module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Combinatorics.SimpleGraph.FiveWheelLike | {
"line": 189,
"column": 6
} | {
"line": 189,
"column": 90
} | {
"line": 190,
"column": 2
} | [
{
"pp": "α : Type u_1\ns : Finset α\nG : SimpleGraph α\nr k : ℕ\ninst✝ : DecidableEq α\nv w₁ w₂ : α\nt : Finset α\nhw : G.IsFiveWheelLike r k v w₁ w₂ s t\nC : G.Coloring (Fin (r + 1))\nh : Set.SurjOn (⇑C) (insert w₁ ↑s) Set.univ\nthis : Set.SurjOn (⇑C) (insert w₂ ↑t) Set.univ\nx : α\nhcx : C x = C v\ny : α\nhcy... | [] | exact hw.isNClique_right.1 (by simp) (by simp [hy]) fun h ↦ hw.notMem_right (h ▸ hy) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 78,
"column": 2
} | {
"line": 79,
"column": 52
} | {
"line": 81,
"column": 0
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nM : G.Subgraph\nh : M.IsMatching\n⊢ Surjective h.toEdge",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"SimpleGraph.Subgraph.edge_vert",
"Sym2.Rel",
"SimpleGraph.Subgraph.IsMatching.toEdge_eq_of_adj",
"Quot.ind",
"Sub... | [] | rintro ⟨⟨x, y⟩, he⟩
exact ⟨⟨x, M.edge_vert he⟩, h.toEdge_eq_of_adj he⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 78,
"column": 2
} | {
"line": 79,
"column": 52
} | {
"line": 81,
"column": 0
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nM : G.Subgraph\nh : M.IsMatching\n⊢ Surjective h.toEdge",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"SimpleGraph.Subgraph.edge_vert",
"Sym2.Rel",
"SimpleGraph.Subgraph.IsMatching.toEdge_eq_of_adj",
"Quot.ind",
"Sub... | [] | rintro ⟨⟨x, y⟩, he⟩
exact ⟨⟨x, M.edge_vert he⟩, h.toEdge_eq_of_adj he⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 156,
"column": 2
} | {
"line": 158,
"column": 23
} | {
"line": 160,
"column": 0
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nv w : V\nh : G.Adj v w\nv✝ : V\nhv : v✝ = v ∨ v✝ = w\n⊢ ∃! w_1, (G.subgraphOfAdj h).Adj v✝ w_1",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Sym2.Rel",
"SimpleGraph.subgraphOfAdj_adj",
"Sym2.eq._s... | [] | cases hv with
| inl => use w; aesop
| inr => use v; aesop | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | Lean.Parser.Tactic.cases |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 169,
"column": 4
} | {
"line": 170,
"column": 28
} | {
"line": 172,
"column": 0
} | [
{
"pp": "case h.refine_2\nV : Type u_1\nG : SimpleGraph V\nG' : G.Subgraph\nM : G'.coe.Subgraph\nhM : M.IsMatching\nv✝ : V\nhv : v✝ ∈ (Subgraph.coeSubgraph M).verts\nw : ↑G'.verts\nhw : (fun w ↦ M.Adj ⟨v✝, ⋯⟩ w) w ∧ ∀ (y : ↑G'.verts), (fun w ↦ M.Adj ⟨v✝, ⋯⟩ w) y → y = w\ny : V\nhy : (fun w ↦ (Subgraph.coeSubgra... | [] | obtain ⟨_, hw', hvw⟩ := (coeSubgraph_adj _ _ _).mp hy
rw [← hw.2 ⟨y, hw'⟩ hvw] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 169,
"column": 4
} | {
"line": 170,
"column": 28
} | {
"line": 172,
"column": 0
} | [
{
"pp": "case h.refine_2\nV : Type u_1\nG : SimpleGraph V\nG' : G.Subgraph\nM : G'.coe.Subgraph\nhM : M.IsMatching\nv✝ : V\nhv : v✝ ∈ (Subgraph.coeSubgraph M).verts\nw : ↑G'.verts\nhw : (fun w ↦ M.Adj ⟨v✝, ⋯⟩ w) w ∧ ∀ (y : ↑G'.verts), (fun w ↦ M.Adj ⟨v✝, ⋯⟩ w) y → y = w\ny : V\nhy : (fun w ↦ (Subgraph.coeSubgra... | [] | obtain ⟨_, hw', hvw⟩ := (coeSubgraph_adj _ _ _).mp hy
rw [← hw.2 ⟨y, hw'⟩ hvw] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.LapMatrix | {
"line": 222,
"column": 87
} | {
"line": 224,
"column": 57
} | {
"line": 226,
"column": 0
} | [
{
"pp": "V : Type u_1\ninst✝² : Fintype V\nG : SimpleGraph V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : DecidableEq V\n⊢ Fintype.card G.ConnectedComponent = finrank ℝ ↥(toLin' (lapMatrix ℝ G)).ker",
"ppTerm": "?m.33",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Pi.Function.module",
... | [] | by
classical
rw [Module.finrank_eq_card_basis G.lapMatrix_ker_basis] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.LineGraph | {
"line": 42,
"column": 67
} | {
"line": 42,
"column": 96
} | {
"line": 44,
"column": 0
} | [
{
"pp": "V : Type u_1\n⊢ ⊥.lineGraph = ⊥",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"iff_false",
"Set.mem_empty_iff_false._simp_1",
"congrArg",
"SimpleGraph.Adj",
"False.elim",
"SimpleGraph.edgeSet_bot",
"Subtype.... | [] | by aesop (add simp lineGraph) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.StronglyRegular | {
"line": 199,
"column": 4
} | {
"line": 201,
"column": 26
} | {
"line": 202,
"column": 4
} | [
{
"pp": "case convert_4\nn k ℓ μ : ℕ\nV : Type u\ninst✝¹ : Fintype V\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nh : G.IsSRGWith n k ℓ μ\nthis : DecidableEq V := Classical.decEq V\nv w : V\nhw : ¬G.Adj v w ∧ w ≠ v\n⊢ #(bipartiteBelow G.Adj (G.neighborFinset v) w) = μ",
"ppTerm": "?convert_4",
"assig... | [
"case convert_4\nn k ℓ μ : ℕ\nV : Type u\ninst✝¹ : Fintype V\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\nh : G.IsSRGWith n k ℓ μ\nthis : DecidableEq V := Classical.decEq V\nv w : V\nhw : ¬G.Adj v w ∧ w ≠ v\n⊢ #(G.neighborSet v ∩ G.neighborSet w).toFinset = #(G.commonNeighbors v w).toFinset"
] | simp_rw [bipartiteBelow, adj_comm, ← mem_neighborFinset, filter_mem_eq_inter,
neighborFinset_def, ← Set.toFinset_inter, ← h.of_not_adj hw.2.symm hw.1,
← Set.toFinset_card] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Combinatorics.SimpleGraph.FiveWheelLike | {
"line": 399,
"column": 8
} | {
"line": 404,
"column": 33
} | {
"line": 405,
"column": 8
} | [
{
"pp": "case pos\nα : Type u_1\nG : SimpleGraph α\nr k : ℕ\nv w₁ w₂ : α\ns t : Finset α\ninst✝² : DecidableEq α\nhw : G.IsFiveWheelLike r k v w₁ w₂ s t\nhcf : G.CliqueFree (r + 2)\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Fintype α\nhm : G.FiveWheelLikeFree r (k + 1)\nX : Finset α := {x | ∀ ⦃y : α⦄, y ∈ s ∩ t → G.... | [
"case neg\nα : Type u_1\nG : SimpleGraph α\nr k : ℕ\nv w₁ w₂ : α\ns t : Finset α\ninst✝² : DecidableEq α\nhw : G.IsFiveWheelLike r k v w₁ w₂ s t\nhcf : G.CliqueFree (r + 2)\ninst✝¹ : DecidableRel G.Adj\ninst✝ : Fintype α\nhm : G.FiveWheelLikeFree r (k + 1)\nX : Finset α := {x | ∀ ⦃y : α⦄, y ∈ s ∩ t → G.Adj x y}\nW ... | · have Xu : X = univ := by
rw [← hw.card_inter, card_eq_zero] at hk
exact eq_univ_of_forall fun _ ↦ by simp [X, hk]
subst k
rw [add_zero] at Wc
simp [Xu, Wc, mul_comm] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Combinatorics.SimpleGraph.VertexCover | {
"line": 179,
"column": 2
} | {
"line": 179,
"column": 34
} | {
"line": 180,
"column": 2
} | [
{
"pp": "case refine_2\nV : Type u_1\na✝ : Nontrivial V\nn : ℕ\nhn : ↑n ≤ ENat.card V - 1\nhh : (completeGraph V).vertexCoverNum < ↑n\nthis✝ : ↑n - 1 ≤ ENat.card V\nt : Set V\nht₁ : t.encard = ↑(n - 1)\nht₂ : (completeGraph V).IsVertexCover t\nthis : 1 < (Set.univ \\ t).encard\na b : V\nleft✝¹ : a ∈ Set.univ \\... | [
"case refine_2\nV : Type u_1\na✝ : Nontrivial V\nn : ℕ\nhn : ↑n ≤ ENat.card V - 1\nhh : (completeGraph V).vertexCoverNum < ↑n\nthis✝¹ : ↑n - 1 ≤ ENat.card V\nt : Set V\nht₁ : t.encard = ↑(n - 1)\nht₂ : (completeGraph V).IsVertexCover t\nthis✝ : 1 < (Set.univ \\ t).encard\na b : V\nleft✝¹ : a ∈ Set.univ \\ t\nleft✝ ... | have := @ht₂ a b (by simp [hne]) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Data.Nat.PSub | {
"line": 58,
"column": 53
} | {
"line": 58,
"column": 69
} | {
"line": 58,
"column": 70
} | [
{
"pp": "m n : ℕ\n⊢ (m - n).ppred.getD 0 = (m.psub (n + 1)).getD 0",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"HSub.hSub",
"Option.getD",
"id",
"instSubNat",
"instOfNatNat",
"instHAdd",
"instHSub",
"HAdd... | [
"m n : ℕ\n⊢ ((m.psub n).getD 0).ppred.getD 0 = (m.psub (n + 1)).getD 0"
] | sub_eq_psub m n, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Computability.Partrec | {
"line": 53,
"column": 4
} | {
"line": 53,
"column": 20
} | {
"line": 54,
"column": 4
} | [
{
"pp": "p : ℕ →. Bool\nH : ∃ n, true ∈ p n ∧ ∀ k < n, (p k).Dom\n⊢ ∀ (a : ℕ), Acc (lbp p) a",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Part",
"Membership.mem",
"Exists",
"_private.Mathlib.Computability.Partrec.0.Nat.wf_lbp.match_1",
"Part.instMembership... | [
"p : ℕ →. Bool\nH : ∃ n, true ∈ p n ∧ ∀ k < n, (p k).Dom\nn : ℕ\npn : true ∈ p n ∧ ∀ k < n, (p k).Dom\n⊢ ∀ (a : ℕ), Acc (lbp p) a"
] | let ⟨n, pn⟩ := H | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Computability.Primrec.Basic | {
"line": 512,
"column": 6
} | {
"line": 517,
"column": 48
} | {
"line": 519,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable β\nf : α → β\ng : α → ℕ × β → β\nhf : Primrec f\nhg : Primrec₂ g\nn : ℕ\n⊢ Nat.unpaired\n (fun z n ↦\n Nat.casesOn n 0 fun y ↦\n Nat.unpaired\n (fun z n ↦\n Nat.rec (encode (Option.map f... | [] | simp only [Nat.unpaired, id_eq, Nat.unpair_pair, decode_prod_val, decode_nat,
Option.bind_some, Option.map_map, Option.map_some]
rcases @decode α _ n.unpair.1 with - | a; · rfl
simp only [Nat.pred_eq_sub_one, encode_some, Nat.succ_eq_add_one, encodek, Option.map_some,
Option.bind_some, Optio... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.Primrec.Basic | {
"line": 512,
"column": 6
} | {
"line": 517,
"column": 48
} | {
"line": 519,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable β\nf : α → β\ng : α → ℕ × β → β\nhf : Primrec f\nhg : Primrec₂ g\nn : ℕ\n⊢ Nat.unpaired\n (fun z n ↦\n Nat.casesOn n 0 fun y ↦\n Nat.unpaired\n (fun z n ↦\n Nat.rec (encode (Option.map f... | [] | simp only [Nat.unpaired, id_eq, Nat.unpair_pair, decode_prod_val, decode_nat,
Option.bind_some, Option.map_map, Option.map_some]
rcases @decode α _ n.unpair.1 with - | a; · rfl
simp only [Nat.pred_eq_sub_one, encode_some, Nat.succ_eq_add_one, encodek, Option.map_some,
Option.bind_some, Optio... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.Partrec | {
"line": 583,
"column": 2
} | {
"line": 583,
"column": 84
} | {
"line": 584,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_4\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : α → β → σ\n⊢ (Computable₂ fun a n ↦ Option.map (f a) (decode n)) ↔ Computable₂ f",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Primcodable.... | [
"case e'_1\nα : Type u_1\nβ : Type u_2\nσ : Type u_4\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : α → β → σ\nx✝¹ : α\nx✝ : ℕ\n⊢ Option.map (f x✝¹) (decode x✝) = (decode x✝).bind (Option.some ∘ f x✝¹)"
] | convert! (bind_decode_iff (f := fun a => Option.some ∘ f a)).trans option_some_iff | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.Computability.Partrec | {
"line": 753,
"column": 8
} | {
"line": 753,
"column": 42
} | {
"line": 754,
"column": 6
} | [
{
"pp": "case refine_2.inl.refine_1\nα : Type u_5\nσ : Type u_6\nf : α →. σ ⊕ α\na : α\nb : σ\nF : α → ℕ →. σ ⊕ α :=\n fun a n ↦ Nat.rec (Part.some (Sum.inr a)) (fun x IH ↦ IH.bind fun s ↦ Sum.casesOn s (fun x ↦ Part.some s) f) n\nh : b ∈ f.fix a\na₁ : α\nh₁ : b ∈ f.fix a₁\na₂ : α\nh₂✝ : b ∈ f.fix a₂\nIH :\n ... | [] | simpa [F] using Or.inr ⟨_, hk, h₂⟩ | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Computability.Partrec | {
"line": 753,
"column": 8
} | {
"line": 753,
"column": 42
} | {
"line": 754,
"column": 6
} | [
{
"pp": "case refine_2.inl.refine_1\nα : Type u_5\nσ : Type u_6\nf : α →. σ ⊕ α\na : α\nb : σ\nF : α → ℕ →. σ ⊕ α :=\n fun a n ↦ Nat.rec (Part.some (Sum.inr a)) (fun x IH ↦ IH.bind fun s ↦ Sum.casesOn s (fun x ↦ Part.some s) f) n\nh : b ∈ f.fix a\na₁ : α\nh₁ : b ∈ f.fix a₁\na₂ : α\nh₂✝ : b ∈ f.fix a₂\nIH :\n ... | [] | simpa [F] using Or.inr ⟨_, hk, h₂⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.Partrec | {
"line": 753,
"column": 8
} | {
"line": 753,
"column": 42
} | {
"line": 754,
"column": 6
} | [
{
"pp": "case refine_2.inl.refine_1\nα : Type u_5\nσ : Type u_6\nf : α →. σ ⊕ α\na : α\nb : σ\nF : α → ℕ →. σ ⊕ α :=\n fun a n ↦ Nat.rec (Part.some (Sum.inr a)) (fun x IH ↦ IH.bind fun s ↦ Sum.casesOn s (fun x ↦ Part.some s) f) n\nh : b ∈ f.fix a\na₁ : α\nh₁ : b ∈ f.fix a₁\na₂ : α\nh₂✝ : b ∈ f.fix a₂\nIH :\n ... | [] | simpa [F] using Or.inr ⟨_, hk, h₂⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.Partrec | {
"line": 720,
"column": 26
} | {
"line": 760,
"column": 11
} | {
"line": 762,
"column": 0
} | [
{
"pp": "α : Type u_5\nσ : Type u_6\nf : α →. σ ⊕ α\na : α\nb : σ\n⊢ let F := fun a n ↦\n Nat.rec (Part.some (Sum.inr a)) (fun x IH ↦ IH.bind fun s ↦ Sum.casesOn s (fun x ↦ Part.some s) f) n;\n (∃ n, ((∃ b', Sum.inl b' ∈ F a n) ∧ ∀ {m : ℕ}, m < n → ∃ b, Sum.inr b ∈ F a m) ∧ Sum.inl b ∈ F a n) ↔ b ∈ f.fix a"... | [] | by
intro F; refine ⟨fun h => ?_, fun h => ?_⟩
· rcases h with ⟨n, ⟨_x, h₁⟩, h₂⟩
have : ∀ m a', Sum.inr a' ∈ F a m → b ∈ PFun.fix f a' → b ∈ PFun.fix f a := by
intro m a' am ba
induction m generalizing a' with simp [F] at am
| zero => rwa [← am]
| succ m IH =>
rcases am with ⟨a₂, ... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.Partrec | {
"line": 768,
"column": 2
} | {
"line": 768,
"column": 95
} | {
"line": 769,
"column": 2
} | [
{
"pp": "α : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf : α →. σ ⊕ α\nhf : Partrec f\nF : α → ℕ →. σ ⊕ α :=\n fun a n ↦ Nat.rec (Part.some (Sum.inr a)) (fun x IH ↦ IH.bind fun s ↦ Sum.casesOn s (fun x ↦ Part.some s) f) n\nhF : Partrec₂ F\n⊢ Partrec f.fix",
"ppTerm": "?m.166",
... | [
"α : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf : α →. σ ⊕ α\nhf : Partrec f\nF : α → ℕ →. σ ⊕ α :=\n fun a n ↦ Nat.rec (Part.some (Sum.inr a)) (fun x IH ↦ IH.bind fun s ↦ Sum.casesOn s (fun x ↦ Part.some s) f) n\nhF : Partrec₂ F\np : α → ℕ → Part Bool := fun a n ↦ Part.map (fun s ↦ S... | let p a n := @Part.map _ Bool (fun s => Sum.casesOn s (fun _ => true) fun _ => false) (F a n) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Computability.Primrec.List | {
"line": 309,
"column": 2
} | {
"line": 362,
"column": 68
} | {
"line": 364,
"column": 0
} | [
{
"pp": "β : Type u_2\nσ : Type u_4\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : β → σ\nm : β → ℕ\nl : β → List β\ng : β → List σ → Option σ\nhm : Primrec m\nhl : Primrec l\nhg : Primrec₂ g\nOrd : ∀ (b b' : β), b' ∈ l b → m b' < m b\nH : ∀ (b : β), g b (List.map f (l b)) = some (f b)\n⊢ Primrec f",
"... | [] | haveI : DecidableEq β := Encodable.decidableEqOfEncodable β
let mapGraph (M : List (β × σ)) (bs : List β) : List σ := bs.flatMap (Option.toList <| M.lookup ·)
let bindList (b : β) : ℕ → List β := fun n ↦ n.rec [b] fun _ bs ↦ bs.flatMap l
let graph (b : β) : ℕ → List (β × σ) := fun i ↦ i.rec [] fun i ih ↦
(bin... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.Primrec.List | {
"line": 309,
"column": 2
} | {
"line": 362,
"column": 68
} | {
"line": 364,
"column": 0
} | [
{
"pp": "β : Type u_2\nσ : Type u_4\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : β → σ\nm : β → ℕ\nl : β → List β\ng : β → List σ → Option σ\nhm : Primrec m\nhl : Primrec l\nhg : Primrec₂ g\nOrd : ∀ (b b' : β), b' ∈ l b → m b' < m b\nH : ∀ (b : β), g b (List.map f (l b)) = some (f b)\n⊢ Primrec f",
"... | [] | haveI : DecidableEq β := Encodable.decidableEqOfEncodable β
let mapGraph (M : List (β × σ)) (bs : List β) : List σ := bs.flatMap (Option.toList <| M.lookup ·)
let bindList (b : β) : ℕ → List β := fun n ↦ n.rec [b] fun _ bs ↦ bs.flatMap l
let graph (b : β) : ℕ → List (β × σ) := fun i ↦ i.rec [] fun i ih ↦
(bin... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 140,
"column": 4
} | {
"line": 140,
"column": 99
} | {
"line": 141,
"column": 4
} | [
{
"pp": "f : ℝ → ℝ\nhf✝ : GrowsPolynomially f\nhf' : ∀ (a : ℝ), ∃ b, a ≤ b ∧ f b = 0\nc₁ : ℝ\nhc₁_mem : c₁ > 0\nc₂ : ℝ\nhc₂_mem : c₂ > 0\nhf : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nx : ℝ\nhx : ∀ (y : ℝ), x ≤ y → ∀ u ∈ Set.Icc (1 / 2 * y) y, f u ∈ Set.Icc (c₁ * f ... | [
"f : ℝ → ℝ\nhf✝ : GrowsPolynomially f\nhf' : ∀ (a : ℝ), ∃ b, a ≤ b ∧ f b = 0\nc₁ : ℝ\nhc₁_mem : c₁ > 0\nc₂ : ℝ\nhc₂_mem : c₂ > 0\nhf : ∀ᶠ (x : ℝ) in atTop, ∀ u ∈ Set.Icc (1 / 2 * x) x, f u ∈ Set.Icc (c₁ * f x) (c₂ * f x)\nx : ℝ\nhx : ∀ (y : ℝ), x ≤ y → ∀ u ∈ Set.Icc (1 / 2 * y) y, f u ∈ Set.Icc (c₁ * f y) (c₂ * f y... | simp only [Int.cast_sub, Int.cast_neg, Int.cast_natCast, Int.cast_one, neg_sub, sub_neg_eq_add] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 278,
"column": 2
} | {
"line": 278,
"column": 86
} | {
"line": 279,
"column": 2
} | [
{
"pp": "case intro\nV : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nh : ∀ (M : G.Subgraph), ¬M.IsPerfectMatching\nhvEven : Even (Nat.card V)\nval✝ : Fintype V\n⊢ ∃ u, G.IsTutteViolator u",
"ppTerm": "?intro",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"SimpleGraph.Subgraph... | [
"case intro\nV : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nh : ∀ (M : G.Subgraph), ¬M.IsPerfectMatching\nhvEven : Even (Nat.card V)\nval✝ : Fintype V\nGmax : SimpleGraph V\nhSubgraph : G ≤ Gmax\nhMatchingFree : Gmax.IsMatchingFree\nhMaximal : ∀ G' > Gmax, ∃ M, M.IsPerfectMatching\n⊢ ∃ u, G.IsTutteViolator u"
] | obtain ⟨Gmax, hSubgraph, hMatchingFree, hMaximal⟩ := exists_maximal_isMatchingFree h | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Computability.AkraBazzi.SumTransform | {
"line": 464,
"column": 6
} | {
"line": 466,
"column": 35
} | {
"line": 467,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\ni : α\nthis : (fun n ↦ log (b i) + log ↑n) = fun n ↦ log ↑n + log (b i)\n⊢ (fun n ↦ log ↑n + log (b i)) ~[atTop] fun n ↦ log ↑n",
"ppTerm": "?m.370",
"assig... | [] | exact IsEquivalent.add_isLittleO IsEquivalent.refl
<| IsLittleO.natCast_atTop (f := fun (_ : ℝ) => log (b i))
isLittleO_const_log_atTop | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Computability.AkraBazzi.AkraBazzi | {
"line": 221,
"column": 2
} | {
"line": 221,
"column": 67
} | {
"line": 222,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nq : ℝ → ℝ\nhq_diff : DifferentiableOn ℝ q (Set.Ioi 1)\nhq_poly : GrowsPolynomially fun x ↦ ‖deriv q x‖\ni : α\nb' : ℝ := b (min_bi b) / 2\n⊢ (fun n ↦ q ↑(r i n) - q... | [
"α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nq : ℝ → ℝ\nhq_diff : DifferentiableOn ℝ q (Set.Ioi 1)\nhq_poly : GrowsPolynomially fun x ↦ ‖deriv q x‖\ni : α\nb' : ℝ := b (min_bi b) / 2\nhb_pos : 0 < b'\n⊢ (fun n ↦ q ↑(r i n... | have hb_pos : 0 < b' := by have := R.b_pos (min_bi b); positivity | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Computability.AkraBazzi.SumTransform | {
"line": 582,
"column": 8
} | {
"line": 582,
"column": 35
} | {
"line": 583,
"column": 8
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nn : ℕ\nhn : 0 < n\n⊢ ↑n ^ p a b * (1 + 0) ≤ ↑n ^ p a b * (1 + ∑ u ∈ range n, g ↑u / ↑u ^ (p a b + 1))",
"ppTerm": "?m.46",
"assigned": true,
"usedConsta... | [
"case h₂\nα : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\nn : ℕ\nhn : 0 < n\n⊢ 0 ≤ ∑ u ∈ range n, g ↑u / ↑u ^ (p a b + 1)"
] | gcongr n ^ p a b * (1 + ?_) | Mathlib.Tactic.GCongr._aux_Mathlib_Tactic_GCongr_Core___elabRules_Mathlib_Tactic_GCongr_gcongr_1 | Mathlib.Tactic.GCongr.gcongr |
Mathlib.Computability.AkraBazzi.AkraBazzi | {
"line": 257,
"column": 4
} | {
"line": 259,
"column": 44
} | {
"line": 260,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\ni : α\nq : ℝ → ℝ := fun x ↦ x ^ p a b * (1 - ε x)\n⊢ DifferentiableOn ℝ q (Set.Ioi 1)",
"ppTerm": "?m.94",
"assigned": true,
"usedConstants": [
"N... | [
"α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\ni : α\nq : ℝ → ℝ := fun x ↦ x ^ p a b * (1 - ε x)\nz : ℝ\nhz : z ∈ Set.Ioi 1\n⊢ z ∈ {0}ᶜ"
] | refine DifferentiableOn.mul
(DifferentiableOn.mono (differentiableOn_rpow_const _) fun z hz => ?_)
differentiableOn_one_sub_smoothingFn | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Computability.AkraBazzi.AkraBazzi | {
"line": 323,
"column": 38
} | {
"line": 323,
"column": 77
} | {
"line": 324,
"column": 14
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\ni : α\nq : ℝ → ℝ := fun x ↦ x ^ p a b * (1 - ε x)\nh_diff_q : DifferentiableOn ℝ q (Set.Ioi 1)\nh_deriv_q : deriv q =O[atTop] fun x ↦ x ^ (p a b - 1)\nh_main_norm :... | [] | by rw [mul_inv_cancel₀ (by positivity)] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.AkraBazzi.AkraBazzi | {
"line": 419,
"column": 38
} | {
"line": 419,
"column": 77
} | {
"line": 420,
"column": 16
} | [
{
"pp": "α : Type u_1\ninst✝¹ : Fintype α\nT : ℕ → ℝ\ng : ℝ → ℝ\na b : α → ℝ\nr : α → ℕ → ℕ\ninst✝ : Nonempty α\nR : AkraBazziRecurrence T g a b r\ni : α\nq : ℝ → ℝ := fun x ↦ x ^ p a b * (1 + ε x)\nh_diff_q : DifferentiableOn ℝ q (Set.Ioi 1)\nh_deriv_q : deriv q =O[atTop] fun x ↦ x ^ (p a b - 1)\nh_main_norm :... | [] | by rw [mul_inv_cancel₀ (by positivity)] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.PartrecCode | {
"line": 502,
"column": 54
} | {
"line": 502,
"column": 81
} | {
"line": 504,
"column": 0
} | [
{
"pp": "n : ℕ\n⊢ Code.id.eval n = Part.some n",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"Nat.Partrec.Code.id.eq_1",
"Part",
"Unit.unit",
"PFun",
"congrArg",
"Part.bind",
"Nat.unpair",
"Part.some",
"Part.bind_some",
"Monad.to... | [] | by simp! [Seq.seq, Code.id] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.PartrecCode | {
"line": 712,
"column": 2
} | {
"line": 712,
"column": 23
} | {
"line": 713,
"column": 4
} | [
{
"pp": "case prec\ncf cg : Code\nhf : ∀ {n x : ℕ}, x ∈ cf.eval n → ∃ k, x ∈ evaln (k + 1) cf n\nhg : ∀ {n x : ℕ}, x ∈ cg.eval n → ∃ k, x ∈ evaln (k + 1) cg n\nn x : ℕ\nh :\n x ∈\n Nat.rec (cf.eval (unpair n).1) (fun y IH ↦ IH.bind fun i ↦ cg.eval (Nat.pair (unpair n).1 (Nat.pair y i)))\n (unpair n).2\... | [] | | prec cf cg hf hg => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | null |
Mathlib.Computability.PartrecCode | {
"line": 748,
"column": 24
} | {
"line": 748,
"column": 89
} | {
"line": 748,
"column": 89
} | [
{
"pp": "cf : Code\nhf : ∀ {n x : ℕ}, x ∈ cf.eval n → ∃ k, x ∈ evaln (k + 1) cf n\nn y : ℕ\nIH :\n ∀ (m : ℕ),\n 0 ∈ cf.eval (Nat.pair (unpair n).1 (y + m)) →\n (∀ {m_1 : ℕ}, m_1 < y → ∃ a ∈ cf.eval (Nat.pair (unpair n).1 (m_1 + m)), ¬a = 0) →\n ∃ k, y + m ∈ evaln (k + 1) cf.rfind' (Nat.pair (unp... | [] | by simpa [Nat.succ_eq_add_one, add_comm, add_left_comm] using hy₁ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Nat.Size | {
"line": 29,
"column": 2
} | {
"line": 29,
"column": 38
} | {
"line": 31,
"column": 0
} | [
{
"pp": "b : Bool\nm : ℕ\nh : m ≠ 0\nn : ℕ\n⊢ shiftLeft' b m n ≠ 0",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Nat.bit",
"False",
"Nat.recAux",
"Nat.bit_eq_zero_iff._simp_1",
"eq_false",
"congrArg",
"false_and",
"Ne",
"instOfNatNat... | [] | induction n <;> simp [shiftLeft', *] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.Nat.Size | {
"line": 29,
"column": 2
} | {
"line": 29,
"column": 38
} | {
"line": 31,
"column": 0
} | [
{
"pp": "b : Bool\nm : ℕ\nh : m ≠ 0\nn : ℕ\n⊢ shiftLeft' b m n ≠ 0",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Nat.bit",
"False",
"Nat.recAux",
"Nat.bit_eq_zero_iff._simp_1",
"eq_false",
"congrArg",
"false_and",
"Ne",
"instOfNatNat... | [] | induction n <;> simp [shiftLeft', *] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Nat.Size | {
"line": 29,
"column": 2
} | {
"line": 29,
"column": 38
} | {
"line": 31,
"column": 0
} | [
{
"pp": "b : Bool\nm : ℕ\nh : m ≠ 0\nn : ℕ\n⊢ shiftLeft' b m n ≠ 0",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Nat.bit",
"False",
"Nat.recAux",
"Nat.bit_eq_zero_iff._simp_1",
"eq_false",
"congrArg",
"false_and",
"Ne",
"instOfNatNat... | [] | induction n <;> simp [shiftLeft', *] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 615,
"column": 2
} | {
"line": 619,
"column": 45
} | {
"line": 620,
"column": 2
} | [
{
"pp": "case lb\nb : ℝ\nhb : b ∈ Set.Ioo 0 1\nhb₀ : 0 < b\nh_tendsto : Tendsto (fun x ↦ 1 / 2 * log x) atTop atTop\nx : ℝ\nhx_pos : 1 < x\nhx : ∀ (y : ℝ), b * id x ≤ y → -log b < 1 / 2 * log y\nu : ℝ\nhu : u ∈ Set.Icc (b * x) x\n⊢ 1 / 2 * log x ≤ log u",
"ppTerm": "?lb",
"assigned": true,
"usedCons... | [
"case ub\nb : ℝ\nhb : b ∈ Set.Ioo 0 1\nhb₀ : 0 < b\nh_tendsto : Tendsto (fun x ↦ 1 / 2 * log x) atTop atTop\nx : ℝ\nhx_pos : 1 < x\nhx : ∀ (y : ℝ), b * id x ≤ y → -log b < 1 / 2 * log y\nu : ℝ\nhu : u ∈ Set.Icc (b * x) x\n⊢ log u ≤ 1 * log x"
] | case lb => calc
1 / 2 * Real.log x = Real.log x + (-1 / 2) * Real.log x := by ring
_ ≤ Real.log x + Real.log b := by grind
_ = Real.log (b * x) := by rw [← Real.log_mul (by positivity) (by positivity), mul_comm]
_ ≤ Real.log u := by gcongr; exact hu.1 | Lean.Elab.Tactic.evalCase | Lean.Parser.Tactic.case |
Mathlib.Computability.PartrecCode | {
"line": 971,
"column": 8
} | {
"line": 977,
"column": 57
} | {
"line": 978,
"column": 2
} | [
{
"pp": "case succ.rfind'\nx✝ : Unit\np n : ℕ\nthis : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))\nk' : ℕ\nk : ℕ := k' + 1\nnk : n ≤ k'\ncf : Code\nhg :\n ∀ {k' : ℕ} {c' : Code} {n : ℕ},\n Nat.pair k' (encode c') < Nat.pair k (encode cf.rfind') →\n lup\n ... | [] | have lf := encode_lt_rfind' cf
rw [hg (Nat.pair_lt_pair_right _ lf)]
rcases evaln k cf n with - | x
· rfl
simp only [Option.bind_some]
cases x <;> simp
rw [hg (Nat.pair_lt_pair_left _ k'.lt_succ_self)] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.PartrecCode | {
"line": 971,
"column": 8
} | {
"line": 977,
"column": 57
} | {
"line": 978,
"column": 2
} | [
{
"pp": "case succ.rfind'\nx✝ : Unit\np n : ℕ\nthis : List.range p = List.range (Nat.pair (unpair p).1 (encode (ofNat Code (unpair p).2)))\nk' : ℕ\nk : ℕ := k' + 1\nnk : n ≤ k'\ncf : Code\nhg :\n ∀ {k' : ℕ} {c' : Code} {n : ℕ},\n Nat.pair k' (encode c') < Nat.pair k (encode cf.rfind') →\n lup\n ... | [] | have lf := encode_lt_rfind' cf
rw [hg (Nat.pair_lt_pair_right _ lf)]
rcases evaln k cf n with - | x
· rfl
simp only [Option.bind_some]
cases x <;> simp
rw [hg (Nat.pair_lt_pair_left _ k'.lt_succ_self)] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.NFA | {
"line": 349,
"column": 57
} | {
"line": 356,
"column": 9
} | {
"line": 358,
"column": 0
} | [
{
"pp": "α : Type u\nσ : Type v\nM : DFA α σ\nstart : σ\ns : List α\n⊢ M.toNFA.evalFrom {start} s = {M.evalFrom start s}",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NFA.step",
"Iff.of_eq",
"congrArg",
"List.foldl.eq_2",
"NFA.evalFrom",
... | [] | by
change List.foldl M.toNFA.stepSet {start} s = {List.foldl M.step start s}
induction s generalizing start with
| nil => tauto
| cons a s ih =>
rw [List.foldl, List.foldl,
show M.toNFA.stepSet {start} a = {M.step start a} by simp [NFA.stepSet]]
tauto | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Num.Lemmas | {
"line": 303,
"column": 6
} | {
"line": 303,
"column": 42
} | {
"line": 304,
"column": 6
} | [
{
"pp": "⊢ Num.ofNat' ↑1 = Num.pos 1",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Num.ofNat'_one",
"Eq.mpr",
"castPosNum",
"Nat.instOne",
"congrArg",
"id",
"instOnePosNum",
"instOneNum",
"Num",
"Nat",
"Num.pos",
"On... | [
"⊢ 1 = Num.pos 1"
] | simp only [cast_one, Num.ofNat'_one] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Computability.MyhillNerode | {
"line": 92,
"column": 2
} | {
"line": 92,
"column": 59
} | {
"line": 93,
"column": 2
} | [
{
"pp": "α : Type u\nL : Language α\nx : List α\n⊢ L.toDFA.eval x ∈ L.toDFA.accept ↔ x ∈ L",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Language.mem_accept_toDFA._simp_1",
"congrArg",
"Membership.mem",
"Language.toDFA",
"Set.Elem",
"Language.leftQuot... | [
"α : Type u\nL : Language α\nx : List α\n⊢ ↑(L.toDFA.eval x) = L.leftQuotient x"
] | suffices L.toDFA.eval x = L.leftQuotient x by simp [this] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticSuffices__1 | Lean.Parser.Tactic.tacticSuffices_ |
Mathlib.Data.Num.Lemmas | {
"line": 592,
"column": 33
} | {
"line": 592,
"column": 46
} | {
"line": 592,
"column": 47
} | [
{
"pp": "α : Type u_1\ninst✝ : NonAssocSemiring α\nm n : PosNum\n⊢ ↑(↑m * ↑n) = ↑m * ↑n",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"NonAssocSemiring.toAddCommMonoidWithOne",
"castPosNum",
"HMul.hMul",
"Nat.instOne",
"congrArg",
"id",... | [
"α : Type u_1\ninst✝ : NonAssocSemiring α\nm n : PosNum\n⊢ ↑↑m * ↑↑n = ↑m * ↑n"
] | Nat.cast_mul, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Computability.RE | {
"line": 82,
"column": 53
} | {
"line": 82,
"column": 95
} | {
"line": 82,
"column": 96
} | [
{
"pp": "case inl\nα : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf g : α →. σ\nhf : Partrec f\nhg : Partrec g\nk : ℕ →. ℕ\nhk : Nat.Partrec k\nH :\n ∀ (a : ℕ),\n (∀ x ∈ k a,\n (x ∈ (↑(decode₂ α a)).bind fun a ↦ Part.map encode (f a)) ∨\n x ∈ (↑(decode₂ α a)).bind... | [
"case inl\nα : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf g : α →. σ\nhf : Partrec f\nhg : Partrec g\nk : ℕ →. ℕ\nhk : Nat.Partrec k\nH :\n ∀ (a : ℕ),\n (∀ x ∈ k a,\n (x ∈ (↑(decode₂ α a)).bind fun a ↦ Part.map encode (f a)) ∨\n x ∈ (↑(decode₂ α a)).bind fun a ↦ Par... | simp only [encodek, Option.some_inj] at hx | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Computability.RE | {
"line": 82,
"column": 53
} | {
"line": 82,
"column": 95
} | {
"line": 82,
"column": 96
} | [
{
"pp": "case inr\nα : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf g : α →. σ\nhf : Partrec f\nhg : Partrec g\nk : ℕ →. ℕ\nhk : Nat.Partrec k\nH :\n ∀ (a : ℕ),\n (∀ x ∈ k a,\n (x ∈ (↑(decode₂ α a)).bind fun a ↦ Part.map encode (f a)) ∨\n x ∈ (↑(decode₂ α a)).bind... | [
"case inr\nα : Type u_1\nσ : Type u_4\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf g : α →. σ\nhf : Partrec f\nhg : Partrec g\nk : ℕ →. ℕ\nhk : Nat.Partrec k\nH :\n ∀ (a : ℕ),\n (∀ x ∈ k a,\n (x ∈ (↑(decode₂ α a)).bind fun a ↦ Part.map encode (f a)) ∨\n x ∈ (↑(decode₂ α a)).bind fun a ↦ Par... | simp only [encodek, Option.some_inj] at hx | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Computability.TuringMachine.Tape | {
"line": 202,
"column": 4
} | {
"line": 202,
"column": 18
} | {
"line": 203,
"column": 2
} | [
{
"pp": "case nil\nΓ : Type u_1\ninst✝ : Inhabited Γ\n⊢ BlankExtends [] (head (Quotient.mk'' []) :: [].tail)",
"ppTerm": "?nil",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"List.replicate",
"Quotient.mk''",
"instOfNatNat",
"List.tail",
"List.cons",
... | [] | exact ⟨1, rfl⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Computability.TuringMachine.Tape | {
"line": 202,
"column": 4
} | {
"line": 202,
"column": 18
} | {
"line": 203,
"column": 2
} | [
{
"pp": "case nil\nΓ : Type u_1\ninst✝ : Inhabited Γ\n⊢ BlankExtends [] (head (Quotient.mk'' []) :: [].tail)",
"ppTerm": "?nil",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"List.replicate",
"Quotient.mk''",
"instOfNatNat",
"List.tail",
"List.cons",
... | [] | exact ⟨1, rfl⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.TuringMachine.Tape | {
"line": 202,
"column": 4
} | {
"line": 202,
"column": 18
} | {
"line": 203,
"column": 2
} | [
{
"pp": "case nil\nΓ : Type u_1\ninst✝ : Inhabited Γ\n⊢ BlankExtends [] (head (Quotient.mk'' []) :: [].tail)",
"ppTerm": "?nil",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"List.replicate",
"Quotient.mk''",
"instOfNatNat",
"List.tail",
"List.cons",
... | [] | exact ⟨1, rfl⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.Tape | {
"line": 300,
"column": 15
} | {
"line": 300,
"column": 47
} | {
"line": 300,
"column": 47
} | [
{
"pp": "case nil\nΓ : Type u_1\nΓ' : Type u_2\ninst✝¹ : Inhabited Γ\ninst✝ : Inhabited Γ'\nf : PointedMap Γ Γ'\n⊢ (List.map f.f []).headI = f.f [].headI",
"ppTerm": "?nil",
"assigned": true,
"usedConstants": [
"Inhabited.default",
"Turing.PointedMap.f",
"Eq.symm",
"Turing.Po... | [] | exact (PointedMap.map_pt f).symm | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Computability.StateTransition | {
"line": 246,
"column": 14
} | {
"line": 249,
"column": 19
} | {
"line": 249,
"column": 19
} | [
{
"pp": "σ₁ σ₂ : Type u_1\nf₁ : σ₁ → Option σ₁\nf₂ : σ₂ → Option σ₂\ntr : σ₁ → σ₂\nH : Respects f₁ f₂ fun a b ↦ tr a = b\na₁ : σ₁\nb₂ : σ₂\nh : b₂ ∈ tr <$> eval f₁ a₁\n⊢ b₂ ∈ eval f₂ (tr a₁)",
"ppTerm": "?m.69",
"assigned": true,
"usedConstants": [
"Part",
"congrArg",
"Membership.m... | [] | by
rcases (Part.mem_map_iff _).1 h with ⟨b₁, ab, bb⟩
rcases tr_eval H rfl ab with ⟨_, rfl, h⟩
rwa [bb] at h | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.TuringMachine.Tape | {
"line": 587,
"column": 14
} | {
"line": 588,
"column": 43
} | {
"line": 590,
"column": 0
} | [
{
"pp": "case mk.left\nΓ : Type u_1\nΓ' : Type u_2\ninst✝¹ : Inhabited Γ\ninst✝ : Inhabited Γ'\nf : PointedMap Γ Γ'\nhead✝ : Γ\nleft✝ right✝ : ListBlank Γ\n⊢ map f (move Dir.left { head := head✝, left := left✝, right := right✝ }) =\n move Dir.left (map f { head := head✝, left := left✝, right := right✝ })",
... | [] | simp only [Tape.move, Tape.map, ListBlank.head_map,
ListBlank.map_cons, ListBlank.tail_map] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Computability.TuringMachine.Tape | {
"line": 587,
"column": 14
} | {
"line": 588,
"column": 43
} | {
"line": 590,
"column": 0
} | [
{
"pp": "case mk.right\nΓ : Type u_1\nΓ' : Type u_2\ninst✝¹ : Inhabited Γ\ninst✝ : Inhabited Γ'\nf : PointedMap Γ Γ'\nhead✝ : Γ\nleft✝ right✝ : ListBlank Γ\n⊢ map f (move Dir.right { head := head✝, left := left✝, right := right✝ }) =\n move Dir.right (map f { head := head✝, left := left✝, right := right✝ })"... | [] | simp only [Tape.move, Tape.map, ListBlank.head_map,
ListBlank.map_cons, ListBlank.tail_map] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Computability.TuringMachine.PostTuringMachine | {
"line": 231,
"column": 4
} | {
"line": 231,
"column": 51
} | {
"line": 232,
"column": 4
} | [
{
"pp": "Γ : Type u_1\ninst✝³ : Inhabited Γ\nΓ' : Type u_2\ninst✝² : Inhabited Γ'\nΛ : Type u_3\ninst✝¹ : Inhabited Λ\nΛ' : Type u_4\ninst✝ : Inhabited Λ'\nM : Machine Γ Λ\nf₁ : PointedMap Γ Γ'\nf₂ : PointedMap Γ' Γ\ng₁ : Λ → Λ'\ng₂ : Λ' → Λ\nS : Set Λ\nf₂₁ : Function.RightInverse f₁.f f₂.f\ng₂₁ : ∀ q ∈ S, g₂ (... | [
"Γ : Type u_1\ninst✝³ : Inhabited Γ\nΓ' : Type u_2\ninst✝² : Inhabited Γ'\nΛ : Type u_3\ninst✝¹ : Inhabited Λ\nΛ' : Type u_4\ninst✝ : Inhabited Λ'\nM : Machine Γ Λ\nf₁ : PointedMap Γ Γ'\nf₂ : PointedMap Γ' Γ\ng₁ : Λ → Λ'\ng₂ : Λ' → Λ\nS : Set Λ\nf₂₁ : Function.RightInverse f₁.f f₂.f\ng₂₁ : ∀ q ∈ S, g₂ (g₁ q) = q\nq... | simp only [Turing.Tape.map_fst, g₂₁ q h, f₂₁ _] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Computability.Reduce | {
"line": 127,
"column": 2
} | {
"line": 130,
"column": 53
} | {
"line": 132,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable β\np : α → Prop\nq : β → Prop\nh₁ : p ≤₀ q\nh₂ : ComputablePred q\n⊢ ComputablePred p",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"congrArg",
"Exists",
"in... | [] | rcases h₁ with ⟨f, c, hf⟩
rw [show p = fun a => q (f a) from Set.ext hf]
rcases computable_iff.1 h₂ with ⟨g, hg, rfl⟩
exact ⟨by infer_instance, by simpa using hg.comp c⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.Reduce | {
"line": 127,
"column": 2
} | {
"line": 130,
"column": 53
} | {
"line": 132,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable β\np : α → Prop\nq : β → Prop\nh₁ : p ≤₀ q\nh₂ : ComputablePred q\n⊢ ComputablePred p",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Set.ext",
"Eq.mpr",
"congrArg",
"Exists",
"in... | [] | rcases h₁ with ⟨f, c, hf⟩
rw [show p = fun a => q (f a) from Set.ext hf]
rcases computable_iff.1 h₂ with ⟨g, hg, rfl⟩
exact ⟨by infer_instance, by simpa using hg.comp c⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.PostTuringMachine | {
"line": 725,
"column": 17
} | {
"line": 725,
"column": 51
} | {
"line": 725,
"column": 52
} | [
{
"pp": "case succ\nΓ : Type u_1\nΛ : Type u_2\nσ : Type u_3\nn : ℕ\ndec : List.Vector Bool n → Γ\nS : Finset (Λ' Γ Λ σ)\nf✝ : Γ → Stmt Bool (Λ' Γ Λ σ) σ\ni : ℕ\nIH :\n ∀ (f : List.Vector Bool i → Stmt Bool (Λ' Γ Λ σ) σ),\n (∀ (v : List.Vector Bool i), SupportsStmt S (f v)) → SupportsStmt S (readAux i f)\nf... | [
"case succ.left\nΓ : Type u_1\nΛ : Type u_2\nσ : Type u_3\nn : ℕ\ndec : List.Vector Bool n → Γ\nS : Finset (Λ' Γ Λ σ)\nf✝ : Γ → Stmt Bool (Λ' Γ Λ σ) σ\ni : ℕ\nIH :\n ∀ (f : List.Vector Bool i → Stmt Bool (Λ' Γ Λ σ) σ),\n (∀ (v : List.Vector Bool i), SupportsStmt S (f v)) → SupportsStmt S (readAux i f)\nf : List... | constructor <;> apply IH <;> intro | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Computability.TuringMachine.StackTuringMachine | {
"line": 231,
"column": 52
} | {
"line": 238,
"column": 85
} | {
"line": 240,
"column": 0
} | [
{
"pp": "K : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\nS : Finset Λ\nq₁ q₂ : Stmt Γ Λ σ\nh : q₁ ∈ stmts₁ q₂\nhs : SupportsStmt S q₂\n⊢ SupportsStmt S q₁",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Turing.TM2.SupportsStmt",
"_private.Mathlib.Computability.Turi... | [] | by
induction q₂ with
simp only [stmts₁, SupportsStmt, Finset.mem_insert, Finset.mem_union, Finset.mem_singleton]
at h hs
| branch f q₁ q₂ IH₁ IH₂ => rcases h with (rfl | h | h); exacts [hs, IH₁ h hs.1, IH₂ h hs.2]
| goto l => subst h; exact hs
| halt => subst h; trivial
| load _ _ IH | _ _ _ _ IH =>... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.TuringMachine.Config | {
"line": 276,
"column": 48
} | {
"line": 276,
"column": 60
} | {
"line": 276,
"column": 60
} | [
{
"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\nx✝ : List.Vector ℕ n.succ\na : ℕ\nas : List ℕ\nproperty✝ : (a :: as).length = n.succ\n⊢ head.eval ↑⟨a :: as, property✝⟩ = pure <$> (↑fun v ↦ v.get 0) ⟨a :: as, property✝⟩",
"ppTerm": "?m.213",
"... | [] | by simp; rfl | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Computability.TuringMachine.Config | {
"line": 343,
"column": 6
} | {
"line": 343,
"column": 14
} | {
"line": 343,
"column": 15
} | [
{
"pp": "case rfind.mp\nn✝ : ℕ\nf✝ : List.Vector ℕ n✝ →. ℕ\nn : ℕ\nf : List.Vector ℕ (n + 1) → ℕ\na✝ : Nat.Partrec' ↑f\ncf : Code\nv : List.Vector ℕ n\nhf : ∀ (a : ℕ), cf.eval (a :: ↑v) = Part.some [f (a ::ᵥ v)]\nv' : List ℕ\n⊢ ∀ (v₁ : List ℕ),\n v' ∈\n PFun.fix\n (fun v ↦\n (cf.ev... | [
"case rfind.mp\nn✝ : ℕ\nf✝ : List.Vector ℕ n✝ →. ℕ\nn : ℕ\nf : List.Vector ℕ (n + 1) → ℕ\na✝ : Nat.Partrec' ↑f\ncf : Code\nv : List.Vector ℕ n\nhf : ∀ (a : ℕ), cf.eval (a :: ↑v) = Part.some [f (a ::ᵥ v)]\nv' v₀ : List ℕ\n⊢ v' ∈\n PFun.fix\n (fun v ↦\n (cf.eval v).bind fun y ↦\n Part.... | intro v₀ | Lean.Elab.Tactic.evalIntro | null |
Mathlib.Data.Num.Lemmas | {
"line": 828,
"column": 2
} | {
"line": 830,
"column": 19
} | {
"line": 831,
"column": 2
} | [
{
"pp": "case pos\nn : ℕ\nm : PosNum\n⊢ ↑(m >>> n) = ↑(pos m) >>> n",
"ppTerm": "?pos",
"assigned": true,
"usedConstants": [
"PosNum.casesOn",
"Nat.instMulZeroClass",
"Nat.recAux",
"Nat.instOne",
"PosNum.bit1",
"instOfNatNat",
"PosNum.instHShiftRightNatNum",... | [
"case pos.succ\nn : ℕ\nIH : ∀ (m : PosNum), ↑(m >>> n) = ↑(pos m) >>> n\nm : PosNum\n⊢ ↑(m >>> (n + 1)) = ↑(pos m) >>> (n + 1)"
] | induction n generalizing m with
| zero => cases m <;> rfl
| succ n IH => ?_ | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Computability.TuringMachine.StackTuringMachine | {
"line": 778,
"column": 6
} | {
"line": 781,
"column": 65
} | {
"line": 782,
"column": 6
} | [
{
"pp": "case refine_1.inl.inl\nK : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝¹ : DecidableEq K\nM : Λ → TM2.Stmt Γ Λ σ\ninst✝ : Inhabited Λ\nS : Finset Λ\nss : TM2.Supports M S\nk✝ : K\ns : StAct K Γ σ k✝\nq✝ : TM2.Stmt Γ Λ σ\nIH :\n TM2.SupportsStmt S q✝ →\n (∀ x ∈ trStmts₁ q✝, x ∈ trSu... | [
"case refine_1.inl.inr\nK : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝¹ : DecidableEq K\nM : Λ → TM2.Stmt Γ Λ σ\ninst✝ : Inhabited Λ\nS : Finset Λ\nss : TM2.Supports M S\nk✝ : K\ns : StAct K Γ σ k✝\nq✝ : TM2.Stmt Γ Λ σ\nIH :\n TM2.SupportsStmt S q✝ →\n (∀ x ∈ trStmts₁ q✝, x ∈ trSupp M S) →\n ... | · cases s
· exact ⟨fun _ _ ↦ hret, fun _ _ ↦ hgo⟩
· exact ⟨fun _ _ ↦ hret, fun _ _ ↦ hgo⟩
· exact ⟨⟨fun _ _ ↦ hret, fun _ _ ↦ hret⟩, fun _ _ ↦ hgo⟩ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.ExtremallyDisconnected | {
"line": 63,
"column": 9
} | {
"line": 63,
"column": 55
} | {
"line": 63,
"column": 55
} | [
{
"pp": "X : Type u\ninst✝² : TopologicalSpace X\ninst✝¹ : ExtremallyDisconnected X\ninst✝ : T2Space X\nx : X\na✝¹ : x ∈ univ\ny : X\na✝ : y ∈ univ\nhxy : x ≠ y\nU V : Set X\nhUV : IsOpen U ∧ IsOpen V ∧ x ∈ U ∧ y ∈ V ∧ Disjoint U V\n⊢ IsOpen (closure U)ᶜ",
"ppTerm": "?m.58",
"assigned": true,
"usedC... | [] | simp only [isOpen_compl_iff, isClosed_closure] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Topology.ExtremallyDisconnected | {
"line": 63,
"column": 9
} | {
"line": 63,
"column": 55
} | {
"line": 63,
"column": 55
} | [
{
"pp": "X : Type u\ninst✝² : TopologicalSpace X\ninst✝¹ : ExtremallyDisconnected X\ninst✝ : T2Space X\nx : X\na✝¹ : x ∈ univ\ny : X\na✝ : y ∈ univ\nhxy : x ≠ y\nU V : Set X\nhUV : IsOpen U ∧ IsOpen V ∧ x ∈ U ∧ y ∈ V ∧ Disjoint U V\n⊢ IsOpen (closure U)ᶜ",
"ppTerm": "?m.58",
"assigned": true,
"usedC... | [] | simp only [isOpen_compl_iff, isClosed_closure] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.ExtremallyDisconnected | {
"line": 63,
"column": 9
} | {
"line": 63,
"column": 55
} | {
"line": 63,
"column": 55
} | [
{
"pp": "X : Type u\ninst✝² : TopologicalSpace X\ninst✝¹ : ExtremallyDisconnected X\ninst✝ : T2Space X\nx : X\na✝¹ : x ∈ univ\ny : X\na✝ : y ∈ univ\nhxy : x ≠ y\nU V : Set X\nhUV : IsOpen U ∧ IsOpen V ∧ x ∈ U ∧ y ∈ V ∧ Disjoint U V\n⊢ IsOpen (closure U)ᶜ",
"ppTerm": "?m.58",
"assigned": true,
"usedC... | [] | simp only [isOpen_compl_iff, isClosed_closure] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 604,
"column": 4
} | {
"line": 604,
"column": 16
} | {
"line": 605,
"column": 4
} | [
{
"pp": "case cons.cons.false\np : Γ' → Bool\nk₁ k₂ : K'\nq : Λ'\no : Option Γ'\nL₂ : List Γ'\nh₁ : k₁ ≠ k₂\na : Γ'\nL₁ : List Γ'\nIH :\n ∀ {s : Option Γ'} {S : K' → List Γ'},\n splitAtPred p (S k₁) = (L₁, o, L₂) →\n Reaches₁ (TM2.step tr) { l := some (Λ'.move p k₁ k₂ q), var := s, stk := S }\n ... | [
"case cons.cons.false\np : Γ' → Bool\nk₁ k₂ : K'\nq : Λ'\no : Option Γ'\nL₂ : List Γ'\nh₁ : k₁ ≠ k₂\na : Γ'\nL₁ : List Γ'\nIH :\n ∀ {s : Option Γ'} {S : K' → List Γ'},\n splitAtPred p (S k₁) = (L₁, o, L₂) →\n Reaches₁ (TM2.step tr) { l := some (Λ'.move p k₁ k₂ q), var := s, stk := S }\n { l := some ... | rw [e₃] at e | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.ExtremallyDisconnected | {
"line": 147,
"column": 2
} | {
"line": 175,
"column": 88
} | {
"line": 177,
"column": 0
} | [
{
"pp": "A D : Type u\ninst✝³ : TopologicalSpace A\ninst✝² : TopologicalSpace D\ninst✝¹ : T1Space A\ninst✝ : CompactSpace D\nX : D → A\nX_cont : Continuous X\nX_surj : Surjective X\n⊢ ∃ E, CompactSpace ↑E ∧ X '' E = univ ∧ ∀ (E₀ : Set ↑E), E₀ ≠ univ → IsClosed E₀ → E.restrict X '' E₀ ≠ univ",
"ppTerm": "?m.... | [] | let S : Set <| Set D := {E : Set D | IsClosed E ∧ X '' E = univ}
suffices ∀ (C : Set <| Set D) (_ : C ⊆ S) (_ : IsChain (· ⊆ ·) C), ∃ s ∈ S, ∀ c ∈ C, s ⊆ c by
rcases zorn_superset S this with ⟨E, E_min⟩
obtain ⟨E_closed, E_surj⟩ := E_min.prop
refine ⟨E, isCompact_iff_compactSpace.mp E_closed.isCompact, E_... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.ExtremallyDisconnected | {
"line": 147,
"column": 2
} | {
"line": 175,
"column": 88
} | {
"line": 177,
"column": 0
} | [
{
"pp": "A D : Type u\ninst✝³ : TopologicalSpace A\ninst✝² : TopologicalSpace D\ninst✝¹ : T1Space A\ninst✝ : CompactSpace D\nX : D → A\nX_cont : Continuous X\nX_surj : Surjective X\n⊢ ∃ E, CompactSpace ↑E ∧ X '' E = univ ∧ ∀ (E₀ : Set ↑E), E₀ ≠ univ → IsClosed E₀ → E.restrict X '' E₀ ≠ univ",
"ppTerm": "?m.... | [] | let S : Set <| Set D := {E : Set D | IsClosed E ∧ X '' E = univ}
suffices ∀ (C : Set <| Set D) (_ : C ⊆ S) (_ : IsChain (· ⊆ ·) C), ∃ s ∈ S, ∀ c ∈ C, s ⊆ c by
rcases zorn_superset S this with ⟨E, E_min⟩
obtain ⟨E_closed, E_surj⟩ := E_min.prop
refine ⟨E, isCompact_iff_compactSpace.mp E_closed.isCompact, E_... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Category.Stonean.Basic | {
"line": 114,
"column": 4
} | {
"line": 117,
"column": 37
} | {
"line": 119,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝² : Finite X\ninst✝¹ : TopologicalSpace X\ninst✝ : DiscreteTopology X\n⊢ ExtremallyDisconnected ↑(CompHaus.of X).toTop",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Finite.compactSpace",
"id",
"TopologicalSpace.DiscreteTopology.metrizableSpa... | [] | dsimp
constructor
intro U _
apply isOpen_discrete (closure U) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Category.Stonean.Basic | {
"line": 114,
"column": 4
} | {
"line": 117,
"column": 37
} | {
"line": 119,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝² : Finite X\ninst✝¹ : TopologicalSpace X\ninst✝ : DiscreteTopology X\n⊢ ExtremallyDisconnected ↑(CompHaus.of X).toTop",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Finite.compactSpace",
"id",
"TopologicalSpace.DiscreteTopology.metrizableSpa... | [] | dsimp
constructor
intro U _
apply isOpen_discrete (closure U) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 661,
"column": 4
} | {
"line": 661,
"column": 16
} | {
"line": 662,
"column": 4
} | [
{
"pp": "case cons.cons.false\np : Γ' → Bool\nk : K'\nq : Λ'\no : Option Γ'\nL₂ : List Γ'\na : Γ'\nL₁ : List Γ'\nIH :\n ∀ {s : Option Γ'} {S : K' → List Γ'},\n splitAtPred p (S k) = (L₁, o, L₂) →\n Reaches₁ (TM2.step tr) { l := some (Λ'.clear p k q), var := s, stk := S }\n { l := some q, var := ... | [
"case cons.cons.false\np : Γ' → Bool\nk : K'\nq : Λ'\no : Option Γ'\nL₂ : List Γ'\na : Γ'\nL₁ : List Γ'\nIH :\n ∀ {s : Option Γ'} {S : K' → List Γ'},\n splitAtPred p (S k) = (L₁, o, L₂) →\n Reaches₁ (TM2.step tr) { l := some (Λ'.clear p k q), var := s, stk := S }\n { l := some q, var := o, stk := up... | rw [e₃] at e | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 769,
"column": 4
} | {
"line": 773,
"column": 32
} | {
"line": 774,
"column": 2
} | [
{
"pp": "q : Λ'\ns : Option Γ'\nn : ℕ\nc d : List Γ'\na : PosNum\nthis :\n ∀ (l₁ : List Γ'),\n ∃ l₁' l₂' s',\n l₁.reverseAux (trPosNum a.succ) = l₁'.reverseAux l₂' ∧\n Reaches₁ (TM2.step tr) { l := some q.succ, var := s, stk := elim (trPosNum a ++ [Γ'.cons]) l₁ c d }\n { l := some (unre... | [] | obtain ⟨l₁', l₂', s', e, h⟩ := this []
simp only [List.reverseAux] at e
refine h.trans ?_
convert! unrev_ok using 2
simp [e, List.reverseAux_eq] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 769,
"column": 4
} | {
"line": 773,
"column": 32
} | {
"line": 774,
"column": 2
} | [
{
"pp": "q : Λ'\ns : Option Γ'\nn : ℕ\nc d : List Γ'\na : PosNum\nthis :\n ∀ (l₁ : List Γ'),\n ∃ l₁' l₂' s',\n l₁.reverseAux (trPosNum a.succ) = l₁'.reverseAux l₂' ∧\n Reaches₁ (TM2.step tr) { l := some q.succ, var := s, stk := elim (trPosNum a ++ [Γ'.cons]) l₁ c d }\n { l := some (unre... | [] | obtain ⟨l₁', l₂', s', e, h⟩ := this []
simp only [List.reverseAux] at e
refine h.trans ?_
convert! unrev_ok using 2
simp [e, List.reverseAux_eq] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 803,
"column": 2
} | {
"line": 807,
"column": 8
} | {
"line": 808,
"column": 2
} | [
{
"pp": "case cons.succ.zero\nq₁ q₂ : Λ'\ns : Option Γ'\nc d : List Γ'\nv : List ℕ\nn : ℕ\n⊢ Reaches₁ (TM2.step tr)\n { l := some (q₁.pred q₂), var := s, stk := elim (trPosNum Num.zero.succ' ++ Γ'.cons :: trList v) [] c d }\n { l := some q₂, var := none,\n stk :=\n elim\n ((match Num.... | [
"case cons.succ.pos\nq₁ q₂ : Λ'\ns : Option Γ'\nc d : List Γ'\nv : List ℕ\nn : ℕ\na : PosNum\n⊢ Reaches₁ (TM2.step tr)\n { l := some (q₁.pred q₂), var := s, stk := elim (trPosNum (Num.pos a).succ' ++ Γ'.cons :: trList v) [] c d }\n { l := some q₂, var := none,\n stk :=\n elim\n ((match Nu... | · simp only [trPosNum, Num.succ', List.singleton_append, List.nil_append]
refine TransGen.head rfl ?_
rw [tr]; simp only [pop', TM2.stepAux]
convert! unrev_ok using 2
simp | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 814,
"column": 4
} | {
"line": 818,
"column": 32
} | {
"line": 819,
"column": 2
} | [
{
"pp": "q₁ q₂ : Λ'\ns : Option Γ'\nc d : List Γ'\nv : List ℕ\nn : ℕ\na : PosNum\nthis :\n ∀ (l₁ : List Γ'),\n ∃ l₁' l₂' s',\n l₁.reverseAux (trPosNum a) = l₁'.reverseAux l₂' ∧\n Reaches₁ (TM2.step tr)\n { l := some (q₁.pred q₂), var := s, stk := elim (trPosNum a.succ ++ Γ'.cons :: trLi... | [] | obtain ⟨l₁', l₂', s', e, h⟩ := this []
simp only [List.reverseAux] at e
refine h.trans ?_
convert! unrev_ok using 2
simp [e, List.reverseAux_eq] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 814,
"column": 4
} | {
"line": 818,
"column": 32
} | {
"line": 819,
"column": 2
} | [
{
"pp": "q₁ q₂ : Λ'\ns : Option Γ'\nc d : List Γ'\nv : List ℕ\nn : ℕ\na : PosNum\nthis :\n ∀ (l₁ : List Γ'),\n ∃ l₁' l₂' s',\n l₁.reverseAux (trPosNum a) = l₁'.reverseAux l₂' ∧\n Reaches₁ (TM2.step tr)\n { l := some (q₁.pred q₂), var := s, stk := elim (trPosNum a.succ ++ Γ'.cons :: trLi... | [] | obtain ⟨l₁', l₂', s', e, h⟩ := this []
simp only [List.reverseAux] at e
refine h.trans ?_
convert! unrev_ok using 2
simp [e, List.reverseAux_eq] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Category.LightProfinite.Basic | {
"line": 376,
"column": 4
} | {
"line": 377,
"column": 51
} | {
"line": 379,
"column": 0
} | [
{
"pp": "X✝ Y✝ : LightDiagram'\na₁✝ a₂✝ : X✝ ⟶ Y✝\nh : LightDiagram'.toLightFunctor.map a₁✝ = LightDiagram'.toLightFunctor.map a₂✝\n⊢ a₁✝ = a₂✝",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Opposite",
"LightDiagram.mk",
"LightDiagram.toProfinite",
"CategoryTheory... | [] | apply InducedCategory.homEquiv.injective
apply InducedCategory.homEquiv.symm.injective h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Category.LightProfinite.Basic | {
"line": 376,
"column": 4
} | {
"line": 377,
"column": 51
} | {
"line": 379,
"column": 0
} | [
{
"pp": "X✝ Y✝ : LightDiagram'\na₁✝ a₂✝ : X✝ ⟶ Y✝\nh : LightDiagram'.toLightFunctor.map a₁✝ = LightDiagram'.toLightFunctor.map a₂✝\n⊢ a₁✝ = a₂✝",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Opposite",
"LightDiagram.mk",
"LightDiagram.toProfinite",
"CategoryTheory... | [] | apply InducedCategory.homEquiv.injective
apply InducedCategory.homEquiv.symm.injective h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case move\np✝ : Γ' → Bool\nk₁✝ k₂✝ : K'\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ Λ'.move p✝ k₁✝ k₂✝ q✝ ∈ trStmts₁ (Λ'.move p✝ k₁✝ k₂✝ q✝)",
"ppTerm": "?move",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Turing.PartrecToTM2.Λ... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case move\np✝ : Γ' → Bool\nk₁✝ k₂✝ : K'\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ Λ'.move p✝ k₁✝ k₂✝ q✝ ∈ trStmts₁ (Λ'.move p✝ k₁✝ k₂✝ q✝)",
"ppTerm": "?move",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Turing.PartrecToTM2.Λ... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case move\np✝ : Γ' → Bool\nk₁✝ k₂✝ : K'\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ Λ'.move p✝ k₁✝ k₂✝ q✝ ∈ trStmts₁ (Λ'.move p✝ k₁✝ k₂✝ q✝)",
"ppTerm": "?move",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Turing.PartrecToTM2.Λ... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case clear\np✝ : Γ' → Bool\nk✝ : K'\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ Λ'.clear p✝ k✝ q✝ ∈ trStmts₁ (Λ'.clear p✝ k✝ q✝)",
"ppTerm": "?clear",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Turing.PartrecToTM2.Λ'.instDecid... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case clear\np✝ : Γ' → Bool\nk✝ : K'\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ Λ'.clear p✝ k✝ q✝ ∈ trStmts₁ (Λ'.clear p✝ k✝ q✝)",
"ppTerm": "?clear",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Turing.PartrecToTM2.Λ'.instDecid... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case clear\np✝ : Γ' → Bool\nk✝ : K'\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ Λ'.clear p✝ k✝ q✝ ∈ trStmts₁ (Λ'.clear p✝ k✝ q✝)",
"ppTerm": "?clear",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Turing.PartrecToTM2.Λ'.instDecid... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case copy\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ q✝.copy ∈ trStmts₁ q✝.copy",
"ppTerm": "?copy",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Turing.PartrecToTM2.Λ'.instDecidableEq",
"Turing.PartrecToTM2.Λ'",
"T... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case copy\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ q✝.copy ∈ trStmts₁ q✝.copy",
"ppTerm": "?copy",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Turing.PartrecToTM2.Λ'.instDecidableEq",
"Turing.PartrecToTM2.Λ'",
"T... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case copy\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ q✝.copy ∈ trStmts₁ q✝.copy",
"ppTerm": "?copy",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Turing.PartrecToTM2.Λ'.instDecidableEq",
"Turing.PartrecToTM2.Λ'",
"T... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case push\nk✝ : K'\ns✝ : Option Γ' → Option Γ'\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ Λ'.push k✝ s✝ q✝ ∈ trStmts₁ (Λ'.push k✝ s✝ q✝)",
"ppTerm": "?push",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Turing.PartrecToTM2.Λ'.p... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case push\nk✝ : K'\ns✝ : Option Γ' → Option Γ'\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ Λ'.push k✝ s✝ q✝ ∈ trStmts₁ (Λ'.push k✝ s✝ q✝)",
"ppTerm": "?push",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Turing.PartrecToTM2.Λ'.p... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case push\nk✝ : K'\ns✝ : Option Γ' → Option Γ'\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ Λ'.push k✝ s✝ q✝ ∈ trStmts₁ (Λ'.push k✝ s✝ q✝)",
"ppTerm": "?push",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Turing.PartrecToTM2.Λ'.p... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case read\nf✝ : Option Γ' → Λ'\nf_ih✝ : ∀ (a : Option Γ'), f✝ a ∈ trStmts₁ (f✝ a)\n⊢ Λ'.read f✝ ∈ trStmts₁ (Λ'.read f✝)",
"ppTerm": "?read",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.univ",
"Finset.mem_insert_self",
"Turing.PartrecT... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case read\nf✝ : Option Γ' → Λ'\nf_ih✝ : ∀ (a : Option Γ'), f✝ a ∈ trStmts₁ (f✝ a)\n⊢ Λ'.read f✝ ∈ trStmts₁ (Λ'.read f✝)",
"ppTerm": "?read",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.univ",
"Finset.mem_insert_self",
"Turing.PartrecT... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case read\nf✝ : Option Γ' → Λ'\nf_ih✝ : ∀ (a : Option Γ'), f✝ a ∈ trStmts₁ (f✝ a)\n⊢ Λ'.read f✝ ∈ trStmts₁ (Λ'.read f✝)",
"ppTerm": "?read",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.univ",
"Finset.mem_insert_self",
"Turing.PartrecT... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case succ\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ q✝.succ ∈ trStmts₁ q✝.succ",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Finset",
"Turing.PartrecToTM2.Λ'.instDecidableEq",
"Turing.PartrecToT... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case succ\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ q✝.succ ∈ trStmts₁ q✝.succ",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Finset",
"Turing.PartrecToTM2.Λ'.instDecidableEq",
"Turing.PartrecToT... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case succ\nq✝ : Λ'\nq_ih✝ : q✝ ∈ trStmts₁ q✝\n⊢ q✝.succ ∈ trStmts₁ q✝.succ",
"ppTerm": "?succ",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Finset",
"Turing.PartrecToTM2.Λ'.instDecidableEq",
"Turing.PartrecToT... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case pred\nq₁✝ q₂✝ : Λ'\nq₁_ih✝ : q₁✝ ∈ trStmts₁ q₁✝\nq₂_ih✝ : q₂✝ ∈ trStmts₁ q₂✝\n⊢ q₁✝.pred q₂✝ ∈ trStmts₁ (q₁✝.pred q₂✝)",
"ppTerm": "?pred",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Finset.instUnion",
"Finset... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case pred\nq₁✝ q₂✝ : Λ'\nq₁_ih✝ : q₁✝ ∈ trStmts₁ q₁✝\nq₂_ih✝ : q₂✝ ∈ trStmts₁ q₂✝\n⊢ q₁✝.pred q₂✝ ∈ trStmts₁ (q₁✝.pred q₂✝)",
"ppTerm": "?pred",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Finset.instUnion",
"Finset... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case pred\nq₁✝ q₂✝ : Λ'\nq₁_ih✝ : q₁✝ ∈ trStmts₁ q₁✝\nq₂_ih✝ : q₂✝ ∈ trStmts₁ q₂✝\n⊢ q₁✝.pred q₂✝ ∈ trStmts₁ (q₁✝.pred q₂✝)",
"ppTerm": "?pred",
"assigned": true,
"usedConstants": [
"Turing.PartrecToTM2.trStmts₁",
"Finset.mem_insert_self",
"Finset.instUnion",
"Finset... | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 992,
"column": 20
} | {
"line": 992,
"column": 90
} | {
"line": 994,
"column": 0
} | [
{
"pp": "case ret\nk✝ : Cont'\n⊢ Λ'.ret k✝ ∈ trStmts₁ (Λ'.ret k✝)",
"ppTerm": "?ret",
"assigned": true,
"usedConstants": [
"Finset.mem_singleton_self",
"Turing.PartrecToTM2.Λ'",
"Turing.PartrecToTM2.Λ'.ret"
],
"usedFVars": [
"k✝"
],
"usedGoals": []
}
] | [] | first | apply Finset.mem_singleton_self | apply Finset.mem_insert_self | Lean.Elab.Tactic.evalFirst | Lean.Parser.Tactic.first |
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