module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.Data.Num.Lemmas | {
"line": 157,
"column": 6
} | {
"line": 157,
"column": 56
} | {
"line": 158,
"column": 2
} | [
{
"pp": "case gt\na b : PosNum\nthis : ↑b < ↑a\n⊢ ↑b + ↑b < ↑a + ↑a + 1",
"ppTerm": "?gt",
"assigned": true,
"usedConstants": [
"castPosNum",
"Nat.instOne",
"Nat.add_lt_add",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"Nat.le_succ_of_le",
"Nat... | [] | exact Nat.le_succ_of_le (Nat.add_lt_add this this) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Num.Lemmas | {
"line": 538,
"column": 21
} | {
"line": 538,
"column": 45
} | {
"line": 539,
"column": 2
} | [
{
"pp": "α : Type u_1\n⊢ ∀ (a b c : PosNum), a * (b + c) = a * b + a * c",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"castPosNum",
"HMul.hMul",
"Nat.instOne",
"congrArg",
"PosNum.instAdd",
"id",
... | [] | transfer; simp [mul_add] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Num.Lemmas | {
"line": 538,
"column": 21
} | {
"line": 538,
"column": 45
} | {
"line": 539,
"column": 2
} | [
{
"pp": "α : Type u_1\n⊢ ∀ (a b c : PosNum), a * (b + c) = a * b + a * c",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Distrib.leftDistribClass",
"Eq.mpr",
"castPosNum",
"HMul.hMul",
"Nat.instOne",
"congrArg",
"PosNum.instAdd",
"id",
... | [] | transfer; simp [mul_add] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.EpsilonNFA | {
"line": 255,
"column": 4
} | {
"line": 255,
"column": 26
} | {
"line": 256,
"column": 4
} | [
{
"pp": "α : Type u\nσ : Type v\nM : εNFA α σ\nx : List α\ns₂ : σ\nleft✝ : s₂ ∈ M.accept\nh : ∃ t ∈ M.start, s₂ ∈ M.evalFrom {t} x\n⊢ ∃ s₁ s₂ x', s₁ ∈ M.start ∧ s₂ ∈ M.accept ∧ x'.reduceOption = x ∧ M.IsPath s₁ s₂ x'",
"ppTerm": "?m.80",
"assigned": true,
"usedConstants": [
"Membership.mem",
... | [
"α : Type u\nσ : Type v\nM : εNFA α σ\nx : List α\ns₂ : σ\nleft✝¹ : s₂ ∈ M.accept\ns₁ : σ\nleft✝ : s₁ ∈ M.start\nh : s₂ ∈ M.evalFrom {s₁} x\n⊢ ∃ s₁ s₂ x', s₁ ∈ M.start ∧ s₂ ∈ M.accept ∧ x'.reduceOption = x ∧ M.IsPath s₁ s₂ x'"
] | obtain ⟨s₁, _, h⟩ := h | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 661,
"column": 24
} | {
"line": 661,
"column": 58
} | {
"line": 662,
"column": 6
} | [
{
"pp": "f g : ℝ → ℝ\nhg✝ : GrowsPolynomially g\nhf : f =Θ[atTop] g\nhf' : ∀ᶠ (x : ℝ) in atTop, 0 ≤ f x\nb : ℝ\nhb : b ∈ Set.Ioo 0 1\nhb_pos : 0 < b\nc₁ : ℝ\nhc₁_pos : 0 < c₁\nhf_lb : ∀ᶠ (x : ℝ) in atTop, c₁ * ‖g x‖ ≤ ‖f x‖\nc₂ : ℝ\nhc₂_pos : 0 < c₂\nhf_ub : ∀ᶠ (x : ℝ) in atTop, ‖f x‖ ≤ c₂ * ‖g x‖\nc₃ : ℝ\nhc₃_... | [] | by gcongr; exact (hg_bound u hu).1 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.EpsilonNFA | {
"line": 311,
"column": 2
} | {
"line": 311,
"column": 9
} | {
"line": 312,
"column": 2
} | [
{
"pp": "α : Type u\nσ : Type v\nM : NFA α σ\nstart : Set σ\n⊢ M.toεNFA.stepSet = M.stepSet",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Set.ext",
"εNFA.stepSet",
"funext",
"NFA.stepSet",
"NFA.toεNFA",
"Set"
],
"usedFVars": [
"σ",
... | [
"α : Type u\nσ : Type v\nM : NFA α σ\nstart S : Set σ\ns : α\nx✝ : σ\n⊢ x✝ ∈ M.toεNFA.stepSet S s ↔ x✝ ∈ M.stepSet S s"
] | ext S s | _private.Lean.Elab.Tactic.Ext.0.Lean.Elab.Tactic.Ext.evalExt | Lean.Elab.Tactic.Ext.ext |
Mathlib.Data.Num.Lemmas | {
"line": 608,
"column": 27
} | {
"line": 609,
"column": 40
} | {
"line": 611,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Semiring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nm n : PosNum\n⊢ ↑m ≤ ↑n ↔ m ≤ n",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"castPosNum",
"Preorder.toLT",
... | [] | by
rw [← not_lt]; exact not_congr cast_lt | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.Halting | {
"line": 57,
"column": 36
} | {
"line": 57,
"column": 89
} | {
"line": 58,
"column": 12
} | [
{
"pp": "case inl\nH : ∀ (cf cg : Code), cf.eval = cg.eval → (cf ∈ ∅ ↔ cg ∈ ∅)\nhC : ∀ (f : Code), f ∈ ∅ ↔ f.eval ∈ eval '' ∅\n⊢ ComputablePred fun c ↦ c ∈ ∅",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Set.mem_empty_iff_false._simp_1",
"congrA... | [
"case inl\nH : ∀ (cf cg : Code), cf.eval = cg.eval → (cf ∈ ∅ ↔ cg ∈ ∅)\nhC : ∀ (f : Code), f ∈ ∅ ↔ f.eval ∈ eval '' ∅\n⊢ Computable fun a ↦ false"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Halting | {
"line": 57,
"column": 36
} | {
"line": 57,
"column": 89
} | {
"line": 58,
"column": 12
} | [
{
"pp": "case inr\nH : ∀ (cf cg : Code), cf.eval = cg.eval → (cf ∈ Set.univ ↔ cg ∈ Set.univ)\nhC : ∀ (f : Code), f ∈ Set.univ ↔ f.eval ∈ eval '' Set.univ\n⊢ ComputablePred fun c ↦ c ∈ Set.univ",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instDecidableTrue",
"... | [
"case inr\nH : ∀ (cf cg : Code), cf.eval = cg.eval → (cf ∈ Set.univ ↔ cg ∈ Set.univ)\nhC : ∀ (f : Code), f ∈ Set.univ ↔ f.eval ∈ eval '' Set.univ\n⊢ Computable fun a ↦ true"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.Lemmas | {
"line": 742,
"column": 27
} | {
"line": 743,
"column": 40
} | {
"line": 745,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝² : Semiring α\ninst✝¹ : LinearOrder α\ninst✝ : IsStrictOrderedRing α\nm n : Num\n⊢ ↑m ≤ ↑n ↔ m ≤ n",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Num.cast_lt",
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"Preorder.toLT",
... | [] | by
rw [← not_lt]; exact not_congr cast_lt | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.RE | {
"line": 39,
"column": 2
} | {
"line": 44,
"column": 56
} | {
"line": 45,
"column": 2
} | [
{
"pp": "cf : Code\nhf : Nat.Partrec cf.eval\ncg : Code\nhg : Nat.Partrec cg.eval\nthis : Nat.Partrec fun n ↦ rfindOpt fun k ↦ Code.evaln k cf n <|> Code.evaln k cg n\nn : ℕ\n⊢ (∀ x ∈ rfindOpt fun k ↦ Code.evaln k cf n <|> Code.evaln k cg n, x ∈ cf.eval n ∨ x ∈ cg.eval n) ∧\n ((rfindOpt fun k ↦ Code.evaln k ... | [
"cf : Code\nhf : Nat.Partrec cf.eval\ncg : Code\nhg : Nat.Partrec cg.eval\nthis✝ : Nat.Partrec fun n ↦ rfindOpt fun k ↦ Code.evaln k cf n <|> Code.evaln k cg n\nn : ℕ\nthis : ∀ x ∈ rfindOpt fun k ↦ Code.evaln k cf n <|> Code.evaln k cg n, x ∈ cf.eval n ∨ x ∈ cg.eval n\n⊢ (∀ x ∈ rfindOpt fun k ↦ Code.evaln k cf n <|... | have : ∀ x ∈ rfindOpt fun k ↦ Code.evaln k cf n <|> Code.evaln k cg n,
x ∈ Code.eval cf n ∨ x ∈ Code.eval cg n := by
intro x h
obtain ⟨k, e⟩ := Nat.rfindOpt_spec h
rw [Option.mem_def, Option.orElse_eq_some, ← Option.mem_def, ← Option.mem_def] at e
obtain e | ⟨-, e⟩ := e <;> simp [Code.evaln_sound ... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Computability.PartrecBasis | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 48
} | {
"line": 82,
"column": 49
} | [
{
"pp": "n : ℕ\nf : List.Vector ℕ n →. ℕ\ng : List.Vector ℕ (n + 1) → ℕ\nhf : Partrec' f\nhg : Partrec' ↑g\n⊢ Partrec' fun v ↦ Part.map (fun a ↦ g (a ::ᵥ v)) (f v)",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Part",
"Eq.mpr",
"congrArg",
"Part.bind",
"Part... | [
"n : ℕ\nf : List.Vector ℕ n →. ℕ\ng : List.Vector ℕ (n + 1) → ℕ\nhf : Partrec' f\nhg : Partrec' ↑g\n⊢ Partrec' fun v ↦ (f v).bind fun y ↦ Part.some (g (y ::ᵥ v))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.PartrecBasis | {
"line": 106,
"column": 2
} | {
"line": 106,
"column": 13
} | {
"line": 106,
"column": 14
} | [
{
"pp": "n : ℕ\nf : ℕ →. ℕ\ng : List.Vector ℕ n → ℕ\nhf : Partrec' fun v ↦ f v.head\nhg : Partrec' ↑g\n⊢ Partrec' fun v ↦ f (g v)",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\nf : ℕ →. ℕ\ng : List.Vector ℕ n → ℕ\nhf : Partrec' fun v ↦ f v.head\nhg : Partrec' ↑g\n⊢ Partrec' fun v ↦ f (g v)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Num.Lemmas | {
"line": 779,
"column": 4
} | {
"line": 779,
"column": 35
} | {
"line": 779,
"column": 36
} | [
{
"pp": "case pos.pos\nf : Num → Num → Num\ng : Bool → Bool → Bool\np : PosNum → PosNum → Num\ngff : g false false = false\nf00 : f 0 0 = 0\nf0n : ∀ (n : PosNum), f 0 (pos n) = bif g false true then pos n else 0\nfn0 : ∀ (n : PosNum), f (pos n) 0 = bif g true false then pos n else 0\nfnn : ∀ (m n : PosNum), f (... | [
"case pos.pos.one\nf : Num → Num → Num\ng : Bool → Bool → Bool\np : PosNum → PosNum → Num\ngff : g false false = false\nf00 : f 0 0 = 0\nf0n : ∀ (n : PosNum), f 0 (pos n) = bif g false true then pos n else 0\nfn0 : ∀ (n : PosNum), f (pos n) 0 = bif g true false then pos n else 0\nfnn : ∀ (m n : PosNum), f (pos m) (... | induction m generalizing n with | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Computability.PartrecBasis | {
"line": 141,
"column": 4
} | {
"line": 141,
"column": 34
} | {
"line": 142,
"column": 6
} | [
{
"pp": "c : Partrec.Code\nhf : Nat.Partrec c.eval\n⊢ Partrec' fun v ↦ c.eval v.head",
"ppTerm": "?m.46",
"assigned": true,
"usedConstants": [
"Part",
"Eq.mpr",
"Nat.Partrec.Code.evaln",
"congrArg",
"List.Vector.head",
"List.Vector",
"id",
"instOfNatNa... | [
"c : Partrec.Code\nhf : Nat.Partrec c.eval\n⊢ Partrec' fun v ↦ Nat.rfindOpt fun k ↦ evaln k c v.head"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.PartrecBasis | {
"line": 167,
"column": 15
} | {
"line": 167,
"column": 42
} | {
"line": 167,
"column": 43
} | [
{
"pp": "m n : ℕ\nf : List.Vector ℕ m → List.Vector ℕ n\nh : Vec f\n⊢ Computable f",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"m n : ℕ\nf : List.Vector ℕ m → List.Vector ℕ n\nh : Vec f\n⊢ Computable f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.RE | {
"line": 199,
"column": 53
} | {
"line": 199,
"column": 64
} | {
"line": 199,
"column": 65
} | [
{
"pp": "α : Type u_1\ninst✝ : Primcodable α\nf : α → Bool\nh : Computable f\n⊢ Computable fun a ↦ decide ((fun a ↦ f a = true) a)",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"inferInstance",
"id",
"instDecidableEqBool",
"Bool.t... | [
"α : Type u_1\ninst✝ : Primcodable α\nf : α → Bool\nh : Computable f\n⊢ Computable fun a ↦ f a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.RE | {
"line": 210,
"column": 2
} | {
"line": 210,
"column": 32
} | {
"line": 210,
"column": 33
} | [
{
"pp": "f₁ f₂ : ℕ → ℕ\nhf₁ : Computable f₁\nhf₂ : Computable f₂\nc : ℕ → Prop\ninst✝ : DecidablePred c\nhc : ComputablePred c\n⊢ Computable fun k ↦ if c k then f₁ k else f₂ k",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f₁ f₂ : ℕ → ℕ\nhf₁ : Computable f₁\nhf₂ : Computable f₂\nc : ℕ → Prop\ninst✝ : DecidablePred c\nhc : ComputablePred c\n⊢ Computable fun k ↦ if c k then f₁ k else f₂ k"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.TuringMachine.Tape | {
"line": 267,
"column": 4
} | {
"line": 268,
"column": 70
} | {
"line": 269,
"column": 2
} | [
{
"pp": "case zero\nΓ : Type u_1\ninst✝ : Inhabited Γ\nf : Γ → Γ\ni : ℕ\nL : ListBlank Γ\n⊢ (modifyNth f 0 L).nth i = if i = 0 then f (L.nth i) else L.nth i",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Turing.ListBlank.modifyNth",
"Turing.ListBlank.nth_zero",
"False",... | [] | cases i <;> simp only [ListBlank.nth_zero, if_true, ListBlank.head_cons, ListBlank.modifyNth,
ListBlank.nth_succ, if_false, ListBlank.tail_cons, reduceCtorEq] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Computability.TuringMachine.Tape | {
"line": 267,
"column": 4
} | {
"line": 268,
"column": 70
} | {
"line": 269,
"column": 2
} | [
{
"pp": "case zero\nΓ : Type u_1\ninst✝ : Inhabited Γ\nf : Γ → Γ\ni : ℕ\nL : ListBlank Γ\n⊢ (modifyNth f 0 L).nth i = if i = 0 then f (L.nth i) else L.nth i",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Turing.ListBlank.modifyNth",
"Turing.ListBlank.nth_zero",
"False",... | [] | cases i <;> simp only [ListBlank.nth_zero, if_true, ListBlank.head_cons, ListBlank.modifyNth,
ListBlank.nth_succ, if_false, ListBlank.tail_cons, reduceCtorEq] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.TuringMachine.Tape | {
"line": 267,
"column": 4
} | {
"line": 268,
"column": 70
} | {
"line": 269,
"column": 2
} | [
{
"pp": "case zero\nΓ : Type u_1\ninst✝ : Inhabited Γ\nf : Γ → Γ\ni : ℕ\nL : ListBlank Γ\n⊢ (modifyNth f 0 L).nth i = if i = 0 then f (L.nth i) else L.nth i",
"ppTerm": "?zero",
"assigned": true,
"usedConstants": [
"Turing.ListBlank.modifyNth",
"Turing.ListBlank.nth_zero",
"False",... | [] | cases i <;> simp only [ListBlank.nth_zero, if_true, ListBlank.head_cons, ListBlank.modifyNth,
ListBlank.nth_succ, if_false, ListBlank.tail_cons, reduceCtorEq] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.RecursiveIn | {
"line": 88,
"column": 86
} | {
"line": 89,
"column": 34
} | {
"line": 91,
"column": 0
} | [
{
"pp": "f : ℕ →. ℕ\nO : Set (ℕ →. ℕ)\n⊢ RecursiveIn O f ↔ Nat.RecursiveIn O f",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Part",
"congrArg",
"Part.bind",
"Primcodable.ofDenumerable",
"Part.some",
"Part.bind_some",
"RecursiveIn",
"iff_sel... | [] | by
simp [RecursiveIn, Part.map_id'] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.TuringMachine.Tape | {
"line": 509,
"column": 2
} | {
"line": 510,
"column": 65
} | {
"line": 512,
"column": 0
} | [
{
"pp": "Γ : Type u_1\ninst✝ : Inhabited Γ\nT : Tape Γ\nn : ℕ\n⊢ T.right₀.nth n = T.nth ↑n",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Turing.ListBlank.nth_zero",
"congrArg",
"Turing.Tape.nth",
"Turing.ListBlank.nth_succ",
"instOfNatNat",
"Int",
... | [] | cases n <;> simp only [Tape.nth, Tape.right₀, ListBlank.nth_zero,
ListBlank.nth_succ, ListBlank.head_cons, ListBlank.tail_cons] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Computability.TuringMachine.Tape | {
"line": 509,
"column": 2
} | {
"line": 510,
"column": 65
} | {
"line": 512,
"column": 0
} | [
{
"pp": "Γ : Type u_1\ninst✝ : Inhabited Γ\nT : Tape Γ\nn : ℕ\n⊢ T.right₀.nth n = T.nth ↑n",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Turing.ListBlank.nth_zero",
"congrArg",
"Turing.Tape.nth",
"Turing.ListBlank.nth_succ",
"instOfNatNat",
"Int",
... | [] | cases n <;> simp only [Tape.nth, Tape.right₀, ListBlank.nth_zero,
ListBlank.nth_succ, ListBlank.head_cons, ListBlank.tail_cons] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.TuringMachine.Tape | {
"line": 509,
"column": 2
} | {
"line": 510,
"column": 65
} | {
"line": 512,
"column": 0
} | [
{
"pp": "Γ : Type u_1\ninst✝ : Inhabited Γ\nT : Tape Γ\nn : ℕ\n⊢ T.right₀.nth n = T.nth ↑n",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Turing.ListBlank.nth_zero",
"congrArg",
"Turing.Tape.nth",
"Turing.ListBlank.nth_succ",
"instOfNatNat",
"Int",
... | [] | cases n <;> simp only [Tape.nth, Tape.right₀, ListBlank.nth_zero,
ListBlank.nth_succ, ListBlank.head_cons, ListBlank.tail_cons] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.RecursiveIn | {
"line": 208,
"column": 31
} | {
"line": 208,
"column": 69
} | {
"line": 208,
"column": 70
} | [
{
"pp": "α : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nO O' : Set (ℕ →. ℕ)\nf : α →. σ\nhf : RecursiveIn O f\nhO : ∀ g ∈ O, RecursiveIn O' g\n⊢ ∀ g ∈ O, Nat.RecursiveIn O' g",
"ppTerm": "?m.22",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals"... | [
"α : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nO O' : Set (ℕ →. ℕ)\nf : α →. σ\nhf : RecursiveIn O f\nhO : ∀ g ∈ O, RecursiveIn O' g\n⊢ ∀ g ∈ O, Nat.RecursiveIn O' g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.RecursiveIn | {
"line": 219,
"column": 40
} | {
"line": 219,
"column": 74
} | {
"line": 219,
"column": 75
} | [
{
"pp": "α : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf : α →. σ\nO : Set (ℕ →. ℕ)\nhO : ∀ g ∈ O, Partrec g\nhf : RecursiveIn O f\n⊢ ∀ g ∈ O, Nat.Partrec g",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf : α →. σ\nO : Set (ℕ →. ℕ)\nhO : ∀ g ∈ O, Partrec g\nhf : RecursiveIn O f\n⊢ ∀ g ∈ O, Nat.Partrec g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Reduce | {
"line": 130,
"column": 31
} | {
"line": 130,
"column": 42
} | {
"line": 130,
"column": 43
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable β\np : α → Prop\nf : α → β\nc : Computable f\ng : β → Bool\nhg : Computable g\nh₂ : ComputablePred fun a ↦ g a = true\nhf : ∀ (a : α), p a ↔ (fun a ↦ g a = true) (f a)\n⊢ Computable fun a ↦ decide ((fun a ↦ (fun a ↦ g a = true) (f ... | [
"α : Type u_1\nβ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable β\np : α → Prop\nf : α → β\nc : Computable f\ng : β → Bool\nhg : Computable g\nh₂ : ComputablePred fun a ↦ g a = true\nhf : ∀ (a : α), p a ↔ (fun a ↦ g a = true) (f a)\n⊢ Computable fun a ↦ g (f a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Reduce | {
"line": 382,
"column": 2
} | {
"line": 382,
"column": 13
} | {
"line": 383,
"column": 2
} | [
{
"pp": "case h.h\np✝¹ p✝ : Set ℕ\n⊢ of p✝¹ ≤ of p✝ → of p✝ ≤ of p✝¹ → of p✝¹ = of p✝",
"ppTerm": "?h.h",
"assigned": true,
"usedConstants": [
"ManyOneDegree.instLE",
"Primcodable.ofDenumerable",
"instInhabitedNat",
"LE.le",
"Nat",
"ManyOneDegree",
"Denumera... | [
"case h.h\np✝¹ p✝ : Set ℕ\nhp : of p✝¹ ≤ of p✝\nhq : of p✝ ≤ of p✝¹\n⊢ of p✝¹ = of p✝"
] | intro hp hq | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Computability.Reduce | {
"line": 428,
"column": 2
} | {
"line": 428,
"column": 39
} | {
"line": 428,
"column": 40
} | [
{
"pp": "case h.h.h\np✝² p✝¹ p✝ : Set ℕ\n⊢ of p✝² + of p✝¹ ≤ of p✝ ↔ of p✝² ≤ of p✝ ∧ of p✝¹ ≤ of p✝",
"ppTerm": "?h.h.h",
"assigned": true,
"usedConstants": [
"ManyOneDegree.instLE",
"Eq.mpr",
"instInhabitedOfMonad",
"congrArg",
"Primcodable.ofDenumerable",
"_pri... | [
"case h.h.h\np✝² p✝¹ p✝ : Set ℕ\n⊢ p✝² ⊕' p✝¹ ≤₀ p✝ ↔ p✝² ≤₀ p✝ ∧ p✝¹ ≤₀ p✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.TuringMachine.PostTuringMachine | {
"line": 579,
"column": 16
} | {
"line": 579,
"column": 44
} | {
"line": 580,
"column": 6
} | [
{
"pp": "case right.some.some.move.refl\nΓ : Type u_1\nΛ : Type u_2\ninst✝² : Inhabited Λ\nσ : Type u_3\ninst✝¹ : Inhabited σ\nM : Λ → TM1.Stmt Γ Λ σ\ninst✝ : Fintype σ\nS : Finset Λ\nss : TM1.Supports M S\na : Γ\nv' : σ\nval✝ : TM1.Stmt Γ Λ σ\nd : Dir\nh₂ : some (TM1.Stmt.move d val✝) ∈ TM1.stmts M S\nhs : TM1... | [
"case right.some.some.move.refl\nΓ : Type u_1\nΛ : Type u_2\ninst✝² : Inhabited Λ\nσ : Type u_3\ninst✝¹ : Inhabited σ\nM : Λ → TM1.Stmt Γ Λ σ\ninst✝ : Fintype σ\nS : Finset Λ\nss : TM1.Supports M S\na : Γ\nv' : σ\nval✝ : TM1.Stmt Γ Λ σ\nd : Dir\nh₂ : some (TM1.Stmt.move d val✝) ∈ TM1.stmts M S\nhs : TM1.SupportsStm... | refine TM1.stmts_trans ?_ h₂ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Computability.TuringMachine.PostTuringMachine | {
"line": 583,
"column": 16
} | {
"line": 583,
"column": 44
} | {
"line": 584,
"column": 6
} | [
{
"pp": "case right.some.some.write.refl\nΓ : Type u_1\nΛ : Type u_2\ninst✝² : Inhabited Λ\nσ : Type u_3\ninst✝¹ : Inhabited σ\nM : Λ → TM1.Stmt Γ Λ σ\ninst✝ : Fintype σ\nS : Finset Λ\nss : TM1.Supports M S\na : Γ\nv' : σ\nval✝ : TM1.Stmt Γ Λ σ\nb : Γ → σ → Γ\nh₂ : some (TM1.Stmt.write b val✝) ∈ TM1.stmts M S\n... | [
"case right.some.some.write.refl\nΓ : Type u_1\nΛ : Type u_2\ninst✝² : Inhabited Λ\nσ : Type u_3\ninst✝¹ : Inhabited σ\nM : Λ → TM1.Stmt Γ Λ σ\ninst✝ : Fintype σ\nS : Finset Λ\nss : TM1.Supports M S\na : Γ\nv' : σ\nval✝ : TM1.Stmt Γ Λ σ\nb : Γ → σ → Γ\nh₂ : some (TM1.Stmt.write b val✝) ∈ TM1.stmts M S\nhs : TM1.Sup... | refine TM1.stmts_trans ?_ h₂ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Computability.RegularExpressions | {
"line": 262,
"column": 8
} | {
"line": 263,
"column": 28
} | {
"line": 264,
"column": 6
} | [
{
"pp": "case mp.nil\nα : Type u_1\ninst✝ : DecidableEq α\nP : RegularExpression α\nIH :\n ∀ (t : List α),\n t.length < [].length → (P.star.rmatch t = true ↔ ∃ S, t = S.flatten ∧ ∀ t ∈ S, t ≠ [] ∧ P.rmatch t = true)\n⊢ P.star.rmatch [] = true → ∃ S, [] = S.flatten ∧ ∀ t ∈ S, t ≠ [] ∧ P.rmatch t = true",
... | [] | intro _h
use []; dsimp; tauto | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.RegularExpressions | {
"line": 262,
"column": 8
} | {
"line": 263,
"column": 28
} | {
"line": 264,
"column": 6
} | [
{
"pp": "case mp.nil\nα : Type u_1\ninst✝ : DecidableEq α\nP : RegularExpression α\nIH :\n ∀ (t : List α),\n t.length < [].length → (P.star.rmatch t = true ↔ ∃ S, t = S.flatten ∧ ∀ t ∈ S, t ≠ [] ∧ P.rmatch t = true)\n⊢ P.star.rmatch [] = true → ∃ S, [] = S.flatten ∧ ∀ t ∈ S, t ≠ [] ∧ P.rmatch t = true",
... | [] | intro _h
use []; dsimp; tauto | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.StackTuringMachine | {
"line": 378,
"column": 4
} | {
"line": 378,
"column": 88
} | {
"line": 379,
"column": 2
} | [
{
"pp": "case zero\nK : Type u_1\nΓ : K → Type u_2\nf : ((k : K) → Option (Γ k)) → (k : K) → Option (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\n⊢ ListBlank.modifyNth (fun a ↦ (a.1, f a.2)) 0 (addBottom L) = addBottom (ListBlank.modifyNth f 0 L)",
"ppTerm": "?zero",
"assigned": true,
"usedConstant... | [] | simp only [addBottom, ListBlank.head_cons, ListBlank.modifyNth, ListBlank.tail_cons] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Computability.TuringMachine.StackTuringMachine | {
"line": 378,
"column": 4
} | {
"line": 378,
"column": 88
} | {
"line": 379,
"column": 2
} | [
{
"pp": "case succ\nK : Type u_1\nΓ : K → Type u_2\nf : ((k : K) → Option (Γ k)) → (k : K) → Option (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nn✝ : ℕ\n⊢ ListBlank.modifyNth (fun a ↦ (a.1, f a.2)) (n✝ + 1) (addBottom L) = addBottom (ListBlank.modifyNth f (n✝ + 1) L)",
"ppTerm": "?succ",
"assigned": t... | [
"case succ\nK : Type u_1\nΓ : K → Type u_2\nf : ((k : K) → Option (Γ k)) → (k : K) → Option (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nn✝ : ℕ\n⊢ ListBlank.cons (true, L.head)\n (ListBlank.modifyNth (fun a ↦ (a.1, f a.2)) n✝ (ListBlank.map { f := Prod.mk false, map_pt' := ⋯ } L.tail)) =\n ListBlank.cons ... | simp only [addBottom, ListBlank.head_cons, ListBlank.modifyNth, ListBlank.tail_cons] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Computability.RegularExpressions | {
"line": 291,
"column": 12
} | {
"line": 291,
"column": 47
} | {
"line": 292,
"column": 12
} | [
{
"pp": "case mpr.cons.cons.cons.refine_1\nα : Type u_1\ninst✝ : DecidableEq α\nP : RegularExpression α\na : α\nx : List α\nIH :\n ∀ (t : List α),\n t.length < (a :: x).length → (P.star.rmatch t = true ↔ ∃ S, t = S.flatten ∧ ∀ t ∈ S, t ≠ [] ∧ P.rmatch t = true)\nU : List (List α)\nb : α\nt : List α\nhelem :... | [
"case mpr.cons.cons.cons.refine_1\nα : Type u_1\ninst✝ : DecidableEq α\nP : RegularExpression α\na : α\nx : List α\nIH :\n ∀ (t : List α),\n t.length < (a :: x).length → (P.star.rmatch t = true ↔ ∃ S, t = S.flatten ∧ ∀ t ∈ S, t ≠ [] ∧ P.rmatch t = true)\nU : List (List α)\nb : α\nt : List α\nhelem : b :: t ≠ []... | specialize helem (b :: t) (by simp) | Lean.Elab.Tactic.evalSpecialize | Lean.Parser.Tactic.specialize |
Mathlib.Computability.TuringMachine.StackTuringMachine | {
"line": 531,
"column": 14
} | {
"line": 531,
"column": 41
} | {
"line": 533,
"column": 0
} | [
{
"pp": "case push\nK : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\nk : K\nq : TM2.Stmt Γ Λ σ\na✝ : σ → Γ k\n⊢ trStmts₁ (stRun (StAct.push a✝) q) = {go k (StAct.push a✝) q, ret q} ∪ trStmts₁ q",
"ppTerm": "?push",
"assigned": true,
"usedConstants": [
"Finset.instUnion",
"cong... | [] | simp only [trStmts₁, stRun] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Computability.TuringMachine.StackTuringMachine | {
"line": 531,
"column": 14
} | {
"line": 531,
"column": 41
} | {
"line": 533,
"column": 0
} | [
{
"pp": "case peek\nK : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\nk : K\nq : TM2.Stmt Γ Λ σ\na✝ : σ → Option (Γ k) → σ\n⊢ trStmts₁ (stRun (StAct.peek a✝) q) = {go k (StAct.peek a✝) q, ret q} ∪ trStmts₁ q",
"ppTerm": "?peek",
"assigned": true,
"usedConstants": [
"Finset.instUnion"... | [] | simp only [trStmts₁, stRun] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Computability.TuringMachine.StackTuringMachine | {
"line": 531,
"column": 14
} | {
"line": 531,
"column": 41
} | {
"line": 533,
"column": 0
} | [
{
"pp": "case pop\nK : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\nk : K\nq : TM2.Stmt Γ Λ σ\na✝ : σ → Option (Γ k) → σ\n⊢ trStmts₁ (stRun (StAct.pop a✝) q) = {go k (StAct.pop a✝) q, ret q} ∪ trStmts₁ q",
"ppTerm": "?pop",
"assigned": true,
"usedConstants": [
"Finset.instUnion",
... | [] | simp only [trStmts₁, stRun] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Num.Lemmas | {
"line": 801,
"column": 2
} | {
"line": 801,
"column": 84
} | {
"line": 803,
"column": 0
} | [
{
"pp": "⊢ ∀ (m n : Num), ↑(m &&& n) = ↑m &&& ↑n",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"cond",
"Num.bit",
"Num.castNum_eq_bitwise",
"Num.instAndOp",
"PosNum.bit",
"Bool.and",
"instOnePosNum",
"Bool.true",
"Num",
"Bool.ca... | [] | apply castNum_eq_bitwise PosNum.land <;> intros <;> (try cases_type* Bool) <;> rfl | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.Num.Lemmas | {
"line": 801,
"column": 2
} | {
"line": 801,
"column": 84
} | {
"line": 803,
"column": 0
} | [
{
"pp": "⊢ ∀ (m n : Num), ↑(m &&& n) = ↑m &&& ↑n",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"cond",
"Num.bit",
"Num.castNum_eq_bitwise",
"Num.instAndOp",
"PosNum.bit",
"Bool.and",
"instOnePosNum",
"Bool.true",
"Num",
"Bool.ca... | [] | apply castNum_eq_bitwise PosNum.land <;> intros <;> (try cases_type* Bool) <;> rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Num.Lemmas | {
"line": 801,
"column": 2
} | {
"line": 801,
"column": 84
} | {
"line": 803,
"column": 0
} | [
{
"pp": "⊢ ∀ (m n : Num), ↑(m &&& n) = ↑m &&& ↑n",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"cond",
"Num.bit",
"Num.castNum_eq_bitwise",
"Num.instAndOp",
"PosNum.bit",
"Bool.and",
"instOnePosNum",
"Bool.true",
"Num",
"Bool.ca... | [] | apply castNum_eq_bitwise PosNum.land <;> intros <;> (try cases_type* Bool) <;> rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.Config | {
"line": 283,
"column": 40
} | {
"line": 283,
"column": 82
} | {
"line": 283,
"column": 83
} | [
{
"pp": "n✝² : ℕ\nf : List.Vector ℕ n✝² →. ℕ\nn✝¹ : ℕ\nf✝ : List.Vector ℕ n✝¹ → ℕ\nn✝ : ℕ\ni✝ : Fin n✝\nn : ℕ\ni : Fin n\nc : Code\nh : ∀ (v : List.Vector ℕ n), c.eval ↑v = pure <$> (↑fun v ↦ v.get i) v\nv : List.Vector ℕ n.succ\n⊢ (c.comp tail).eval ↑v = pure <$> (↑fun v ↦ v.get i.succ) v",
"ppTerm": "?m.2... | [
"n✝² : ℕ\nf : List.Vector ℕ n✝² →. ℕ\nn✝¹ : ℕ\nf✝ : List.Vector ℕ n✝¹ → ℕ\nn✝ : ℕ\ni✝ : Fin n✝\nn : ℕ\ni : Fin n\nc : Code\nh : ∀ (v : List.Vector ℕ n), c.eval ↑v = pure <$> (↑fun v ↦ v.get i) v\nv : List.Vector ℕ n.succ\n⊢ c.eval (↑v).tail = pure <$> Part.some (v.get i.succ)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.TuringMachine.Config | {
"line": 285,
"column": 6
} | {
"line": 285,
"column": 37
} | {
"line": 285,
"column": 38
} | [
{
"pp": "case prim.comp\nn : ℕ\nf : List.Vector ℕ n →. ℕ\nn✝¹ : ℕ\nf✝¹ : List.Vector ℕ n✝¹ → ℕ\nm✝ n✝ : ℕ\nf✝ : List.Vector ℕ n✝ → ℕ\ng : Fin n✝ → List.Vector ℕ m✝ → ℕ\nhf : Nat.Primrec' f✝\nhg : ∀ (i : Fin n✝), Nat.Primrec' (g i)\nIHf : ∃ c, ∀ (v : List.Vector ℕ n✝), c.eval ↑v = pure <$> ↑f✝ v\nIHg : ∀ (i : Fi... | [
"case prim.comp\nn : ℕ\nf : List.Vector ℕ n →. ℕ\nn✝¹ : ℕ\nf✝¹ : List.Vector ℕ n✝¹ → ℕ\nm✝ n✝ : ℕ\nf✝ : List.Vector ℕ n✝ → ℕ\ng : Fin n✝ → List.Vector ℕ m✝ → ℕ\nhf : Nat.Primrec' f✝\nhg : ∀ (i : Fin n✝), Nat.Primrec' (g i)\nIHf : ∃ c, ∀ (v : List.Vector ℕ n✝), c.eval ↑v = pure <$> ↑f✝ v\nIHg : ∀ (i : Fin n✝), ∃ c, ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.TuringMachine.StackTuringMachine | {
"line": 568,
"column": 8
} | {
"line": 568,
"column": 63
} | {
"line": 568,
"column": 64
} | [
{
"pp": "case neg.inl.h\nK : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝ : DecidableEq K\nk : K\nq : TM1.Stmt (Γ' K Γ) (Λ' K Γ Λ σ) σ\nv : σ\nS : (k : K) → List (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nhL : ∀ (k : K), ListBlank.map (proj k) L = ListBlank.mk (List.map some (S k)).reverse\... | [
"case neg.inl.h\nK : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝ : DecidableEq K\nk : K\nq : TM1.Stmt (Γ' K Γ) (Λ' K Γ Λ σ) σ\nv : σ\nS : (k : K) → List (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nhL : ∀ (k : K), ListBlank.map (proj k) L = ListBlank.mk (List.map some (S k)).reverse\nf : σ → Γ k... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.TuringDegree | {
"line": 80,
"column": 15
} | {
"line": 80,
"column": 26
} | {
"line": 80,
"column": 27
} | [
{
"pp": "f g h : ℕ →. ℕ\nhg : f ≤ᵀ g\nhh : g ≤ᵀ h\n⊢ ∀ g_1 ∈ {g}, RecursiveIn {h} g_1",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"PFun",
"Primcodable.ofDenumerable",
"RecursiveIn",
"Membership.mem",
"Set.instSingletonSet",
"id",
... | [
"f g h : ℕ →. ℕ\nhg : f ≤ᵀ g\nhh : g ≤ᵀ h\n⊢ RecursiveIn {h} g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.TuringMachine.StackTuringMachine | {
"line": 609,
"column": 10
} | {
"line": 609,
"column": 65
} | {
"line": 609,
"column": 66
} | [
{
"pp": "case neg.inl.h\nK : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝ : DecidableEq K\nk : K\nq : TM1.Stmt (Γ' K Γ) (Λ' K Γ Λ σ) σ\nv : σ\nS : (k : K) → List (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nhL : ∀ (k : K), ListBlank.map (proj k) L = ListBlank.mk (List.map some (S k)).reverse\... | [
"case neg.inl.h\nK : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝ : DecidableEq K\nk : K\nq : TM1.Stmt (Γ' K Γ) (Λ' K Γ Λ σ) σ\nv : σ\nS : (k : K) → List (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nhL : ∀ (k : K), ListBlank.map (proj k) L = ListBlank.mk (List.map some (S k)).reverse\nf : σ → Opt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.CompHaus.EffectiveEpi | {
"line": 79,
"column": 4
} | {
"line": 79,
"column": 15
} | {
"line": 79,
"column": 16
} | [
{
"pp": "α : Type\ninst✝ : Finite α\nB : CompHaus\nX : α → CompHaus\nπ : (a : α) → X a ⟶ B\ntfae_2_to_1 : Epi (Sigma.desc π) → EffectiveEpiFamily X π\ntfae_1_to_2 : EffectiveEpiFamily X π → Epi (Sigma.desc π)\nx✝ : ∀ (b : ↑B.toTop), ∃ a x, (ConcreteCategory.hom (π a)) x = b\ne : ∀ (b : ↑B.toTop), ∃ a x, (Concre... | [
"α : Type\ninst✝ : Finite α\nB : CompHaus\nX : α → CompHaus\nπ : (a : α) → X a ⟶ B\ntfae_2_to_1 : Epi (Sigma.desc π) → EffectiveEpiFamily X π\ntfae_1_to_2 : EffectiveEpiFamily X π → Epi (Sigma.desc π)\nx✝ : ∀ (b : ↑B.toTop), ∃ a x, (ConcreteCategory.hom (π a)) x = b\ne : ∀ (b : ↑B.toTop), ∃ a x, (ConcreteCategory.h... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.TuringMachine.StackTuringMachine | {
"line": 694,
"column": 2
} | {
"line": 694,
"column": 20
} | {
"line": 695,
"column": 2
} | [
{
"pp": "K : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝ : DecidableEq K\nM : Λ → TM2.Stmt Γ Λ σ\nv : σ\nS : (k : K) → List (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nhT : ∀ (k : K), ListBlank.map (proj k) L = ListBlank.mk (List.map some (S k)).reverse\nl : Λ\n⊢ ∃ b,\n TrCfg (TM2.stepAu... | [
"K : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝ : DecidableEq K\nM : Λ → TM2.Stmt Γ Λ σ\nv : σ\nS : (k : K) → List (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nhT : ∀ (k : K), ListBlank.map (proj k) L = ListBlank.mk (List.map some (S k)).reverse\nl : Λ\nN : TM2.Stmt Γ Λ σ\n⊢ ∃ b, TrCfg (TM2.ste... | generalize M l = N | Lean.Elab.Tactic.evalGeneralize | Lean.Parser.Tactic.generalize |
Mathlib.Topology.Separation.Profinite | {
"line": 109,
"column": 4
} | {
"line": 109,
"column": 69
} | {
"line": 110,
"column": 4
} | [
{
"pp": "H : Type u_3\ninst✝³ : TopologicalSpace H\ninst✝² : LocallyCompactSpace H\ninst✝¹ : T2Space H\ninst✝ : TotallyDisconnectedSpace H\nU : Set H\nhU : IsOpen[inst✝³] U\ns : Set H\ncomp : IsCompact s\nsU : s ⊆ U\nu : Set ↑s := Subtype.val ⁻¹' interior s\nu_open_in_s : IsOpen[instTopologicalSpaceSubtype] u\n... | [
"H : Type u_3\ninst✝³ : TopologicalSpace H\ninst✝² : LocallyCompactSpace H\ninst✝¹ : T2Space H\ninst✝ : TotallyDisconnectedSpace H\nU : Set H\nhU : IsOpen[inst✝³] U\ns : Set H\ncomp : IsCompact s\nsU : s ⊆ U\nu : Set ↑s := Subtype.val ⁻¹' interior s\nu_open_in_s : IsOpen[instTopologicalSpaceSubtype] u\nx : { x // x... | have f2 : IsOpen v := VisClopen.2.preimage continuous_subtype_val | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Topology.Separation.Profinite | {
"line": 159,
"column": 58
} | {
"line": 159,
"column": 69
} | {
"line": 159,
"column": 70
} | [
{
"pp": "X : Type u_4\nI : Type u_5\ninst✝⁴ : TopologicalSpace X\ninst✝³ : CompactSpace X\ninst✝² : T2Space X\ninst✝¹ : TotallyDisconnectedSpace X\ninst✝ : Finite I\nα✝ β✝ : Type u_5\ne : α✝ ≃ β✝\nIH :\n ∀ {Z D : α✝ → Set X},\n (∀ (i : α✝), IsClosed[inst✝⁴] (Z i)) →\n (∀ (i : α✝), IsClopen (D i)) →\n ... | [
"X : Type u_4\nI : Type u_5\ninst✝⁴ : TopologicalSpace X\ninst✝³ : CompactSpace X\ninst✝² : T2Space X\ninst✝¹ : TotallyDisconnectedSpace X\ninst✝ : Finite I\nα✝ β✝ : Type u_5\ne : α✝ ≃ β✝\nIH :\n ∀ {Z D : α✝ → Set X},\n (∀ (i : α✝), IsClosed[inst✝⁴] (Z i)) →\n (∀ (i : α✝), IsClopen (D i)) →\n (∀ (i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.Profinite | {
"line": 160,
"column": 17
} | {
"line": 160,
"column": 28
} | {
"line": 160,
"column": 29
} | [
{
"pp": "X : Type u_4\nI : Type u_5\ninst✝⁴ : TopologicalSpace X\ninst✝³ : CompactSpace X\ninst✝² : T2Space X\ninst✝¹ : TotallyDisconnectedSpace X\ninst✝ : Finite I\nα✝ β✝ : Type u_5\ne : α✝ ≃ β✝\nIH :\n ∀ {Z D : α✝ → Set X},\n (∀ (i : α✝), IsClosed[inst✝⁴] (Z i)) →\n (∀ (i : α✝), IsClopen (D i)) →\n ... | [
"X : Type u_4\nI : Type u_5\ninst✝⁴ : TopologicalSpace X\ninst✝³ : CompactSpace X\ninst✝² : T2Space X\ninst✝¹ : TotallyDisconnectedSpace X\ninst✝ : Finite I\nα✝ β✝ : Type u_5\ne : α✝ ≃ β✝\nIH :\n ∀ {Z D : α✝ → Set X},\n (∀ (i : α✝), IsClosed[inst✝⁴] (Z i)) →\n (∀ (i : α✝), IsClopen (D i)) →\n (∀ (i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.Profinite | {
"line": 163,
"column": 4
} | {
"line": 163,
"column": 49
} | {
"line": 163,
"column": 50
} | [
{
"pp": "case of_equiv\nX : Type u_4\nI : Type u_5\ninst✝⁴ : TopologicalSpace X\ninst✝³ : CompactSpace X\ninst✝² : T2Space X\ninst✝¹ : TotallyDisconnectedSpace X\ninst✝ : Finite I\nα✝ β✝ : Type u_5\ne : α✝ ≃ β✝\nIH :\n ∀ {Z D : α✝ → Set X},\n (∀ (i : α✝), IsClosed[inst✝⁴] (Z i)) →\n (∀ (i : α✝), IsClop... | [
"case of_equiv\nX : Type u_4\nI : Type u_5\ninst✝⁴ : TopologicalSpace X\ninst✝³ : CompactSpace X\ninst✝² : T2Space X\ninst✝¹ : TotallyDisconnectedSpace X\ninst✝ : Finite I\nα✝ β✝ : Type u_5\ne : α✝ ≃ β✝\nIH :\n ∀ {Z D : α✝ → Set X},\n (∀ (i : α✝), IsClosed[inst✝⁴] (Z i)) →\n (∀ (i : α✝), IsClopen (D i)) →\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.Profinite | {
"line": 178,
"column": 6
} | {
"line": 178,
"column": 17
} | {
"line": 178,
"column": 18
} | [
{
"pp": "X : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n (∀ (i : I), IsClopen (D i)) →\n... | [
"X : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n (∀ (i : I), IsClopen (D i)) →\n (∀ (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ExtremallyDisconnected | {
"line": 186,
"column": 4
} | {
"line": 186,
"column": 43
} | {
"line": 186,
"column": 44
} | [
{
"pp": "case pos\nA E : Type u\ninst✝¹ : TopologicalSpace A\ninst✝ : TopologicalSpace E\nρ : E → A\nρ_cont : Continuous ρ\nρ_surj : Surjective ρ\nzorn_subset : ∀ (E₀ : Set E), E₀ ≠ univ → IsClosed E₀ → ρ '' E₀ ≠ univ\nG : Set E\nhG : IsOpen G\nG_empty : G = ∅\n⊢ ρ '' G ⊆ closure (ρ '' Gᶜ)ᶜ",
"ppTerm": "?po... | [
"case pos\nA E : Type u\ninst✝¹ : TopologicalSpace A\ninst✝ : TopologicalSpace E\nρ : E → A\nρ_cont : Continuous ρ\nρ_surj : Surjective ρ\nzorn_subset : ∀ (E₀ : Set E), E₀ ≠ univ → IsClosed E₀ → ρ '' E₀ ≠ univ\nG : Set E\nhG : IsOpen G\nG_empty : G = ∅\n⊢ ∅ ⊆ closure (ρ '' ∅ᶜ)ᶜ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ExtremallyDisconnected | {
"line": 202,
"column": 36
} | {
"line": 202,
"column": 47
} | {
"line": 202,
"column": 48
} | [
{
"pp": "A E : Type u\ninst✝¹ : TopologicalSpace A\ninst✝ : TopologicalSpace E\nρ : E → A\nρ_cont : Continuous ρ\nρ_surj : Surjective ρ\nzorn_subset : ∀ (E₀ : Set E), E₀ ≠ univ → IsClosed E₀ → ρ '' E₀ ≠ univ\nG : Set E\nhG : IsOpen G\nG_empty : ¬G = ∅\nN : Set A\nN_open : IsOpen N\ne : E\nhe : e ∈ G\nha : ρ e ∈... | [
"A E : Type u\ninst✝¹ : TopologicalSpace A\ninst✝ : TopologicalSpace E\nρ : E → A\nρ_cont : Continuous ρ\nρ_surj : Surjective ρ\nzorn_subset : ∀ (E₀ : Set E), E₀ ≠ univ → IsClosed E₀ → ρ '' E₀ ≠ univ\nG : Set E\nhG : IsOpen G\nG_empty : ¬G = ∅\nN : Set A\nN_open : IsOpen N\ne : E\nhe : e ∈ G\nha : ρ e ∈ ρ '' G\nhN ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.Profinite | {
"line": 216,
"column": 8
} | {
"line": 216,
"column": 93
} | {
"line": 217,
"column": 10
} | [
{
"pp": "case h_option.refine_5.none.some\nX : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n ... | [
"case h_option.refine_5.none.some\nX : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n (∀ (i : I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.Profinite | {
"line": 218,
"column": 8
} | {
"line": 218,
"column": 93
} | {
"line": 219,
"column": 10
} | [
{
"pp": "case h_option.refine_5.some.none\nX : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n ... | [
"case h_option.refine_5.some.none\nX : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n (∀ (i : I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.Profinite | {
"line": 220,
"column": 8
} | {
"line": 220,
"column": 19
} | {
"line": 220,
"column": 20
} | [
{
"pp": "case h_option.refine_5.some.some\nX : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n ... | [
"case h_option.refine_5.some.some\nX : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n (∀ (i : I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.DiscreteQuotient | {
"line": 391,
"column": 2
} | {
"line": 391,
"column": 14
} | {
"line": 391,
"column": 15
} | [
{
"pp": "X : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\n⊢ Injective fun x ↦\n match x with\n | { toSetoid := f, isOpen_setOfPred_rel := isOpen_setOfPred_rel } => f.classes",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Topology.DiscreteQuo... | [
"X : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\ntoSetoid✝ : Setoid X\nisOpen_setOfPred_rel✝ : ∀ (x : X), IsOpen[inst✝¹] (ofPred (toSetoid✝ x))\n⊢ ∀ ⦃a₂ : DiscreteQuotient X⦄,\n (fun x ↦\n match x with\n | { toSetoid := f, isOpen_setOfPred_rel := isOpen_setOfPred_rel } =>... | intro ⟨_, _⟩ | Lean.Elab.Tactic.evalIntro | null |
Mathlib.Topology.Category.Profinite.CofilteredLimit | {
"line": 87,
"column": 4
} | {
"line": 92,
"column": 55
} | {
"line": 93,
"column": 2
} | [
{
"pp": "case refine_3.refine_1\nJ : Type v\ninst✝¹ : SmallCategory J\ninst✝ : IsCofiltered J\nF : J ⥤ Profinite\nC : Cone F\nU : Set ↑C.pt.toTop\nhC : IsLimit C\nhU : IsClopen U\nS : Set (Set ↑(toTopCat.mapCone C).pt)\nhS : S ⊆ {U | ∃ j, ∃ V ∈ {W | IsClopen W}, U = ⇑(ConcreteCategory.hom ((toTopCat.mapCone C).... | [] | apply isClopen_biUnion_finset
intro s hs
dsimp [W]
rw [dif_pos hs]
exact ⟨(hV s).1.1.preimage (F.map _).hom.hom.continuous,
(hV s).1.2.preimage (F.map _).hom.hom.continuous⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Category.Profinite.CofilteredLimit | {
"line": 87,
"column": 4
} | {
"line": 92,
"column": 55
} | {
"line": 93,
"column": 2
} | [
{
"pp": "case refine_3.refine_1\nJ : Type v\ninst✝¹ : SmallCategory J\ninst✝ : IsCofiltered J\nF : J ⥤ Profinite\nC : Cone F\nU : Set ↑C.pt.toTop\nhC : IsLimit C\nhU : IsClopen U\nS : Set (Set ↑(toTopCat.mapCone C).pt)\nhS : S ⊆ {U | ∃ j, ∃ V ∈ {W | IsClopen W}, U = ⇑(ConcreteCategory.hom ((toTopCat.mapCone C).... | [] | apply isClopen_biUnion_finset
intro s hs
dsimp [W]
rw [dif_pos hs]
exact ⟨(hV s).1.1.preimage (F.map _).hom.hom.continuous,
(hV s).1.2.preimage (F.map _).hom.hom.continuous⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Category.Profinite.CofilteredLimit | {
"line": 132,
"column": 2
} | {
"line": 132,
"column": 41
} | {
"line": 133,
"column": 2
} | [
{
"pp": "case intro\nJ : Type v\ninst✝² : SmallCategory J\ninst✝¹ : IsCofiltered J\nF : J ⥤ Profinite\nC : Cone F\nα : Type u_1\ninst✝ : Finite α\nhC : IsLimit C\nf : LocallyConstant (↑C.pt.toTop) α\nval✝ : Fintype α\nι : α → α → Fin 2 := fun x y ↦ if x = y then 0 else 1\nff : α → LocallyConstant (↑C.pt.toTop) ... | [
"case intro\nJ : Type v\ninst✝² : SmallCategory J\ninst✝¹ : IsCofiltered J\nF : J ⥤ Profinite\nC : Cone F\nα : Type u_1\ninst✝ : Finite α\nhC : IsLimit C\nf : LocallyConstant (↑C.pt.toTop) α\nval✝ : Fintype α\nι : α → α → Fin 2 := fun x y ↦ if x = y then 0 else 1\nff : α → LocallyConstant (↑C.pt.toTop) (Fin 2) := (... | let G : Finset J := Finset.univ.image j | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Condensed.TopComparison | {
"line": 57,
"column": 2
} | {
"line": 57,
"column": 13
} | {
"line": 57,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nG : C ⥤ TopCat\nX : Type w'\ninst✝² : TopologicalSpace X\nZ B : C\nπ : Z ⟶ B\ninst✝¹ : HasPullback π π\ninst✝ : PreservesLimit (cospan π π) G\na : C(↑(G.obj Z), X)\nha : ⇑a ∘ ⇑(ConcreteCategory.hom (G.map (pullback.fst π π))) = ⇑a ∘ ⇑(ConcreteCategory.hom (G.map ... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nG : C ⥤ TopCat\nX : Type w'\ninst✝² : TopologicalSpace X\nZ B : C\nπ : Z ⟶ B\ninst✝¹ : HasPullback π π\ninst✝ : PreservesLimit (cospan π π) G\na : C(↑(G.obj Z), X)\nha : ⇑a ∘ ⇑(ConcreteCategory.hom (G.map (pullback.fst π π))) = ⇑a ∘ ⇑(ConcreteCategory.hom (G.map (pullback.sn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 1149,
"column": 2
} | {
"line": 1149,
"column": 24
} | {
"line": 1149,
"column": 25
} | [
{
"pp": "K : Option Γ' → Finset Λ'\nS : Finset Λ'\n⊢ Supports (Finset.univ.biUnion K) S ↔ ∀ (a : Option Γ'), Supports (K a) S",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Turing.TM2.SupportsStmt",
"Turing.PartrecToTM2.tr",
"Finset.univ",
"Turing.P... | [
"K : Option Γ' → Finset Λ'\nS : Finset Λ'\n⊢ (∀ (q : Λ') (x : Option Γ'), q ∈ K x → TM2.SupportsStmt S (tr q)) ↔\n ∀ (a : Option Γ'), ∀ q ∈ K a, TM2.SupportsStmt S (tr q)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.LightProfinite.AsLimit | {
"line": 125,
"column": 2
} | {
"line": 125,
"column": 45
} | {
"line": 125,
"column": 46
} | [
{
"pp": "S : LightProfinite\nn : ℕ\n⊢ Function.Surjective (⇑(ConcreteCategory.hom (S.transitionMap n)) ∘ ⇑(ConcreteCategory.hom (S.proj (n + 1))))",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom"... | [
"S : LightProfinite\nn : ℕ\n⊢ Function.Surjective ⇑(ConcreteCategory.hom (S.proj n))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.LightProfinite.AsLimit | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 47
} | {
"line": 130,
"column": 48
} | [
{
"pp": "S : LightProfinite\nn m : ℕ\nh : n ≤ m\n⊢ Function.Surjective (⇑(ConcreteCategory.hom (S.transitionMapLE h)) ∘ ⇑(ConcreteCategory.hom (S.proj m)))",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"LightProfinite.proj_comp_transitionMapLE'",
... | [
"S : LightProfinite\nn m : ℕ\nh : n ≤ m\n⊢ Function.Surjective ⇑(ConcreteCategory.hom (S.proj n))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Condensed.Discrete.LocallyConstant | {
"line": 360,
"column": 9
} | {
"line": 360,
"column": 93
} | {
"line": 360,
"column": 93
} | [
{
"pp": "P : TopCat → Prop\ninst✝⁴ : ∀ (S : CompHausLike P) (p : ↑S.toTop → Prop), HasProp P (Subtype p)\nS : CompHausLike P\nY : (CompHausLike P)ᵒᵖ ⥤ Type (max u w)\ninst✝³ : HasProp P PUnit.{u + 1}\nf : LocallyConstant (↑S.toTop) (Y.obj (op (of P PUnit.{u + 1})))\nT : CompHausLike P\ng : T ⟶ S\nX✝ : TopCat\ni... | [
"P : TopCat → Prop\ninst✝⁴ : ∀ (S : CompHausLike P) (p : ↑S.toTop → Prop), HasProp P (Subtype p)\nS : CompHausLike P\nY : (CompHausLike P)ᵒᵖ ⥤ Type (max u w)\ninst✝³ : HasProp P PUnit.{u + 1}\nf : LocallyConstant (↑S.toTop) (Y.obj (op (of P PUnit.{u + 1})))\nT : CompHausLike P\ng : T ⟶ S\nX✝ : TopCat\ninst✝² : HasE... | ← map_eq_image _ a ⟨PUnit.unit, by simp [mem_iff_eq_image, ← map_preimage_eq_image]⟩ | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Condensed.Discrete.Colimit | {
"line": 159,
"column": 16
} | {
"line": 159,
"column": 27
} | {
"line": 159,
"column": 28
} | [
{
"pp": "S : Profinite\nF : Profiniteᵒᵖ ⥤ Type (u + 1)\nhF : (S : Profinite) → IsColimit (F.mapCocone S.asLimitCone.op)\nX✝ Y✝ : Profiniteᵒᵖ\nx✝ : X✝ ⟶ Y✝\n⊢ (lanPresheaf F).map x✝ ≫\n (match Y✝ with\n | Opposite.op S => lanPresheafIso (hF S)).hom =\n (match X✝ with\n | Opposite.op S => la... | [
"S : Profinite\nF : Profiniteᵒᵖ ⥤ Type (u + 1)\nhF : (S : Profinite) → IsColimit (F.mapCocone S.asLimitCone.op)\nX✝ Y✝ : Profiniteᵒᵖ\nx✝ : X✝ ⟶ Y✝\n⊢ colimit.desc (CostructuredArrow.proj toProfinite.op X✝ ⋙ toProfinite.op ⋙ F)\n { pt := colimit (CostructuredArrow.proj toProfinite.op Y✝ ⋙ toProfinite.op ⋙ F),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Condensed.Light.InternallyProjective | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 53
} | {
"line": 82,
"column": 0
} | [
{
"pp": "case e_6\nR : Type u\ninst✝ : CommRing R\nA B P : LightCondMod R\nS : LightProfinite\ne : A ⟶ B\nx : ↑((P ⟹ A).obj.obj (Opposite.op S))\n⊢ (coherentTopology LightProfinite).yonedaEquiv\n ((coherentTopology LightProfinite).yonedaEquiv.symm\n ((ConcreteCategory.hom (((ihom P).map e).hom.app (... | [] | simp [dsimp% GrothendieckTopology.yonedaEquiv_comp] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Topology.Category.LightProfinite.Injective | {
"line": 114,
"column": 4
} | {
"line": 114,
"column": 37
} | {
"line": 114,
"column": 38
} | [
{
"pp": "case refine_2\nX : Type u_1\nY : Type u_2\nS : Type u_3\nT : Type u_4\ninst✝¹⁰ : TopologicalSpace X\ninst✝⁹ : CompactSpace X\ninst✝⁸ : TopologicalSpace Y\ninst✝⁷ : CompactSpace Y\ninst✝⁶ : T2Space Y\ninst✝⁵ : TotallyDisconnectedSpace Y\ninst✝⁴ : TopologicalSpace S\ninst✝³ : T2Space S\ninst✝² : Finite S... | [
"case refine_2\nX : Type u_1\nY : Type u_2\nS : Type u_3\nT : Type u_4\ninst✝¹⁰ : TopologicalSpace X\ninst✝⁹ : CompactSpace X\ninst✝⁸ : TopologicalSpace Y\ninst✝⁷ : CompactSpace Y\ninst✝⁶ : T2Space Y\ninst✝⁵ : TotallyDisconnectedSpace Y\ninst✝⁴ : TopologicalSpace S\ninst✝³ : T2Space S\ninst✝² : Finite S\ninst✝¹ : T... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.LightProfinite.Injective | {
"line": 116,
"column": 51
} | {
"line": 116,
"column": 74
} | {
"line": 116,
"column": 75
} | [
{
"pp": "X : Type u_1\nY : Type u_2\nS : Type u_3\nT : Type u_4\ninst✝¹⁰ : TopologicalSpace X\ninst✝⁹ : CompactSpace X\ninst✝⁸ : TopologicalSpace Y\ninst✝⁷ : CompactSpace Y\ninst✝⁶ : T2Space Y\ninst✝⁵ : TotallyDisconnectedSpace Y\ninst✝⁴ : TopologicalSpace S\ninst✝³ : T2Space S\ninst✝² : Finite S\ninst✝¹ : Topo... | [
"X : Type u_1\nY : Type u_2\nS : Type u_3\nT : Type u_4\ninst✝¹⁰ : TopologicalSpace X\ninst✝⁹ : CompactSpace X\ninst✝⁸ : TopologicalSpace Y\ninst✝⁷ : CompactSpace Y\ninst✝⁶ : T2Space Y\ninst✝⁵ : TotallyDisconnectedSpace Y\ninst✝⁴ : TopologicalSpace S\ninst✝³ : T2Space S\ninst✝² : Finite S\ninst✝¹ : TopologicalSpace... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Control.Functor.Multivariate | {
"line": 178,
"column": 4
} | {
"line": 178,
"column": 91
} | {
"line": 179,
"column": 4
} | [
{
"pp": "case h₁\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u_1\ninst✝¹ : MvFunctor F\ninst✝ : LawfulMvFunctor F\nα : TypeVec.{u} n\nβ : Type u\nP : β → Prop\nx : F (α ::: β)\nu✝ : F fun i ↦ { p_1 // ofRepeat (α.PredLast' P i p_1) }\n⊢ (fun i ↦ Subtype.val) <$$> u✝ = x ↔ (fun i x ↦ ↑(f P n α i x)) <$$> u✝ = x",
... | [
"case h₁\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u_1\ninst✝¹ : MvFunctor F\ninst✝ : LawfulMvFunctor F\nα : TypeVec.{u} n\nβ : Type u\nP : β → Prop\nx : F (α ::: β)\nu✝ : F fun i ↦ { p_1 // ofRepeat (α.PredLast' P i p_1) }\n⊢ (fun i ↦ Subtype.val) = fun i x ↦ ↑(f P n α i x)"
] | suffices (fun i => Subtype.val) = (fun i x => (MvFunctor.f P n α i x).val) by rw [this] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticSuffices__1 | Lean.Parser.Tactic.tacticSuffices_ |
Mathlib.Control.Monad.Cont | {
"line": 224,
"column": 4
} | {
"line": 224,
"column": 57
} | {
"line": 225,
"column": 6
} | [
{
"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",
"ppTerm": "?m.17... | [
"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⊢ (do\n let x ← x✝¹.run\n callCC fun f ↦ x.elim (pure none) fun x ↦ (x✝ (OptionT.mkLabel f) x).run) =\n do\n let __do_lift... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Condensed.Light.Sequence | {
"line": 68,
"column": 15
} | {
"line": 68,
"column": 32
} | {
"line": 68,
"column": 33
} | [
{
"pp": "S : Type u_1\nT : Type u_2\nX : Type u_3\nπ : T → S × Option X\nσ : Option X → S → T\nhσ' : ∀ (x : Option X) (s : S), (π (σ x s)).2 = x\nx : T\nx✝ : ∃ i, (∀ (x_1 : S), ¬σ (Option.some i) x_1 = x) ∧ (π x).2 = ↑i\nn : X\nhn : ∀ (x_1 : S), ¬σ (Option.some n) x_1 = x\nhn' : (π x).2 = ↑n\n⊢ ¬(π x).2 = none"... | [
"S : Type u_1\nT : Type u_2\nX : Type u_3\nπ : T → S × Option X\nσ : Option X → S → T\nhσ' : ∀ (x : Option X) (s : S), (π (σ x s)).2 = x\nx : T\nx✝ : ∃ i, (∀ (x_1 : S), ¬σ (Option.some i) x_1 = x) ∧ (π x).2 = ↑i\nn : X\nhn : ∀ (x_1 : S), ¬σ (Option.some n) x_1 = x\nhn' : (π x).2 = ↑n\n⊢ ¬↑n = none"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Condensed.Light.Sequence | {
"line": 81,
"column": 4
} | {
"line": 81,
"column": 15
} | {
"line": 81,
"column": 16
} | [
{
"pp": "case refine_1\nS : Type u_1\nT : Type u_2\nX : Type u_3\ninst✝⁵ : TopologicalSpace S\ninst✝⁴ : TopologicalSpace T\ninst✝³ : TopologicalSpace X\ninst✝² : DiscreteTopology X\ninst✝¹ : T2Space T\ninst✝ : CompactSpace S\nπ : T → S × OnePoint X\nhπ : Continuous π\nσ : Option X → S → T\nhσ : ∀ (x : Option X)... | [
"case refine_1\nS : Type u_1\nT : Type u_2\nX : Type u_3\ninst✝⁵ : TopologicalSpace S\ninst✝⁴ : TopologicalSpace T\ninst✝³ : TopologicalSpace X\ninst✝² : DiscreteTopology X\ninst✝¹ : T2Space T\ninst✝ : CompactSpace S\nπ : T → S × OnePoint X\nhπ : Continuous π\nσ : Option X → S → T\nhσ : ∀ (x : Option X), Continuous... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Control.LawfulFix | {
"line": 132,
"column": 4
} | {
"line": 135,
"column": 25
} | {
"line": 137,
"column": 0
} | [
{
"pp": "case a\nα : Type u_1\nβ : α → Type u_2\nf : ((a : α) → Part (β a)) →o (a : α) → Part (β a)\n⊢ ωSup (approxChain f) ≤ Part.fix ⇑f",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Part",
"Pi.preorder",
"instOmegaCompletePartialOrderForall",
"Part.Fix.approx_le_... | [] | apply ωSup_le _ _ _
simp only [Fix.approxChain]
intro y x
apply approx_le_fix f | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Control.LawfulFix | {
"line": 132,
"column": 4
} | {
"line": 135,
"column": 25
} | {
"line": 137,
"column": 0
} | [
{
"pp": "case a\nα : Type u_1\nβ : α → Type u_2\nf : ((a : α) → Part (β a)) →o (a : α) → Part (β a)\n⊢ ωSup (approxChain f) ≤ Part.fix ⇑f",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Part",
"Pi.preorder",
"instOmegaCompletePartialOrderForall",
"Part.Fix.approx_le_... | [] | apply ωSup_le _ _ _
simp only [Fix.approxChain]
intro y x
apply approx_le_fix f | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Control.LawfulFix | {
"line": 189,
"column": 4
} | {
"line": 189,
"column": 80
} | {
"line": 189,
"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)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Part",
"Eq.mpr",
"Unit.unit",
"Pi.preorder",
"con... | [] | rw [Part.fix_eq_of_ωScottContinuous (ωScottContinuous_toUnitMono f hc)]; rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Control.LawfulFix | {
"line": 189,
"column": 4
} | {
"line": 189,
"column": 80
} | {
"line": 189,
"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)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Part",
"Eq.mpr",
"Unit.unit",
"Pi.preorder",
"con... | [] | rw [Part.fix_eq_of_ωScottContinuous (ωScottContinuous_toUnitMono f hc)]; rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.TypeVec | {
"line": 675,
"column": 2
} | {
"line": 676,
"column": 56
} | {
"line": 677,
"column": 2
} | [
{
"pp": "n : 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",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Fin2.rec",
"Fin2.fz",
"TypeVec.ofRepeat",
"TypeVec.prod.mk",
"id",
... | [
"case fz\nn n✝ : ℕ\nα : TypeVec.{u_1} (n✝ + 1)\nr : α ⊗ α ⟹ «repeat» (n✝ + 1) Prop\nx : Subtype_ r Fin2.fz\n⊢ ⟨↑x, ⋯⟩ = x",
"case fs\nn n✝ : ℕ\na✝ : Fin2 n✝\na_ih✝ :\n ∀ {α : TypeVec.{u_1} n✝} (r : α ⊗ α ⟹ «repeat» n✝ Prop) (x : Subtype_ r a✝), toSubtype' r a✝ (ofSubtype' r a✝ x) = x\nα : TypeVec.{u_1} (n✝ + 1)\... | 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
} | {
"line": 69,
"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 a)",
"ppTerm": "?m.49",
... | [
"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 (g (E.symm a) (E.symm b)) ≤ f (E.symm a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Filter | {
"line": 70,
"column": 35
} | {
"line": 70,
"column": 46
} | {
"line": 70,
"column": 47
} | [
{
"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)",
"ppTerm": "?m.62",
... | [
"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 (g (E.symm a) (E.symm b)) ≤ f (E.symm b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Filter | {
"line": 129,
"column": 34
} | {
"line": 129,
"column": 45
} | {
"line": 129,
"column": 46
} | [
{
"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",
"ppTerm": "?m.41",
"assigned": false,
"usedConstants": [... | [
"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"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 71,
"column": 28
} | {
"line": 71,
"column": 39
} | {
"line": 71,
"column": 40
} | [
{
"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 ... | [
"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 h) ⊆ f a ∩ f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 73,
"column": 36
} | {
"line": 73,
"column": 47
} | {
"line": 73,
"column": 48
} | [
{
"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 ... | [
"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 h) ⊆ f a ∩ f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 74,
"column": 36
} | {
"line": 74,
"column": 47
} | {
"line": 74,
"column": 48
} | [
{
"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 ... | [
"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 h) ⊆ f a ∩ f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 146,
"column": 33
} | {
"line": 146,
"column": 44
} | {
"line": 146,
"column": 45
} | [
{
"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)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership... | [
"α : Type u_1\ninst✝ : TopologicalSpace α\nF : Realizer α\ns : F.σ\na : α\nm : a ∈ F.F.f s\n⊢ F.F.f s ∈ 𝓝 a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 178,
"column": 31
} | {
"line": 178,
"column": 42
} | {
"line": 178,
"column": 43
} | [
{
"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✝",
"ppTerm": "?m.7... | [
"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 ∈ F.F.f s ∧ F.F.f s ⊆ s✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 178,
"column": 74
} | {
"line": 178,
"column": 85
} | {
"line": 178,
"column": 86
} | [
{
"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.... | [
"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.f (E.symm t)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Erased | {
"line": 63,
"column": 71
} | {
"line": 63,
"column": 82
} | {
"line": 63,
"column": 83
} | [
{
"pp": "α : Sort u_1\na b : Erased α\nh : a.out = b.out\n⊢ a = b",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Sort u_1\na b : Erased α\nh : a.out = b.out\n⊢ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.FP.Basic | {
"line": 87,
"column": 10
} | {
"line": 87,
"column": 24
} | {
"line": 87,
"column": 24
} | [
{
"pp": "C : FloatCfg\nthis : prec ≤ 2 * emax\n⊢ emin + ↑prec - 1 ≤ ↑emax",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"FP.prec",
"congrArg",
"FP.emax",
"Eq.mp",
"instMulNat",
"instOfNatNat",
"Int",
"LE.le",
"instL... | [
"C : FloatCfg\nthis : ↑prec ≤ ↑(2 * emax)\n⊢ emin + ↑prec - 1 ≤ ↑emax"
] | ← Int.ofNat_le | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Fin.FlagRange | {
"line": 42,
"column": 27
} | {
"line": 42,
"column": 46
} | {
"line": 42,
"column": 47
} | [
{
"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... | [
"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 : Fin (n + 1)), ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.FlagRange | {
"line": 45,
"column": 12
} | {
"line": 45,
"column": 47
} | {
"line": 45,
"column": 48
} | [
{
"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 ... | [
"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 : ∀ (y : Fin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Semiquot | {
"line": 187,
"column": 20
} | {
"line": 187,
"column": 31
} | {
"line": 187,
"column": 32
} | [
{
"pp": "α : Type u_1\nq : Semiquot α\np : q.IsPure\na : α\n⊢ a ∈ q ↔ a ∈ pure (q.get p)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Pure.pure",
"Semiquot.instMonad",
"Eq.mpr",
"congrArg",
"Monad.toApplicative",
"Membership.mem",
"id",
"... | [
"α : Type u_1\nq : Semiquot α\np : q.IsPure\na : α\n⊢ a ∈ q ↔ a = q.get p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Semiquot | {
"line": 204,
"column": 43
} | {
"line": 204,
"column": 54
} | {
"line": 204,
"column": 55
} | [
{
"pp": "α : Type u_1\ns t : Semiquot α\nh : t.IsPure\nst : s ≤ t\n⊢ pure (t.get h) ≤ pure (s.get ⋯)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Pure.pure",
"Semiquot.instMonad",
"Semiquot.pure_le._simp_1",
"Eq.mpr",
"Monad.toApplicative",
"PartialO... | [
"α : Type u_1\ns t : Semiquot α\nh : t.IsPure\nst : s ≤ t\n⊢ t.get h = s.get ⋯"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 28,
"column": 2
} | {
"line": 28,
"column": 13
} | {
"line": 28,
"column": 14
} | [
{
"pp": "m n : ℕ\nf : Fin m → Fin n\nhf : Function.Injective f\n⊢ m ≤ n",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"m n : ℕ\nf : Fin m → Fin n\nhf : Function.Injective f\n⊢ m ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 35,
"column": 2
} | {
"line": 35,
"column": 13
} | {
"line": 35,
"column": 14
} | [
{
"pp": "m n : ℕ\nf : Fin m ↪ Fin n\n⊢ m ≤ n",
"ppTerm": "?m.3",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"m n : ℕ\nf : Fin m ↪ Fin n\n⊢ m ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 44,
"column": 2
} | {
"line": 44,
"column": 13
} | {
"line": 44,
"column": 14
} | [
{
"pp": "m n : ℕ\nf : Fin m → Fin n\nhf : Function.Injective f\nb : Fin n\nhb : b ∉ Set.range f\n⊢ m < n",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"m n : ℕ\nf : Fin m → Fin n\nhf : Function.Injective f\nb : Fin n\nhb : b ∉ Set.range f\n⊢ m < n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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