FinEnum α\nβ : α → Type u_2\ninst✝ : (a : α) → FinEnum (β a)\nf : (a : α) → β a\n⊢ f ∈ enum β",
"usedConstants": [
"Eq.mpr",
"FinEnum.toList",
"Membership.mem",
"Exists",
"id",
"FinEnum.mem_toList",
"List.Pi.enum",
"List",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.FinEnum | {
"line": 336,
"column": 59
} | {
"line": 336,
"column": 70
} | [
{
"pp": "α✝ : Type u_1\ninst✝³ : FinEnum α✝\nβ : α✝ → Type u_2\ninst✝² : (a : α✝) → FinEnum (β a)\np : Prop\ninst✝¹ : Decidable p\nα : p → Type\ninst✝ : (hp : p) → FinEnum (α hp)\nhp : p\nx : (hp : p) → α hp\n⊢ x ∈ map (fun x x_1 ↦ x) (FinEnum.toList (α hp))",
"usedConstants": [
"Eq.mpr",
"FinEn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.DenselyOrdered | {
"line": 33,
"column": 4
} | {
"line": 33,
"column": 52
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : DenselyOrdered α\ns t : Finset α\ninst✝² : NoMaxOrder α\ninst✝¹ : NoMinOrder α\ninst✝ : Nonempty α\nH : ∀ x ∈ s, ∀ y ∈ t, x < y\nhs : ¬s.Nonempty\nht : ¬t.Nonempty\n⊢ ∃ b, (∀ x ∈ s, x < b) ∧ ∀ y ∈ t, b < y",
"usedConstants": [
"False",
... | exact Nonempty.elim ‹_› fun p ↦ ⟨p, by simp_all⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Finset.DenselyOrdered | {
"line": 33,
"column": 4
} | {
"line": 33,
"column": 52
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : DenselyOrdered α\ns t : Finset α\ninst✝² : NoMaxOrder α\ninst✝¹ : NoMinOrder α\ninst✝ : Nonempty α\nH : ∀ x ∈ s, ∀ y ∈ t, x < y\nhs : ¬s.Nonempty\nht : ¬t.Nonempty\n⊢ ∃ b, (∀ x ∈ s, x < b) ∧ ∀ y ∈ t, b < y",
"usedConstants": [
"False",
... | exact Nonempty.elim ‹_› fun p ↦ ⟨p, by simp_all⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.DenselyOrdered | {
"line": 33,
"column": 4
} | {
"line": 33,
"column": 52
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : DenselyOrdered α\ns t : Finset α\ninst✝² : NoMaxOrder α\ninst✝¹ : NoMinOrder α\ninst✝ : Nonempty α\nH : ∀ x ∈ s, ∀ y ∈ t, x < y\nhs : ¬s.Nonempty\nht : ¬t.Nonempty\n⊢ ∃ b, (∀ x ∈ s, x < b) ∧ ∀ y ∈ t, b < y",
"usedConstants": [
"False",
... | exact Nonempty.elim ‹_› fun p ↦ ⟨p, by simp_all⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.AList | {
"line": 323,
"column": 2
} | {
"line": 323,
"column": 22
} | [
{
"pp": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nc : Sigma β\nl : List (Sigma β)\nh : (c :: l).NodupKeys\n⊢ { entries := c :: l, nodupKeys := h } = insert c.fst c.snd { entries := l, nodupKeys := ⋯ }",
"usedConstants": [
"Eq.mpr",
"AList.mk.injEq",
"AList.mk",
"congrArg",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Functor | {
"line": 54,
"column": 4
} | {
"line": 54,
"column": 30
} | [
{
"pp": "case cons\nF : Type u → Type u\ninst✝¹ : Applicative F\ninst✝ : CommApplicative F\nα' β' : Type u\nf : α' → F β'\na b : List α'\nx : α'\nl₁ l₂ : List α'\na✝ : l₁ ~ l₂\nh : ofList <$> Traversable.traverse f l₁ = ofList <$> Traversable.traverse f l₂\nthis : cons <$> f x <*> ofList <$> Traversable.travers... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Functor | {
"line": 62,
"column": 6
} | {
"line": 62,
"column": 24
} | [
{
"pp": "case e_a.e_a.h.h.h\nF : Type u → Type u\ninst✝¹ : Applicative F\ninst✝ : CommApplicative F\nα' β' : Type u\nf : α' → F β'\na✝ b✝ : List α'\nx y : α'\nl✝ : List α'\na b : β'\nl : List β'\n⊢ flip (fun a b l ↦ ↑(a :: b :: l)) a b l = ↑(a :: b :: l)",
"usedConstants": [
"Eq.mpr",
"Multiset"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sigma | {
"line": 252,
"column": 6
} | {
"line": 254,
"column": 38
} | [
{
"pp": "α : Type u\nα' : Type u'\nβ : Type v\nf : α → α'\nhf : Function.Injective f\nhd : (_ : α) × β\ntl : List ((_ : α) × β)\nih : tl.NodupKeys → (map (Sigma.map f fun x ↦ id) tl).NodupKeys\nnd : ¬hd.fst ∈ tl.keys ∧ tl.NodupKeys\nh : (Sigma.map f (fun x ↦ id) hd).fst ∈ (map (Sigma.map f fun x ↦ id) tl).keys\... | simp only [keys, map_map] at h ⊢
obtain ⟨x, hm, he⟩ := mem_map.mp h
exact mem_map.mpr ⟨x, hm, hf he⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Sigma | {
"line": 252,
"column": 6
} | {
"line": 254,
"column": 38
} | [
{
"pp": "α : Type u\nα' : Type u'\nβ : Type v\nf : α → α'\nhf : Function.Injective f\nhd : (_ : α) × β\ntl : List ((_ : α) × β)\nih : tl.NodupKeys → (map (Sigma.map f fun x ↦ id) tl).NodupKeys\nnd : ¬hd.fst ∈ tl.keys ∧ tl.NodupKeys\nh : (Sigma.map f (fun x ↦ id) hd).fst ∈ (map (Sigma.map f fun x ↦ id) tl).keys\... | simp only [keys, map_map] at h ⊢
obtain ⟨x, hm, he⟩ := mem_map.mp h
exact mem_map.mpr ⟨x, hm, hf he⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finset.Lattice.Pi | {
"line": 48,
"column": 4
} | {
"line": 48,
"column": 88
} | [
{
"pp": "case insert.refine_2\nα : Type u_1\nι : Type u_2\ninst✝² : DistribLattice α\ninst✝¹ : BoundedOrder α\ninst✝ : DecidableEq ι\nκ : ι → Type u_3\nt : (i : ι) → Finset (κ i)\nf : (i : ι) → κ i → α\ni : ι\ns : Finset ι\nhi : i ∉ s\nih : (s.inf fun i ↦ (t i).sup (f i)) = (s.pi t).sup fun g ↦ s.attach.inf fun... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Lattice.Pi | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 44
} | [
{
"pp": "case insert.refine_1.inr\nα : Type u_1\nι : Type u_2\ninst✝² : DistribLattice α\ninst✝¹ : BoundedOrder α\ninst✝ : DecidableEq ι\nκ : ι → Type u_3\nt : (i : ι) → Finset (κ i)\nf : (i : ι) → κ i → α\ni : ι\ns : Finset ι\nhi : i ∉ s\nih : (s.inf fun i ↦ (t i).sup (f i)) = (s.pi t).sup fun g ↦ s.attach.inf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finmap | {
"line": 306,
"column": 4
} | {
"line": 306,
"column": 15
} | [
{
"pp": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nf : { f // ∀ (i : α), (f.2 i).isSome = true ↔ i ∈ f.1 }\ni : α\nx : β i\nleft✝¹ : ⟨i, x⟩.fst ∈ (↑f).1\nhx : (↑f).2 ⟨i, x⟩.fst = some ⟨i, x⟩.snd\ny : β i\nleft✝ : ⟨i, y⟩.fst ∈ (↑f).1\nhy : (↑f).2 ⟨i, y⟩.fst = some ⟨i, y⟩.snd\n⊢ ⟨i, x⟩ = ⟨i, y⟩",
"us... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sigma | {
"line": 455,
"column": 46
} | {
"line": 455,
"column": 67
} | [
{
"pp": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na₁ a₂ : α\nl : List (Sigma β)\nh : a₁ ≠ a₂\np✝ : a₁ ∈ l.keys\nw✝² : β a₂\nw✝¹ w✝ : List (Sigma β)\nleft✝ : ¬a₂ ∈ w✝¹.keys\np : a₁ ∈ (w✝¹ ++ ⟨a₂, w✝²⟩ :: w✝).keys\nq : a₂ ∈ (w✝¹ ++ ⟨a₂, w✝²⟩ :: w✝).keys\n⊢ a₁ ∈ (w✝¹ ++ w✝).keys",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.PiInduction | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 28
} | [
{
"pp": "case h.e'_1\nι : Type u_1\nα : ι → Type u_2\ninst✝² : Finite ι\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → DecidableEq (α i)\nr : (i : ι) → α i → Finset (α i) → Prop\nH_ex : ∀ (i : ι) (s : Finset (α i)), s.Nonempty → ∃ x ∈ s, r i x (s.erase x)\np : ((i : ι) → Finset (α i)) → Prop\nh0 : p fun x ↦ ∅\nstep... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.BigOperators | {
"line": 52,
"column": 2
} | {
"line": 53,
"column": 25
} | [
{
"pp": "case h\nι : Type u_1\nM : Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : AddCommMonoid M\na✝ : List (ι →₀ M)\n⊢ (sum (Quot.mk (⇑(List.isSetoid (ι →₀ M))) a✝)).support ⊆\n (map Finsupp.support (Quot.mk (⇑(List.isSetoid (ι →₀ M))) a✝)).sup",
"usedConstants": [
"Multiset.sum",
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.BigOperators | {
"line": 71,
"column": 4
} | {
"line": 72,
"column": 9
} | [
{
"pp": "ι : Type u_1\nM : Type u_2\ninst✝¹ : DecidableEq ι\ninst✝ : Zero M\ns : Multiset (ι →₀ M)\nx : ι\nx✝ : List (ι →₀ M)\n⊢ x ∈ (map Finsupp.support (Quot.mk (⇑(List.isSetoid (ι →₀ M))) x✝)).sup ↔\n ∃ f ∈ Quot.mk (⇑(List.isSetoid (ι →₀ M))) x✝, x ∈ f.support",
"usedConstants": [
"Eq.mpr",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.NeLocus | {
"line": 44,
"column": 2
} | {
"line": 45,
"column": 32
} | [
{
"pp": "α : Type u_1\nN : Type u_3\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : Zero N\nf g : α →₀ N\na : α\n⊢ a ∈ f.neLocus g ↔ f a ≠ g a",
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"instDecidableNot",
"Finset.instUnion",
"congrArg",
"_private.Math... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.NeLocus | {
"line": 83,
"column": 14
} | {
"line": 83,
"column": 73
} | [
{
"pp": "α : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁴ : DecidableEq α\ninst✝³ : DecidableEq N\ninst✝² : Zero N\ninst✝¹ : DecidableEq M\ninst✝ : Zero M\nf g : α →₀ N\nF : N → M\nF0 : F 0 = 0\nx : α\n⊢ x ∈ (mapRange F F0 f).neLocus (mapRange F F0 g) → x ∈ f.neLocus g",
"usedConstants": [
"Finsupp.in... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.NeLocus | {
"line": 90,
"column": 2
} | {
"line": 90,
"column": 32
} | [
{
"pp": "case h\nα : Type u_1\nM : Type u_2\nN : Type u_3\nP : Type u_4\ninst✝⁵ : DecidableEq α\ninst✝⁴ : DecidableEq N\ninst✝³ : Zero M\ninst✝² : DecidableEq P\ninst✝¹ : Zero P\ninst✝ : Zero N\nF : M → N → P\nF0 : F 0 0 = 0\nf : α →₀ M\ng₁ g₂ : α →₀ N\nhF : ∀ (f : M), Function.Injective fun g ↦ F f g\na✝ : α\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.NeLocus | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 32
} | [
{
"pp": "case h\nα : Type u_1\nM : Type u_2\nN : Type u_3\nP : Type u_4\ninst✝⁵ : DecidableEq α\ninst✝⁴ : DecidableEq M\ninst✝³ : Zero M\ninst✝² : DecidableEq P\ninst✝¹ : Zero P\ninst✝ : Zero N\nF : M → N → P\nF0 : F 0 0 = 0\nf₁ f₂ : α →₀ M\ng : α →₀ N\nhF : ∀ (g : N), Function.Injective fun f ↦ F f g\na✝ : α\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.NeLocus | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 32
} | [
{
"pp": "case h\nα : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁴ : DecidableEq α\ninst✝³ : DecidableEq N\ninst✝² : DecidableEq M\ninst✝¹ : Zero M\ninst✝ : Zero N\nf g : α →₀ N\nF : N → M\nF0 : F 0 = 0\nhF : Function.Injective F\na✝ : α\n⊢ a✝ ∈ (mapRange F F0 f).neLocus (mapRange F F0 g) ↔ a✝ ∈ f.neLocus g",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.NeLocus | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 35
} | [
{
"pp": "α : Type u_1\nN : Type u_3\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : AddGroup N\nf₁ f₂ g : α →₀ N\n⊢ (f₁ - g).neLocus (f₂ - g) = f₁.neLocus f₂",
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"congrArg",
"Finsupp.neLocus",
"Finset",
"... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.AList | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 28
} | [
{
"pp": "α : Type u_1\nM : Type u_2\ninst✝² : Zero M\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq M\nl : AList fun _x ↦ M\n⊢ l.lookupFinsupp.support = (filter (fun x ↦ decide (x.snd ≠ 0)) l.entries).keys.toFinset",
"usedConstants": [
"instDecidableNot",
"Finset",
"List.keys",
"Finsup... | dsimp only [lookupFinsupp] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.Data.Finsupp.AList | {
"line": 91,
"column": 60
} | {
"line": 93,
"column": 39
} | [
{
"pp": "α : Type u_1\nM : Type u_2\ninst✝¹ : Zero M\ninst✝ : DecidableEq α\nl : AList fun _x ↦ M\na : α\n⊢ l.lookupFinsupp a = 0 ↔ a ∉ l ∨ 0 ∈ lookup a l",
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"False",
"Option.ctorIdx",
"congrArg",
"Option.instMembership",... | by
rw [lookupFinsupp_apply, ← lookup_eq_none]
rcases lookup a l with - | m <;> simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.List.Sigma | {
"line": 748,
"column": 4
} | {
"line": 752,
"column": 35
} | [
{
"pp": "case cons\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns : Sigma β\ntail✝ : List (Sigma β)\nih : ∀ {l₂ : List (Sigma β)}, b ∈ dlookup a (tail✝.kunion l₂) ↔ b ∈ dlookup a tail✝ ∨ ¬a ∈ tail✝.keys ∧ b ∈ dlookup a l₂\nl₂ : List (Sigma β)\n⊢ b ∈ dlookup a ((s :: tail✝).kunion l₂) ↔ b ... | obtain ⟨a'⟩ := s
by_cases h₁ : a = a'
· subst h₁
simp
· simp [h₁, @ih (kerase a' l₂)] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Sigma | {
"line": 748,
"column": 4
} | {
"line": 752,
"column": 35
} | [
{
"pp": "case cons\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns : Sigma β\ntail✝ : List (Sigma β)\nih : ∀ {l₂ : List (Sigma β)}, b ∈ dlookup a (tail✝.kunion l₂) ↔ b ∈ dlookup a tail✝ ∨ ¬a ∈ tail✝.keys ∧ b ∈ dlookup a l₂\nl₂ : List (Sigma β)\n⊢ b ∈ dlookup a ((s :: tail✝).kunion l₂) ↔ b ... | obtain ⟨a'⟩ := s
by_cases h₁ : a = a'
· subst h₁
simp
· simp [h₁, @ih (kerase a' l₂)] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finsupp.AList | {
"line": 119,
"column": 6
} | {
"line": 119,
"column": 17
} | [
{
"pp": "case neg\nα : Type u_1\nM : Type u_2\ninst✝ : Zero M\nf : α →₀ M\na : α\nh : ¬f a = 0\n⊢ ⟨a, f a⟩ ∈ f.toAList.entries",
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"Prod.toSigma",
"congrArg",
"Finset",
"List.map",
"Prod.exists._simp_1",
"heq_e... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.Sigma | {
"line": 90,
"column": 2
} | {
"line": 90,
"column": 13
} | [
{
"pp": "case h\nκ : Type u_1\nι : κ → Type u_2\nM : Type u_3\ninst✝ : Zero M\nk : κ\nf g : ι k →₀ M\nh : f.embSigma = g.embSigma\ni : ι k\nthis : f.embSigma ⟨k, i⟩ = g.embSigma ⟨k, i⟩\n⊢ f i = g i",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Holor | {
"line": 151,
"column": 4
} | {
"line": 151,
"column": 14
} | [
{
"pp": "α : Type\nds₁ ds₂ ds₃ : List ℕ\ninst✝ : Semigroup α\nx : Holor α ds₁\ny : Holor α ds₂\nz : Holor α ds₃\nt : HolorIndex (ds₁ ++ ds₂ ++ ds₃)\n⊢ (x ⊗ y ⊗ z) t = cast ⋯ (x ⊗ (y ⊗ z)) t",
"usedConstants": [
"Semigroup.toMul",
"cast",
"id",
"instHAppendOfAppend",
"List",
... | unfold mul | Lean.Elab.Tactic.evalUnfold | Lean.Parser.Tactic.unfold |
Mathlib.Data.Holor | {
"line": 242,
"column": 28
} | {
"line": 242,
"column": 82
} | [
{
"pp": "α : Type\nd : ℕ\nds : List ℕ\ninst✝ : Semiring α\nx : Holor α (d :: ds)\ni : ℕ\nhid : i < d\nb : ↥(Finset.range d)\na✝ : b ∈ (Finset.range d).attach\nhbi : b ≠ ⟨i, ⋯⟩\n⊢ i ≠ ↑b",
"usedConstants": [
"Finset",
"Membership.mem",
"id",
"Ne",
"Finset.range",
"Finset.i... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Holor | {
"line": 280,
"column": 6
} | {
"line": 280,
"column": 59
} | [
{
"pp": "α : Type\nds : List ℕ\ninst✝¹ : Mul α\ninst✝ : AddMonoid α\nm n : ℕ\ny x₁ x₂ : Holor α ds\nhx₁ : x₁.CPRankMax1\nhx₂ : CPRankMax m x₂\nhy : CPRankMax n y\nthis : CPRankMax (m + n + 1) (x₁ + (x₂ + y))\n⊢ CPRankMax (m + 1 + n) (x₁ + x₂ + y)",
"usedConstants": [
"Eq.mpr",
"AddMonoid.toAddSe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Holor | {
"line": 327,
"column": 4
} | {
"line": 327,
"column": 19
} | [
{
"pp": "α : Type\ninst✝ : Semiring α\nd : ℕ\nds : List ℕ\nx : Holor α (d :: ds)\nh_summands : ∀ (i : ↥(Finset.range d)), CPRankMax ds.prod (unitVec d ↑i ⊗ x.slice ↑i ⋯)\nh_dds_prod : (d :: ds).prod = (Finset.range d).card * ds.prod\nthis : CPRankMax ((Finset.range d).attach.card * ds.prod) (∑ i ∈ (Finset.range... | rw [h_dds_prod] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Int.Lemmas | {
"line": 56,
"column": 2
} | {
"line": 56,
"column": 44
} | [
{
"pp": "a b : ℤ\nha : a ≤ 0\nhb : b ≤ 0\n⊢ a.natAbs = b.natAbs ↔ a = b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.Lemmas | {
"line": 61,
"column": 2
} | {
"line": 61,
"column": 35
} | [
{
"pp": "a b : ℤ\nha : 0 ≤ a\nhb : b ≤ 0\n⊢ a.natAbs = b.natAbs ↔ a = -b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.Lemmas | {
"line": 65,
"column": 2
} | {
"line": 65,
"column": 35
} | [
{
"pp": "a b : ℤ\nha : a ≤ 0\nhb : 0 ≤ b\n⊢ a.natAbs = b.natAbs ↔ -a = b",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.Lemmas | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 30
} | [
{
"pp": "a : ℤ\nx✝ : a ∈ Iic 0\nb : ℤ\nhb : b ∈ Iic 0\nhab : a < b\n⊢ b.natAbs < a.natAbs",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.CardIntervalMod | {
"line": 61,
"column": 2
} | {
"line": 62,
"column": 76
} | [
{
"pp": "case h\na b r : ℤ\nhr : 0 < r\nx : ℤ\n⊢ x ∈ {x ∈ Ioc a b | r ∣ x} ↔ x ∈ map { toFun := fun x ↦ x * r, inj' := ⋯ } (Ioc ⌊↑a / ↑r⌋ ⌊↑b / ↑r⌋)",
"usedConstants": [
"Int.decidableDvd",
"Iff.mpr",
"Int.cast",
"Eq.mpr",
"GroupWithZero.toMonoidWithZero",
"Preorder.toLT"... | simp only [mem_map, mem_filter, mem_Ioc, floor_lt, le_floor, div_lt_iff₀, le_div_iff₀,
dvd_iff_exists_eq_mul_left, cast_pos.2 hr, ← cast_mul, cast_lt, cast_le] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Int.Star | {
"line": 29,
"column": 36
} | {
"line": 29,
"column": 66
} | [
{
"pp": "n : ℕ\nhn : Even n\nx : ℤ\nhx : x ∈ nonneg ℤ\n⊢ x = x.natAbs • 1 ^ n",
"usedConstants": [
"Int.instAddCommGroup",
"one_pow",
"Eq.mpr",
"MulOne.toOne",
"instHSMul",
"HMul.hMul",
"Monoid.toMulOneClass",
"abs",
"congrArg",
"Int.instLinearOrde... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.Star | {
"line": 35,
"column": 2
} | {
"line": 35,
"column": 23
} | [
{
"pp": "⊢ closure (range fun x ↦ x * x) = nonneg ℤ",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 110,
"column": 8
} | {
"line": 110,
"column": 19
} | [
{
"pp": "case false\nα : Type u_1\np : α → Bool\nl : List α\nhead : α\ntail : List α\nhi : find? p tail = (dropWhile (fun x ↦ !p x) tail).head?\nphh : false = p head\nphh' : ¬p head = true\n⊢ (!p head) = true",
"usedConstants": [
"Eq.mpr",
"Bool.not",
"congrArg",
"id",
"Bool.tr... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 113,
"column": 8
} | {
"line": 113,
"column": 19
} | [
{
"pp": "case true\nα : Type u_1\np : α → Bool\nl : List α\nhead : α\ntail : List α\nhi : find? p tail = (dropWhile (fun x ↦ !p x) tail).head?\nphh : true = p head\n⊢ ¬(!p head) = true",
"usedConstants": [
"Eq.mpr",
"Bool.not",
"Bool.not_eq_false",
"congrArg",
"id",
"Bool... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 123,
"column": 62
} | {
"line": 123,
"column": 73
} | [
{
"pp": "α : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ p x = true\n⊢ dropWhile (fun x ↦ !p x) l ≠ []",
"usedConstants": [
"Eq.mpr",
"List.dropWhile_eq_nil_iff._simp_1",
"Bool.not",
"Bool.not_eq_false",
"congrArg",
"Membership.mem",
"Exists",
"id",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 127,
"column": 62
} | {
"line": 127,
"column": 73
} | [
{
"pp": "α : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ ¬p x = true\n⊢ dropWhile p l ≠ []",
"usedConstants": [
"Eq.mpr",
"List.dropWhile_eq_nil_iff._simp_1",
"congrArg",
"Membership.mem",
"Exists",
"id",
"Ne",
"Bool.true",
"funext",
"List... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.TakeWhile | {
"line": 130,
"column": 4
} | {
"line": 130,
"column": 15
} | [
{
"pp": "case convert_2\nα : Type u_1\np : α → Bool\nl : List α\nh : ∃ x, x ∈ l ∧ ¬p x = true\n⊢ ∃ x, x ∈ l ∧ (!p x) = true",
"usedConstants": [
"Eq.mpr",
"Bool.not",
"congrArg",
"Membership.mem",
"Exists",
"id",
"Bool.true",
"funext",
"List",
"And... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.ModifyLast | {
"line": 43,
"column": 30
} | {
"line": 43,
"column": 52
} | [
{
"pp": "case cons\nα : Type u_1\nf : α → α\na head✝ : α\ntl : List α\n⊢ (#[].push head✝).toListAppend (modifyLast.go f (tl ++ [a]) #[]) = head✝ :: (tl ++ [f a])",
"usedConstants": [
"Eq.mpr",
"Array.toListAppend_eq",
"Array.push",
"congrArg",
"List.modifyLast.go",
"id",
... | Array.toListAppend_eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.Lemmas | {
"line": 42,
"column": 8
} | {
"line": 42,
"column": 42
} | [
{
"pp": "case cons.succ.succ.refine_1\nα : Type u_1\nx hd : α\ntl : List α\nIH :\n ¬x ∈ tl →\n ∀ ⦃n : ℕ⦄,\n n ∈ {n | n ≤ tl.length} →\n ∀ ⦃m : ℕ⦄, m ∈ {n | n ≤ tl.length} → (fun k ↦ tl.insertIdx k x) n = (fun k ↦ tl.insertIdx k x) m → n = m\nhx : ¬x = hd ∧ ¬x ∈ tl\nn✝¹ : ℕ\nhn : n✝¹ + 1 ≤ tl.len... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lemmas | {
"line": 43,
"column": 8
} | {
"line": 43,
"column": 42
} | [
{
"pp": "case cons.succ.succ.refine_2\nα : Type u_1\nx hd : α\ntl : List α\nIH :\n ¬x ∈ tl →\n ∀ ⦃n : ℕ⦄,\n n ∈ {n | n ≤ tl.length} →\n ∀ ⦃m : ℕ⦄, m ∈ {n | n ≤ tl.length} → (fun k ↦ tl.insertIdx k x) n = (fun k ↦ tl.insertIdx k x) m → n = m\nhx : ¬x = hd ∧ ¬x ∈ tl\nn✝¹ : ℕ\nhn : n✝¹ + 1 ≤ tl.len... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Intervals | {
"line": 62,
"column": 54
} | {
"line": 62,
"column": 70
} | [
{
"pp": "n m l : ℕ\nthis : n ≤ l ∧ l < n + (m - n) ↔ n ≤ l ∧ l < m\n⊢ l ∈ Ico n m ↔ n ≤ l ∧ l < m",
"usedConstants": [
"List.mem_range'_1._simp_1",
"congrArg",
"List.range'",
"HSub.hSub",
"Membership.mem",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENa... | simp [Ico, this] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.List.Intervals | {
"line": 62,
"column": 54
} | {
"line": 62,
"column": 70
} | [
{
"pp": "n m l : ℕ\nthis : n ≤ l ∧ l < n + (m - n) ↔ n ≤ l ∧ l < m\n⊢ l ∈ Ico n m ↔ n ≤ l ∧ l < m",
"usedConstants": [
"List.mem_range'_1._simp_1",
"congrArg",
"List.range'",
"HSub.hSub",
"Membership.mem",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENa... | simp [Ico, this] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Intervals | {
"line": 62,
"column": 54
} | {
"line": 62,
"column": 70
} | [
{
"pp": "n m l : ℕ\nthis : n ≤ l ∧ l < n + (m - n) ↔ n ≤ l ∧ l < m\n⊢ l ∈ Ico n m ↔ n ≤ l ∧ l < m",
"usedConstants": [
"List.mem_range'_1._simp_1",
"congrArg",
"List.range'",
"HSub.hSub",
"Membership.mem",
"instSubNat",
"instOfNatNat",
"LE.le",
"instLENa... | simp [Ico, this] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Intervals | {
"line": 69,
"column": 59
} | {
"line": 69,
"column": 75
} | [
{
"pp": "n m k : ℕ\n⊢ range' (k + n) (m - n) = range' (n + k) (m - n)",
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.range'",
"HSub.hSub",
"id",
"instSubNat",
"instOfNatNat",
"List",
"instHAdd",
"instHSub",
"HAdd.hAdd",
"Nat",
"... | Nat.add_comm n k | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.List.Intervals | {
"line": 189,
"column": 4
} | {
"line": 189,
"column": 15
} | [
{
"pp": "n m : ℕ\nhnm : n < m\nx✝¹ : ℕ\nx✝ : x✝¹ ∈ Ico n m\n⊢ decide (x✝¹ ≤ n) = decide (x✝¹ < n + 1)",
"usedConstants": [
"Eq.mpr",
"id",
"instOfNatNat",
"LE.le",
"instLENat",
"instHAdd",
"Iff",
"HAdd.hAdd",
"Nat",
"LT.lt",
"Bool",
"Na... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Palindrome | {
"line": 66,
"column": 69
} | {
"line": 68,
"column": 38
} | [
{
"pp": "α : Type u_1\nl : List α\n⊢ (l ++ l.reverse).Palindrome",
"usedConstants": [
"List.Palindrome.of_reverse_eq",
"Eq.mpr",
"congrArg",
"id",
"instHAppendOfAppend",
"List",
"List.reverse_reverse",
"List.reverse",
"Eq.refl",
"List.instAppend",
... | by
apply of_reverse_eq
rw [reverse_append, reverse_reverse] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.List.SplitLengths | {
"line": 53,
"column": 46
} | {
"line": 53,
"column": 57
} | [
{
"pp": "α : Type u_1\nl : List α\nsz : List ℕ\ni : ℕ\nhi : i < (sz.splitLengths l).length\n⊢ i < sz.length",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitLengths | {
"line": 68,
"column": 4
} | {
"line": 68,
"column": 26
} | [
{
"pp": "case h\nα : Type u_1\nhead : ℕ\ntail : List ℕ\nih : ∀ (l : List α), l.length ≤ tail.sum → (tail.splitLengths l).flatten = l\nl : List α\nh : l.length ≤ (head :: tail).sum\n⊢ (drop head l).length ≤ tail.sum",
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.length_drop",
"AddMo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitLengths | {
"line": 93,
"column": 46
} | {
"line": 93,
"column": 57
} | [
{
"pp": "α✝ : Type u_1\nl✝ : List α✝\nsz✝ : List ℕ\nα : Type u_2\nl : List α\nsz : List ℕ\nh : sz.sum ≤ l.length\ni : ℕ\nhi : i < (sz.splitLengths l).length\n⊢ i < sz.length",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitLengths | {
"line": 97,
"column": 4
} | {
"line": 97,
"column": 15
} | [
{
"pp": "α : Type u_2\nl : List α\nsz : List ℕ\nh : sz.sum ≤ l.length\ni : ℕ\nhi : i < (sz.splitLengths l).length\nthis : map length (sz.splitLengths l) = sz\n⊢ i < (map length (sz.splitLengths l)).length",
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.map",
"id",
"List",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitLengths | {
"line": 104,
"column": 23
} | {
"line": 104,
"column": 34
} | [
{
"pp": "α : Type u_2\nl : List α\nsz : List ℕ\nb : ℕ\nh : ∀ (n : ℕ), n ∈ sz → n ≤ b\ni : ℕ\nhi : i < (sz.splitLengths l).length\nthis : (sz.splitLengths l)[i].length ≤ sz[i]\n⊢ i < sz.length",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitBy | {
"line": 61,
"column": 2
} | {
"line": 61,
"column": 29
} | [
{
"pp": "α : Type u_1\nr : α → α → Bool\nl : List α\n⊢ splitBy r l = [] ↔ l = []",
"usedConstants": [
"List.splitBy",
"List",
"List.flatten_splitBy",
"Eq",
"List.flatten"
]
}
] | have := flatten_splitBy r l | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.List.SplitBy | {
"line": 76,
"column": 6
} | {
"line": 76,
"column": 17
} | [
{
"pp": "case h_2\nα : Type u_1\nr : α → α → Bool\nb : α\nl : List α\nIH : ∀ {a : α} {g : List α}, ¬[] ∈ splitBy.loop r l a g []\na : α\ng : List α\nx✝ : Bool\nheq✝ : r a b = false\n⊢ ¬([] ∈ [(a :: g).reverse].reverse ∨ [] ∈ splitBy.loop r l b [] [])",
"usedConstants": [
"Eq.mpr",
"False",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitBy | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 15
} | [
{
"pp": "case nil\nα : Type u_1\nr : α → α → Bool\na : α\ng : List α\ngs : List (List α)\nhgs' : ¬[] ∈ gs\nhgs : IsChain (fun b a ↦ ∃ ha hb, r (a.getLast ha) (b.head hb) = false) gs\nhga : ∀ (m : List α), m ∈ gs.head? → ∃ ha hb, r (m.getLast ha) ((g.reverse ++ [a]).head hb) = false\n⊢ IsChain (fun b a ↦ ∃ ha hb... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.SplitBy | {
"line": 143,
"column": 8
} | {
"line": 143,
"column": 19
} | [
{
"pp": "case h_2.hgs'\nα : Type u_1\nr : α → α → Bool\nb : α\nl : List α\nIH :\n ∀ {a : α} {g : List α} {gs : List (List α)},\n ¬[] ∈ gs →\n IsChain (fun b a ↦ ∃ ha hb, r (a.getLast ha) (b.head hb) = false) gs →\n (∀ (m : List α), m ∈ gs.head? → ∃ ha hb, r (m.getLast ha) ((g.reverse ++ [a]).hea... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Matrix.Bilinear | {
"line": 148,
"column": 4
} | {
"line": 148,
"column": 15
} | [
{
"pp": "case mp.a\nl : Type u_1\nm : Type u_2\nn : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : Semiring R\ninst✝³ : Semiring A\ninst✝² : Module R A\ninst✝¹ : SMulCommClass R A A\ninst✝ : Nonempty n\na : Matrix l m A\ninhabited_h : Inhabited n\ni : l\nj : m\nh : (mulLeftLinearMap n R a) (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Matrix.Bilinear | {
"line": 159,
"column": 50
} | {
"line": 159,
"column": 73
} | [
{
"pp": "m : Type u_2\nn✝ : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq m\ninst✝³ : Semiring R\ninst✝² : Semiring A\ninst✝¹ : Module R A\ninst✝ : SMulCommClass R A A\na : Matrix m m A\nk n : ℕ\n⊢ mulLeftLinearMap n✝ R a ^ n * mulLeftLinearMap n✝ R a = mulLeftLinearMap n✝ R (a ... | Module.End.mul_eq_comp, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Matrix.Bilinear | {
"line": 181,
"column": 4
} | {
"line": 181,
"column": 15
} | [
{
"pp": "case mp.a\nl : Type u_1\nm : Type u_2\nn : Type u_3\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : Semiring R\ninst✝³ : Semiring A\ninst✝² : Module R A\ninst✝¹ : IsScalarTower R A A\na : Matrix m n A\ninst✝ : Nonempty l\ninhabited_h : Inhabited l\ni : m\nj : n\nh : (mulRightLinearMap l R a) ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Matrix.Bilinear | {
"line": 192,
"column": 52
} | {
"line": 192,
"column": 75
} | [
{
"pp": "l : Type u_1\nm : Type u_2\nR : Type u_5\nA : Type u_6\ninst✝⁵ : Fintype m\ninst✝⁴ : DecidableEq m\ninst✝³ : Semiring R\ninst✝² : Semiring A\ninst✝¹ : Module R A\ninst✝ : IsScalarTower R A A\na : Matrix m m A\nk n : ℕ\n⊢ mulRightLinearMap l R a ^ n * mulRightLinearMap l R a = mulRightLinearMap l R (a ^... | Module.End.mul_eq_comp, | Lean.Elab.Tactic.evalRewriteSeq | null |
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