module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Data.List.Infix | {
"line": 131,
"column": 6
} | {
"line": 131,
"column": 17
} | {
"line": 131,
"column": 18
} | [
{
"pp": "case cons.cons\nα : Type u_1\ntail✝¹ : List α\nih : ∀ {l₁ : List α}, l₁ <+: tail✝¹ → tail✝¹ = l₁ ++ drop l₁.length tail✝¹\nhead✝ : α\ntail✝ : List α\nh' : tail✝ <+: tail✝¹\nh : head✝ :: tail✝ <+: head✝ :: tail✝¹\n⊢ head✝ :: tail✝¹ = head✝ :: tail✝ ++ drop (head✝ :: tail✝).length (head✝ :: tail✝¹)",
... | [
"case cons.cons\nα : Type u_1\ntail✝¹ : List α\nih : ∀ {l₁ : List α}, l₁ <+: tail✝¹ → tail✝¹ = l₁ ++ drop l₁.length tail✝¹\nhead✝ : α\ntail✝ : List α\nh' : tail✝ <+: tail✝¹\nh : head✝ :: tail✝ <+: head✝ :: tail✝¹\n⊢ tail✝¹ = tail✝ ++ drop tail✝.length tail✝¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Infix | {
"line": 288,
"column": 19
} | {
"line": 288,
"column": 30
} | {
"line": 288,
"column": 31
} | [
{
"pp": "case cons\nα : Type u_1\nx : α\nl : List α\nIH : l.tails.length = l.length + 1\n⊢ (x :: l).tails.length = (x :: l).length + 1",
"ppTerm": "?cons",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"instOfNatNat",
"List.cons",
"List",
"instHAdd",
... | [
"case cons\nα : Type u_1\nx : α\nl : List α\nIH : l.tails.length = l.length + 1\n⊢ l.tails.length = l.length + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Infix | {
"line": 326,
"column": 2
} | {
"line": 326,
"column": 19
} | {
"line": 326,
"column": 20
} | [
{
"pp": "α : Type u_1\nl : List α\nn : ℕ\n⊢ (take n l).inits = take (n + 1) l.inits",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"List.ext_getElem",
"instOfNatNat",
"List",
"instHAdd",
"HAdd.hAdd",
"Nat",
"instAddNat",
"OfNat.ofNat",
... | [
"case hl\nα : Type u_1\nl : List α\nn : ℕ\n⊢ (take n l).inits.length = (take (n + 1) l.inits).length",
"case h\nα : Type u_1\nl : List α\nn : ℕ\n⊢ ∀ (i : ℕ) (h₁ : i < (take n l).inits.length) (h₂ : i < (take (n + 1) l.inits).length),\n (take n l).inits[i] = (take (n + 1) l.inits)[i]"
] | apply ext_getElem | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Data.Multiset.Filter | {
"line": 393,
"column": 4
} | {
"line": 393,
"column": 44
} | {
"line": 393,
"column": 45
} | [
{
"pp": "α : Type u_1\nβ : Type v\nf : α → β\nhf : Injective f\ns t : Multiset α\nh : map f s ≤ map f t\na : α\n⊢ count a s ≤ count a t",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type v\nf : α → β\nhf : Injective f\ns t : Multiset α\nh : map f s ≤ map f t\na : α\n⊢ count a s ≤ count a t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Multiset.Filter | {
"line": 393,
"column": 4
} | {
"line": 393,
"column": 68
} | {
"line": 395,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type v\nf : α → β\nhf : Injective f\ns t : Multiset α\nh : map f s ≤ map f t\na : α\n⊢ count a s ≤ count a t",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Multiset.le_iff_count",
"Multiset.map",
"congrArg",
"PartialOrder.toPreorder",
... | [] | simpa [count_map_eq_count' f _ hf] using le_iff_count.mp h (f a) | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Data.Finset.Filter | {
"line": 210,
"column": 42
} | {
"line": 210,
"column": 53
} | {
"line": 210,
"column": 54
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : DecidableEq β\nf : α → β\ns : Set β\nt : Finset α\ni j : β\nh : i ≠ j\nu : Finset α\nhi : u ⊆ (fun x ↦ filter (fun x_1 ↦ f x_1 = x) t) i\nhj : u ⊆ (fun x ↦ filter (fun x_1 ↦ f x_1 = x) t) j\nx : α\nhx : x ∈ u\n⊢ x ∈ t ∧ f x = i",
"ppTerm": "?m.41",
"assigned"... | [
"α : Type u_1\nβ : Type u_2\ninst✝ : DecidableEq β\nf : α → β\ns : Set β\nt : Finset α\ni j : β\nh : i ≠ j\nu : Finset α\nhi : u ⊆ (fun x ↦ filter (fun x_1 ↦ f x_1 = x) t) i\nhj : u ⊆ (fun x ↦ filter (fun x_1 ↦ f x_1 = x) t) j\nx : α\nhx : x ∈ u\n⊢ x ∈ t ∧ f x = i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Filter | {
"line": 211,
"column": 42
} | {
"line": 211,
"column": 53
} | {
"line": 211,
"column": 54
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : DecidableEq β\nf : α → β\ns : Set β\nt : Finset α\nj : β\nu : Finset α\nhj : u ⊆ (fun x ↦ filter (fun x_1 ↦ f x_1 = x) t) j\nx : α\nhx : x ∈ u\nh : f x ≠ j\nhi : u ⊆ (fun x ↦ filter (fun x_1 ↦ f x_1 = x) t) (f x)\n⊢ x ∈ t ∧ f x = j",
"ppTerm": "?m.76",
"assig... | [
"α : Type u_1\nβ : Type u_2\ninst✝ : DecidableEq β\nf : α → β\ns : Set β\nt : Finset α\nj : β\nu : Finset α\nhj : u ⊆ (fun x ↦ filter (fun x_1 ↦ f x_1 = x) t) j\nx : α\nhx : x ∈ u\nh : f x ≠ j\nhi : u ⊆ (fun x ↦ filter (fun x_1 ↦ f x_1 = x) t) (f x)\n⊢ x ∈ t ∧ f x = j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Basic | {
"line": 321,
"column": 2
} | {
"line": 321,
"column": 22
} | {
"line": 321,
"column": 23
} | [
{
"pp": "α : Type u_1\ns t : Finset α\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\nh : ∀ (i : α), Disjoint (p i) (q i)\na : α\nleft✝¹ : a ∈ s\nhp : p a\nleft✝ : a ∈ t\nhq : q a\n⊢ False",
"ppTerm": "?m.50",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"used... | [
"α : Type u_1\ns t : Finset α\np q : α → Prop\ninst✝¹ : DecidablePred p\ninst✝ : DecidablePred q\nh : ∀ (i : α), Disjoint (p i) (q i)\na : α\nleft✝¹ : a ∈ s\nhp : p a\nleft✝ : a ∈ t\nhq : q a\n⊢ False"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.OfMap | {
"line": 42,
"column": 18
} | {
"line": 42,
"column": 29
} | {
"line": 42,
"column": 30
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : DecidableEq α\ns : Multiset α\nH : ∀ (x : α), x ∈ s\n⊢ ∀ (x : α), x ∈ s.toFinset",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Multiset.toFinset",
"Eq.mpr",
"Finset",
"Membership.mem",
"Multiset",
... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : DecidableEq α\ns : Multiset α\nH : ∀ (x : α), x ∈ s\n⊢ ∀ (x : α), x ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.OfMap | {
"line": 47,
"column": 18
} | {
"line": 47,
"column": 29
} | {
"line": 47,
"column": 30
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : DecidableEq α\nl : List α\nH : ∀ (x : α), x ∈ l\n⊢ ∀ (x : α), x ∈ l.toFinset",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset",
"Membership.mem",
"id",
"List.toFinset",
"List.mem_... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝ : DecidableEq α\nl : List α\nH : ∀ (x : α), x ∈ l\n⊢ ∀ (x : α), x ∈ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Image | {
"line": 145,
"column": 4
} | {
"line": 145,
"column": 15
} | {
"line": 145,
"column": 16
} | [
{
"pp": "case mp\nα : Type u_1\nβ : Type u_2\ns : Finset α\nt : Finset β\nf : α ≃ β\nh : s ⊆ map f.symm.toEmbedding t\nx : β\nhx : f.symm x ∈ s\n⊢ x ∈ t",
"ppTerm": "?mp",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case mp\nα : Type u_1\nβ : Type u_2\ns : Finset α\nt : Finset β\nf : α ≃ β\nh : s ⊆ map f.symm.toEmbedding t\nx : β\nhx : f.symm x ∈ s\n⊢ x ∈ t"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Image | {
"line": 233,
"column": 51
} | {
"line": 233,
"column": 62
} | {
"line": 233,
"column": 63
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf✝ : α ↪ β\ns✝ : Finset α\nf : α ↪ β\na : α\ns : Finset α\nha : a ∉ s\n⊢ f a ∉ map f s",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset",
"Finset.mem_map'._simp_1",
"Finset.map",
... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\nf✝ : α ↪ β\ns✝ : Finset α\nf : α ↪ β\na : α\ns : Finset α\nha : a ∉ s\n⊢ a ∉ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.Sets | {
"line": 114,
"column": 53
} | {
"line": 114,
"column": 96
} | {
"line": 116,
"column": 0
} | [
{
"pp": "α : Type u_1\ns t : Set α\ninst✝¹ : Fintype ↑s\ninst✝ : Fintype ↑t\n⊢ Disjoint s.toFinset t.toFinset ↔ Disjoint s t",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"congrArg",
"Finset",
"Disjoint",
"SemilatticeInf.toPartialOrder",
"BiheytingAlgebra.to... | [] | by simp only [← disjoint_coe, coe_toFinset] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Fintype.Sets | {
"line": 254,
"column": 32
} | {
"line": 254,
"column": 43
} | {
"line": 254,
"column": 44
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\n⊢ ∀ (x : Prop), x ∈ { val := {True, False}, nodup := fintype._proof_1 }",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"False",
"Multiset.Nodup",
"LinearOrder.toDecidableEq",
"iff_false",
"con... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\n⊢ ∀ (x : Prop), x ∨ ¬x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Image | {
"line": 542,
"column": 40
} | {
"line": 542,
"column": 51
} | {
"line": 542,
"column": 52
} | [
{
"pp": "α : Type u_1\na : α\ns : Finset α\nha : a ∉ s\nx : α\nhx : x ∈ cons a s ha\n⊢ ⟨x, hx⟩ ∈ (cons a s ha).attach ↔ ⟨x, hx⟩ ∈ cons ⟨a, ⋯⟩ (map { toFun := fun x ↦ ⟨↑x, ⋯⟩, inj' := ⋯ } s.attach) ⋯",
"ppTerm": "?m.53",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.attach_cons._... | [
"α : Type u_1\na : α\ns : Finset α\nha : a ∉ s\nx : α\nhx : x ∈ cons a s ha\n⊢ x = a ∨ x ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Image | {
"line": 548,
"column": 84
} | {
"line": 548,
"column": 95
} | {
"line": 548,
"column": 96
} | [
{
"pp": "α : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\na x : α\nhx : x ∈ insert a s\n⊢ ⟨x, hx⟩ ∈ (insert a s).attach ↔ ⟨x, hx⟩ ∈ insert ⟨a, ⋯⟩ (image (fun x ↦ ⟨↑x, ⋯⟩) s.attach)",
"ppTerm": "?m.52",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.mem_insert_self",
"Iff.... | [
"α : Type u_1\ninst✝ : DecidableEq α\ns : Finset α\na x : α\nhx : x ∈ insert a s\n⊢ x = a ∨ x ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Image | {
"line": 627,
"column": 23
} | {
"line": 627,
"column": 34
} | {
"line": 627,
"column": 35
} | [
{
"pp": "α✝ : Type u_1\nβ : Type u_2\nγ : Type u_3\nα : Type ?u.18\np : α → Prop\ninst✝ : DecidablePred p\ns : Finset α\nx : ↥(filter p s)\n⊢ p ↑x",
"ppTerm": "?m.42",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α✝ : Type u_1\nβ : Type u_2\nγ : Type u_3\nα : Type ?u.18\np : α → Prop\ninst✝ : DecidablePred p\ns : Finset α\nx : ↥(filter p s)\n⊢ p ↑x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Image | {
"line": 653,
"column": 61
} | {
"line": 653,
"column": 86
} | {
"line": 653,
"column": 87
} | [
{
"pp": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\ns : Finset α\nh : ∀ x ∈ s, p x\n⊢ ∀ (a : α), a ∈ map (Embedding.subtype p) (Finset.subtype p s) ↔ a ∈ s",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.mem_filter._simp_1",
"congrArg",
"... | [
"α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\ns : Finset α\nh : ∀ x ∈ s, p x\n⊢ ∀ a ∈ s, p a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Image | {
"line": 653,
"column": 61
} | {
"line": 653,
"column": 88
} | {
"line": 655,
"column": 0
} | [
{
"pp": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\ns : Finset α\nh : ∀ x ∈ s, p x\n⊢ ∀ (a : α), a ∈ map (Embedding.subtype p) (Finset.subtype p s) ↔ a ∈ s",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.mem_filter._simp_1",
"congrArg",
"... | [] | simpa [subtype_map] using h | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Data.Finset.Image | {
"line": 653,
"column": 61
} | {
"line": 653,
"column": 88
} | {
"line": 655,
"column": 0
} | [
{
"pp": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\ns : Finset α\nh : ∀ x ∈ s, p x\n⊢ ∀ (a : α), a ∈ map (Embedding.subtype p) (Finset.subtype p s) ↔ a ∈ s",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.mem_filter._simp_1",
"congrArg",
"... | [] | simpa [subtype_map] using h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.Image | {
"line": 653,
"column": 61
} | {
"line": 653,
"column": 88
} | {
"line": 655,
"column": 0
} | [
{
"pp": "α : Type u_1\np : α → Prop\ninst✝ : DecidablePred p\ns : Finset α\nh : ∀ x ∈ s, p x\n⊢ ∀ (a : α), a ∈ map (Embedding.subtype p) (Finset.subtype p s) ↔ a ∈ s",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Finset.mem_filter._simp_1",
"congrArg",
"... | [] | simpa [subtype_map] using h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fin.Embedding | {
"line": 97,
"column": 4
} | {
"line": 97,
"column": 72
} | {
"line": 97,
"column": 73
} | [
{
"pp": "case succ\nn : ℕ\nihn : ∀ {m : ℕ}, Nonempty (Fin n ↪ Fin m) → n ≤ m\nm : ℕ\ne : Fin (n + 1) ↪ Fin m.succ\ni j : Fin n\nh : (fun i ↦ ((e.setValue 0 0) i.succ).pred ⋯) i = (fun i ↦ ((e.setValue 0 0) i.succ).pred ⋯) j\n⊢ i = j",
"ppTerm": "?succ",
"assigned": false,
"usedConstants": [],
"u... | [
"case succ\nn : ℕ\nihn : ∀ {m : ℕ}, Nonempty (Fin n ↪ Fin m) → n ≤ m\nm : ℕ\ne : Fin (n + 1) ↪ Fin m.succ\ni j : Fin n\nh : (fun i ↦ ((e.setValue 0 0) i.succ).pred ⋯) i = (fun i ↦ ((e.setValue 0 0) i.succ).pred ⋯) j\n⊢ i = j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Basic | {
"line": 219,
"column": 19
} | {
"line": 219,
"column": 45
} | {
"line": 219,
"column": 46
} | [
{
"pp": "k l : ℕ\nh : k = l\na b : Fin k\nhab : Fin.cast h a = Fin.cast h b\n⊢ a = b",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"id",
"Fin.val",
"Nat",
"_private.Mathlib.Data.Fin.Basic.0.Fin.cast_injective._simp_1_1",
"Fin",
"Eq"
... | [
"k l : ℕ\nh : k = l\na b : Fin k\nhab : Fin.cast h a = Fin.cast h b\n⊢ ↑a = ↑b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Card | {
"line": 357,
"column": 4
} | {
"line": 357,
"column": 16
} | {
"line": 357,
"column": 17
} | [
{
"pp": "case calc_1\nα : Type u_1\nβ : Type u_2\ns : Finset α\nt : Finset β\ni : (a : α) → a ∈ s → β\nhi : ∀ (a : α) (ha : a ∈ s), i a ha ∈ t\ni_inj : ∀ (a₁ : α) (ha₁ : a₁ ∈ s) (a₂ : α) (ha₂ : a₂ ∈ s), i a₁ ha₁ = i a₂ ha₂ → a₁ = a₂\ni_surj : ∀ b ∈ t, ∃ a, ∃ (ha : a ∈ s), i a ha = b\n⊢ Injective fun a ↦ i ↑a ⋯"... | [
"case calc_1\nα : Type u_1\nβ : Type u_2\ns : Finset α\nt : Finset β\ni : (a : α) → a ∈ s → β\nhi : ∀ (a : α) (ha : a ∈ s), i a ha ∈ t\ni_inj : ∀ (a₁ : α) (ha₁ : a₁ ∈ s) (a₂ : α) (ha₂ : a₂ ∈ s), i a₁ ha₁ = i a₂ ha₂ → a₁ = a₂\ni_surj : ∀ b ∈ t, ∃ a, ∃ (ha : a ∈ s), i a ha = b\nval✝ : α\nproperty✝ : val✝ ∈ s\n⊢ ∀ ⦃a₂... | intro ⟨_, _⟩ | Lean.Elab.Tactic.evalIntro | null |
Mathlib.Data.Finset.Card | {
"line": 358,
"column": 4
} | {
"line": 358,
"column": 15
} | {
"line": 358,
"column": 16
} | [
{
"pp": "case calc_1\nα : Type u_1\nβ : Type u_2\ns : Finset α\nt : Finset β\ni : (a : α) → a ∈ s → β\nhi : ∀ (a : α) (ha : a ∈ s), i a ha ∈ t\ni_inj : ∀ (a₁ : α) (ha₁ : a₁ ∈ s) (a₂ : α) (ha₂ : a₂ ∈ s), i a₁ ha₁ = i a₂ ha₂ → a₁ = a₂\ni_surj : ∀ b ∈ t, ∃ a, ∃ (ha : a ∈ s), i a ha = b\nval✝¹ : α\nproperty✝¹ : val... | [
"case calc_1\nα : Type u_1\nβ : Type u_2\ns : Finset α\nt : Finset β\ni : (a : α) → a ∈ s → β\nhi : ∀ (a : α) (ha : a ∈ s), i a ha ∈ t\ni_inj : ∀ (a₁ : α) (ha₁ : a₁ ∈ s) (a₂ : α) (ha₂ : a₂ ∈ s), i a₁ ha₁ = i a₂ ha₂ → a₁ = a₂\ni_surj : ∀ b ∈ t, ∃ a, ∃ (ha : a ∈ s), i a ha = b\nval✝¹ : α\nproperty✝¹ : val✝¹ ∈ s\nval✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Basic | {
"line": 544,
"column": 2
} | {
"line": 544,
"column": 23
} | {
"line": 544,
"column": 24
} | [
{
"pp": "n : ℕ\ni : Fin n\nh : ↑i + 1 < n\n⊢ ↑(i + 1) = ↑i + 1",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Fin.pos",
"Fin.neZero",
"Fin.mk",
"id",
"Fin.instOfNat",
"Nat.instMod",
"instHMod",
"instOfNatNa... | [
"n : ℕ\ni : Fin n\nh : ↑i + 1 < n\n⊢ (↑i + 1) % n = ↑i + 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Card | {
"line": 478,
"column": 42
} | {
"line": 478,
"column": 77
} | {
"line": 478,
"column": 78
} | [
{
"pp": "α : Type u_1\ns : Finset α\nn : ℕ\nf : ℕ → α\nhf : ∀ i < n, f i ∈ s\nf_inj : ∀ i < n, ∀ j < n, f i = f j → i = j\n⊢ Set.MapsTo f ↑(range n) ↑s",
"ppTerm": "?m.32",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"SetLike.mem_coe._simp_1",
"Preorder.toLT",
"Finset.coe_... | [
"α : Type u_1\ns : Finset α\nn : ℕ\nf : ℕ → α\nhf : ∀ i < n, f i ∈ s\nf_inj : ∀ i < n, ∀ j < n, f i = f j → i = j\n⊢ ∀ ⦃x : ℕ⦄, x < n → f x ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.OfFn | {
"line": 75,
"column": 25
} | {
"line": 75,
"column": 33
} | {
"line": 75,
"column": 33
} | [
{
"pp": "case succ\nα : Type u\nn m : ℕ\nIH : ∀ (f : Fin (m * n) → α), ofFn f = (ofFn fun i ↦ ofFn fun j ↦ f ⟨↑i * n + ↑j, ⋯⟩).flatten\nf : Fin ((m + 1) * n) → α\n⊢ ofFn f =\n ((ofFn fun i ↦ ofFn fun j ↦ f ⟨↑i.castSucc * n + ↑j, ⋯⟩).concat\n (ofFn fun j ↦ f ⟨↑(Fin.last m) * n + ↑j, ⋯⟩)).flatten",
... | [
"case succ\nα : Type u\nn m : ℕ\nIH : ∀ (f : Fin (m * n) → α), ofFn f = (ofFn fun i ↦ ofFn fun j ↦ f ⟨↑i * n + ↑j, ⋯⟩).flatten\nf : Fin ((m + 1) * n) → α\n⊢ (ofFn fun i ↦ f (Fin.cast ⋯ i)) =\n ((ofFn fun i ↦ ofFn fun j ↦ f ⟨↑i.castSucc * n + ↑j, ⋯⟩).concat\n (ofFn fun j ↦ f ⟨↑(Fin.last m) * n + ↑j, ⋯⟩)).f... | succ_mul | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Data.Finset.Card | {
"line": 530,
"column": 58
} | {
"line": 530,
"column": 74
} | {
"line": 530,
"column": 75
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Finset α\nt : Finset β\nf : (a : α) → a ∈ s → β\nhf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t\nhsurj : ∀ b ∈ t, ∃ a, ∃ (ha : a ∈ s), f a ha = b\nhst : #s ≤ #t\na₁ : α\nha₁ : a₁ ∈ s\na₂ : α\nha₂ : a₂ ∈ s\nha₁a₂ : f a₁ ha₁ = f a₂ ha₂\nf' : ↥s → β := fun a ↦ f ↑a ⋯\nx : β\nhx : ... | [
"α : Type u_1\nβ : Type u_2\ns : Finset α\nt : Finset β\nf : (a : α) → a ∈ s → β\nhf : ∀ (a : α) (ha : a ∈ s), f a ha ∈ t\nhsurj : ∀ b ∈ t, ∃ a, ∃ (ha : a ∈ s), f a ha = b\nhst : #s ≤ #t\na₁ : α\nha₁ : a₁ ∈ s\na₂ : α\nha₂ : a₂ ∈ s\nha₁a₂ : f a₁ ha₁ = f a₂ ha₂\nf' : ↥s → β := fun a ↦ f ↑a ⋯\nx : β\nhx : x ∈ ↑t\n⊢ ∃ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Card | {
"line": 611,
"column": 12
} | {
"line": 611,
"column": 41
} | {
"line": 611,
"column": 42
} | [
{
"pp": "α : Type u_1\ns t : Finset α\nh : #s < #t\n⊢ ∃ e ∈ t, e ∉ s",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ns t : Finset α\nh : #s < #t\n⊢ ∃ e ∈ t, e ∉ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.FinRange | {
"line": 34,
"column": 2
} | {
"line": 34,
"column": 13
} | {
"line": 34,
"column": 14
} | [
{
"pp": "k : ℕ\ni : Fin k\n⊢ idxOf i (finRange k) = ↑i",
"ppTerm": "?m.4",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"k : ℕ\ni : Fin k\n⊢ idxOf i (finRange k) = ↑i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.FinRange | {
"line": 54,
"column": 2
} | {
"line": 54,
"column": 52
} | {
"line": 55,
"column": 2
} | [
{
"pp": "α : Type u\nn : ℕ\nf : Fin n → α\n⊢ (ofFn f).Nodup → Function.Injective f",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"List.ofFn",
"Fin.consInduction",
"List.Nodup",
"Nat",
"Function.Injective",
"Fin"
],
"usedFVars": [
"α",
... | [
"case refine_1\nα : Type u\nn : ℕ\nf : Fin n → α\n⊢ (ofFn Fin.elim0).Nodup → Function.Injective Fin.elim0",
"case refine_2\nα : Type u\nn : ℕ\nf : Fin n → α\nn✝ : ℕ\nx₀ : α\nxs : Fin n✝ → α\nih : (ofFn xs).Nodup → Function.Injective xs\n⊢ (ofFn (Fin.cons x₀ xs)).Nodup → Function.Injective (Fin.cons x₀ xs)"
] | refine Fin.consInduction ?_ (fun x₀ xs ih => ?_) f | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 143,
"column": 36
} | {
"line": 143,
"column": 47
} | {
"line": 143,
"column": 48
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Sort u\nx₀ y₀ : α 0\nx y : (i : Fin n) → α i.succ\nh : cons x₀ x = cons y₀ y\ni : Fin n\n⊢ x i = y i",
"ppTerm": "?m.35",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\nα : Fin (n + 1) → Sort u\nx₀ y₀ : α 0\nx y : (i : Fin n) → α i.succ\nh : cons x₀ x = cons y₀ y\ni : Fin n\n⊢ x i = y i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Card | {
"line": 664,
"column": 2
} | {
"line": 664,
"column": 13
} | {
"line": 664,
"column": 14
} | [
{
"pp": "α : Type u_1\ns : Finset α\nn : ℕ\nhns : n ≤ #s\n⊢ ∃ t ⊆ s, #t = n",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ns : Finset α\nn : ℕ\nhns : n ≤ #s\n⊢ ∃ t ⊆ s, #t = n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Card | {
"line": 752,
"column": 2
} | {
"line": 752,
"column": 44
} | {
"line": 752,
"column": 45
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ns : Finset α\nf : α → β\nt : Finset β\ninst✝ : DecidableEq β\nhf : Set.InjOn f ↑s\nhf' : Set.MapsTo f ↑s ↑t\nh : #t = #s + 1\nthis : #(t \\ image f s) = 1\n⊢ ∃! x, x ∈ t ∧ x ∉ image f s",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
... | [
"α : Type u_1\nβ : Type u_2\ns : Finset α\nf : α → β\nt : Finset β\ninst✝ : DecidableEq β\nhf : Set.InjOn f ↑s\nhf' : Set.MapsTo f ↑s ↑t\nh : #t = #s + 1\nthis : #(t \\ image f s) = 1\n⊢ ∃! x, x ∈ t ∧ ∀ x_1 ∈ s, ¬f x_1 = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.SuccPred | {
"line": 469,
"column": 60
} | {
"line": 469,
"column": 86
} | {
"line": 469,
"column": 87
} | [
{
"pp": "n m : ℕ\na b : Fin m\nha : ↑a < n\nh : b ≤ a\n⊢ b.castLT ⋯ ≤ a.castLT ha",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.Data.Fin.SuccPred.0.Fin.val_sub_castLT_of_le._simp_1_1",
"lt_of_le_of_lt",
"id",
"LE.le",
"instL... | [
"n m : ℕ\na b : Fin m\nha : ↑a < n\nh : b ≤ a\n⊢ ↑b ≤ ↑a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Card | {
"line": 805,
"column": 4
} | {
"line": 806,
"column": 53
} | {
"line": 807,
"column": 4
} | [
{
"pp": "α : Type u_1\ns : Finset α\n⊢ 2 < #s ↔ ∃ a b c, a ∈ s ∧ b ∈ s ∧ c ∈ s ∧ a ≠ b ∧ a ≠ c ∧ b ≠ c",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"_private.Mathlib.Data.Finset.Card.0.Finset.two_lt_card_iff._simp_1_3",
"congrArg",
"Finset",
"Part... | [
"α : Type u_1\ns : Finset α\n⊢ (∃ b b_1 b_2, ∃ a ⊆ s, b ≠ b_1 ∧ b ≠ b_2 ∧ b_1 ≠ b_2 ∧ a = {b, b_1, b_2}) ↔\n ∃ a b c, a ∈ s ∧ b ∈ s ∧ c ∈ s ∧ a ≠ b ∧ a ≠ c ∧ b ≠ c"
] | simp_rw [lt_iff_add_one_le, le_card_iff_exists_subset_card, reduceAdd, card_eq_three,
← exists_and_left, exists_comm (α := Finset α)] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Data.Fin.SuccPred | {
"line": 660,
"column": 4
} | {
"line": 660,
"column": 48
} | {
"line": 660,
"column": 49
} | [
{
"pp": "case pos\nn : ℕ\ninst✝ : NeZero n\np : Fin (n + 1)\ni : Fin n\nh : 0 < i\nH : i.castSucc < p\n⊢ 0 < p.succAbove i",
"ppTerm": "?pos✝",
"assigned": true,
"usedConstants": [
"Fin.succAbove",
"Eq.mpr",
"instNeZeroNatHAdd_1",
"congrArg",
"Fin.castSucc_pos_iff._simp... | [
"case pos\nn : ℕ\ninst✝ : NeZero n\np : Fin (n + 1)\ni : Fin n\nh : 0 < i\nH : i.castSucc < p\n⊢ 0 < i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.SuccPred | {
"line": 670,
"column": 38
} | {
"line": 670,
"column": 91
} | {
"line": 672,
"column": 0
} | [
{
"pp": "n : ℕ\nx : Fin n\ny : Fin (n + 1)\nh : y ≤ x.castSucc\nh' : y.succAbove x ≠ 0\n⊢ (y.succAbove x).pred h' = x",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Fin.succAbove_of_le_castSucc",
"Fin.succAbove",
"instNeZeroNatHAdd_1",
"Fin.succ",
"Fin.pred"... | [] | simp only [succAbove_of_le_castSucc _ _ h, pred_succ] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Fin.SuccPred | {
"line": 670,
"column": 38
} | {
"line": 670,
"column": 91
} | {
"line": 672,
"column": 0
} | [
{
"pp": "n : ℕ\nx : Fin n\ny : Fin (n + 1)\nh : y ≤ x.castSucc\nh' : y.succAbove x ≠ 0\n⊢ (y.succAbove x).pred h' = x",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Fin.succAbove_of_le_castSucc",
"Fin.succAbove",
"instNeZeroNatHAdd_1",
"Fin.succ",
"Fin.pred"... | [] | simp only [succAbove_of_le_castSucc _ _ h, pred_succ] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fin.SuccPred | {
"line": 670,
"column": 38
} | {
"line": 670,
"column": 91
} | {
"line": 672,
"column": 0
} | [
{
"pp": "n : ℕ\nx : Fin n\ny : Fin (n + 1)\nh : y ≤ x.castSucc\nh' : y.succAbove x ≠ 0\n⊢ (y.succAbove x).pred h' = x",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Fin.succAbove_of_le_castSucc",
"Fin.succAbove",
"instNeZeroNatHAdd_1",
"Fin.succ",
"Fin.pred"... | [] | simp only [succAbove_of_le_castSucc _ _ h, pred_succ] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fin.SuccPred | {
"line": 688,
"column": 2
} | {
"line": 688,
"column": 31
} | {
"line": 688,
"column": 32
} | [
{
"pp": "n : ℕ\nx✝¹ x✝ : Fin (n + 1)\nh : x✝¹.succAbove = x✝.succAbove\n⊢ x✝¹ = x✝",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\nx✝¹ x✝ : Fin (n + 1)\nh : x✝¹.succAbove = x✝.succAbove\n⊢ x✝¹ = x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.Card | {
"line": 262,
"column": 4
} | {
"line": 262,
"column": 15
} | {
"line": 262,
"column": 16
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝² : Fintype α\ninst✝¹ : Fintype β\ninst✝ : DecidableEq β\nf : α → β\nhf : Injective f\nh : card β = card α + 1\n⊢ ∃! x, x ∉ image f univ",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"not_exists._simp_1",
"Finset.univ"... | [
"α : Type u_1\nβ : Type u_2\ninst✝² : Fintype α\ninst✝¹ : Fintype β\ninst✝ : DecidableEq β\nf : α → β\nhf : Injective f\nh : card β = card α + 1\n⊢ ∃! x, ∀ (x_1 : α), ¬f x_1 = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.Card | {
"line": 275,
"column": 83
} | {
"line": 275,
"column": 94
} | {
"line": 275,
"column": 95
} | [
{
"pp": "α : Type u_4\nβ : Type u_5\nf : α → β\ninst✝¹ : Fintype α\ninst✝ : Fintype ↑(Set.range f)\nx✝ : ↑(Set.range f)\nval✝ : β\na : α\nha : f a = val✝\n⊢ (fun a ↦ ⟨f a, ⋯⟩) a = ⟨val✝, ⋯⟩",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Membership.mem",
"Exist... | [
"α : Type u_4\nβ : Type u_5\nf : α → β\ninst✝¹ : Fintype α\ninst✝ : Fintype ↑(Set.range f)\nx✝ : ↑(Set.range f)\nval✝ : β\na : α\nha : f a = val✝\n⊢ f a = val✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.Card | {
"line": 905,
"column": 88
} | {
"line": 906,
"column": 30
} | {
"line": 908,
"column": 0
} | [
{
"pp": "α : Type u_1\nn : ℕ\np : Finset α → Sort u_4\nH : (t₁ : Finset α) → ({t₂ : Finset α} → #t₂ ≤ n → t₁ ⊂ t₂ → p t₂) → #t₁ ≤ n → p t₁\ns : Finset α\n⊢ strongDownwardInduction H s = H s fun {t} ht x ↦ strongDownwardInduction H t ht",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
... | [] | by
rw [strongDownwardInduction] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.List.Duplicate | {
"line": 80,
"column": 4
} | {
"line": 80,
"column": 23
} | {
"line": 81,
"column": 4
} | [
{
"pp": "case refine_1\nα : Type u_1\nl : List α\nx y : α\nh : x ∈+ y :: l\n⊢ y = x ∧ x ∈ l ∨ x ∈+ l",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"List.Duplicate.cons_duplicate",
"List.Duplicate.cons_mem",
"HEq.refl",
"Membership.mem",
"List.cons",
... | [
"case refine_1.cons_mem\nα : Type u_1\nl : List α\nx : α\nhm : x ∈ l\n⊢ x = x ∧ x ∈ l ∨ x ∈+ l",
"case refine_1.cons_duplicate\nα : Type u_1\nl : List α\nx y : α\nhm : x ∈+ l\n⊢ y = x ∧ x ∈ l ∨ x ∈+ l"
] | obtain hm | hm := h | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Data.List.Duplicate | {
"line": 88,
"column": 2
} | {
"line": 88,
"column": 43
} | {
"line": 88,
"column": 44
} | [
{
"pp": "α : Type u_1\nl : List α\nx y : α\nh : x ∈+ y :: l\nhx : x ≠ y\n⊢ x ∈+ l",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nl : List α\nx y : α\nh : x ∈+ y :: l\nhx : x ≠ y\n⊢ x ∈+ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.SuccPred | {
"line": 740,
"column": 2
} | {
"line": 741,
"column": 9
} | {
"line": 741,
"column": 10
} | [
{
"pp": "n : ℕ\n⊢ succAbove 1 1 = 2",
"ppTerm": "?m.21",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\n⊢ succAbove 1 1 = 2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.Card | {
"line": 350,
"column": 4
} | {
"line": 350,
"column": 31
} | {
"line": 350,
"column": 32
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : Finite α\nf : α → β\ne : α ≃ β\nthis : Injective (⇑e.symm ∘ f) ↔ Surjective (⇑e.symm ∘ f)\nhinj : Injective f\n⊢ Surjective f",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\ninst✝ : Finite α\nf : α → β\ne : α ≃ β\nthis : Injective (⇑e.symm ∘ f) ↔ Surjective (⇑e.symm ∘ f)\nhinj : Injective f\n⊢ Surjective f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.Card | {
"line": 352,
"column": 4
} | {
"line": 352,
"column": 31
} | {
"line": 352,
"column": 32
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝ : Finite α\nf : α → β\ne : α ≃ β\nthis : Injective (⇑e.symm ∘ f) ↔ Surjective (⇑e.symm ∘ f)\nhsurj : Surjective f\n⊢ Injective f",
"ppTerm": "?m.30",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nβ : Type u_2\ninst✝ : Finite α\nf : α → β\ne : α ≃ β\nthis : Injective (⇑e.symm ∘ f) ↔ Surjective (⇑e.symm ∘ f)\nhsurj : Surjective f\n⊢ Injective f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.Card | {
"line": 377,
"column": 30
} | {
"line": 377,
"column": 41
} | {
"line": 377,
"column": 42
} | [
{
"pp": "α : Type u_1\ninst✝ : Fintype α\nn : ℕ\ns : Finset α\nhsn : #s ≤ n\nhnα : n ≤ Fintype.card α\n⊢ ∃ t, s ⊆ t ∧ #t = n",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ninst✝ : Fintype α\nn : ℕ\ns : Finset α\nhsn : #s ≤ n\nhnα : n ≤ Fintype.card α\n⊢ ∃ t, s ⊆ t ∧ #t = n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 576,
"column": 21
} | {
"line": 576,
"column": 32
} | {
"line": 576,
"column": 33
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Sort u_1\nx y : (i : Fin n) → α i.castSucc\nxₙ yₙ : α (last n)\nh : snoc x xₙ = snoc y yₙ\ni : Fin n\n⊢ x i = y i",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\nα : Fin (n + 1) → Sort u_1\nx y : (i : Fin n) → α i.castSucc\nxₙ yₙ : α (last n)\nh : snoc x xₙ = snoc y yₙ\ni : Fin n\n⊢ x i = y i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 576,
"column": 62
} | {
"line": 576,
"column": 73
} | {
"line": 576,
"column": 74
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Sort u_1\nx y : (i : Fin n) → α i.castSucc\nxₙ yₙ : α (last n)\nh : snoc x xₙ = snoc y yₙ\n⊢ xₙ = yₙ",
"ppTerm": "?m.27",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\nα : Fin (n + 1) → Sort u_1\nx y : (i : Fin n) → α i.castSucc\nxₙ yₙ : α (last n)\nh : snoc x xₙ = snoc y yₙ\n⊢ xₙ = yₙ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Duplicate | {
"line": 135,
"column": 23
} | {
"line": 135,
"column": 58
} | {
"line": 135,
"column": 59
} | [
{
"pp": "α : Type u_1\nl✝ : List α\nx✝ : α\ninst✝ : DecidableEq α\nx y : α\nl : List α\nh : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)\nhx : ¬(y = x ∧ x ∈ l)\n⊢ failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)",
... | [
"α : Type u_1\nl✝ : List α\nx✝ : α\ninst✝ : DecidableEq α\nx y : α\nl : List α\nh : failed to pretty print expression (use 'set_option pp.rawOnError true' for raw representation)\nhx : ¬(y = x ∧ x ∈ l)\n⊢ y = x → ¬x ∈ l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.Card | {
"line": 530,
"column": 2
} | {
"line": 530,
"column": 37
} | {
"line": 530,
"column": 38
} | [
{
"pp": "n : ℕ\ns : Finset (Fin n)\n⊢ #s ≤ n",
"ppTerm": "?m.4",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\ns : Finset (Fin n)\n⊢ #s ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.NodupEquivFin | {
"line": 117,
"column": 34
} | {
"line": 117,
"column": 45
} | {
"line": 117,
"column": 46
} | [
{
"pp": "α : Type u_1\nhd : α\ntl : List α\nIH : ∀ {l' : List α} (f : ℕ ↪o ℕ), (∀ (ix : ℕ), tl[ix]? = l'[f ix]?) → tl <+ l'\nl' : List α\nf : ℕ ↪o ℕ\nhf : ∀ (ix : ℕ), (hd :: tl)[ix]? = l'[f ix]?\n⊢ some hd = l'[f 0]?",
"ppTerm": "?m.45",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"α : Type u_1\nhd : α\ntl : List α\nIH : ∀ {l' : List α} (f : ℕ ↪o ℕ), (∀ (ix : ℕ), tl[ix]? = l'[f ix]?) → tl <+ l'\nl' : List α\nf : ℕ ↪o ℕ\nhf : ∀ (ix : ℕ), (hd :: tl)[ix]? = l'[f ix]?\n⊢ some hd = l'[f 0]?"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 741,
"column": 6
} | {
"line": 741,
"column": 75
} | {
"line": 741,
"column": 76
} | [
{
"pp": "case cast.cast\nn : ℕ\nα : Type u_2\nx₀ : α\nx : Fin n → α\nhx : Injective x\nhx₀ : ¬x₀ ∈ Set.range x\ni j : Fin n\nh : snoc x x₀ i.castSucc = snoc x x₀ j.castSucc\n⊢ i.castSucc = j.castSucc",
"ppTerm": "?cast.cast",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Function.Injec... | [
"case cast.cast\nn : ℕ\nα : Type u_2\nx₀ : α\nx : Fin n → α\nhx : Injective x\nhx₀ : ¬x₀ ∈ Set.range x\ni j : Fin n\nh : snoc x x₀ i.castSucc = snoc x x₀ j.castSucc\n⊢ x i = x j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 757,
"column": 4
} | {
"line": 757,
"column": 31
} | {
"line": 757,
"column": 32
} | [
{
"pp": "case refine_1\nn : ℕ\nα : Type u_2\nx₀ : α\nx : Fin n → α\nh : Injective (snoc x x₀)\n⊢ Injective x",
"ppTerm": "?refine_1",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"case refine_1\nn : ℕ\nα : Type u_2\nx₀ : α\nx : Fin n → α\nh : Injective (snoc x x₀)\n⊢ Injective x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.EquivFin | {
"line": 457,
"column": 14
} | {
"line": 457,
"column": 46
} | {
"line": 457,
"column": 47
} | [
{
"pp": "α✝ : Type u_1\nβ : Type u_2\nγ : Type u_3\nα : Type u_4\ninst✝ : Infinite α\nx : α\n_hx : x ∉ ∅\ny : α\nhy : y ∉ {x}\n⊢ y ≠ x",
"ppTerm": "?m.25",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α✝ : Type u_1\nβ : Type u_2\nγ : Type u_3\nα : Type u_4\ninst✝ : Infinite α\nx : α\n_hx : x ∉ ∅\ny : α\nhy : y ∉ {x}\n⊢ y ≠ x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 110,
"column": 6
} | {
"line": 110,
"column": 21
} | {
"line": 110,
"column": 22
} | [
{
"pp": "case neg\nα : Type u_1\nr : α → α → Prop\ninst✝ : DecidableRel r\na b : α\nl : List α\nh : ¬r a b\n⊢ orderedInsert r a (b :: l) ~ a :: b :: l",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.orderedInsert_cons",
"eq_false",
"congrArg",
... | [
"case neg\nα : Type u_1\nr : α → α → Prop\ninst✝ : DecidableRel r\na b : α\nl : List α\nh : ¬r a b\n⊢ b :: orderedInsert r a l ~ a :: b :: l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.NodupEquivFin | {
"line": 149,
"column": 6
} | {
"line": 149,
"column": 17
} | {
"line": 149,
"column": 18
} | [
{
"pp": "case mp.cons\nα : Type u_1\nl l' l₁✝ l₂✝ : List α\na✝¹ : α\na✝ : l₁✝ <+ l₂✝\nf : ℕ ↪o ℕ\nhf : ∀ (ix : ℕ), l₁✝[ix]? = l₂✝[f ix]?\n⊢ ∀ (ix : ℕ), l₁✝[ix]? = (a✝¹ :: l₂✝)[(RelEmbedding.trans f (OrderEmbedding.ofStrictMono (fun x ↦ x + 1) ⋯)) ix]?",
"ppTerm": "?mp.cons",
"assigned": true,
"usedC... | [
"case mp.cons\nα : Type u_1\nl l' l₁✝ l₂✝ : List α\na✝¹ : α\na✝ : l₁✝ <+ l₂✝\nf : ℕ ↪o ℕ\nhf : ∀ (ix : ℕ), l₁✝[ix]? = l₂✝[f ix]?\n⊢ ∀ (ix : ℕ), l₁✝[ix]? = l₂✝[f ix]?"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fintype.EquivFin | {
"line": 558,
"column": 38
} | {
"line": 558,
"column": 63
} | {
"line": 558,
"column": 63
} | [
{
"pp": "α : Type u_4\ninst✝ : Infinite α\nn : ℕ\n⊢ #(map (natEmbedding α) (range n)) = n",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset.card_map",
"Finset.card_range",
"Finset.map",
"id",
"Finset.range",
"Nat",
... | [] | rw [card_map, card_range] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Fintype.EquivFin | {
"line": 558,
"column": 38
} | {
"line": 558,
"column": 63
} | {
"line": 558,
"column": 63
} | [
{
"pp": "α : Type u_4\ninst✝ : Infinite α\nn : ℕ\n⊢ #(map (natEmbedding α) (range n)) = n",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset.card_map",
"Finset.card_range",
"Finset.map",
"id",
"Finset.range",
"Nat",
... | [] | rw [card_map, card_range] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Fintype.EquivFin | {
"line": 558,
"column": 38
} | {
"line": 558,
"column": 63
} | {
"line": 558,
"column": 63
} | [
{
"pp": "α : Type u_4\ninst✝ : Infinite α\nn : ℕ\n⊢ #(map (natEmbedding α) (range n)) = n",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset.card_map",
"Finset.card_range",
"Finset.map",
"id",
"Finset.range",
"Nat",
... | [] | rw [card_map, card_range] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 893,
"column": 2
} | {
"line": 893,
"column": 23
} | {
"line": 893,
"column": 24
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Sort u_1\np : Fin (n + 1)\na : α p\nf : (i : Fin n) → α (p.succAbove i)\ng : (j : Fin (n + 1)) → α j\n⊢ g = p.insertNth a f ↔ g p = a ∧ p.removeNth g = f",
"ppTerm": "?m.23",
"assigned": true,
"usedConstants": [
"Fin.succAbove",
"Eq.mpr",
"congrArg... | [
"n : ℕ\nα : Fin (n + 1) → Sort u_1\np : Fin (n + 1)\na : α p\nf : (i : Fin n) → α (p.succAbove i)\ng : (j : Fin (n + 1)) → α j\n⊢ g = p.insertNth a f ↔ a = g p ∧ f = p.removeNth g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 898,
"column": 6
} | {
"line": 898,
"column": 17
} | {
"line": 898,
"column": 18
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Sort u_1\np : Fin (n + 1)\nxₚ yₚ : α p\nx y : (j : Fin n) → α (p.succAbove j)\nh : p.insertNth xₚ x = p.insertNth yₚ y\n⊢ xₚ = yₚ",
"ppTerm": "?m.23",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\nα : Fin (n + 1) → Sort u_1\np : Fin (n + 1)\nxₚ yₚ : α p\nx y : (j : Fin n) → α (p.succAbove j)\nh : p.insertNth xₚ x = p.insertNth yₚ y\n⊢ xₚ = yₚ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.NodupEquivFin | {
"line": 157,
"column": 10
} | {
"line": 157,
"column": 21
} | {
"line": 157,
"column": 22
} | [
{
"pp": "case mp.cons_cons.refine_2.succ\nα : Type u_1\nl l' l₁✝ l₂✝ : List α\na✝¹ : α\na✝ : l₁✝ <+ l₂✝\nf : ℕ ↪o ℕ\nhf : ∀ (ix : ℕ), l₁✝[ix]? = l₂✝[f ix]?\nn✝ : ℕ\n⊢ (a✝¹ :: l₁✝)[n✝ + 1]? =\n (a✝¹ :: l₂✝)[(OrderEmbedding.ofMapLEIff (fun ix ↦ if ix = 0 then 0 else (f ix.pred).succ) ⋯) (n✝ + 1)]?",
"ppTer... | [
"case mp.cons_cons.refine_2.succ\nα : Type u_1\nl l' l₁✝ l₂✝ : List α\na✝¹ : α\na✝ : l₁✝ <+ l₂✝\nf : ℕ ↪o ℕ\nhf : ∀ (ix : ℕ), l₁✝[ix]? = l₂✝[f ix]?\nn✝ : ℕ\n⊢ l₁✝[n✝]? = l₂✝[f n✝]?"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 898,
"column": 51
} | {
"line": 898,
"column": 62
} | {
"line": 898,
"column": 63
} | [
{
"pp": "n : ℕ\nα : Fin (n + 1) → Sort u_1\np : Fin (n + 1)\nxₚ yₚ : α p\nx y : (j : Fin n) → α (p.succAbove j)\nh : p.insertNth xₚ x = p.insertNth yₚ y\ni : Fin n\n⊢ x i = y i",
"ppTerm": "?m.29",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"n : ℕ\nα : Fin (n + 1) → Sort u_1\np : Fin (n + 1)\nxₚ yₚ : α p\nx y : (j : Fin n) → α (p.succAbove j)\nh : p.insertNth xₚ x = p.insertNth yₚ y\ni : Fin n\n⊢ x i = y i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 147,
"column": 6
} | {
"line": 147,
"column": 42
} | {
"line": 147,
"column": 43
} | [
{
"pp": "case cons.hl₁\nα : Type u_1\nβ : Type u_2\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : DecidableRel r\ninst✝ : DecidableRel s\nf : α → β\nx : α\nxs : List α\nih :\n (∀ (a : α), a ∈ xs → ∀ (b : α), b ∈ xs → (r a b ↔ s (f a) (f b))) →\n map f (insertionSort r xs) = insertionSort s (map f xs)\nhl :\n... | [
"case cons.hl₁\nα : Type u_1\nβ : Type u_2\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : DecidableRel r\ninst✝ : DecidableRel s\nf : α → β\nx : α\nxs : List α\nih :\n (∀ (a : α), a ∈ xs → ∀ (b : α), b ∈ xs → (r a b ↔ s (f a) (f b))) →\n map f (insertionSort r xs) = insertionSort s (map f xs)\nhl :\n ((r x x ↔ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.NodupEquivFin | {
"line": 182,
"column": 6
} | {
"line": 182,
"column": 72
} | {
"line": 182,
"column": 73
} | [
{
"pp": "case mp.refine_2\nα : Type u_1\nl l' : List α\nf : ℕ ↪o ℕ\nhf : ∀ (ix : ℕ), l[ix]? = l'[f ix]?\nh : ∀ {i : ℕ}, i < l.length → f i < l'.length\ni : Fin l.length\n⊢ some (l.get i) = some (l'.get ((OrderEmbedding.ofMapLEIff (fun ix ↦ ⟨f ↑ix, ⋯⟩) ⋯) i))",
"ppTerm": "?mp.refine_2",
"assigned": true,... | [
"case mp.refine_2\nα : Type u_1\nl l' : List α\nf : ℕ ↪o ℕ\nhf : ∀ (ix : ℕ), l[ix]? = l'[f ix]?\nh : ∀ {i : ℕ}, i < l.length → f i < l'.length\ni : Fin l.length\n⊢ l[↑i] = l'[f ↑i]"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 148,
"column": 6
} | {
"line": 148,
"column": 42
} | {
"line": 148,
"column": 43
} | [
{
"pp": "case cons.hl₂\nα : Type u_1\nβ : Type u_2\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : DecidableRel r\ninst✝ : DecidableRel s\nf : α → β\nx : α\nxs : List α\nih :\n (∀ (a : α), a ∈ xs → ∀ (b : α), b ∈ xs → (r a b ↔ s (f a) (f b))) →\n map f (insertionSort r xs) = insertionSort s (map f xs)\nhl :\n... | [
"case cons.hl₂\nα : Type u_1\nβ : Type u_2\nr : α → α → Prop\ns : β → β → Prop\ninst✝¹ : DecidableRel r\ninst✝ : DecidableRel s\nf : α → β\nx : α\nxs : List α\nih :\n (∀ (a : α), a ∈ xs → ∀ (b : α), b ∈ xs → (r a b ↔ s (f a) (f b))) →\n map f (insertionSort r xs) = insertionSort s (map f xs)\nhl :\n ((r x x ↔ ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 974,
"column": 2
} | {
"line": 974,
"column": 13
} | {
"line": 974,
"column": 14
} | [
{
"pp": "α : Sort u_3\nn : ℕ\na : α\nf : Fin n → α\ni : Fin (n + 1)\n⊢ cons a f i.rev = snoc (f ∘ rev) a i",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Sort u_3\nn : ℕ\na : α\nf : Fin n → α\ni : Fin (n + 1)\n⊢ cons a f i.rev = snoc (f ∘ rev) a i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 982,
"column": 2
} | {
"line": 982,
"column": 13
} | {
"line": 982,
"column": 14
} | [
{
"pp": "α : Sort u_3\nn : ℕ\na : α\nf : Fin n → α\ni : Fin (n + 1)\n⊢ snoc f a i.rev = cons a (f ∘ rev) i",
"ppTerm": "?m.26",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Sort u_3\nn : ℕ\na : α\nf : Fin n → α\ni : Fin (n + 1)\n⊢ snoc f a i.rev = cons a (f ∘ rev) i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.NodupEquivFin | {
"line": 194,
"column": 8
} | {
"line": 194,
"column": 19
} | {
"line": 194,
"column": 20
} | [
{
"pp": "case neg\nα : Type u_1\nl l' : List α\nf : Fin l.length ↪o Fin l'.length\nhf : ∀ (ix : Fin l.length), l.get ix = l'.get (f ix)\ni j : ℕ\nh : i < j\nhi : ¬i < l.length\nhj : ¬j < l.length\n⊢ i + l'.length < j + l'.length",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Eq.mpr... | [
"case neg\nα : Type u_1\nl l' : List α\nf : Fin l.length ↪o Fin l'.length\nhf : ∀ (ix : Fin l.length), l.get ix = l'.get (f ix)\ni j : ℕ\nh : i < j\nhi : ¬i < l.length\nhj : ¬j < l.length\n⊢ i < j"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.NodupEquivFin | {
"line": 221,
"column": 10
} | {
"line": 221,
"column": 21
} | {
"line": 221,
"column": 22
} | [
{
"pp": "case mpr.refine_2.zero\nα : Type u_1\nl : List α\nx : α\nn m : Fin l.length\nhnm : n < m\nh : x = l.get n\nh' : x = l.get m\nhi : 0 < (replicate 2 x).length\n⊢ (replicate 2 x).get ⟨0, hi⟩ = l.get ((OrderEmbedding.ofStrictMono (fun i ↦ if ↑i = 0 then n else m) ⋯) ⟨0, hi⟩)",
"ppTerm": "?mpr.refine_2.... | [
"case mpr.refine_2.zero\nα : Type u_1\nl : List α\nx : α\nn m : Fin l.length\nhnm : n < m\nh : x = l.get n\nh' : x = l.get m\nhi : 0 < (replicate 2 x).length\n⊢ x = l[↑n]"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.NodupEquivFin | {
"line": 222,
"column": 10
} | {
"line": 222,
"column": 21
} | {
"line": 222,
"column": 22
} | [
{
"pp": "case mpr.refine_2.succ\nα : Type u_1\nl : List α\nx : α\nn m : Fin l.length\nhnm : n < m\nh : x = l.get n\nh' : x = l.get m\nn✝ : ℕ\nhi : n✝ + 1 < (replicate 2 x).length\n⊢ (replicate 2 x).get ⟨n✝ + 1, hi⟩ =\n l.get ((OrderEmbedding.ofStrictMono (fun i ↦ if ↑i = 0 then n else m) ⋯) ⟨n✝ + 1, hi⟩)",
... | [
"case mpr.refine_2.succ\nα : Type u_1\nl : List α\nx : α\nn m : Fin l.length\nhnm : n < m\nh : x = l.get n\nh' : x = l.get m\nn✝ : ℕ\nhi : n✝ + 1 < (replicate 2 x).length\n⊢ x = l[↑m]"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 333,
"column": 2
} | {
"line": 333,
"column": 13
} | {
"line": 333,
"column": 14
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\n⊢ Pairwise r (l.merge l' fun x1 x2 ↦ decide (r x1 x2))",
"ppTerm": "?m.12",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
... | [
"α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\n⊢ Pairwise r (l.merge l' fun x1 x2 ↦ decide (r x1 x2))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 334,
"column": 27
} | {
"line": 334,
"column": 38
} | {
"line": 334,
"column": 39
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\na b c : α\nh₁ : decide (r a b) = true\nh₂ : decide (r b c) = true\n⊢ decide (r a c) = true",
"ppTerm": "?m.21",
"assigned": true,
"usedCon... | [
"α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\na b c : α\nh₁ : decide (r a b) = true\nh₂ : decide (r b c) = true\n⊢ r a c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 334,
"column": 56
} | {
"line": 334,
"column": 67
} | {
"line": 334,
"column": 68
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\na b c : α\nh₁ : decide (r a b) = true\nh₂ : decide (r b c) = true\n⊢ r a ?m.42",
"ppTerm": "?m.45",
"assigned": false,
"usedConstants": []... | [
"α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\na b c : α\nh₁ : decide (r a b) = true\nh₂ : decide (r b c) = true\n⊢ r a ?m.42"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 334,
"column": 76
} | {
"line": 334,
"column": 87
} | {
"line": 334,
"column": 88
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\na b c : α\nh₁ : decide (r a b) = true\nh₂ : decide (r b c) = true\n⊢ r b c",
"ppTerm": "?m.46",
"assigned": false,
"usedConstants": [],
... | [
"α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\na b c : α\nh₁ : decide (r a b) = true\nh₂ : decide (r b c) = true\n⊢ r b c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 335,
"column": 19
} | {
"line": 335,
"column": 30
} | {
"line": 335,
"column": 31
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\na b : α\n⊢ (decide (r a b) || decide (r b a)) = true",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"cong... | [
"α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\na b : α\n⊢ r a b ∨ r b a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 336,
"column": 13
} | {
"line": 336,
"column": 24
} | {
"line": 336,
"column": 25
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\n⊢ Pairwise (fun a b ↦ decide (r a b) = true) l",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.Pairw... | [
"α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\n⊢ Pairwise (fun a b ↦ r a b) l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 336,
"column": 32
} | {
"line": 336,
"column": 43
} | {
"line": 336,
"column": 44
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\n⊢ Pairwise (fun a b ↦ decide (r a b) = true) l'",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"List.Pair... | [
"α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl l' : List α\nh : Pairwise r l\nh' : Pairwise r l'\n⊢ Pairwise (fun a b ↦ r a b) l'"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 344,
"column": 2
} | {
"line": 344,
"column": 13
} | {
"line": 344,
"column": 14
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl : List α\n⊢ Pairwise r (l.mergeSort fun x1 x2 ↦ decide (r x1 x2))",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl : List α\n⊢ Pairwise r (l.mergeSort fun x1 x2 ↦ decide (r x1 x2))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 345,
"column": 21
} | {
"line": 345,
"column": 32
} | {
"line": 345,
"column": 33
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl : List α\nx✝² x✝¹ x✝ : α\n⊢ decide (r x✝² x✝¹) = true → decide (r x✝¹ x✝) = true → decide (r x✝² x✝) = true",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"... | [
"α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl : List α\nx✝² x✝¹ x✝ : α\n⊢ r x✝² x✝¹ → r x✝¹ x✝ → r x✝² x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 346,
"column": 8
} | {
"line": 346,
"column": 19
} | {
"line": 346,
"column": 20
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl : List α\n⊢ ∀ (a b : α), (decide (r a b) || decide (r b a)) = true",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"id",
"Bool.true",... | [
"α : Type u_1\nr : α → α → Prop\ninst✝² : DecidableRel r\ninst✝¹ : Std.Total r\ninst✝ : IsTrans α r\nl : List α\n⊢ ∀ (a b : α), r a b ∨ r b a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 694,
"column": 79
} | {
"line": 694,
"column": 90
} | {
"line": 694,
"column": 91
} | [
{
"pp": "α : Type u_1\ninst✝ : PartialOrder α\nl₁ l₂ : List α\nh : ∀ (a : α), a ∈ l₁ ↔ a ∈ l₂\nhl₁ : l₁.SortedLT\nhl₂ : l₂.SortedGT\n⊢ ∀ (a : α), a ∈ l₁ ↔ a ∈ l₂.reverse",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"List.mem_reverse._simp_1",
"Eq.mpr",
"congrArg",
... | [
"α : Type u_1\ninst✝ : PartialOrder α\nl₁ l₂ : List α\nh : ∀ (a : α), a ∈ l₁ ↔ a ∈ l₂\nhl₁ : l₁.SortedLT\nhl₂ : l₂.SortedGT\n⊢ ∀ (a : α), a ∈ l₁ ↔ a ∈ l₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sort | {
"line": 699,
"column": 36
} | {
"line": 699,
"column": 47
} | {
"line": 699,
"column": 48
} | [
{
"pp": "α : Type u_1\ninst✝ : PartialOrder α\nl₁ l₂ : List α\nh : ∀ (a : α), a ∈ l₁ ↔ a ∈ l₂\nhl₁ : l₁.SortedGT\nhl₂ : l₂.SortedLT\n⊢ ∀ (a : α), a ∈ l₁ ↔ a ∈ l₂.reverse",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"List.mem_reverse._simp_1",
"Eq.mpr",
"congrArg",
... | [
"α : Type u_1\ninst✝ : PartialOrder α\nl₁ l₂ : List α\nh : ∀ (a : α), a ∈ l₁ ↔ a ∈ l₂\nhl₁ : l₁.SortedGT\nhl₂ : l₂.SortedLT\n⊢ ∀ (a : α), a ∈ l₁ ↔ a ∈ l₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Basic | {
"line": 339,
"column": 2
} | {
"line": 339,
"column": 31
} | {
"line": 339,
"column": 32
} | [
{
"pp": "α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nn : ℕ\n⊢ Fintype ↑{i | i ≤ n}",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nβ : Type v\nι : Sort w\nγ : Type x\nn : ℕ\n⊢ Fintype ↑{i | i ≤ n}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Basic | {
"line": 372,
"column": 16
} | {
"line": 372,
"column": 27
} | {
"line": 372,
"column": 28
} | [
{
"pp": "α : Type u\np : Finset α → Prop\nh : ∀ (s : Set α) (hs : s.Finite), p hs.toFinset\ns : Finset α\n⊢ p s",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\np : Finset α → Prop\nh : ∀ (s : Set α) (hs : s.Finite), p hs.toFinset\ns : Finset α\n⊢ p s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Basic | {
"line": 686,
"column": 2
} | {
"line": 686,
"column": 31
} | {
"line": 686,
"column": 32
} | [
{
"pp": "α : Type u\nβ : Type v\nf : α → β\nhf : Injective f\n⊢ (range f).Finite ↔ Finite α",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nβ : Type v\nf : α → β\nhf : Injective f\n⊢ (range f).Finite ↔ Finite α"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Basic | {
"line": 724,
"column": 22
} | {
"line": 724,
"column": 33
} | {
"line": 724,
"column": 34
} | [
{
"pp": "case cons\nα : Type u\nmotive : (s : Set α) → s.Finite → Prop\nempty : motive ∅ ⋯\ninsert : ∀ {a : α} {s : Set α}, a ∉ s → ∀ (hs : s.Finite), motive s hs → motive (Insert.insert a s) ⋯\na : α\ns : Finset α\nha : a ∉ s\nih : ∀ (hs : (↑s).Finite), motive (↑s) hs\nhs : (↑(Finset.cons a s ha)).Finite\n⊢ mo... | [
"case cons\nα : Type u\nmotive : (s : Set α) → s.Finite → Prop\nempty : motive ∅ ⋯\ninsert : ∀ {a : α} {s : Set α}, a ∉ s → ∀ (hs : s.Finite), motive s hs → motive (Insert.insert a s) ⋯\na : α\ns : Finset α\nha : a ∉ s\nih : ∀ (hs : (↑s).Finite), motive (↑s) hs\nhs : (↑(Finset.cons a s ha)).Finite\n⊢ motive (Insert... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Tuple.Basic | {
"line": 1293,
"column": 4
} | {
"line": 1293,
"column": 15
} | {
"line": 1293,
"column": 16
} | [
{
"pp": "α : Type u_1\nai : ℕ\na b : Fin ai → α\nh : ⟨ai, a⟩.snd = ⟨ai, b⟩.snd ∘ Fin.cast ⋯\n⊢ ⟨ai, a⟩ = ⟨ai, b⟩",
"ppTerm": "?m.64",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"heq_eq_eq",
"id",
"Sigma.mk.injEq",
"And",
"Nat",
"congr",... | [
"α : Type u_1\nai : ℕ\na b : Fin ai → α\nh : ⟨ai, a⟩.snd = ⟨ai, b⟩.snd ∘ Fin.cast ⋯\n⊢ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Basic | {
"line": 858,
"column": 33
} | {
"line": 858,
"column": 44
} | {
"line": 858,
"column": 45
} | [
{
"pp": "α : Type u\ninst✝ : Infinite α\ns : Set α\nhs : sᶜ.Finite\nh : s.Finite\n⊢ univ.Finite",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ninst✝ : Infinite α\ns : Set α\nhs : sᶜ.Finite\nh : s.Finite\n⊢ univ.Finite"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Basic | {
"line": 861,
"column": 33
} | {
"line": 861,
"column": 44
} | {
"line": 861,
"column": 45
} | [
{
"pp": "α : Type u\ninst✝ : Infinite α\ns : Set α\nhs : s.Finite\nh : sᶜ.Finite\n⊢ univ.Finite",
"ppTerm": "?m.7",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\ninst✝ : Infinite α\ns : Set α\nhs : s.Finite\nh : sᶜ.Finite\n⊢ univ.Finite"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Basic | {
"line": 870,
"column": 2
} | {
"line": 870,
"column": 13
} | {
"line": 870,
"column": 14
} | [
{
"pp": "α : Type u_1\ns t : Set α\nhs : s.Infinite\nht : (s \\ t).Finite\n⊢ (s ∩ t).Infinite",
"ppTerm": "?m.8",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u_1\ns t : Set α\nhs : s.Infinite\nht : (s \\ t).Finite\n⊢ (s ∩ t).Infinite"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Basic | {
"line": 887,
"column": 2
} | {
"line": 887,
"column": 13
} | {
"line": 887,
"column": 14
} | [
{
"pp": "α : Type u\nβ : Type v\nf : α → β\nhf : Injective f\n⊢ (range f).Infinite ↔ Infinite α",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Type u\nβ : Type v\nf : α → β\nhf : Injective f\n⊢ (range f).Infinite ↔ Infinite α"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Set.Finite.Basic | {
"line": 954,
"column": 2
} | {
"line": 954,
"column": 19
} | {
"line": 954,
"column": 20
} | [
{
"pp": "α : Type u\ninst✝ : LinearOrder α\nh : ∀ ⦃x y z : α⦄, x < y → y < z → False\na✝ : Nontrivial α\nx y : α\nhne : x ≠ y\nz : α\n⊢ z ∈ {x, y}",
"ppTerm": "?m.38",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"LinearOrder.toDecidableEq",
"congrArg",
"Finset",
"Mem... | [
"α : Type u\ninst✝ : LinearOrder α\nh : ∀ ⦃x y z : α⦄, x < y → y < z → False\na✝ : Nontrivial α\nx y : α\nhne : x ≠ y\nz : α\n⊢ z = x ∨ z = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Pairwise | {
"line": 71,
"column": 16
} | {
"line": 71,
"column": 44
} | {
"line": 72,
"column": 4
} | [
{
"pp": "case a\nα : Type u_1\nR : α → α → Prop\nl : List α\ninst✝ : Std.Refl R\nh : ∀ (a : α), a ∈ l → ∀ (b : α), b ∈ l → a ≠ b → R a b\na b : α\nhab : [a, b] <+ l\nheq : ¬a = b\n⊢ a ∈ l",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"true_or",
... | [] | try (apply hab.subset; simp) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticTry__1 | Lean.Parser.Tactic.tacticTry_ |
Mathlib.Data.List.Pairwise | {
"line": 71,
"column": 16
} | {
"line": 71,
"column": 44
} | {
"line": 72,
"column": 4
} | [
{
"pp": "case a\nα : Type u_1\nR : α → α → Prop\nl : List α\ninst✝ : Std.Refl R\nh : ∀ (a : α), a ∈ l → ∀ (b : α), b ∈ l → a ≠ b → R a b\na b : α\nhab : [a, b] <+ l\nheq : ¬a = b\n⊢ b ∈ l",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"False",
"congrArg",
"Membership.mem",... | [] | try (apply hab.subset; simp) | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticTry__1 | Lean.Parser.Tactic.tacticTry_ |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.