module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite | {
"line": 419,
"column": 6
} | {
"line": 419,
"column": 17
} | {
"line": 419,
"column": 18
} | [
{
"pp": "case neg.refine_1\nα : Type u\nG✝ : SimpleGraph α\ns : Set α\nV : Type u_1\nG : SimpleGraph V\nr t : ℕ\nK : G.CompleteEquipartiteSubgraph r t\nf : (completeEquipartiteGraph r t).Copy G\nht : ¬t = 0\ni : Fin r\nx✝¹ x✝ : Fin t\nh : (fun j ↦ f (i, j)) x✝¹ = (fun j ↦ f (i, j)) x✝\n⊢ x✝¹ = x✝",
"ppTerm"... | [
"case neg.refine_1\nα : Type u\nG✝ : SimpleGraph α\ns : Set α\nV : Type u_1\nG : SimpleGraph V\nr t : ℕ\nK : G.CompleteEquipartiteSubgraph r t\nf : (completeEquipartiteGraph r t).Copy G\nht : ¬t = 0\ni : Fin r\nx✝¹ x✝ : Fin t\nh : (fun j ↦ f (i, j)) x✝¹ = (fun j ↦ f (i, j)) x✝\n⊢ x✝¹ = x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.CompleteMultipartite | {
"line": 422,
"column": 57
} | {
"line": 422,
"column": 68
} | {
"line": 422,
"column": 69
} | [
{
"pp": "α : Type u\nG✝ : SimpleGraph α\ns : Set α\nV : Type u_1\nG : SimpleGraph V\nr t : ℕ\nK : G.CompleteEquipartiteSubgraph r t\nf : (completeEquipartiteGraph r t).Copy G\nht : ¬t = 0\ni₁ i₂ : Fin r\nh :\n ∀ (a : V),\n a ∈ map { toFun := fun j ↦ f (i₁, j), inj' := ⋯ } univ ↔ a ∈ map { toFun := fun j ↦ f... | [
"α : Type u\nG✝ : SimpleGraph α\ns : Set α\nV : Type u_1\nG : SimpleGraph V\nr t : ℕ\nK : G.CompleteEquipartiteSubgraph r t\nf : (completeEquipartiteGraph r t).Copy G\nht : ¬t = 0\ni₁ i₂ : Fin r\nh :\n ∀ (a : V),\n a ∈ map { toFun := fun j ↦ f (i₁, j), inj' := ⋯ } univ ↔ a ∈ map { toFun := fun j ↦ f (i₂, j), in... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Diam | {
"line": 377,
"column": 2
} | {
"line": 378,
"column": 17
} | {
"line": 379,
"column": 2
} | [
{
"pp": "case refine_1\nα : Type u_1\nG : SimpleGraph α\nh : G.radius = 0\n⊢ Nonempty α",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"iInf",
"instCompleteLinearOrderENat",
"congrArg",
"CommSemiring.toSemiring",
"ENat.iInf_... | [
"case refine_2\nα : Type u_1\nG : SimpleGraph α\nh : G.radius = 0\n⊢ Subsingleton α",
"case refine_3\nα : Type u_1\nG : SimpleGraph α\nx✝ : Nonempty α ∧ Subsingleton α\nleft✝ : Nonempty α\nright✝ : Subsingleton α\n⊢ G.radius = 0"
] | · contrapose! h
simp [radius] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Combinatorics.SimpleGraph.Diam | {
"line": 383,
"column": 4
} | {
"line": 383,
"column": 24
} | {
"line": 383,
"column": 25
} | [
{
"pp": "case h\nα : Type u_1\nG : SimpleGraph α\nx✝ : Nonempty α ∧ Subsingleton α\nleft✝ : Nonempty α\nright✝ : Subsingleton α\n⊢ G.eccent Classical.ofNonempty = 0",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"SimpleGraph.edist_eq_zero_iff._simp_1",
"Eq.mpr",
"Classical.... | [
"case h\nα : Type u_1\nG : SimpleGraph α\nx✝ : Nonempty α ∧ Subsingleton α\nleft✝ : Nonempty α\nright✝ : Subsingleton α\n⊢ ∀ (i : α), Classical.ofNonempty = i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Finsubgraph | {
"line": 162,
"column": 4
} | {
"line": 162,
"column": 12
} | {
"line": 163,
"column": 4
} | [
{
"pp": "V : Type u\nW : Type v\nG : SimpleGraph V\nF : SimpleGraph W\ninst✝ : Finite W\nh : (G' : G.Subgraph) → G'.verts.Finite → G'.coe →g F\nval✝ : Fintype W\nthis : ∀ (G' : G.Finsubgraphᵒᵖ), Nonempty ((G.finsubgraphHomFunctor F).obj G')\n⊢ (G' : G.Finsubgraphᵒᵖ) → Fintype ((G.finsubgraphHomFunctor F).obj G'... | [
"V : Type u\nW : Type v\nG : SimpleGraph V\nF : SimpleGraph W\ninst✝ : Finite W\nh : (G' : G.Subgraph) → G'.verts.Finite → G'.coe →g F\nval✝ : Fintype W\nthis : ∀ (G' : G.Finsubgraphᵒᵖ), Nonempty ((G.finsubgraphHomFunctor F).obj G')\nG' : G.Finsubgraphᵒᵖ\n⊢ Fintype ((G.finsubgraphHomFunctor F).obj G')"
] | intro G' | Lean.Elab.Tactic.evalIntro | null |
Mathlib.Combinatorics.SimpleGraph.Finsubgraph | {
"line": 162,
"column": 4
} | {
"line": 162,
"column": 12
} | {
"line": 163,
"column": 4
} | [
{
"pp": "V : Type u\nW : Type v\nG : SimpleGraph V\nF : SimpleGraph W\ninst✝ : Finite W\nh : (G' : G.Subgraph) → G'.verts.Finite → G'.coe →g F\nval✝ : Fintype W\nthis : ∀ (G' : G.Finsubgraphᵒᵖ), Nonempty ((G.finsubgraphHomFunctor F).obj G')\n⊢ (G' : G.Finsubgraphᵒᵖ) → Fintype ((G.finsubgraphHomFunctor F).obj G'... | [
"V : Type u\nW : Type v\nG : SimpleGraph V\nF : SimpleGraph W\ninst✝ : Finite W\nh : (G' : G.Subgraph) → G'.verts.Finite → G'.coe →g F\nval✝ : Fintype W\nthis : ∀ (G' : G.Finsubgraphᵒᵖ), Nonempty ((G.finsubgraphHomFunctor F).obj G')\nG' : G.Finsubgraphᵒᵖ\n⊢ Fintype ((G.finsubgraphHomFunctor F).obj G')"
] | intro G' | Lean.Elab.Tactic.evalIntro | Lean.Parser.Tactic.intro |
Mathlib.Combinatorics.SimpleGraph.Girth | {
"line": 76,
"column": 2
} | {
"line": 76,
"column": 13
} | {
"line": 76,
"column": 14
} | [
{
"pp": "α : Type u_1\nG : SimpleGraph α\n⊢ 3 ≤ G.egirth",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"SimpleGraph.le_egirth._simp_1",
"Eq.mpr",
"instCompleteLinearOrderENat",
"instCharZeroENat",
"instAddMonoidWithOneENat",
"ChainCompletePartialOrder.i... | [
"α : Type u_1\nG : SimpleGraph α\n⊢ ∀ (a : α) (w : G.Walk a a), w.IsCycle → 3 ≤ w.length"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity | {
"line": 129,
"column": 2
} | {
"line": 129,
"column": 45
} | {
"line": 130,
"column": 2
} | [
{
"pp": "W : Type u_1\nH : SimpleGraph W\nε : ℝ\nhε_pos : 0 < ε\nh : ∀ (a : ℕ), ∃ b, a ≤ b ∧ ∃ G inst, ↑(#G.edgeFinset) ≥ (H.turanDensity + ε) * ↑(b.choose 2) ∧ IsEmpty (H.Copy G)\n⊢ H.turanDensity + ε ≤ sInf {x | ∃ n ∈ Set.Ici 2, ↑(extremalNumber n H) / ↑(n.choose 2) = x}",
"ppTerm": "?m.61",
"assigned... | [
"case refine_1\nW : Type u_1\nH : SimpleGraph W\nε : ℝ\nhε_pos : 0 < ε\nh : ∀ (a : ℕ), ∃ b, a ≤ b ∧ ∃ G inst, ↑(#G.edgeFinset) ≥ (H.turanDensity + ε) * ↑(b.choose 2) ∧ IsEmpty (H.Copy G)\n⊢ {x | ∃ n ∈ Set.Ici 2, ↑(extremalNumber n H) / ↑(n.choose 2) = x}.Nonempty",
"case refine_2\nW : Type u_1\nH : SimpleGraph W\... | refine le_csInf ?_ (fun x ⟨m, hm, hx⟩ ↦ ?_) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits | {
"line": 77,
"column": 25
} | {
"line": 77,
"column": 41
} | {
"line": 77,
"column": 42
} | [
{
"pp": "n : ℕ\nG : SimpleGraph (Fin n)\ninst✝ : DecidableRel G.Adj\nr t t' : ℕ\nK : G.CompleteEquipartiteSubgraph r t'\nv : Fin n\nht'_pos : 0 < t'\nhv : v ∈ K.vertsᶜ\np : Finset (Fin n)\nhp : p ∈ K.parts\nhs : ∀ (x : Finset (Fin n)), x ∉ powersetCard t p ∨ ∃ x_1 ∈ x, ¬G.Adj v x_1\n⊢ #(K.parts.disjiUnion (fun ... | [
"n : ℕ\nG : SimpleGraph (Fin n)\ninst✝ : DecidableRel G.Adj\nr t t' : ℕ\nK : G.CompleteEquipartiteSubgraph r t'\nv : Fin n\nht'_pos : 0 < t'\nhv : v ∈ K.vertsᶜ\np : Finset (Fin n)\nhp : p ∈ K.parts\nhs : ∀ (x : Finset (Fin n)), x ∉ powersetCard t p ∨ ∃ x_1 ∈ x, ¬G.Adj v x_1\n⊢ ∑ a ∈ K.parts, #({v_1 ∈ id a | (betwee... | card_disjiUnion, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Combinatorics.SimpleGraph.Extremal.TuranDensity | {
"line": 166,
"column": 2
} | {
"line": 166,
"column": 59
} | {
"line": 166,
"column": 60
} | [
{
"pp": "W : Type u_1\nH : SimpleGraph W\nε : ℝ\nhε_pos : 0 < ε\nV : Type u_2\ninst✝¹ : Fintype V\nh_verts : Fintype.card V ≥ H.turanDensityConst ε\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\n⊢ Nat.find ⋯ ≤ Fintype.card V",
"ppTerm": "?m.73",
"assigned": false,
"usedConstants": [],
"usedFVar... | [
"W : Type u_1\nH : SimpleGraph W\nε : ℝ\nhε_pos : 0 < ε\nV : Type u_2\ninst✝¹ : Fintype V\nh_verts : Fintype.card V ≥ H.turanDensityConst ε\nG : SimpleGraph V\ninst✝ : DecidableRel G.Adj\n⊢ Nat.find ⋯ ≤ Fintype.card V"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits | {
"line": 110,
"column": 10
} | {
"line": 111,
"column": 78
} | {
"line": 112,
"column": 4
} | [
{
"pp": "case h₂\nn : ℕ\nG : SimpleGraph (Fin n)\ninst✝ : DecidableRel G.Adj\nr t t' : ℕ\nK : G.CompleteEquipartiteSubgraph r t'\nhr_pos : 0 < r\nht'_pos : 0 < t'\nv : Fin n\nhv : v ∈ filter K t\n⊢ ↑((between (↑K.verts) (↑K.verts)ᶜ G).degree v) ≤ ↑(#K.verts)",
"ppTerm": "?h₂",
"assigned": true,
"use... | [] | exact_mod_cast isBipartiteWith_degree_le'
(between_verts_isBipartiteWith K) (filter_subset_compl_verts K hv) | Lean.Parser.Tactic._aux_Init_TacticsExtra___macroRules_Lean_Parser_Tactic_tacticExact_mod_cast__1 | Lean.Parser.Tactic.tacticExact_mod_cast_ |
Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits | {
"line": 110,
"column": 10
} | {
"line": 111,
"column": 78
} | {
"line": 112,
"column": 4
} | [
{
"pp": "case h₂\nn : ℕ\nG : SimpleGraph (Fin n)\ninst✝ : DecidableRel G.Adj\nr t t' : ℕ\nK : G.CompleteEquipartiteSubgraph r t'\nhr_pos : 0 < r\nht'_pos : 0 < t'\nv : Fin n\nhv : v ∈ filter K t\n⊢ ↑((between (↑K.verts) (↑K.verts)ᶜ G).degree v) ≤ ↑(#K.verts)",
"ppTerm": "?h₂",
"assigned": true,
"use... | [] | exact_mod_cast isBipartiteWith_degree_le'
(between_verts_isBipartiteWith K) (filter_subset_compl_verts K hv) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits | {
"line": 110,
"column": 10
} | {
"line": 111,
"column": 78
} | {
"line": 112,
"column": 4
} | [
{
"pp": "case h₂\nn : ℕ\nG : SimpleGraph (Fin n)\ninst✝ : DecidableRel G.Adj\nr t t' : ℕ\nK : G.CompleteEquipartiteSubgraph r t'\nhr_pos : 0 < r\nht'_pos : 0 < t'\nv : Fin n\nhv : v ∈ filter K t\n⊢ ↑((between (↑K.verts) (↑K.verts)ᶜ G).degree v) ≤ ↑(#K.verts)",
"ppTerm": "?h₂",
"assigned": true,
"use... | [] | exact_mod_cast isBipartiteWith_degree_le'
(between_verts_isBipartiteWith K) (filter_subset_compl_verts K hv) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Card.Arithmetic | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 51
} | {
"line": 138,
"column": 52
} | [
{
"pp": "α : Type u_1\nι : Type u_2\nt : Set ι\nht : t.Finite\ns : ι → Set α\n⊢ (⋃ i ∈ t, s i).ncard ≤ ∑ᶠ (i : ι) (_ : i ∈ t), (s i).ncard",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nι : Type u_2\nt : Set ι\nht : t.Finite\ns : ι → Set α\n⊢ (⋃ i ∈ t, s i).ncard ≤ ∑ᶠ (i : ι) (_ : i ∈ t), (s i).ncard"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Card.Arithmetic | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 51
} | {
"line": 142,
"column": 52
} | [
{
"pp": "α : Type u_1\nι : Type u_2\nt : Set ι\nht : t.Finite\ns : ι → Set α\n⊢ (⋃ i ∈ t, s i).encard ≤ ∑ᶠ (i : ι) (_ : i ∈ t), (s i).encard",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nι : Type u_2\nt : Set ι\nht : t.Finite\ns : ι → Set α\n⊢ (⋃ i ∈ t, s i).encard ≤ ∑ᶠ (i : ι) (_ : i ∈ t), (s i).encard"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Card.Arithmetic | {
"line": 146,
"column": 2
} | {
"line": 146,
"column": 13
} | {
"line": 146,
"column": 14
} | [
{
"pp": "α : Type u_1\nι : Type u_2\ninst✝ : Fintype ι\ns : ι → Set α\n⊢ (⋃ i, s i).ncard ≤ ∑ i, (s i).ncard",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nι : Type u_2\ninst✝ : Fintype ι\ns : ι → Set α\n⊢ (⋃ i, s i).ncard ≤ ∑ i, (s i).ncard"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Card.Arithmetic | {
"line": 150,
"column": 2
} | {
"line": 150,
"column": 13
} | {
"line": 150,
"column": 14
} | [
{
"pp": "α : Type u_1\nι : Type u_2\ninst✝ : Fintype ι\ns : ι → Set α\n⊢ (⋃ i, s i).encard ≤ ∑ i, (s i).encard",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nι : Type u_2\ninst✝ : Fintype ι\ns : ι → Set α\n⊢ (⋃ i, s i).encard ≤ ∑ i, (s i).encard"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Card.Arithmetic | {
"line": 154,
"column": 2
} | {
"line": 154,
"column": 13
} | {
"line": 154,
"column": 14
} | [
{
"pp": "α : Type u_1\nι : Type u_2\ninst✝ : Finite ι\ns : ι → Set α\n⊢ (⋃ i, s i).ncard ≤ ∑ᶠ (i : ι), (s i).ncard",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nι : Type u_2\ninst✝ : Finite ι\ns : ι → Set α\n⊢ (⋃ i, s i).ncard ≤ ∑ᶠ (i : ι), (s i).ncard"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Card.Arithmetic | {
"line": 158,
"column": 2
} | {
"line": 158,
"column": 13
} | {
"line": 158,
"column": 14
} | [
{
"pp": "α : Type u_1\nι : Type u_2\ninst✝ : Finite ι\ns : ι → Set α\n⊢ (⋃ i, s i).encard ≤ ∑ᶠ (i : ι), (s i).encard",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nι : Type u_2\ninst✝ : Finite ι\ns : ι → Set α\n⊢ (⋃ i, s i).encard ≤ ∑ᶠ (i : ι), (s i).encard"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Hall | {
"line": 49,
"column": 4
} | {
"line": 49,
"column": 18
} | {
"line": 50,
"column": 4
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\np : Set V\ninst✝ : DecidablePred fun x ↦ x ∈ p\nf : ↑p → V\nh₁ : ∀ (x : ↑p), f x ∉ p\nh₂ : ∀ (x : ↑p), G.Adj (↑x) (f x)\nv w : V\nh : if h : v ∈ p then f ⟨v, h⟩ = w else if h : w ∈ p then f ⟨w, h⟩ = v else False\n⊢ G.Adj v w",
"ppTerm": "?m.47",
"assigned": true... | [
"case pos\nV : Type u_1\nG : SimpleGraph V\np : Set V\ninst✝ : DecidablePred fun x ↦ x ∈ p\nf : ↑p → V\nh₁ : ∀ (x : ↑p), f x ∉ p\nh₂ : ∀ (x : ↑p), G.Adj (↑x) (f x)\nv w : V\nh✝ : v ∈ p\nh : f ⟨v, h✝⟩ = w\n⊢ G.Adj v w",
"case pos\nV : Type u_1\nG : SimpleGraph V\np : Set V\ninst✝ : DecidablePred fun x ↦ x ∈ p\nf :... | split_ifs at h | Mathlib.Tactic._aux_Mathlib_Tactic_SplitIfs___elabRules_Mathlib_Tactic_splitIfs_1 | Mathlib.Tactic.splitIfs |
Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits | {
"line": 177,
"column": 8
} | {
"line": 177,
"column": 51
} | {
"line": 178,
"column": 4
} | [
{
"pp": "n : ℕ\nG : SimpleGraph (Fin n)\ninst✝ : DecidableRel G.Adj\nε : ℝ\nr t t' : ℕ\nK : G.CompleteEquipartiteSubgraph r t'\nhr_pos : 0 < r\nht'_pos : 0 < t'\nht_lt_t' : t < t'\nhδ : ↑G.minDegree ≥ (1 - 1 / ↑r + ε) * ↑n\nhN : (↑(t'.choose t) ^ r * ↑t + ↑r * ↑t') * (↑t' - ↑t) ≤ ↑n * (↑r * ↑t' * ε - ↑t)\nthis ... | [] | simp_rw [Finset.card_pi, card_powersetCard] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits | {
"line": 177,
"column": 8
} | {
"line": 177,
"column": 51
} | {
"line": 178,
"column": 4
} | [
{
"pp": "n : ℕ\nG : SimpleGraph (Fin n)\ninst✝ : DecidableRel G.Adj\nε : ℝ\nr t t' : ℕ\nK : G.CompleteEquipartiteSubgraph r t'\nhr_pos : 0 < r\nht'_pos : 0 < t'\nht_lt_t' : t < t'\nhδ : ↑G.minDegree ≥ (1 - 1 / ↑r + ε) * ↑n\nhN : (↑(t'.choose t) ^ r * ↑t + ↑r * ↑t') * (↑t' - ↑t) ≤ ↑n * (↑r * ↑t' * ε - ↑t)\nthis ... | [] | simp_rw [Finset.card_pi, card_powersetCard] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Extremal.ErdosStoneSimonovits | {
"line": 177,
"column": 8
} | {
"line": 177,
"column": 51
} | {
"line": 178,
"column": 4
} | [
{
"pp": "n : ℕ\nG : SimpleGraph (Fin n)\ninst✝ : DecidableRel G.Adj\nε : ℝ\nr t t' : ℕ\nK : G.CompleteEquipartiteSubgraph r t'\nhr_pos : 0 < r\nht'_pos : 0 < t'\nht_lt_t' : t < t'\nhδ : ↑G.minDegree ≥ (1 - 1 / ↑r + ε) * ↑n\nhN : (↑(t'.choose t) ^ r * ↑t + ↑r * ↑t') * (↑t' - ↑t) ≤ ↑n * (↑r * ↑t' * ε - ↑t)\nthis ... | [] | simp_rw [Finset.card_pi, card_powersetCard] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Hamiltonian | {
"line": 143,
"column": 11
} | {
"line": 143,
"column": 26
} | {
"line": 143,
"column": 27
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝¹ : DecidableEq α\nG : SimpleGraph α\na b : α\np : G.Walk a b\ninst✝ : Fintype α\nh✝ : Nonempty α\nx✝ : p.IsPath ∧ p.length = Fintype.card α - 1\nhp : p.IsPath\nh : p.length = Fintype.card α - 1\nthis : Injective fun x ↦ p.support.get x\n⊢ Fintype.card α = p.support.length"... | [
"case neg\nα : Type u_1\ninst✝¹ : DecidableEq α\nG : SimpleGraph α\na b : α\np : G.Walk a b\ninst✝ : Fintype α\nh✝ : Nonempty α\nx✝ : p.IsPath ∧ p.length = Fintype.card α - 1\nhp : p.IsPath\nh : p.length = Fintype.card α - 1\nthis : Injective fun x ↦ p.support.get x\n⊢ Fintype.card α = p.length + 1"
] | length_support, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Combinatorics.SimpleGraph.Hamiltonian | {
"line": 164,
"column": 4
} | {
"line": 164,
"column": 15
} | {
"line": 164,
"column": 16
} | [
{
"pp": "case cons\nα : Type u_1\ninst✝¹ : DecidableEq α\nG : SimpleGraph α\nβ : Type u_2\ninst✝ : DecidableEq β\nH : SimpleGraph β\na : α\nf : G →g H\nhf : Bijective ⇑f\nx v✝ : α\ny : G.Adj a v✝\np : G.Walk v✝ a\nhp : (cons y p).IsHamiltonianCycle\n__IsCycle✝ : (Walk.map f (cons y p)).IsCycle := IsCycle.map (B... | [
"case cons\nα : Type u_1\ninst✝¹ : DecidableEq α\nG : SimpleGraph α\nβ : Type u_2\ninst✝ : DecidableEq β\nH : SimpleGraph β\na : α\nf : G →g H\nhf : Bijective ⇑f\nx v✝ : α\ny : G.Adj a v✝\np : G.Walk v✝ a\nhp : (cons y p).IsHamiltonianCycle\n__IsCycle✝ : (Walk.map f (cons y p)).IsCycle := IsCycle.map (Bijective.inj... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Hamiltonian | {
"line": 191,
"column": 2
} | {
"line": 193,
"column": 11
} | {
"line": 195,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\nG : SimpleGraph α\na : α\np : G.Walk a a\ninst✝ : Fintype α\nhp : p.IsHamiltonianCycle\n⊢ p.length = Fintype.card α",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SimpleGraph.Walk.length_tail_add_one",
"SimpleGrap... | [] | rw [← length_tail_add_one hp.not_nil, hp.isHamiltonian_tail.length_eq, Nat.sub_add_cancel]
rw [Nat.succ_le_iff, Fintype.card_pos_iff]
exact ⟨a⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.Hamiltonian | {
"line": 191,
"column": 2
} | {
"line": 193,
"column": 11
} | {
"line": 195,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝¹ : DecidableEq α\nG : SimpleGraph α\na : α\np : G.Walk a a\ninst✝ : Fintype α\nhp : p.IsHamiltonianCycle\n⊢ p.length = Fintype.card α",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SimpleGraph.Walk.length_tail_add_one",
"SimpleGrap... | [] | rw [← length_tail_add_one hp.not_nil, hp.isHamiltonian_tail.length_eq, Nat.sub_add_cancel]
rw [Nat.succ_le_iff, Fintype.card_pos_iff]
exact ⟨a⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 103,
"column": 2
} | {
"line": 103,
"column": 13
} | {
"line": 103,
"column": 14
} | [
{
"pp": "case h\nV : Type u_1\nG G' : SimpleGraph V\nM : G.Subgraph\nh : M.IsMatching\nhGG' : G ≤ G'\nv✝ : V\nhv✝ : v✝ ∈ (Subgraph.map (Hom.ofLE hGG') M).verts\nw✝ : V\nhv : w✝ ∈ M.verts\nhv' : (Hom.ofLE hGG') w✝ = v✝\nw : V\nhw : (fun w ↦ M.Adj w✝ w) w ∧ ∀ (y : V), (fun w ↦ M.Adj w✝ w) y → y = w\n⊢ (fun w ↦ (S... | [
"case h\nV : Type u_1\nG G' : SimpleGraph V\nM : G.Subgraph\nh : M.IsMatching\nhGG' : G ≤ G'\nv✝ : V\nhv✝ : v✝ ∈ (Subgraph.map (Hom.ofLE hGG') M).verts\nw✝ : V\nhv : w✝ ∈ M.verts\nhv' : (Hom.ofLE hGG') w✝ = v✝\nw : V\nhw : (fun w ↦ M.Adj w✝ w) w ∧ ∀ (y : V), (fun w ↦ M.Adj w✝ w) y → y = w\n⊢ M.Adj v✝ w ∧ ∀ (y : V),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 130,
"column": 6
} | {
"line": 130,
"column": 77
} | {
"line": 130,
"column": 78
} | [
{
"pp": "case h.inr\nV : Type u_1\nG : SimpleGraph V\nM M' : G.Subgraph\nhM : M.IsMatching\nhM' : M'.IsMatching\nhd✝ : Disjoint M.support M'.support\nv : V\nhv : v ∈ (M ⊔ M').verts\nN N' : G.Subgraph\nhN : N.IsMatching\nhd : ∀ ⦃a : V⦄, a ∈ N.support → a ∉ N'.support\nhmN : v ∈ N.verts\nw : V\nhw : (fun w ↦ N.Ad... | [
"case h.inr\nV : Type u_1\nG : SimpleGraph V\nM M' : G.Subgraph\nhM : M.IsMatching\nhM' : M'.IsMatching\nhd✝ : Disjoint M.support M'.support\nv : V\nhv : v ∈ (M ⊔ M').verts\nN N' : G.Subgraph\nhN : N.IsMatching\nhd : ∀ ⦃a : V⦄, a ∈ N.support → a ∉ N'.support\nhmN : v ∈ N.verts\nw : V\nhw : (fun w ↦ N.Adj v w) w ∧ ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 151,
"column": 4
} | {
"line": 151,
"column": 77
} | {
"line": 151,
"column": 78
} | [
{
"pp": "case neg\nV : Type u_1\nG : SimpleGraph V\nι : Type u_3\nf : ι → G.Subgraph\nhM : ∀ (i : ι), (f i).IsMatching\nhd : Pairwise fun i j ↦ Disjoint (f i).support (f j).support\nv : V\nhv : v ∈ (⨆ i, f i).verts\ni : ι\nhi : v ∈ (f i).verts\nw : V\nhw : (fun w ↦ (f i).Adj v w) w ∧ ∀ (y : V), (fun w ↦ (f i).A... | [
"case neg\nV : Type u_1\nG : SimpleGraph V\nι : Type u_3\nf : ι → G.Subgraph\nhM : ∀ (i : ι), (f i).IsMatching\nhd : Pairwise fun i j ↦ Disjoint (f i).support (f j).support\nv : V\nhv : v ∈ (⨆ i, f i).verts\ni : ι\nhi : v ∈ (f i).verts\nw : V\nhw : (fun w ↦ (f i).Adj v w) w ∧ ∀ (y : V), (fun w ↦ (f i).Adj v w) y → ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 212,
"column": 13
} | {
"line": 212,
"column": 37
} | {
"line": 212,
"column": 38
} | [
{
"pp": "V : Type u_1\nW : Type u_2\nG : SimpleGraph V\nG' : SimpleGraph W\nM : G.Subgraph\nf : G ≃g G'\nh : (Subgraph.map f.toHom M).IsMatching\n⊢ M.IsMatching",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\nW : Type u_2\nG : SimpleGraph V\nG' : SimpleGraph W\nM : G.Subgraph\nf : G ≃g G'\nh : (Subgraph.map f.toHom M).IsMatching\n⊢ M.IsMatching"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 265,
"column": 2
} | {
"line": 265,
"column": 35
} | {
"line": 265,
"column": 36
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nM : G.Subgraph\ninst✝ : Fintype V\nh : M.IsPerfectMatching\n⊢ Even (Fintype.card V)",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\nG : SimpleGraph V\nM : G.Subgraph\ninst✝ : Fintype V\nh : M.IsPerfectMatching\n⊢ Even (Fintype.card V)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 273,
"column": 2
} | {
"line": 273,
"column": 77
} | {
"line": 273,
"column": 78
} | [
{
"pp": "case h\nV : Type u_1\nG : SimpleGraph V\nM : G.Subgraph\nh : M.IsMatching\nv✝ : V\nhv : v✝ ∈ M.verts\nw : V\nhvw : M.Adj v✝ w\nhw : ∀ (y : V), (fun w ↦ M.Adj v✝ w) y → y = w\n⊢ (fun w ↦ (M.induce (M.verts ∩ (G.connectedComponentMk v✝).supp)).Adj v✝ w) w ∧\n ∀ (y : V), (fun w ↦ (M.induce (M.verts ∩ (... | [
"case h\nV : Type u_1\nG : SimpleGraph V\nM : G.Subgraph\nh : M.IsMatching\nv✝ : V\nhv : v✝ ∈ M.verts\nw : V\nhvw : M.Adj v✝ w\nhw : ∀ (y : V), (fun w ↦ M.Adj v✝ w) y → y = w\n⊢ ∀ y ∈ M.verts, G.Reachable y v✝ → M.Adj v✝ y → y = w"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 277,
"column": 2
} | {
"line": 277,
"column": 33
} | {
"line": 277,
"column": 34
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nM : G.Subgraph\nh : M.IsPerfectMatching\nc : G.ConnectedComponent\n⊢ (M.induce c.supp).IsMatching",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\nG : SimpleGraph V\nM : G.Subgraph\nh : M.IsPerfectMatching\nc : G.ConnectedComponent\n⊢ (M.induce c.supp).IsMatching"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 337,
"column": 2
} | {
"line": 337,
"column": 46
} | {
"line": 337,
"column": 47
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nM : G.Subgraph\ninst✝ : Finite V\nu : Set V\nhM : M.IsPerfectMatching\nc : ↑(⊤.deleteVerts u).coe.oddComponents\nh : ∀ w ∈ u, ∀ (v : ↑(⊤.deleteVerts u).verts), M.Adj (↑v) w → v ∉ (↑c).supp\nhMmatch : (M.induce (Subtype.val '' (↑c).supp)).IsMatching\nthis✝ : Fintype ↑(M.... | [
"V : Type u_1\nG : SimpleGraph V\nM : G.Subgraph\ninst✝ : Finite V\nu : Set V\nhM : M.IsPerfectMatching\nc : ↑(⊤.deleteVerts u).coe.oddComponents\nh : ∀ w ∈ u, ∀ (v : ↑(⊤.deleteVerts u).verts), M.Adj (↑v) w → v ∉ (↑c).supp\nhMmatch : (M.induce (Subtype.val '' (↑c).supp)).IsMatching\nthis✝ : Fintype ↑(M.induce (Subt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.StronglyRegular | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 13
} | {
"line": 130,
"column": 14
} | [
{
"pp": "V : Type u\ninst✝² : Fintype V\nG : SimpleGraph V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : DecidableEq V\nv w : V\nh : G.Adj v w\n⊢ ((G.neighborFinset v)ᶜ ∩ (G.neighborFinset w)ᶜ) \\ ({w} ∪ {v}) = (G.neighborFinset v)ᶜ ∩ (G.neighborFinset w)ᶜ",
"ppTerm": "?m.36",
"assigned": true,
"usedConstan... | [
"V : Type u\ninst✝² : Fintype V\nG : SimpleGraph V\ninst✝¹ : DecidableRel G.Adj\ninst✝ : DecidableEq V\nv w : V\nh : G.Adj v w\n⊢ G.Adj v w ∧ G.Adj w v"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.StronglyRegular | {
"line": 150,
"column": 27
} | {
"line": 150,
"column": 49
} | {
"line": 150,
"column": 50
} | [
{
"pp": "case inl\nV : Type u\ninst✝² : Fintype V\nG : SimpleGraph V\ninst✝¹ : DecidableRel G.Adj\nn k ℓ μ : ℕ\ninst✝ : DecidableEq V\nh : G.IsSRGWith n k ℓ μ\nv u : V\nha : v ≠ u ∧ ¬G.Adj v u\nhne : v ≠ u\n⊢ ¬G.Adj v u ∧ ¬G.Adj u u",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"Eq.... | [
"case inl\nV : Type u\ninst✝² : Fintype V\nG : SimpleGraph V\ninst✝¹ : DecidableRel G.Adj\nn k ℓ μ : ℕ\ninst✝ : DecidableEq V\nh : G.IsSRGWith n k ℓ μ\nv u : V\nha : v ≠ u ∧ ¬G.Adj v u\nhne : v ≠ u\n⊢ ¬G.Adj v u"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.StronglyRegular | {
"line": 150,
"column": 27
} | {
"line": 150,
"column": 49
} | {
"line": 150,
"column": 50
} | [
{
"pp": "case inr\nV : Type u\ninst✝² : Fintype V\nG : SimpleGraph V\ninst✝¹ : DecidableRel G.Adj\nn k ℓ μ : ℕ\ninst✝ : DecidableEq V\nh : G.IsSRGWith n k ℓ μ\nw u : V\nha : u ≠ w ∧ ¬G.Adj u w\nhne : u ≠ w\n⊢ ¬G.Adj u u ∧ ¬G.Adj w u",
"ppTerm": "?inr",
"assigned": true,
"usedConstants": [
"Eq.... | [
"case inr\nV : Type u\ninst✝² : Fintype V\nG : SimpleGraph V\ninst✝¹ : DecidableRel G.Adj\nn k ℓ μ : ℕ\ninst✝ : DecidableEq V\nh : G.IsSRGWith n k ℓ μ\nw u : V\nha : u ≠ w ∧ ¬G.Adj u w\nhne : u ≠ w\n⊢ ¬G.Adj w u"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 608,
"column": 47
} | {
"line": 608,
"column": 58
} | {
"line": 608,
"column": 59
} | [
{
"pp": "V : Type u_1\nG G' : SimpleGraph V\nM : G.Subgraph\nhM : M.IsPerfectMatching\nhG' : G'.IsAlternating M.spanningCoe\nhG'cyc : G'.IsCycles\nv w : V\nhw : (fun w ↦ M.Adj v w) w ∧ ∀ (y : V), (fun w ↦ M.Adj v w) y → y = w\nh : G'.Adj v w\nw' : V\nhw' : w ≠ w' ∧ G'.Adj v w'\n⊢ M.Adj v w ↔ ¬M.Adj v w'",
"... | [
"V : Type u_1\nG G' : SimpleGraph V\nM : G.Subgraph\nhM : M.IsPerfectMatching\nhG' : G'.IsAlternating M.spanningCoe\nhG'cyc : G'.IsCycles\nv w : V\nhw : (fun w ↦ M.Adj v w) w ∧ ∀ (y : V), (fun w ↦ M.Adj v w) y → y = w\nh : G'.Adj v w\nw' : V\nhw' : w ≠ w' ∧ G'.Adj v w'\n⊢ M.Adj v w ↔ ¬M.Adj v w'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 616,
"column": 48
} | {
"line": 616,
"column": 59
} | {
"line": 616,
"column": 60
} | [
{
"pp": "V : Type u_1\nG G' : SimpleGraph V\nM : G.Subgraph\nhM : M.IsPerfectMatching\nhG' : G'.IsAlternating M.spanningCoe\nhG'cyc : G'.IsCycles\nv w : V\nhw : (fun w ↦ M.Adj v w) w ∧ ∀ (y : V), (fun w ↦ M.Adj v w) y → y = w\nh : G'.Adj v w\nw' : V\nhw' : w ≠ w' ∧ G'.Adj v w'\nhmadj : M.Adj v w ↔ ¬M.Adj v w'\n... | [
"V : Type u_1\nG G' : SimpleGraph V\nM : G.Subgraph\nhM : M.IsPerfectMatching\nhG' : G'.IsAlternating M.spanningCoe\nhG'cyc : G'.IsCycles\nv w : V\nhw : (fun w ↦ M.Adj v w) w ∧ ∀ (y : V), (fun w ↦ M.Adj v w) y → y = w\nh : G'.Adj v w\nw' : V\nhw' : w ≠ w' ∧ G'.Adj v w'\nhmadj : M.Adj v w ↔ ¬M.Adj v w'\ny : V\nhr : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.StronglyRegular | {
"line": 211,
"column": 2
} | {
"line": 212,
"column": 31
} | {
"line": 213,
"column": 2
} | [
{
"pp": "V : Type u\ninst✝³ : Fintype V\nG : SimpleGraph V\ninst✝² : DecidableRel G.Adj\nn k ℓ μ : ℕ\ninst✝¹ : DecidableEq V\nα : Type u_1\ninst✝ : Semiring α\nh : G.IsSRGWith n k ℓ μ\nv w : V\n⊢ (adjMatrix α G ^ 2) v w = (k • 1 + ℓ • adjMatrix α G + μ • adjMatrix α Gᶜ) v w",
"ppTerm": "?m.64",
"assigne... | [
"V : Type u\ninst✝³ : Fintype V\nG : SimpleGraph V\ninst✝² : DecidableRel G.Adj\nn k ℓ μ : ℕ\ninst✝¹ : DecidableEq V\nα : Type u_1\ninst✝ : Semiring α\nh : G.IsSRGWith n k ℓ μ\nv w : V\n⊢ ↑(Fintype.card ↑{p | p.length = 2}) =\n (k • 1 v w + ℓ • if G.Adj v w then 1 else 0) + μ • if v ≠ w ∧ ¬G.Adj v w then 1 else ... | simp only [adjMatrix_pow_apply_eq_card_walk, Matrix.add_apply, Matrix.smul_apply,
adjMatrix_apply, compl_adj] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 623,
"column": 48
} | {
"line": 623,
"column": 59
} | {
"line": 623,
"column": 60
} | [
{
"pp": "V : Type u_1\nG G' : SimpleGraph V\nM : G.Subgraph\nhM : M.IsPerfectMatching\nhG' : G'.IsAlternating M.spanningCoe\nhG'cyc : G'.IsCycles\nv w : V\nhw : (fun w ↦ M.Adj v w) w ∧ ∀ (y : V), (fun w ↦ M.Adj v w) y → y = w\nh : ¬G'.Adj v w\ny : V\nhr : G'.Adj v y ∧ ¬M.Adj v y\nw' : V\nhw' : y ≠ w' ∧ G'.Adj v... | [
"V : Type u_1\nG G' : SimpleGraph V\nM : G.Subgraph\nhM : M.IsPerfectMatching\nhG' : G'.IsAlternating M.spanningCoe\nhG'cyc : G'.IsCycles\nv w : V\nhw : (fun w ↦ M.Adj v w) w ∧ ∀ (y : V), (fun w ↦ M.Adj v w) y → y = w\nh : ¬G'.Adj v w\ny : V\nhr : G'.Adj v y ∧ ¬M.Adj v y\nw' : V\nhw' : y ≠ w' ∧ G'.Adj v w'\n⊢ M.Adj... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Matching | {
"line": 637,
"column": 2
} | {
"line": 637,
"column": 29
} | {
"line": 637,
"column": 30
} | [
{
"pp": "V : Type u_1\nG G' : SimpleGraph V\nM : G.Subgraph\nM' : G'.Subgraph\nhM : M.IsPerfectMatching\nhM' : M'.IsPerfectMatching\n⊢ (M.spanningCoe ∆ M'.spanningCoe).IsAlternating M'.spanningCoe",
"ppTerm": "?m.18",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"V : Type u_1\nG G' : SimpleGraph V\nM : G.Subgraph\nM' : G'.Subgraph\nhM : M.IsPerfectMatching\nhM' : M'.IsPerfectMatching\n⊢ (M.spanningCoe ∆ M'.spanningCoe).IsAlternating M'.spanningCoe"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.UniversalVerts | {
"line": 61,
"column": 2
} | {
"line": 61,
"column": 78
} | {
"line": 62,
"column": 4
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ns : Set ↑G.deleteUniversalVerts.verts\n⊢ Disjoint (Subtype.val '' s) G.universalVerts",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\nG : SimpleGraph V\ns : Set ↑G.deleteUniversalVerts.verts\n⊢ Disjoint (Subtype.val '' s) G.universalVerts"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Trails | {
"line": 92,
"column": 16
} | {
"line": 92,
"column": 45
} | {
"line": 92,
"column": 46
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : DecidableEq V\nu v : V\np : G.Walk u v\nh : p.IsEulerian\ne : Sym2 V\nhe : e ∈ G.edgeSet\n⊢ e ∈ p.edges",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\nG : SimpleGraph V\ninst✝ : DecidableEq V\nu v : V\np : G.Walk u v\nh : p.IsEulerian\ne : Sym2 V\nhe : e ∈ G.edgeSet\n⊢ e ∈ p.edges"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.FiveWheelLike | {
"line": 364,
"column": 10
} | {
"line": 364,
"column": 25
} | {
"line": 364,
"column": 26
} | [
{
"pp": "α : 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}\n... | [
"α : 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 : Finset α... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.FiveWheelLike | {
"line": 380,
"column": 6
} | {
"line": 380,
"column": 21
} | {
"line": 380,
"column": 22
} | [
{
"pp": "α : 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}\n... | [
"α : 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 : Finset α... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.FiveWheelLike | {
"line": 400,
"column": 12
} | {
"line": 400,
"column": 52
} | {
"line": 401,
"column": 12
} | [
{
"pp": "α : 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}\n... | [
"α : 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 : Finset α... | rw [← hw.card_inter, card_eq_zero] at hk | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Combinatorics.SimpleGraph.VertexCover | {
"line": 79,
"column": 4
} | {
"line": 80,
"column": 11
} | {
"line": 80,
"column": 12
} | [
{
"pp": "V : Type u_1\nW : Type u_2\nG : SimpleGraph V\nH : SimpleGraph W\nf : G ≃g H\nc : Set W\nh : G.IsVertexCover (⇑f ⁻¹' c)\n⊢ H.IsVertexCover c",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\nW : Type u_2\nG : SimpleGraph V\nH : SimpleGraph W\nf : G ≃g H\nc : Set W\nh : G.IsVertexCover (⇑f ⁻¹' c)\n⊢ H.IsVertexCover c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.VertexCover | {
"line": 128,
"column": 2
} | {
"line": 128,
"column": 17
} | {
"line": 128,
"column": 18
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\nh : G.vertexCoverNum = 0\n⊢ G = ⊥",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"V : Type u_1\nG : SimpleGraph V\nh : G.vertexCoverNum = 0\n⊢ G = ⊥"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.VertexCover | {
"line": 135,
"column": 34
} | {
"line": 135,
"column": 64
} | {
"line": 135,
"column": 64
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\na✝ : Nontrivial V\nx : V\nn : ℕ\nhn : ∀ (i : Set V), G.IsVertexCover i → ↑n ≤ i.encard\n⊢ G.IsVertexCover (Set.univ \\ {x})",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.... | [] | grind [IsVertexCover, Adj.ne'] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.Combinatorics.SimpleGraph.VertexCover | {
"line": 135,
"column": 34
} | {
"line": 135,
"column": 64
} | {
"line": 135,
"column": 64
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\na✝ : Nontrivial V\nx : V\nn : ℕ\nhn : ∀ (i : Set V), G.IsVertexCover i → ↑n ≤ i.encard\n⊢ G.IsVertexCover (Set.univ \\ {x})",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.... | [] | grind [IsVertexCover, Adj.ne'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.SimpleGraph.VertexCover | {
"line": 135,
"column": 34
} | {
"line": 135,
"column": 64
} | {
"line": 135,
"column": 64
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\na✝ : Nontrivial V\nx : V\nn : ℕ\nhn : ∀ (i : Set V), G.IsVertexCover i → ↑n ≤ i.encard\n⊢ G.IsVertexCover (Set.univ \\ {x})",
"ppTerm": "?m.51",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Combinatorics.SimpleGraph.VertexCover.0.SimpleGraph.... | [] | grind [IsVertexCover, Adj.ne'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.VertexCover | {
"line": 136,
"column": 2
} | {
"line": 136,
"column": 66
} | {
"line": 136,
"column": 67
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\na✝ : Nontrivial V\nx : V\nn : ℕ\nhn : ∀ (i : Set V), G.IsVertexCover i → ↑n ≤ i.encard\nthis : ↑n ≤ (Set.univ \\ {x}).encard\n⊢ ↑n ≤ ENat.card V - 1",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instAddMonoidWithOneENat",
... | [
"V : Type u_1\nG : SimpleGraph V\na✝ : Nontrivial V\nx : V\nn : ℕ\nhn : ∀ (i : Set V), G.IsVertexCover i → ↑n ≤ i.encard\nthis : ↑n ≤ (Set.univ \\ {x}).encard\n⊢ ↑n ≤ ENat.card V - 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 56,
"column": 4
} | {
"line": 56,
"column": 78
} | {
"line": 56,
"column": 79
} | [
{
"pp": "case refine_4\nV : Type u_1\nG G' : SimpleGraph V\nx b a c : V\nM : (G ⊔ edge a c).Subgraph\np : G'.Walk a x\nhp : p.IsPath\nhcalt : G'.IsAlternating M.spanningCoe\nhM2nadj : ¬M.Adj x a\nhpac : p.toSubgraph.Adj a c\nhnpxb : ¬p.toSubgraph.Adj x b\nhM2ac : M.Adj a c\nhgadj : G.Adj x a\nhnxc : x ≠ c\nhnab... | [
"case refine_4\nV : Type u_1\nG G' : SimpleGraph V\nx b a c : V\nM : (G ⊔ edge a c).Subgraph\np : G'.Walk a x\nhp : p.IsPath\nhcalt : G'.IsAlternating M.spanningCoe\nhM2nadj : ¬M.Adj x a\nhpac : p.toSubgraph.Adj a c\nhnpxb : ¬p.toSubgraph.Adj x b\nhM2ac : M.Adj a c\nhgadj : G.Adj x a\nhnxc : x ≠ c\nhnab : a ≠ b\nhl... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 133,
"column": 29
} | {
"line": 134,
"column": 42
} | {
"line": 134,
"column": 43
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nhveven : Even (Nat.card V)\nh : ¬G.IsTutteViolator G.universalVerts\nh' : ∀ (K : G.deleteUniversalVerts.coe.ConnectedComponent), G.deleteUniversalVerts.coe.IsClique K.supp\nval✝ : Fintype V\nM : G.Subgraph\nhM : M.IsMatching\nhsub : M.vertsᶜ ⊆ G.univer... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nhveven : Even (Nat.card V)\nh : ¬G.IsTutteViolator G.universalVerts\nh' : ∀ (K : G.deleteUniversalVerts.coe.ConnectedComponent), G.deleteUniversalVerts.coe.IsClique K.supp\nval✝ : Fintype V\nM : G.Subgraph\nhM : M.IsMatching\nhsub : M.vertsᶜ ⊆ G.universalVerts\n⊢ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 142,
"column": 47
} | {
"line": 142,
"column": 58
} | {
"line": 142,
"column": 59
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nhodd : Odd (Nat.card V)\n⊢ Odd (Nat.card ↑(⊤.deleteVerts ∅).verts)",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"SimpleGraph.Subgraph",
"Set.univ",
"Odd",
"Set.Elem",
... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nhodd : Odd (Nat.card V)\n⊢ Odd (Nat.card V)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 68
} | {
"line": 144,
"column": 0
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nhodd : Odd (Nat.card V)\n⊢ 0 < (⊤.deleteVerts ∅).coe.oddComponents.ncard",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Iff.mpr",
"Eq.mpr",
"Nat.instCanonicallyOrderedAdd",
"Nat.instNontrivial",
"co... | [] | exact ((odd_ncard_oddComponents _).mpr <| by simpa using hodd).pos | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Combinatorics.Young.SemistandardTableau | {
"line": 71,
"column": 4
} | {
"line": 73,
"column": 9
} | {
"line": 75,
"column": 0
} | [
{
"pp": "μ : YoungDiagram\nT T' : SemistandardYoungTableau μ\nh : T.entry = T'.entry\n⊢ T = T'",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"YoungDiagram",
"SemistandardYoungTableau.mk",
"Membership.mem",
"Eq.rec",
"Prod.mk",
"instOfNatNat",
"LE... | [] | cases T
cases T'
congr | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Combinatorics.Young.SemistandardTableau | {
"line": 71,
"column": 4
} | {
"line": 73,
"column": 9
} | {
"line": 75,
"column": 0
} | [
{
"pp": "μ : YoungDiagram\nT T' : SemistandardYoungTableau μ\nh : T.entry = T'.entry\n⊢ T = T'",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"YoungDiagram",
"SemistandardYoungTableau.mk",
"Membership.mem",
"Eq.rec",
"Prod.mk",
"instOfNatNat",
"LE... | [] | cases T
cases T'
congr | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 173,
"column": 42
} | {
"line": 174,
"column": 9
} | {
"line": 174,
"column": 10
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nx a b c : V\nM1 : (G ⊔ edge x b).Subgraph\nM2 : (G ⊔ edge a c).Subgraph\nhxa : G.Adj x a\nhab : G.Adj a b\nhnGxb : ¬G.Adj x b\nhnGac : ¬G.Adj a c\nhnxb : x ≠ b\nhnxc : x ≠ c\nhnac : a ≠ c\nhnbc : b ≠ c\nhM1 : M1.IsPerfectMatching\nhM2 : M2.IsPerfectMat... | [
"V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nx a b c : V\nM1 : (G ⊔ edge x b).Subgraph\nM2 : (G ⊔ edge a c).Subgraph\nhxa : G.Adj x a\nhab : G.Adj a b\nhnGxb : ¬G.Adj x b\nhnGac : ¬G.Adj a c\nhnxb : x ≠ b\nhnxc : x ≠ c\nhnac : a ≠ c\nhnbc : b ≠ c\nhM1 : M1.IsPerfectMatching\nhM2 : M2.IsPerfectMatching\nhM1xb... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Young.YoungDiagram | {
"line": 448,
"column": 2
} | {
"line": 448,
"column": 54
} | {
"line": 448,
"column": 55
} | [
{
"pp": "μ : YoungDiagram\ni j : ℕ\n⊢ (∃ (_ : i < μ.colLen 0), j < μ.rowLen i) ↔ (i, j) ∈ μ",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.Combinatorics.Young.YoungDiagram.0.YoungDiagram.ofRowLens_to_rowLens_eq_self._simp_1_4",
"YoungDiagram",... | [
"μ : YoungDiagram\ni j : ℕ\n⊢ j < μ.rowLen i → 0 < μ.rowLen i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.Tiling.Tile | {
"line": 242,
"column": 6
} | {
"line": 242,
"column": 49
} | {
"line": 242,
"column": 50
} | [
{
"pp": "G : Type u_1\nX : Type u_2\nιₚ : Type u_3\ninst✝¹ : Group G\ninst✝ : MulAction G X\nps : Protoset G X ιₚ\ng : G\npt : PlacedTile ps\na b : G\nr : a⁻¹ * b ∈ Subgroup.map (MulAction.stabilizer G ↑(↑ps pt.index)).subtype (↑ps pt.index).symmetries\n⊢ { index := pt.index, groupElts := ↑(g * a) }.groupElts ≍... | [
"G : Type u_1\nX : Type u_2\nιₚ : Type u_3\ninst✝¹ : Group G\ninst✝ : MulAction G X\nps : Protoset G X ιₚ\ng : G\npt : PlacedTile ps\na b : G\nr : a⁻¹ * b ∈ Subgroup.map (MulAction.stabilizer G ↑(↑ps pt.index)).subtype (↑ps pt.index).symmetries\n⊢ ∃ (x : (a⁻¹ * b) • ↑(↑ps pt.index) = ↑(↑ps pt.index)), ⟨a⁻¹ * b, ⋯⟩ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.Basic | {
"line": 366,
"column": 42
} | {
"line": 366,
"column": 66
} | {
"line": 366,
"column": 66
} | [
{
"pp": "⊢ Primrec₂ Nat.pair",
"ppTerm": "?m.7",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Nat.Primrec",
"Denumerable.prod",
"Equiv.instEquivLike",
"congrArg",
"Primcodable.ofDenumerable",
"Nat.unpair",
"Option.some",
"Option.encodable",
... | [
"⊢ Nat.Primrec fun n ↦ n + 1"
] | simp [Primrec₂, Primrec] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 228,
"column": 4
} | {
"line": 228,
"column": 87
} | {
"line": 228,
"column": 87
} | [
{
"pp": "V : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nx a b c : V\nM1 : (G ⊔ edge x b).Subgraph\nM2 : (G ⊔ edge a c).Subgraph\nhxa : G.Adj x a\nhab : G.Adj a b\nhnGxb : ¬G.Adj x b\nhnGac : ¬G.Adj a c\nhnxb : x ≠ b\nhnxc : x ≠ c\nhnac : a ≠ c\nhnbc : b ≠ c\nhM1 : M1.IsPerfectMatching\nhM2 : M2.IsPerfectMat... | [
"case refine_1\nV : Type u_1\nG : SimpleGraph V\ninst✝ : Finite V\nx a b c : V\nM1 : (G ⊔ edge x b).Subgraph\nM2 : (G ⊔ edge a c).Subgraph\nhxa : G.Adj x a\nhab : G.Adj a b\nhnGxb : ¬G.Adj x b\nhnGac : ¬G.Adj a c\nhnxb : x ≠ b\nhnxc : x ≠ c\nhnac : a ≠ c\nhnbc : b ≠ c\nhM1 : M1.IsPerfectMatching\nhM2 : M2.IsPerfect... | refine ⟨x', hx', p'.takeUntil x' hx'p, hp'.1.isPath_takeUntil hx'p, ?_, fun h ↦ ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Computability.Partrec | {
"line": 76,
"column": 10
} | {
"line": 76,
"column": 17
} | {
"line": 77,
"column": 10
} | [
{
"pp": "case inr.inl\np : ℕ →. Bool\nm : ℕ\nIH : (y : ℕ) → lbp p y m → (∀ n < y, false ∈ p n) → { n // true ∈ p n ∧ ∀ m < n, false ∈ p m }\nal : ∀ n < m, false ∈ p n\nn : ℕ\nh₁ : true ∈ p n\nh₂ : ∀ k < n, (p k).Dom\nh₃ : m = n\n⊢ (p m).Dom",
"ppTerm": "?inr.inl",
"assigned": true,
"usedConstants": ... | [
"case inr.inl\np : ℕ →. Bool\nm : ℕ\nIH : (y : ℕ) → lbp p y m → (∀ n < y, false ∈ p n) → { n // true ∈ p n ∧ ∀ m < n, false ∈ p m }\nal : ∀ n < m, false ∈ p n\nn : ℕ\nh₁ : true ∈ p n\nh₂ : ∀ k < n, (p k).Dom\nh₃ : m = n\n⊢ (p n).Dom"
] | rw [h₃] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Computability.Primrec.Basic | {
"line": 608,
"column": 2
} | {
"line": 608,
"column": 32
} | {
"line": 608,
"column": 33
} | [
{
"pp": "α : Type u_1\nσ : Type u_3\ninst✝² : Primcodable α\ninst✝¹ : Primcodable σ\nc : α → Prop\ninst✝ : DecidablePred c\nf g : α → σ\nhc : PrimrecPred c\nhf : Primrec f\nhg : Primrec g\n⊢ Primrec fun a ↦ if c a then f a else g a",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"us... | [
"α : Type u_1\nσ : Type u_3\ninst✝² : Primcodable α\ninst✝¹ : Primcodable σ\nc : α → Prop\ninst✝ : DecidablePred c\nf g : α → σ\nhc : PrimrecPred c\nhf : Primrec f\nhg : Primrec g\n⊢ Primrec fun a ↦ if c a then f a else g a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.Basic | {
"line": 665,
"column": 10
} | {
"line": 665,
"column": 21
} | {
"line": 665,
"column": 22
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\np : α → β → Prop\ninst✝ : DecidableRel p\nhp : PrimrecRel p\nf : α → β\nhf : Primrec f\n⊢ PrimrecPred fun a ↦ (fun b ↦ decide (p a b)) (f a) = true",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\np : α → β → Prop\ninst✝ : DecidableRel p\nhp : PrimrecRel p\nf : α → β\nhf : Primrec f\n⊢ PrimrecPred fun a ↦ p a (f a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 147,
"column": 23
} | {
"line": 147,
"column": 34
} | {
"line": 147,
"column": 35
} | [
{
"pp": "α : Type u_1\nf : ℕ → Option α\nh : ∃ n a, a ∈ f n\nh' : ∃ n, (f n).isSome = true\ns : (f (Nat.find h')).isSome = true\n⊢ true ∈ (fun n ↦ ↑(Option.some (f n).isSome)) (Nat.find h')",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
"Part",
"Eq.mpr",
"Part.some",
... | [
"α : Type u_1\nf : ℕ → Option α\nh : ∃ n a, a ∈ f n\nh' : ∃ n, (f n).isSome = true\ns : (f (Nat.find h')).isSome = true\n⊢ (f (Nat.find h')).isSome = true"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 15
} | {
"line": 150,
"column": 16
} | [
{
"pp": "α : Type u_1\nf : ℕ → Option α\nh : ∃ n a, a ∈ f n\nh' : ∃ n, (f n).isSome = true\ns : (f (Nat.find h')).isSome = true\nfd : (rfind fun n ↦ ↑(Option.some (f n).isSome)).Dom\nthis : true ∈ ↑(Option.some (f ((rfind fun n ↦ ↑(Option.some (f n).isSome)).get fd)).isSome)\n⊢ ((fun b ↦ (fun n ↦ ↑(f n)) ((rfin... | [
"α : Type u_1\nf : ℕ → Option α\nh : ∃ n a, a ∈ f n\nh' : ∃ n, (f n).isSome = true\ns : (f (Nat.find h')).isSome = true\nfd : (rfind fun n ↦ ↑(Option.some (f n).isSome)).Dom\nthis : true ∈ ↑(Option.some (f ((rfind fun n ↦ ↑(Option.some (f n).isSome)).get fd)).isSome)\n⊢ (f ((rfind fun n ↦ Part.some (f n).isSome).ge... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.Basic | {
"line": 839,
"column": 20
} | {
"line": 839,
"column": 31
} | {
"line": 839,
"column": 32
} | [
{
"pp": "α : Type u_1\ninst✝ : Primcodable α\n⊢ PrimrecPred fun p ↦ (fun a ↦ decide (encode a = p.1)) p.2 = true",
"ppTerm": "?m.49",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Primcodable.ofDenumerable",
"id",
"Prod.fst",
"Primcodable.prod",
... | [
"α : Type u_1\ninst✝ : Primcodable α\n⊢ PrimrecPred fun p ↦ encode p.2 = p.1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 409,
"column": 2
} | {
"line": 409,
"column": 32
} | {
"line": 409,
"column": 33
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : α →. β\ng : α → β → σ\nhf : Partrec f\nhg : Computable₂ g\n⊢ Partrec fun a ↦ Part.map (g a) (f a)",
"ppTerm": "?m.19",
"assigned": false,
"usedConstants": [],
"usedFVars"... | [
"α : Type u_1\nβ : Type u_2\nσ : Type u_3\ninst✝² : Primcodable α\ninst✝¹ : Primcodable β\ninst✝ : Primcodable σ\nf : α →. β\ng : α → β → σ\nhf : Partrec f\nhg : Computable₂ g\n⊢ Partrec fun a ↦ Part.map (g a) (f a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 527,
"column": 27
} | {
"line": 527,
"column": 49
} | {
"line": 527,
"column": 50
} | [
{
"pp": "α : Type u_1\nσ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf : α →. σ\nh : Nat.Partrec fun n ↦ (↑(decode₂ α n)).bind fun a ↦ Part.map encode (f a)\n⊢ Partrec fun a ↦ Part.map encode (f a)",
"ppTerm": "?m.94",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"... | [
"α : Type u_1\nσ : Type u_2\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nf : α →. σ\nh : Nat.Partrec fun n ↦ (↑(decode₂ α n)).bind fun a ↦ Part.map encode (f a)\n⊢ Partrec fun a ↦ Part.map encode (f a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 341,
"column": 39
} | {
"line": 341,
"column": 50
} | {
"line": 341,
"column": 51
} | [
{
"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)\nthis✝¹ : DecidableE... | [
"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)\nthis✝¹ : DecidableEq β\nmapGrap... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 346,
"column": 41
} | {
"line": 346,
"column": 52
} | {
"line": 346,
"column": 53
} | [
{
"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)\nthis✝ : DecidableEq... | [
"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)\nthis✝ : DecidableEq β\nmapGraph... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 348,
"column": 10
} | {
"line": 348,
"column": 46
} | {
"line": 348,
"column": 47
} | [
{
"pp": "case cons\nβ : 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)\nthis✝ : ... | [
"case cons\nβ : 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)\nthis✝ : DecidableEq ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 354,
"column": 22
} | {
"line": 354,
"column": 41
} | {
"line": 354,
"column": 42
} | [
{
"pp": "case zero\nβ : 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)\nthis✝ : ... | [
"case zero\nβ : 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)\nthis✝ : DecidableEq ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 753,
"column": 8
} | {
"line": 753,
"column": 23
} | {
"line": 753,
"column": 24
} | [
{
"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 ... | [
"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 ∀ (a'' : α),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 755,
"column": 33
} | {
"line": 755,
"column": 48
} | {
"line": 755,
"column": 49
} | [
{
"pp": "α : 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 ∀ (a'' : α),\n Sum.inr a''... | [
"α : 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 ∀ (a'' : α),\n Sum.inr a'' ∈ f a₂ →\n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Partrec | {
"line": 772,
"column": 29
} | {
"line": 772,
"column": 44
} | {
"line": 772,
"column": 45
} | [
{
"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\np : α → ℕ → Part Bool := fun a n ↦ Part.ma... | [
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Ackermann | {
"line": 125,
"column": 23
} | {
"line": 125,
"column": 34
} | {
"line": 125,
"column": 35
} | [
{
"pp": "n₁ n₂ : ℕ\nh : n₁ < n₂\n⊢ ack 0 n₁ < ack 0 n₂",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"Eq.mpr",
"ack",
"Preorder.toLT",
"Nat.instIsOrderedAddMonoid",
"AddLeftCancelSemigroup.toIsLeft... | [
"n₁ n₂ : ℕ\nh : n₁ < n₂\n⊢ n₁ < n₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Ackermann | {
"line": 157,
"column": 19
} | {
"line": 157,
"column": 30
} | {
"line": 157,
"column": 31
} | [
{
"pp": "m : ℕ\n⊢ m + 1 + 0 < ack (m + 1) 0",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ack",
"congrArg",
"AddMonoid.toAddZeroClass",
"ack_succ_zero",
"Nat.instAddMonoid",
"id",
"instOfNatNat",
"instHAdd",
"HAdd.hAd... | [
"m : ℕ\n⊢ m + 1 < ack m 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Ackermann | {
"line": 179,
"column": 32
} | {
"line": 179,
"column": 43
} | {
"line": 179,
"column": 44
} | [
{
"pp": "m : ℕ\n_h : 0 < m + 1\n⊢ ack 0 0 < ack (m + 1) 0",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ack",
"congrArg",
"AddMonoid.toAddZeroClass",
"ack_succ_zero",
"Nat.instAddMonoid",
"id",
"instOfNatNat",
"zero_add",
... | [
"m : ℕ\n_h : 0 < m + 1\n⊢ 1 < ack m 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 539,
"column": 28
} | {
"line": 539,
"column": 39
} | {
"line": 539,
"column": 40
} | [
{
"pp": "α : Type u_1\ninst✝ : Primcodable α\nn : ℕ\n⊢ Primrec fun a ↦ (a.1 ::ᵥ a.2).toList",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List.Vector",
"id",
"Primcodable.vector",
"List.Vector.toList_cons",
"Prod.fst",
... | [
"α : Type u_1\ninst✝ : Primcodable α\nn : ℕ\n⊢ Primrec fun a ↦ a.1 :: a.2.toList"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 559,
"column": 4
} | {
"line": 559,
"column": 15
} | {
"line": 559,
"column": 16
} | [
{
"pp": "α : Type u_1\nσ : Type u_3\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nn : ℕ\nf : Fin (n + 1) → α → σ\nhf : ∀ (i : Fin (n + 1)), Primrec (f i)\n⊢ Primrec fun a ↦ List.ofFn fun i ↦ f i a",
"ppTerm": "?m.34",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1"... | [
"α : Type u_1\nσ : Type u_3\ninst✝¹ : Primcodable α\ninst✝ : Primcodable σ\nn : ℕ\nf : Fin (n + 1) → α → σ\nhf : ∀ (i : Fin (n + 1)), Primrec (f i)\n⊢ Primrec fun a ↦ f 0 a :: List.ofFn fun i ↦ f i.succ a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Ackermann | {
"line": 187,
"column": 4
} | {
"line": 187,
"column": 15
} | {
"line": 187,
"column": 16
} | [
{
"pp": "m₁ m₂ : ℕ\nh : m₁ + 1 < m₂ + 1\n⊢ ack (m₁ + 1) 0 < ack (m₂ + 1) 0",
"ppTerm": "?m.71",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ack",
"congrArg",
"ack_succ_zero",
"id",
"instOfNatNat",
"instHAdd",
"HAdd.hAdd",
"Nat",
"congr"... | [
"m₁ m₂ : ℕ\nh : m₁ + 1 < m₂ + 1\n⊢ ack m₁ 1 < ack m₂ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Ackermann | {
"line": 236,
"column": 15
} | {
"line": 236,
"column": 26
} | {
"line": 236,
"column": 27
} | [
{
"pp": "n : ℕ\n⊢ (ack 0 n + 1) ^ 2 ≤ ack (0 + 3) n",
"ppTerm": "?m.41",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"ack",
"congrArg",
"Nat.instMonoid",
"AddMonoid.toAddZeroClass",
"HSub.hSub",
"Nat.instAddMonoid",
"ack_three",
"id",
"i... | [
"n : ℕ\n⊢ (n + 1 + 1) ^ 2 ≤ 2 ^ (n + 3) - 3"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 664,
"column": 2
} | {
"line": 664,
"column": 13
} | {
"line": 664,
"column": 14
} | [
{
"pp": "f : ℕ → ℕ → ℕ\nhf : Primrec' fun v ↦ f v.head v.tail.head\nn : ℕ\ng h : List.Vector ℕ n → ℕ\nhg : Primrec' g\nhh : Primrec' h\n⊢ Primrec' fun v ↦ f (g v) (h v)",
"ppTerm": "?m.15",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"f : ℕ → ℕ → ℕ\nhf : Primrec' fun v ↦ f v.head v.tail.head\nn : ℕ\ng h : List.Vector ℕ n → ℕ\nhg : Primrec' g\nhh : Primrec' h\n⊢ Primrec' fun v ↦ f (g v) (h v)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 668,
"column": 2
} | {
"line": 668,
"column": 13
} | {
"line": 668,
"column": 14
} | [
{
"pp": "n : ℕ\nf g : List.Vector ℕ n → ℕ\nh : List.Vector ℕ (n + 2) → ℕ\nhf : Primrec' f\nhg : Primrec' g\nhh : Primrec' h\n⊢ Primrec' fun v ↦ Nat.rec (g v) (fun y IH ↦ h (y ::ᵥ IH ::ᵥ v)) (f v)",
"ppTerm": "?m.24",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
... | [
"n : ℕ\nf g : List.Vector ℕ n → ℕ\nh : List.Vector ℕ (n + 2) → ℕ\nhf : Primrec' f\nhg : Primrec' g\nhh : Primrec' h\n⊢ Primrec' fun v ↦ Nat.rec (g v) (fun y IH ↦ h (y ::ᵥ IH ::ᵥ v)) (f v)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Primrec.List | {
"line": 681,
"column": 2
} | {
"line": 681,
"column": 13
} | {
"line": 681,
"column": 14
} | [
{
"pp": "this : Primrec' fun v ↦ (fun a b ↦ b - a) v.head v.tail.head\n⊢ Primrec' fun v ↦ v.head - v.tail.head",
"ppTerm": "?m.37",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"this : Primrec' fun v ↦ (fun a b ↦ b - a) v.head v.tail.head\n⊢ Primrec' fun v ↦ v.head - v.tail.head"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Ackermann | {
"line": 312,
"column": 8
} | {
"line": 313,
"column": 26
} | {
"line": 314,
"column": 8
} | [
{
"pp": "case inl\nf✝ f g : ℕ → ℕ\nhf : Nat.Primrec f\nhg : Nat.Primrec g\na : ℕ\nha : ∀ (n : ℕ), f n < ack a n\nb : ℕ\nhb : ∀ (n : ℕ), g n < ack b n\nm n : ℕ\nIH : rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n < ack (max a b + 9) (m + n)\nh₁ : ?m.338 < m\n⊢ ack (b + 4) (max m (pair n (rec (f m) (fun y IH ↦ g... | [
"case inr\nf✝ f g : ℕ → ℕ\nhf : Nat.Primrec f\nhg : Nat.Primrec g\na : ℕ\nha : ∀ (n : ℕ), f n < ack a n\nb : ℕ\nhb : ∀ (n : ℕ), g n < ack b n\nm n : ℕ\nIH : rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n < ack (max a b + 9) (m + n)\nh₁ : m ≤ pair n (rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n)\n⊢ ack (b + 4) (... | · rw [max_eq_left h₁.le]
gcongr <;> omega | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Computability.Primrec.List | {
"line": 754,
"column": 4
} | {
"line": 754,
"column": 15
} | {
"line": 755,
"column": 6
} | [
{
"pp": "case prec\nn : ℕ\nf✝¹ : List.Vector ℕ n → ℕ\nf f✝ g✝ : ℕ → ℕ\na✝¹ : Nat.Primrec f✝\na✝ : Nat.Primrec g✝\nhf : Primrec' fun v ↦ f✝ v.head\nhg : Primrec' fun v ↦ g✝ v.head\n⊢ Primrec' fun v ↦ unpaired (fun z n ↦ Nat.rec (f✝ z) (fun y IH ↦ g✝ (pair z (pair y IH))) n) v.head",
"ppTerm": "?prec",
"a... | [
"case prec\nn : ℕ\nf✝¹ : List.Vector ℕ n → ℕ\nf f✝ g✝ : ℕ → ℕ\na✝¹ : Nat.Primrec f✝\na✝ : Nat.Primrec g✝\nhf : Primrec' fun v ↦ f✝ v.head\nhg : Primrec' fun v ↦ g✝ v.head\n⊢ Primrec' fun v ↦ Nat.rec (f✝ (unpair v.head).1) (fun y IH ↦ g✝ (pair (unpair v.head).1 (pair y IH))) (unpair v.head).2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.Ackermann | {
"line": 319,
"column": 10
} | {
"line": 322,
"column": 57
} | {
"line": 323,
"column": 8
} | [
{
"pp": "case inr.inl\nf✝ f g : ℕ → ℕ\nhf : Nat.Primrec f\nhg : Nat.Primrec g\na : ℕ\nha : ∀ (n : ℕ), f n < ack a n\nb : ℕ\nhb : ∀ (n : ℕ), g n < ack b n\nm n : ℕ\nIH : rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n < ack (max a b + 9) (m + n)\nh₁ : m ≤ pair n (rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n)\... | [] | rw [max_eq_left h₂.le, add_assoc]
exact
ack_le_ack (Nat.add_le_add (le_max_right a b) <| by simp)
((le_succ n).trans <| self_le_add_left _ _) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Computability.Ackermann | {
"line": 319,
"column": 10
} | {
"line": 322,
"column": 57
} | {
"line": 323,
"column": 8
} | [
{
"pp": "case inr.inl\nf✝ f g : ℕ → ℕ\nhf : Nat.Primrec f\nhg : Nat.Primrec g\na : ℕ\nha : ∀ (n : ℕ), f n < ack a n\nb : ℕ\nhb : ∀ (n : ℕ), g n < ack b n\nm n : ℕ\nIH : rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n < ack (max a b + 9) (m + n)\nh₁ : m ≤ pair n (rec (f m) (fun y IH ↦ g (pair m (pair y IH))) n)\... | [] | rw [max_eq_left h₂.le, add_assoc]
exact
ack_le_ack (Nat.add_le_add (le_max_right a b) <| by simp)
((le_succ n).trans <| self_le_add_left _ _) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.Primrec.List | {
"line": 774,
"column": 15
} | {
"line": 774,
"column": 26
} | {
"line": 774,
"column": 27
} | [
{
"pp": "m n : ℕ\nf : List.Vector ℕ m → List.Vector ℕ n\nh : Vec f\n⊢ Primrec 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⊢ Primrec f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.AkraBazzi.SumTransform | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 13
} | {
"line": 130,
"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\n⊢ ∀ᶠ (x : ℕ) in atTop, ‖↑(r i x) - b i * ↑x‖ ≤ ↑x / log ↑x ^ 2",
"ppTerm": "?m.58",
"assigned": true,
"usedConstants": [
"Norm.norm",
... | [
"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\n⊢ ∃ a, ∀ (b_1 : ℕ), a ≤ b_1 → |↑(r i b_1) - b i * ↑b_1| ≤ ↑b_1 / log ↑b_1 ^ 2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.AkraBazzi.GrowsPolynomially | {
"line": 113,
"column": 19
} | {
"line": 113,
"column": 77
} | {
"line": 114,
"column": 6
} | [
{
"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 ... | [] | by simp only [neg_add, ← sub_eq_add_neg] at hz; exact hz.2 | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 289,
"column": 10
} | {
"line": 289,
"column": 39
} | {
"line": 289,
"column": 40
} | [
{
"pp": "V : 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\nh' : ∀ (K : Gmax.deleteUniver... | [
"V : 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\nh' : ∀ (K : Gmax.deleteUniversalVerts.coe... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Combinatorics.SimpleGraph.Tutte | {
"line": 302,
"column": 6
} | {
"line": 302,
"column": 47
} | {
"line": 302,
"column": 48
} | [
{
"pp": "V : 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\nhc : ¬Fintype.card ↑Gmax.univ... | [
"V : 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\nhc : ¬Fintype.card ↑Gmax.universalVerts <... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.AkraBazzi.AkraBazzi | {
"line": 94,
"column": 8
} | {
"line": 94,
"column": 15
} | {
"line": 94,
"column": 16
} | [
{
"pp": "p x : ℝ\nhx : 1 < x\nhderiv : deriv (fun x ↦ 1 - ε x) x = x⁻¹ / log x ^ 2\n⊢ deriv (fun x ↦ x ^ p) x * (1 - ε x) + x ^ p * deriv (fun x ↦ 1 - ε x) x =\n p * x ^ (p - 1) * (1 - ε x) + x ^ p * (x⁻¹ / log x ^ 2)",
"ppTerm": "?m.399",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"p x : ℝ\nhx : 1 < x\nhderiv : deriv (fun x ↦ 1 - ε x) x = x⁻¹ / log x ^ 2\n⊢ deriv (fun x ↦ x ^ p) x * (1 - ε x) + x ^ p * (x⁻¹ / log x ^ 2) =\n p * x ^ (p - 1) * (1 - ε x) + x ^ p * (x⁻¹ / log x ^ 2)"
] | hderiv, | Lean.Elab.Tactic.evalRewriteSeq | null |
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