module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Data.Num.Lemmas | {
"line": 801,
"column": 2
} | {
"line": 801,
"column": 84
} | {
"line": 803,
"column": 0
} | [
{
"pp": "⊢ ∀ (m n : Num), ↑(m &&& n) = ↑m &&& ↑n",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"cond",
"Num.bit",
"Num.castNum_eq_bitwise",
"Num.instAndOp",
"PosNum.bit",
"Bool.and",
"instOnePosNum",
"Bool.true",
"Num",
"Bool.ca... | [] | apply castNum_eq_bitwise PosNum.land <;> intros <;> (try cases_type* Bool) <;> rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Num.Lemmas | {
"line": 801,
"column": 2
} | {
"line": 801,
"column": 84
} | {
"line": 803,
"column": 0
} | [
{
"pp": "⊢ ∀ (m n : Num), ↑(m &&& n) = ↑m &&& ↑n",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"cond",
"Num.bit",
"Num.castNum_eq_bitwise",
"Num.instAndOp",
"PosNum.bit",
"Bool.and",
"instOnePosNum",
"Bool.true",
"Num",
"Bool.ca... | [] | apply castNum_eq_bitwise PosNum.land <;> intros <;> (try cases_type* Bool) <;> rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Computability.TuringMachine.StackTuringMachine | {
"line": 607,
"column": 10
} | {
"line": 607,
"column": 65
} | {
"line": 607,
"column": 66
} | [
{
"pp": "case neg.inl.h\nK : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝ : DecidableEq K\nk : K\nq : TM1.Stmt (Γ' K Γ) (Λ' K Γ Λ σ) σ\nv : σ\nS : (k : K) → List (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nhL : ∀ (k : K), ListBlank.map (proj k) L = ListBlank.mk (List.map some (S k)).reverse\... | [
"case neg.inl.h\nK : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝ : DecidableEq K\nk : K\nq : TM1.Stmt (Γ' K Γ) (Λ' K Γ Λ σ) σ\nv : σ\nS : (k : K) → List (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nhL : ∀ (k : K), ListBlank.map (proj k) L = ListBlank.mk (List.map some (S k)).reverse\nf : σ → Opt... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.TuringDegree | {
"line": 80,
"column": 15
} | {
"line": 80,
"column": 26
} | {
"line": 80,
"column": 27
} | [
{
"pp": "f g h : ℕ →. ℕ\nhg : f ≤ᵀ g\nhh : g ≤ᵀ h\n⊢ ∀ g_1 ∈ {g}, RecursiveIn {h} g_1",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"PFun",
"Primcodable.ofDenumerable",
"RecursiveIn",
"Membership.mem",
"Set.instSingletonSet",
"id",
... | [
"f g h : ℕ →. ℕ\nhg : f ≤ᵀ g\nhh : g ≤ᵀ h\n⊢ RecursiveIn {h} g"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Computability.TuringMachine.StackTuringMachine | {
"line": 692,
"column": 2
} | {
"line": 692,
"column": 20
} | {
"line": 693,
"column": 2
} | [
{
"pp": "K : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝ : DecidableEq K\nM : Λ → TM2.Stmt Γ Λ σ\nv : σ\nS : (k : K) → List (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nhT : ∀ (k : K), ListBlank.map (proj k) L = ListBlank.mk (List.map some (S k)).reverse\nl : Λ\n⊢ ∃ b,\n TrCfg (TM2.stepAu... | [
"K : Type u_1\nΓ : K → Type u_2\nΛ : Type u_3\nσ : Type u_4\ninst✝ : DecidableEq K\nM : Λ → TM2.Stmt Γ Λ σ\nv : σ\nS : (k : K) → List (Γ k)\nL : ListBlank ((k : K) → Option (Γ k))\nhT : ∀ (k : K), ListBlank.map (proj k) L = ListBlank.mk (List.map some (S k)).reverse\nl : Λ\nN : TM2.Stmt Γ Λ σ\n⊢ ∃ b, TrCfg (TM2.ste... | generalize M l = N | Lean.Elab.Tactic.evalGeneralize | Lean.Parser.Tactic.generalize |
Mathlib.Topology.Category.CompHaus.EffectiveEpi | {
"line": 79,
"column": 4
} | {
"line": 79,
"column": 15
} | {
"line": 79,
"column": 16
} | [
{
"pp": "α : Type\ninst✝ : Finite α\nB : CompHaus\nX : α → CompHaus\nπ : (a : α) → X a ⟶ B\ntfae_2_to_1 : Epi (Sigma.desc π) → EffectiveEpiFamily X π\ntfae_1_to_2 : EffectiveEpiFamily X π → Epi (Sigma.desc π)\nx✝ : ∀ (b : ↑B.toTop), ∃ a x, (ConcreteCategory.hom (π a)) x = b\ne : ∀ (b : ↑B.toTop), ∃ a x, (Concre... | [
"α : Type\ninst✝ : Finite α\nB : CompHaus\nX : α → CompHaus\nπ : (a : α) → X a ⟶ B\ntfae_2_to_1 : Epi (Sigma.desc π) → EffectiveEpiFamily X π\ntfae_1_to_2 : EffectiveEpiFamily X π → Epi (Sigma.desc π)\nx✝ : ∀ (b : ↑B.toTop), ∃ a x, (ConcreteCategory.hom (π a)) x = b\ne : ∀ (b : ↑B.toTop), ∃ a x, (ConcreteCategory.h... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.Profinite | {
"line": 109,
"column": 4
} | {
"line": 109,
"column": 69
} | {
"line": 110,
"column": 4
} | [
{
"pp": "H : Type u_3\ninst✝³ : TopologicalSpace H\ninst✝² : LocallyCompactSpace H\ninst✝¹ : T2Space H\ninst✝ : TotallyDisconnectedSpace H\nU : Set H\nhU : IsOpen[inst✝³] U\ns : Set H\ncomp : IsCompact s\nsU : s ⊆ U\nu : Set ↑s := Subtype.val ⁻¹' interior s\nu_open_in_s : IsOpen[instTopologicalSpaceSubtype] u\n... | [
"H : Type u_3\ninst✝³ : TopologicalSpace H\ninst✝² : LocallyCompactSpace H\ninst✝¹ : T2Space H\ninst✝ : TotallyDisconnectedSpace H\nU : Set H\nhU : IsOpen[inst✝³] U\ns : Set H\ncomp : IsCompact s\nsU : s ⊆ U\nu : Set ↑s := Subtype.val ⁻¹' interior s\nu_open_in_s : IsOpen[instTopologicalSpaceSubtype] u\nx : { x // x... | have f2 : IsOpen v := VisClopen.2.preimage continuous_subtype_val | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Topology.Separation.Profinite | {
"line": 159,
"column": 58
} | {
"line": 159,
"column": 69
} | {
"line": 159,
"column": 70
} | [
{
"pp": "X : Type u_4\nI : Type u_5\ninst✝⁴ : TopologicalSpace X\ninst✝³ : CompactSpace X\ninst✝² : T2Space X\ninst✝¹ : TotallyDisconnectedSpace X\ninst✝ : Finite I\nα✝ β✝ : Type u_5\ne : α✝ ≃ β✝\nIH :\n ∀ {Z D : α✝ → Set X},\n (∀ (i : α✝), IsClosed[inst✝⁴] (Z i)) →\n (∀ (i : α✝), IsClopen (D i)) →\n ... | [
"X : Type u_4\nI : Type u_5\ninst✝⁴ : TopologicalSpace X\ninst✝³ : CompactSpace X\ninst✝² : T2Space X\ninst✝¹ : TotallyDisconnectedSpace X\ninst✝ : Finite I\nα✝ β✝ : Type u_5\ne : α✝ ≃ β✝\nIH :\n ∀ {Z D : α✝ → Set X},\n (∀ (i : α✝), IsClosed[inst✝⁴] (Z i)) →\n (∀ (i : α✝), IsClopen (D i)) →\n (∀ (i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.Profinite | {
"line": 160,
"column": 17
} | {
"line": 160,
"column": 28
} | {
"line": 160,
"column": 29
} | [
{
"pp": "X : Type u_4\nI : Type u_5\ninst✝⁴ : TopologicalSpace X\ninst✝³ : CompactSpace X\ninst✝² : T2Space X\ninst✝¹ : TotallyDisconnectedSpace X\ninst✝ : Finite I\nα✝ β✝ : Type u_5\ne : α✝ ≃ β✝\nIH :\n ∀ {Z D : α✝ → Set X},\n (∀ (i : α✝), IsClosed[inst✝⁴] (Z i)) →\n (∀ (i : α✝), IsClopen (D i)) →\n ... | [
"X : Type u_4\nI : Type u_5\ninst✝⁴ : TopologicalSpace X\ninst✝³ : CompactSpace X\ninst✝² : T2Space X\ninst✝¹ : TotallyDisconnectedSpace X\ninst✝ : Finite I\nα✝ β✝ : Type u_5\ne : α✝ ≃ β✝\nIH :\n ∀ {Z D : α✝ → Set X},\n (∀ (i : α✝), IsClosed[inst✝⁴] (Z i)) →\n (∀ (i : α✝), IsClopen (D i)) →\n (∀ (i ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.Profinite | {
"line": 163,
"column": 4
} | {
"line": 163,
"column": 49
} | {
"line": 163,
"column": 50
} | [
{
"pp": "case of_equiv\nX : Type u_4\nI : Type u_5\ninst✝⁴ : TopologicalSpace X\ninst✝³ : CompactSpace X\ninst✝² : T2Space X\ninst✝¹ : TotallyDisconnectedSpace X\ninst✝ : Finite I\nα✝ β✝ : Type u_5\ne : α✝ ≃ β✝\nIH :\n ∀ {Z D : α✝ → Set X},\n (∀ (i : α✝), IsClosed[inst✝⁴] (Z i)) →\n (∀ (i : α✝), IsClop... | [
"case of_equiv\nX : Type u_4\nI : Type u_5\ninst✝⁴ : TopologicalSpace X\ninst✝³ : CompactSpace X\ninst✝² : T2Space X\ninst✝¹ : TotallyDisconnectedSpace X\ninst✝ : Finite I\nα✝ β✝ : Type u_5\ne : α✝ ≃ β✝\nIH :\n ∀ {Z D : α✝ → Set X},\n (∀ (i : α✝), IsClosed[inst✝⁴] (Z i)) →\n (∀ (i : α✝), IsClopen (D i)) →\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.Profinite | {
"line": 178,
"column": 6
} | {
"line": 178,
"column": 17
} | {
"line": 178,
"column": 18
} | [
{
"pp": "X : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n (∀ (i : I), IsClopen (D i)) →\n... | [
"X : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n (∀ (i : I), IsClopen (D i)) →\n (∀ (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ExtremallyDisconnected | {
"line": 186,
"column": 4
} | {
"line": 186,
"column": 43
} | {
"line": 186,
"column": 44
} | [
{
"pp": "case pos\nA E : Type u\ninst✝¹ : TopologicalSpace A\ninst✝ : TopologicalSpace E\nρ : E → A\nρ_cont : Continuous ρ\nρ_surj : Surjective ρ\nzorn_subset : ∀ (E₀ : Set E), E₀ ≠ univ → IsClosed E₀ → ρ '' E₀ ≠ univ\nG : Set E\nhG : IsOpen G\nG_empty : G = ∅\n⊢ ρ '' G ⊆ closure (ρ '' Gᶜ)ᶜ",
"ppTerm": "?po... | [
"case pos\nA E : Type u\ninst✝¹ : TopologicalSpace A\ninst✝ : TopologicalSpace E\nρ : E → A\nρ_cont : Continuous ρ\nρ_surj : Surjective ρ\nzorn_subset : ∀ (E₀ : Set E), E₀ ≠ univ → IsClosed E₀ → ρ '' E₀ ≠ univ\nG : Set E\nhG : IsOpen G\nG_empty : G = ∅\n⊢ ∅ ⊆ closure (ρ '' ∅ᶜ)ᶜ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.ExtremallyDisconnected | {
"line": 202,
"column": 36
} | {
"line": 202,
"column": 47
} | {
"line": 202,
"column": 48
} | [
{
"pp": "A E : Type u\ninst✝¹ : TopologicalSpace A\ninst✝ : TopologicalSpace E\nρ : E → A\nρ_cont : Continuous ρ\nρ_surj : Surjective ρ\nzorn_subset : ∀ (E₀ : Set E), E₀ ≠ univ → IsClosed E₀ → ρ '' E₀ ≠ univ\nG : Set E\nhG : IsOpen G\nG_empty : ¬G = ∅\nN : Set A\nN_open : IsOpen N\ne : E\nhe : e ∈ G\nha : ρ e ∈... | [
"A E : Type u\ninst✝¹ : TopologicalSpace A\ninst✝ : TopologicalSpace E\nρ : E → A\nρ_cont : Continuous ρ\nρ_surj : Surjective ρ\nzorn_subset : ∀ (E₀ : Set E), E₀ ≠ univ → IsClosed E₀ → ρ '' E₀ ≠ univ\nG : Set E\nhG : IsOpen G\nG_empty : ¬G = ∅\nN : Set A\nN_open : IsOpen N\ne : E\nhe : e ∈ G\nha : ρ e ∈ ρ '' G\nhN ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.DiscreteQuotient | {
"line": 384,
"column": 2
} | {
"line": 384,
"column": 14
} | {
"line": 384,
"column": 15
} | [
{
"pp": "X : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\n⊢ Injective fun x ↦\n match x with\n | { toSetoid := f, isOpen_setOf_rel := isOpen_setOf_rel } => f.classes",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Topology.DiscreteQuotient.0.... | [
"X : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\ntoSetoid✝ : Setoid X\nisOpen_setOf_rel✝ : ∀ (x : X), IsOpen[inst✝¹] (setOf (toSetoid✝ x))\n⊢ ∀ ⦃a₂ : DiscreteQuotient X⦄,\n (fun x ↦\n match x with\n | { toSetoid := f, isOpen_setOf_rel := isOpen_setOf_rel } => f.classes)\n... | intro ⟨_, _⟩ | Lean.Elab.Tactic.evalIntro | null |
Mathlib.Topology.Separation.Profinite | {
"line": 216,
"column": 8
} | {
"line": 216,
"column": 93
} | {
"line": 217,
"column": 10
} | [
{
"pp": "case h_option.refine_5.none.some\nX : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n ... | [
"case h_option.refine_5.none.some\nX : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n (∀ (i : I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.Profinite | {
"line": 218,
"column": 8
} | {
"line": 218,
"column": 93
} | {
"line": 219,
"column": 10
} | [
{
"pp": "case h_option.refine_5.some.none\nX : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n ... | [
"case h_option.refine_5.some.none\nX : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n (∀ (i : I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.Profinite | {
"line": 220,
"column": 8
} | {
"line": 220,
"column": 19
} | {
"line": 220,
"column": 20
} | [
{
"pp": "case h_option.refine_5.some.some\nX : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n ... | [
"case h_option.refine_5.some.some\nX : Type u_4\nI✝ : Type u_5\ninst✝⁵ : TopologicalSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : Finite I✝\nI : Type u_5\ninst✝ : Fintype I\nIH :\n ∀ {Z D : I → Set X},\n (∀ (i : I), IsClosed[inst✝⁵] (Z i)) →\n (∀ (i : I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.Profinite.CofilteredLimit | {
"line": 87,
"column": 4
} | {
"line": 92,
"column": 55
} | {
"line": 93,
"column": 2
} | [
{
"pp": "case refine_3.refine_1\nJ : Type v\ninst✝¹ : SmallCategory J\ninst✝ : IsCofiltered J\nF : J ⥤ Profinite\nC : Cone F\nU : Set ↑C.pt.toTop\nhC : IsLimit C\nhU : IsClopen U\nS : Set (Set ↑(toTopCat.mapCone C).pt)\nhS : S ⊆ {U | ∃ j, ∃ V ∈ {W | IsClopen W}, U = ⇑(ConcreteCategory.hom ((toTopCat.mapCone C).... | [] | apply isClopen_biUnion_finset
intro s hs
dsimp [W]
rw [dif_pos hs]
exact ⟨(hV s).1.1.preimage (F.map _).hom.hom.continuous,
(hV s).1.2.preimage (F.map _).hom.hom.continuous⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Category.Profinite.CofilteredLimit | {
"line": 87,
"column": 4
} | {
"line": 92,
"column": 55
} | {
"line": 93,
"column": 2
} | [
{
"pp": "case refine_3.refine_1\nJ : Type v\ninst✝¹ : SmallCategory J\ninst✝ : IsCofiltered J\nF : J ⥤ Profinite\nC : Cone F\nU : Set ↑C.pt.toTop\nhC : IsLimit C\nhU : IsClopen U\nS : Set (Set ↑(toTopCat.mapCone C).pt)\nhS : S ⊆ {U | ∃ j, ∃ V ∈ {W | IsClopen W}, U = ⇑(ConcreteCategory.hom ((toTopCat.mapCone C).... | [] | apply isClopen_biUnion_finset
intro s hs
dsimp [W]
rw [dif_pos hs]
exact ⟨(hV s).1.1.preimage (F.map _).hom.hom.continuous,
(hV s).1.2.preimage (F.map _).hom.hom.continuous⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Category.Profinite.CofilteredLimit | {
"line": 132,
"column": 2
} | {
"line": 132,
"column": 41
} | {
"line": 133,
"column": 2
} | [
{
"pp": "case intro\nJ : Type v\ninst✝² : SmallCategory J\ninst✝¹ : IsCofiltered J\nF : J ⥤ Profinite\nC : Cone F\nα : Type u_1\ninst✝ : Finite α\nhC : IsLimit C\nf : LocallyConstant (↑C.pt.toTop) α\nval✝ : Fintype α\nι : α → α → Fin 2 := fun x y ↦ if x = y then 0 else 1\nff : α → LocallyConstant (↑C.pt.toTop) ... | [
"case intro\nJ : Type v\ninst✝² : SmallCategory J\ninst✝¹ : IsCofiltered J\nF : J ⥤ Profinite\nC : Cone F\nα : Type u_1\ninst✝ : Finite α\nhC : IsLimit C\nf : LocallyConstant (↑C.pt.toTop) α\nval✝ : Fintype α\nι : α → α → Fin 2 := fun x y ↦ if x = y then 0 else 1\nff : α → LocallyConstant (↑C.pt.toTop) (Fin 2) := (... | let G : Finset J := Finset.univ.image j | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Computability.TuringMachine.ToPartrec | {
"line": 1144,
"column": 2
} | {
"line": 1144,
"column": 24
} | {
"line": 1144,
"column": 25
} | [
{
"pp": "K : Option Γ' → Finset Λ'\nS : Finset Λ'\n⊢ Supports (Finset.univ.biUnion K) S ↔ ∀ (a : Option Γ'), Supports (K a) S",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Turing.TM2.SupportsStmt",
"Turing.PartrecToTM2.tr",
"Finset.univ",
"Turing.P... | [
"K : Option Γ' → Finset Λ'\nS : Finset Λ'\n⊢ (∀ (q : Λ') (x : Option Γ'), q ∈ K x → TM2.SupportsStmt S (tr q)) ↔\n ∀ (a : Option Γ'), ∀ q ∈ K a, TM2.SupportsStmt S (tr q)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Condensed.TopComparison | {
"line": 57,
"column": 2
} | {
"line": 57,
"column": 13
} | {
"line": 57,
"column": 14
} | [
{
"pp": "C : Type u\ninst✝³ : Category.{v, u} C\nG : C ⥤ TopCat\nX : Type w'\ninst✝² : TopologicalSpace X\nZ B : C\nπ : Z ⟶ B\ninst✝¹ : HasPullback π π\ninst✝ : PreservesLimit (cospan π π) G\na : C(↑(G.obj Z), X)\nha : ⇑a ∘ ⇑(ConcreteCategory.hom (G.map (pullback.fst π π))) = ⇑a ∘ ⇑(ConcreteCategory.hom (G.map ... | [
"C : Type u\ninst✝³ : Category.{v, u} C\nG : C ⥤ TopCat\nX : Type w'\ninst✝² : TopologicalSpace X\nZ B : C\nπ : Z ⟶ B\ninst✝¹ : HasPullback π π\ninst✝ : PreservesLimit (cospan π π) G\na : C(↑(G.obj Z), X)\nha : ⇑a ∘ ⇑(ConcreteCategory.hom (G.map (pullback.fst π π))) = ⇑a ∘ ⇑(ConcreteCategory.hom (G.map (pullback.sn... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.LightProfinite.AsLimit | {
"line": 125,
"column": 2
} | {
"line": 125,
"column": 45
} | {
"line": 125,
"column": 46
} | [
{
"pp": "S : LightProfinite\nn : ℕ\n⊢ Function.Surjective (⇑(ConcreteCategory.hom (S.transitionMap n)) ∘ ⇑(ConcreteCategory.hom (S.proj (n + 1))))",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"congrArg",
"CategoryTheory.ConcreteCategory.hom"... | [
"S : LightProfinite\nn : ℕ\n⊢ Function.Surjective ⇑(ConcreteCategory.hom (S.proj n))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.LightProfinite.AsLimit | {
"line": 130,
"column": 2
} | {
"line": 130,
"column": 47
} | {
"line": 130,
"column": 48
} | [
{
"pp": "S : LightProfinite\nn m : ℕ\nh : n ≤ m\n⊢ Function.Surjective (⇑(ConcreteCategory.hom (S.transitionMapLE h)) ∘ ⇑(ConcreteCategory.hom (S.proj m)))",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Opposite",
"LightProfinite.proj_comp_transitionMapLE'",
... | [
"S : LightProfinite\nn m : ℕ\nh : n ≤ m\n⊢ Function.Surjective ⇑(ConcreteCategory.hom (S.proj n))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Condensed.Discrete.LocallyConstant | {
"line": 359,
"column": 9
} | {
"line": 359,
"column": 93
} | {
"line": 359,
"column": 93
} | [
{
"pp": "P : TopCat → Prop\ninst✝⁴ : ∀ (S : CompHausLike P) (p : ↑S.toTop → Prop), HasProp P (Subtype p)\nS : CompHausLike P\nY : (CompHausLike P)ᵒᵖ ⥤ Type (max u w)\ninst✝³ : HasProp P PUnit.{u + 1}\nf : LocallyConstant (↑S.toTop) (Y.obj (op (of P PUnit.{u + 1})))\nT : CompHausLike P\ng : T ⟶ S\nX✝ : TopCat\ni... | [
"P : TopCat → Prop\ninst✝⁴ : ∀ (S : CompHausLike P) (p : ↑S.toTop → Prop), HasProp P (Subtype p)\nS : CompHausLike P\nY : (CompHausLike P)ᵒᵖ ⥤ Type (max u w)\ninst✝³ : HasProp P PUnit.{u + 1}\nf : LocallyConstant (↑S.toTop) (Y.obj (op (of P PUnit.{u + 1})))\nT : CompHausLike P\ng : T ⟶ S\nX✝ : TopCat\ninst✝² : HasE... | ← map_eq_image _ a ⟨PUnit.unit, by simp [mem_iff_eq_image, ← map_preimage_eq_image]⟩ | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Condensed.Discrete.Colimit | {
"line": 154,
"column": 16
} | {
"line": 154,
"column": 27
} | {
"line": 154,
"column": 28
} | [
{
"pp": "S : Profinite\nF : Profiniteᵒᵖ ⥤ Type (u + 1)\nhF : (S : Profinite) → IsColimit (F.mapCocone S.asLimitCone.op)\nX✝ Y✝ : Profiniteᵒᵖ\nx✝ : X✝ ⟶ Y✝\n⊢ (lanPresheaf F).map x✝ ≫\n (match Y✝ with\n | Opposite.op S => lanPresheafIso (hF S)).hom =\n (match X✝ with\n | Opposite.op S => la... | [
"S : Profinite\nF : Profiniteᵒᵖ ⥤ Type (u + 1)\nhF : (S : Profinite) → IsColimit (F.mapCocone S.asLimitCone.op)\nX✝ Y✝ : Profiniteᵒᵖ\nx✝ : X✝ ⟶ Y✝\n⊢ colimit.desc (CostructuredArrow.proj toProfinite.op X✝ ⋙ toProfinite.op ⋙ F)\n { pt := colimit (CostructuredArrow.proj toProfinite.op Y✝ ⋙ toProfinite.op ⋙ F),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Condensed.Light.InternallyProjective | {
"line": 80,
"column": 2
} | {
"line": 80,
"column": 53
} | {
"line": 82,
"column": 0
} | [
{
"pp": "case e_6\nR : Type u\ninst✝ : CommRing R\nA B P : LightCondMod R\nS : LightProfinite\ne : A ⟶ B\nx : ↑((P ⟹ A).obj.obj (Opposite.op S))\n⊢ (coherentTopology LightProfinite).yonedaEquiv\n ((coherentTopology LightProfinite).yonedaEquiv.symm\n ((ConcreteCategory.hom (((ihom P).map e).hom.app (... | [] | simp [dsimp% GrothendieckTopology.yonedaEquiv_comp] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Topology.Category.LightProfinite.Injective | {
"line": 114,
"column": 4
} | {
"line": 114,
"column": 37
} | {
"line": 114,
"column": 38
} | [
{
"pp": "case refine_2\nX : Type u_1\nY : Type u_2\nS : Type u_3\nT : Type u_4\ninst✝¹⁰ : TopologicalSpace X\ninst✝⁹ : CompactSpace X\ninst✝⁸ : TopologicalSpace Y\ninst✝⁷ : CompactSpace Y\ninst✝⁶ : T2Space Y\ninst✝⁵ : TotallyDisconnectedSpace Y\ninst✝⁴ : TopologicalSpace S\ninst✝³ : T2Space S\ninst✝² : Finite S... | [
"case refine_2\nX : Type u_1\nY : Type u_2\nS : Type u_3\nT : Type u_4\ninst✝¹⁰ : TopologicalSpace X\ninst✝⁹ : CompactSpace X\ninst✝⁸ : TopologicalSpace Y\ninst✝⁷ : CompactSpace Y\ninst✝⁶ : T2Space Y\ninst✝⁵ : TotallyDisconnectedSpace Y\ninst✝⁴ : TopologicalSpace S\ninst✝³ : T2Space S\ninst✝² : Finite S\ninst✝¹ : T... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Category.LightProfinite.Injective | {
"line": 116,
"column": 51
} | {
"line": 116,
"column": 74
} | {
"line": 116,
"column": 75
} | [
{
"pp": "X : Type u_1\nY : Type u_2\nS : Type u_3\nT : Type u_4\ninst✝¹⁰ : TopologicalSpace X\ninst✝⁹ : CompactSpace X\ninst✝⁸ : TopologicalSpace Y\ninst✝⁷ : CompactSpace Y\ninst✝⁶ : T2Space Y\ninst✝⁵ : TotallyDisconnectedSpace Y\ninst✝⁴ : TopologicalSpace S\ninst✝³ : T2Space S\ninst✝² : Finite S\ninst✝¹ : Topo... | [
"X : Type u_1\nY : Type u_2\nS : Type u_3\nT : Type u_4\ninst✝¹⁰ : TopologicalSpace X\ninst✝⁹ : CompactSpace X\ninst✝⁸ : TopologicalSpace Y\ninst✝⁷ : CompactSpace Y\ninst✝⁶ : T2Space Y\ninst✝⁵ : TotallyDisconnectedSpace Y\ninst✝⁴ : TopologicalSpace S\ninst✝³ : T2Space S\ninst✝² : Finite S\ninst✝¹ : TopologicalSpace... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Condensed.Light.Sequence | {
"line": 68,
"column": 15
} | {
"line": 68,
"column": 32
} | {
"line": 68,
"column": 33
} | [
{
"pp": "S : Type u_1\nT : Type u_2\nX : Type u_3\nπ : T → S × Option X\nσ : Option X → S → T\nhσ' : ∀ (x : Option X) (s : S), (π (σ x s)).2 = x\nx : T\nx✝ : ∃ i, (∀ (x_1 : S), ¬σ (Option.some i) x_1 = x) ∧ (π x).2 = ↑i\nn : X\nhn : ∀ (x_1 : S), ¬σ (Option.some n) x_1 = x\nhn' : (π x).2 = ↑n\n⊢ ¬(π x).2 = none"... | [
"S : Type u_1\nT : Type u_2\nX : Type u_3\nπ : T → S × Option X\nσ : Option X → S → T\nhσ' : ∀ (x : Option X) (s : S), (π (σ x s)).2 = x\nx : T\nx✝ : ∃ i, (∀ (x_1 : S), ¬σ (Option.some i) x_1 = x) ∧ (π x).2 = ↑i\nn : X\nhn : ∀ (x_1 : S), ¬σ (Option.some n) x_1 = x\nhn' : (π x).2 = ↑n\n⊢ ¬↑n = none"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Condensed.Light.Sequence | {
"line": 81,
"column": 4
} | {
"line": 81,
"column": 15
} | {
"line": 81,
"column": 16
} | [
{
"pp": "case refine_1\nS : Type u_1\nT : Type u_2\nX : Type u_3\ninst✝⁵ : TopologicalSpace S\ninst✝⁴ : TopologicalSpace T\ninst✝³ : TopologicalSpace X\ninst✝² : DiscreteTopology X\ninst✝¹ : T2Space T\ninst✝ : CompactSpace S\nπ : T → S × OnePoint X\nhπ : Continuous π\nσ : Option X → S → T\nhσ : ∀ (x : Option X)... | [
"case refine_1\nS : Type u_1\nT : Type u_2\nX : Type u_3\ninst✝⁵ : TopologicalSpace S\ninst✝⁴ : TopologicalSpace T\ninst✝³ : TopologicalSpace X\ninst✝² : DiscreteTopology X\ninst✝¹ : T2Space T\ninst✝ : CompactSpace S\nπ : T → S × OnePoint X\nhπ : Continuous π\nσ : Option X → S → T\nhσ : ∀ (x : Option X), Continuous... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Control.Functor.Multivariate | {
"line": 174,
"column": 4
} | {
"line": 174,
"column": 91
} | {
"line": 175,
"column": 4
} | [
{
"pp": "case h₁\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u_1\ninst✝¹ : MvFunctor F\ninst✝ : LawfulMvFunctor F\nα : TypeVec.{u} n\nβ : Type u\nP : β → Prop\nx : F (α ::: β)\nu✝ : F fun i ↦ { p_1 // ofRepeat (α.PredLast' P i p_1) }\n⊢ (fun i ↦ Subtype.val) <$$> u✝ = x ↔ (fun i x ↦ ↑(f P n α i x)) <$$> u✝ = x",
... | [
"case h₁\nn : ℕ\nF : TypeVec.{u} (n + 1) → Type u_1\ninst✝¹ : MvFunctor F\ninst✝ : LawfulMvFunctor F\nα : TypeVec.{u} n\nβ : Type u\nP : β → Prop\nx : F (α ::: β)\nu✝ : F fun i ↦ { p_1 // ofRepeat (α.PredLast' P i p_1) }\n⊢ (fun i ↦ Subtype.val) = fun i x ↦ ↑(f P n α i x)"
] | suffices (fun i => Subtype.val) = (fun i x => (MvFunctor.f P n α i x).val) by rw [this] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticSuffices__1 | Lean.Parser.Tactic.tacticSuffices_ |
Mathlib.Control.Monad.Cont | {
"line": 225,
"column": 4
} | {
"line": 225,
"column": 57
} | {
"line": 226,
"column": 6
} | [
{
"pp": "m : Type u → Type v\ninst✝² : Monad m\ninst✝¹ : MonadCont m\ninst✝ : LawfulMonadCont m\nα✝ ω✝ γ✝ : Type u\nx✝¹ : OptionT m α✝\nx✝ : Label ω✝ (OptionT m) γ✝ → α✝ → OptionT m ω✝\n⊢ (callCC fun f ↦ x✝¹ >>= x✝ f).run =\n (do\n let x ← x✝¹\n callCC fun f ↦ x✝ f x).run",
"ppTerm": "?m.17... | [
"m : Type u → Type v\ninst✝² : Monad m\ninst✝¹ : MonadCont m\ninst✝ : LawfulMonadCont m\nα✝ ω✝ γ✝ : Type u\nx✝¹ : OptionT m α✝\nx✝ : Label ω✝ (OptionT m) γ✝ → α✝ → OptionT m ω✝\n⊢ (do\n let x ← x✝¹.run\n callCC fun f ↦ x.elim (pure none) fun x ↦ (x✝ (OptionT.mkLabel f) x).run) =\n do\n let __do_lift... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Control.LawfulFix | {
"line": 132,
"column": 4
} | {
"line": 135,
"column": 25
} | {
"line": 137,
"column": 0
} | [
{
"pp": "case a\nα : Type u_1\nβ : α → Type u_2\nf : ((a : α) → Part (β a)) →o (a : α) → Part (β a)\n⊢ ωSup (approxChain f) ≤ Part.fix ⇑f",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Part",
"Pi.preorder",
"instOmegaCompletePartialOrderForall",
"Part.Fix.approx_le_... | [] | apply ωSup_le _ _ _
simp only [Fix.approxChain]
intro y x
apply approx_le_fix f | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Control.LawfulFix | {
"line": 132,
"column": 4
} | {
"line": 135,
"column": 25
} | {
"line": 137,
"column": 0
} | [
{
"pp": "case a\nα : Type u_1\nβ : α → Type u_2\nf : ((a : α) → Part (β a)) →o (a : α) → Part (β a)\n⊢ ωSup (approxChain f) ≤ Part.fix ⇑f",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"Part",
"Pi.preorder",
"instOmegaCompletePartialOrderForall",
"Part.Fix.approx_le_... | [] | apply ωSup_le _ _ _
simp only [Fix.approxChain]
intro y x
apply approx_le_fix f | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Control.LawfulFix | {
"line": 189,
"column": 4
} | {
"line": 189,
"column": 80
} | {
"line": 189,
"column": 80
} | [
{
"pp": "α : Type u_1\nβ : α → Type u_2\nf : Part α → Part α\nhc : ωScottContinuous f\n⊢ Part.fix ⇑(toUnitMono { toFun := f, monotone' := ⋯ }) () = f (Fix.fix f)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Part",
"Eq.mpr",
"Unit.unit",
"Pi.preorder",
"con... | [] | rw [Part.fix_eq_of_ωScottContinuous (ωScottContinuous_toUnitMono f hc)]; rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Control.LawfulFix | {
"line": 189,
"column": 4
} | {
"line": 189,
"column": 80
} | {
"line": 189,
"column": 80
} | [
{
"pp": "α : Type u_1\nβ : α → Type u_2\nf : Part α → Part α\nhc : ωScottContinuous f\n⊢ Part.fix ⇑(toUnitMono { toFun := f, monotone' := ⋯ }) () = f (Fix.fix f)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Part",
"Eq.mpr",
"Unit.unit",
"Pi.preorder",
"con... | [] | rw [Part.fix_eq_of_ωScottContinuous (ωScottContinuous_toUnitMono f hc)]; rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.TypeVec | {
"line": 668,
"column": 2
} | {
"line": 669,
"column": 56
} | {
"line": 670,
"column": 2
} | [
{
"pp": "n : ℕ\nα : TypeVec.{u_1} n\nr : α ⊗ α ⟹ «repeat» n Prop\ni : Fin2 n\nx : Subtype_ r i\n⊢ (toSubtype' r ⊚ ofSubtype' r) i x = id i x",
"ppTerm": "?m.28",
"assigned": true,
"usedConstants": [
"Fin2.rec",
"Fin2.fz",
"TypeVec.ofRepeat",
"TypeVec.prod.mk",
"id",
... | [
"case fz\nn n✝ : ℕ\nα : TypeVec.{u_1} (n✝ + 1)\nr : α ⊗ α ⟹ «repeat» (n✝ + 1) Prop\nx : Subtype_ r Fin2.fz\n⊢ ⟨↑x, ⋯⟩ = x",
"case fs\nn n✝ : ℕ\na✝ : Fin2 n✝\na_ih✝ :\n ∀ {α : TypeVec.{u_1} n✝} (r : α ⊗ α ⟹ «repeat» n✝ Prop) (x : Subtype_ r a✝), toSubtype' r a✝ (ofSubtype' r a✝ x) = x\nα : TypeVec.{u_1} (n✝ + 1)\... | induction i
<;> dsimp only [id, toSubtype', comp, ofSubtype'] at * | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Data.Analysis.Topology | {
"line": 71,
"column": 28
} | {
"line": 71,
"column": 39
} | {
"line": 71,
"column": 40
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\nF : Ctop α σ\nE : σ ≃ τ\nf : σ → Set α\nT : α → σ\nh₁ : ∀ (x : α), x ∈ f (T x)\nI : (a b : σ) → (x : α) → x ∈ f a ∩ f b → σ\nh₂ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), x ∈ f (I a b x h)\nh₃ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), f (I a b x ... | [
"α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\nF : Ctop α σ\nE : σ ≃ τ\nf : σ → Set α\nT : α → σ\nh₁ : ∀ (x : α), x ∈ f (T x)\nI : (a b : σ) → (x : α) → x ∈ f a ∩ f b → σ\nh₂ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), x ∈ f (I a b x h)\nh₃ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), f (I a b x h) ⊆ f a ∩ f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 73,
"column": 36
} | {
"line": 73,
"column": 47
} | {
"line": 73,
"column": 48
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\nF : Ctop α σ\nE : σ ≃ τ\nf : σ → Set α\nT : α → σ\nh₁ : ∀ (x : α), x ∈ f (T x)\nI : (a b : σ) → (x : α) → x ∈ f a ∩ f b → σ\nh₂ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), x ∈ f (I a b x h)\nh₃ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), f (I a b x ... | [
"α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\nF : Ctop α σ\nE : σ ≃ τ\nf : σ → Set α\nT : α → σ\nh₁ : ∀ (x : α), x ∈ f (T x)\nI : (a b : σ) → (x : α) → x ∈ f a ∩ f b → σ\nh₂ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), x ∈ f (I a b x h)\nh₃ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), f (I a b x h) ⊆ f a ∩ f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 74,
"column": 36
} | {
"line": 74,
"column": 47
} | {
"line": 74,
"column": 48
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\nF : Ctop α σ\nE : σ ≃ τ\nf : σ → Set α\nT : α → σ\nh₁ : ∀ (x : α), x ∈ f (T x)\nI : (a b : σ) → (x : α) → x ∈ f a ∩ f b → σ\nh₂ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), x ∈ f (I a b x h)\nh₃ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), f (I a b x ... | [
"α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\nF : Ctop α σ\nE : σ ≃ τ\nf : σ → Set α\nT : α → σ\nh₁ : ∀ (x : α), x ∈ f (T x)\nI : (a b : σ) → (x : α) → x ∈ f a ∩ f b → σ\nh₂ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), x ∈ f (I a b x h)\nh₃ : ∀ (a b : σ) (x : α) (h : x ∈ f a ∩ f b), f (I a b x h) ⊆ f a ∩ f... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Filter | {
"line": 69,
"column": 34
} | {
"line": 69,
"column": 45
} | {
"line": 69,
"column": 46
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\ninst✝ : PartialOrder α\nF : CFilter α σ\nE : σ ≃ τ\nf : σ → α\np : σ\ng : σ → σ → σ\nh₁ : ∀ (a b : σ), f (g a b) ≤ f a\nh₂ : ∀ (a b : σ), f (g a b) ≤ f b\na b : τ\n⊢ f (E.symm (E (g (E.symm a) (E.symm b)))) ≤ f (E.symm a)",
"ppTerm": "?m.49",
... | [
"α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\ninst✝ : PartialOrder α\nF : CFilter α σ\nE : σ ≃ τ\nf : σ → α\np : σ\ng : σ → σ → σ\nh₁ : ∀ (a b : σ), f (g a b) ≤ f a\nh₂ : ∀ (a b : σ), f (g a b) ≤ f b\na b : τ\n⊢ f (g (E.symm a) (E.symm b)) ≤ f (E.symm a)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Filter | {
"line": 70,
"column": 35
} | {
"line": 70,
"column": 46
} | {
"line": 70,
"column": 47
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\ninst✝ : PartialOrder α\nF : CFilter α σ\nE : σ ≃ τ\nf : σ → α\np : σ\ng : σ → σ → σ\nh₁ : ∀ (a b : σ), f (g a b) ≤ f a\nh₂ : ∀ (a b : σ), f (g a b) ≤ f b\na b : τ\n⊢ f (E.symm (E (g (E.symm a) (E.symm b)))) ≤ f (E.symm b)",
"ppTerm": "?m.62",
... | [
"α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\ninst✝ : PartialOrder α\nF : CFilter α σ\nE : σ ≃ τ\nf : σ → α\np : σ\ng : σ → σ → σ\nh₁ : ∀ (a b : σ), f (g a b) ≤ f a\nh₂ : ∀ (a b : σ), f (g a b) ≤ f b\na b : τ\n⊢ f (g (E.symm a) (E.symm b)) ≤ f (E.symm b)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Filter | {
"line": 129,
"column": 34
} | {
"line": 129,
"column": 45
} | {
"line": 129,
"column": 46
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\nf : Filter α\nF : f.Realizer\nE : F.σ ≃ τ\nx✝¹ : Set α\nx✝ : x✝¹ ∈ (CFilter.ofEquiv E F.F).toFilter.sets\ns : τ\nh : (CFilter.ofEquiv E F.F).f s ⊆ x✝¹\n⊢ F.F.f (E.symm s) ⊆ x✝¹",
"ppTerm": "?m.41",
"assigned": false,
"usedConstants": [... | [
"α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\nf : Filter α\nF : f.Realizer\nE : F.σ ≃ τ\nx✝¹ : Set α\nx✝ : x✝¹ ∈ (CFilter.ofEquiv E F.F).toFilter.sets\ns : τ\nh : (CFilter.ofEquiv E F.F).f s ⊆ x✝¹\n⊢ F.F.f (E.symm s) ⊆ x✝¹"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 146,
"column": 33
} | {
"line": 146,
"column": 44
} | {
"line": 146,
"column": 45
} | [
{
"pp": "α : Type u_1\ninst✝ : TopologicalSpace α\nF : Realizer α\ns : F.σ\na : α\nm : a ∈ F.F.f s\n⊢ 𝓝 a ≤ 𝓟 (F.F.f s)",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"PartialOrder.toPreorder",
"Preorder.toLE",
"Membership... | [
"α : Type u_1\ninst✝ : TopologicalSpace α\nF : Realizer α\ns : F.σ\na : α\nm : a ∈ F.F.f s\n⊢ F.F.f s ∈ 𝓝 a"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 178,
"column": 31
} | {
"line": 178,
"column": 42
} | {
"line": 178,
"column": 43
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\ninst✝ : TopologicalSpace α\nF : Realizer α\nE : F.σ ≃ τ\na : α\ns✝ : Set α\nx✝ : ∃ b, a ∈ F.F.f b ∧ F.F.f b ⊆ s✝\ns : F.σ\nh : a ∈ F.F.f s ∧ F.F.f s ⊆ s✝\n⊢ a ∈ (Ctop.ofEquiv E F.F).f (E s) ∧ (Ctop.ofEquiv E F.F).f (E s) ⊆ s✝",
"ppTerm": "?m.7... | [
"α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\ninst✝ : TopologicalSpace α\nF : Realizer α\nE : F.σ ≃ τ\na : α\ns✝ : Set α\nx✝ : ∃ b, a ∈ F.F.f b ∧ F.F.f b ⊆ s✝\ns : F.σ\nh : a ∈ F.F.f s ∧ F.F.f s ⊆ s✝\n⊢ a ∈ F.F.f s ∧ F.F.f s ⊆ s✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Analysis.Topology | {
"line": 178,
"column": 74
} | {
"line": 178,
"column": 85
} | {
"line": 178,
"column": 86
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\ninst✝ : TopologicalSpace α\nF : Realizer α\nE : F.σ ≃ τ\na : α\ns : Set α\nx✝ : ∃ b, a ∈ (Ctop.ofEquiv E F.F).f b ∧ (Ctop.ofEquiv E F.F).f b ⊆ s\nt : τ\nh : a ∈ (Ctop.ofEquiv E F.F).f t ∧ (Ctop.ofEquiv E F.F).f t ⊆ s\n⊢ a ∈ F.F.f (E.symm t) ∧ F.F.... | [
"α : Type u_1\nβ : Type u_2\nσ : Type u_3\nτ : Type u_4\ninst✝ : TopologicalSpace α\nF : Realizer α\nE : F.σ ≃ τ\na : α\ns : Set α\nx✝ : ∃ b, a ∈ (Ctop.ofEquiv E F.F).f b ∧ (Ctop.ofEquiv E F.F).f b ⊆ s\nt : τ\nh : a ∈ (Ctop.ofEquiv E F.F).f t ∧ (Ctop.ofEquiv E F.F).f t ⊆ s\n⊢ a ∈ F.F.f (E.symm t) ∧ F.F.f (E.symm t)... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Erased | {
"line": 63,
"column": 71
} | {
"line": 63,
"column": 82
} | {
"line": 63,
"column": 83
} | [
{
"pp": "α : Sort u_1\na b : Erased α\nh : a.out = b.out\n⊢ a = b",
"ppTerm": "?m.6",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"α : Sort u_1\na b : Erased α\nh : a.out = b.out\n⊢ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.FP.Basic | {
"line": 87,
"column": 10
} | {
"line": 87,
"column": 24
} | {
"line": 87,
"column": 24
} | [
{
"pp": "C : FloatCfg\nthis : prec ≤ 2 * emax\n⊢ emin + ↑prec - 1 ≤ ↑emax",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"HMul.hMul",
"FP.prec",
"congrArg",
"FP.emax",
"Eq.mp",
"instMulNat",
"instOfNatNat",
"Int",
"LE.le",
"instL... | [
"C : FloatCfg\nthis : ↑prec ≤ ↑(2 * emax)\n⊢ emin + ↑prec - 1 ≤ ↑emax"
] | ← Int.ofNat_le | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Data.Fin.FlagRange | {
"line": 42,
"column": 27
} | {
"line": 42,
"column": 46
} | {
"line": 42,
"column": 47
} | [
{
"pp": "α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : BoundedOrder α\nn : ℕ\nf : Fin (n + 1) → α\nh0 : f 0 = ⊥\nhlast : f (Fin.last n) = ⊤\nhcovBy : ∀ (k : Fin n), f k.castSucc ⩿ f k.succ\nhmono : Monotone f\nt : Set α\nhtc : IsChain (fun x1 x2 ↦ x1 ≤ x2) t\nhbt : range f ⊆ t\nx : α\nhx : x ∈ t\nh : ∀ (y : Fi... | [
"α : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : BoundedOrder α\nn : ℕ\nf : Fin (n + 1) → α\nh0 : f 0 = ⊥\nhlast : f (Fin.last n) = ⊤\nhcovBy : ∀ (k : Fin n), f k.castSucc ⩿ f k.succ\nhmono : Monotone f\nt : Set α\nhtc : IsChain (fun x1 x2 ↦ x1 ≤ x2) t\nhbt : range f ⊆ t\nx : α\nhx : x ∈ t\nh : ∀ (y : Fin (n + 1)), ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.FlagRange | {
"line": 45,
"column": 12
} | {
"line": 45,
"column": 47
} | {
"line": 45,
"column": 48
} | [
{
"pp": "case zero\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : BoundedOrder α\nn : ℕ\nf : Fin (n + 1) → α\nh0 : f 0 = ⊥\nhlast : f (Fin.last n) = ⊤\nhcovBy : ∀ (k : Fin n), f k.castSucc ⩿ f k.succ\nhmono : Monotone f\nt : Set α\nhtc : IsChain (fun x1 x2 ↦ x1 ≤ x2) t\nhbt : range f ⊆ t\nx : α\nhx : x ∈ t\nh ... | [
"case zero\nα : Type u_1\ninst✝¹ : PartialOrder α\ninst✝ : BoundedOrder α\nn : ℕ\nf : Fin (n + 1) → α\nh0 : f 0 = ⊥\nhlast : f (Fin.last n) = ⊤\nhcovBy : ∀ (k : Fin n), f k.castSucc ⩿ f k.succ\nhmono : Monotone f\nt : Set α\nhtc : IsChain (fun x1 x2 ↦ x1 ≤ x2) t\nhbt : range f ⊆ t\nx : α\nhx : x ∈ t\nh : ∀ (y : Fin... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Semiquot | {
"line": 186,
"column": 20
} | {
"line": 186,
"column": 31
} | {
"line": 186,
"column": 32
} | [
{
"pp": "α : Type u_1\nq : Semiquot α\np : q.IsPure\na : α\n⊢ a ∈ q ↔ a ∈ pure (q.get p)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Pure.pure",
"Semiquot.instMonad",
"Eq.mpr",
"congrArg",
"Monad.toApplicative",
"Membership.mem",
"id",
"... | [
"α : Type u_1\nq : Semiquot α\np : q.IsPure\na : α\n⊢ a ∈ q ↔ a = q.get p"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Semiquot | {
"line": 203,
"column": 43
} | {
"line": 203,
"column": 54
} | {
"line": 203,
"column": 55
} | [
{
"pp": "α : Type u_1\ns t : Semiquot α\nh : t.IsPure\nst : s ≤ t\n⊢ pure (t.get h) ≤ pure (s.get ⋯)",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"Pure.pure",
"Semiquot.instMonad",
"Semiquot.pure_le._simp_1",
"Eq.mpr",
"Monad.toApplicative",
"PartialO... | [
"α : Type u_1\ns t : Semiquot α\nh : t.IsPure\nst : s ≤ t\n⊢ t.get h = s.get ⋯"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 28,
"column": 2
} | {
"line": 28,
"column": 13
} | {
"line": 28,
"column": 14
} | [
{
"pp": "m n : ℕ\nf : Fin m → Fin n\nhf : Function.Injective f\n⊢ m ≤ n",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"m n : ℕ\nf : Fin m → Fin n\nhf : Function.Injective f\n⊢ m ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 35,
"column": 2
} | {
"line": 35,
"column": 13
} | {
"line": 35,
"column": 14
} | [
{
"pp": "m n : ℕ\nf : Fin m ↪ Fin n\n⊢ m ≤ n",
"ppTerm": "?m.3",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"m n : ℕ\nf : Fin m ↪ Fin n\n⊢ m ≤ n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 44,
"column": 2
} | {
"line": 44,
"column": 13
} | {
"line": 44,
"column": 14
} | [
{
"pp": "m n : ℕ\nf : Fin m → Fin n\nhf : Function.Injective f\nb : Fin n\nhb : b ∉ Set.range f\n⊢ m < n",
"ppTerm": "?m.10",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"m n : ℕ\nf : Fin m → Fin n\nhf : Function.Injective f\nb : Fin n\nhb : b ∉ Set.range f\n⊢ m < n"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 51,
"column": 2
} | {
"line": 51,
"column": 13
} | {
"line": 51,
"column": 14
} | [
{
"pp": "m n : ℕ\nf : Fin m → Fin n\nhf : Function.Surjective f\n⊢ n ≤ m",
"ppTerm": "?m.5",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"m n : ℕ\nf : Fin m → Fin n\nhf : Function.Surjective f\n⊢ n ≤ m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Fin.Pigeonhole | {
"line": 59,
"column": 2
} | {
"line": 59,
"column": 13
} | {
"line": 59,
"column": 14
} | [
{
"pp": "m : ℕ\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf : Fin m → α\n⊢ Fintype.card ↑(Set.range f) ≤ m",
"ppTerm": "?m.6",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Fintype.card_ofFinset",
"Finset.univ",
"Finset.univ_filter_exists",
"Iff.of_eq",... | [
"m : ℕ\nα : Type u_1\ninst✝¹ : Fintype α\ninst✝ : DecidableEq α\nf : Fin m → α\n⊢ (Finset.image f Finset.univ).card ≤ m"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Condensed.Light.Sequence | {
"line": 326,
"column": 19
} | {
"line": 326,
"column": 30
} | {
"line": 326,
"column": 31
} | [
{
"pp": "R : Type\ninst✝ : CommRing R\nX Y : LightCondMod R\np : X ⟶ Y\nhp : Epi p\nS : LightProfinite\nf : (free R).obj (S ⊗ ℕ∪{∞}).toCondensed ⟶ Y\nT : LightProfinite\nπ : T ⟶ S ⊗ ℕ∪{∞}\ng : (free R).obj T.toCondensed ⟶ X\nhπ : Epi π\ncomm : (lightProfiniteToLightCondSet ⋙ free R).map π ≫ f = g ≫ p\nS' T' : L... | [
"R : Type\ninst✝ : CommRing R\nX Y : LightCondMod R\np : X ⟶ Y\nhp : Epi p\nS : LightProfinite\nf : (free R).obj (S ⊗ ℕ∪{∞}).toCondensed ⟶ Y\nT : LightProfinite\nπ : T ⟶ S ⊗ ℕ∪{∞}\ng : (free R).obj T.toCondensed ⟶ X\nhπ : Epi π\ncomm : (lightProfiniteToLightCondSet ⋙ free R).map π ≫ f = g ≫ p\nS' T' : LightProfinit... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finite.Perm | {
"line": 49,
"column": 2
} | {
"line": 49,
"column": 25
} | {
"line": 49,
"column": 26
} | [
{
"pp": "α : Type u_1\ninst✝ : Finite α\nhα : Nat.card α ≤ 2\n⊢ Nat.card (Perm α) ∣ 2",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Dvd.dvd",
"congrArg",
"Nat.card_perm",
"id",
"Nat.card",
"instOfNatNat",
"Nat.instDvd",
"Na... | [
"α : Type u_1\ninst✝ : Finite α\nhα : Nat.card α ≤ 2\n⊢ (Nat.card α)! ∣ 2"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finite.Perm | {
"line": 60,
"column": 2
} | {
"line": 60,
"column": 46
} | {
"line": 60,
"column": 47
} | [
{
"pp": "α : Type u_1\ninst✝ : Finite α\na b c : α\nleft✝² : a ∈ _root_.Set.univ\nleft✝¹ : b ∈ _root_.Set.univ\nleft✝ : c ∈ _root_.Set.univ\nhab : a ≠ b\nhac : a ≠ c\nhbc : b ≠ c\nh : ∀ (a b : Perm α) (x : α), (a * b) x = (b * a) x\n⊢ b = c",
"ppTerm": "?m.108",
"assigned": false,
"usedConstants": [... | [
"α : Type u_1\ninst✝ : Finite α\na b c : α\nleft✝² : a ∈ _root_.Set.univ\nleft✝¹ : b ∈ _root_.Set.univ\nleft✝ : c ∈ _root_.Set.univ\nhab : a ≠ b\nhac : a ≠ c\nhbc : b ≠ c\nh : ∀ (a b : Perm α) (x : α), (a * b) x = (b * a) x\n⊢ b = c"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.FinEnum | {
"line": 83,
"column": 39
} | {
"line": 83,
"column": 50
} | {
"line": 83,
"column": 51
} | [
{
"pp": "α : Type u\nβ✝ : α → Type v\nβ : Type ?u.19\nf : β → α\ninst✝¹ : DecidableEq α\ninst✝ : FinEnum β\nh : Surjective f\nx✝ : α\n⊢ x✝ ∈ List.map f (toList β)",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"FinEnum.toList",
"congrArg",
"List.map",
... | [
"α : Type u\nβ✝ : α → Type v\nβ : Type ?u.19\nf : β → α\ninst✝¹ : DecidableEq α\ninst✝ : FinEnum β\nh : Surjective f\nx✝ : α\n⊢ ∃ a, f a = x✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.FinEnum | {
"line": 328,
"column": 24
} | {
"line": 328,
"column": 45
} | {
"line": 328,
"column": 46
} | [
{
"pp": "α : Type u_1\ninst✝¹ : FinEnum α\nβ : α → Type u_2\ninst✝ : (a : α) → FinEnum (β a)\nf : (a : α) → β a\n⊢ f ∈ enum β",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"FinEnum.toList",
"Membership.mem",
"Exists",
"id",
"FinEnum.mem_toList... | [
"α : Type u_1\ninst✝¹ : FinEnum α\nβ : α → Type u_2\ninst✝ : (a : α) → FinEnum (β a)\nf : (a : α) → β a\n⊢ ∃ a ∈ (FinEnum.toList α).pi fun x ↦ FinEnum.toList (β x), (fun x ↦ a x ⋯) = f"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 83,
"column": 6
} | {
"line": 83,
"column": 22
} | {
"line": 83,
"column": 23
} | [
{
"pp": "case none\nα : Type u_1\nβ : Type u_2\nf : α → Option α\ng : α → β\nh : ∀ (a b : α), b ∈ f a → g a = g b\na : α\nl : List α\nh' : f a = none\n⊢ map g (lookmap f (a :: l)) = map g (a :: l)",
"ppTerm": "?none",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"List... | [
"case none\nα : Type u_1\nβ : Type u_2\nf : α → Option α\ng : α → β\nh : ∀ (a b : α), b ∈ f a → g a = g b\na : α\nl : List α\nh' : f a = none\n⊢ map g (lookmap f l) = map g l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.FinEnum | {
"line": 336,
"column": 59
} | {
"line": 336,
"column": 70
} | {
"line": 336,
"column": 71
} | [
{
"pp": "α✝ : Type u_1\ninst✝³ : FinEnum α✝\nβ : α✝ → Type u_2\ninst✝² : (a : α✝) → FinEnum (β a)\np : Prop\ninst✝¹ : Decidable p\nα : p → Type\ninst✝ : (hp : p) → FinEnum (α hp)\nhp : p\nx : (hp : p) → α hp\n⊢ x ∈ map (fun x x_1 ↦ x) (FinEnum.toList (α hp))",
"ppTerm": "?m.30",
"assigned": true,
"u... | [
"α✝ : Type u_1\ninst✝³ : FinEnum α✝\nβ : α✝ → Type u_2\ninst✝² : (a : α✝) → FinEnum (β a)\np : Prop\ninst✝¹ : Decidable p\nα : p → Type\ninst✝ : (hp : p) → FinEnum (α hp)\nhp : p\nx : (hp : p) → α hp\n⊢ ∃ a, (fun x ↦ a) = x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 101,
"column": 6
} | {
"line": 101,
"column": 21
} | {
"line": 101,
"column": 22
} | [
{
"pp": "case cons.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na : α\nl₁✝ l₂✝ : List α\np : l₁✝ ~ l₂✝\nIH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) l₁✝ → lookmap f l₁✝ ~ lookmap f l₂✝\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d)... | [
"case cons.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na : α\nl₁✝ l₂✝ : List α\np : l₁✝ ~ l₂✝\nIH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) l₁✝ → lookmap f l₁✝ ~ lookmap f l₂✝\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (a :: l₁✝)\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 105,
"column": 6
} | {
"line": 105,
"column": 26
} | {
"line": 105,
"column": 27
} | [
{
"pp": "case swap.none.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nh₁ : f a = none\nh₂ : f b = none\n⊢ lookmap f (b :: a :: l) ~ lookmap f (a :: b :: l)",
"ppTerm": "?swap.none.non... | [
"case swap.none.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nh₁ : f a = none\nh₂ : f b = none\n⊢ b :: a :: lookmap f l ~ a :: b :: lookmap f l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 106,
"column": 6
} | {
"line": 106,
"column": 48
} | {
"line": 106,
"column": 49
} | [
{
"pp": "case swap.none.some\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nh₁ : f a = none\nd : α\nh₂ : f b = some d\n⊢ lookmap f (b :: a :: l) ~ lookmap f (a :: b :: l)",
"ppTerm": "?swap... | [
"case swap.none.some\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nh₁ : f a = none\nd : α\nh₂ : f b = some d\n⊢ d :: a :: l ~ a :: d :: l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Lookmap | {
"line": 107,
"column": 6
} | {
"line": 107,
"column": 48
} | {
"line": 107,
"column": 49
} | [
{
"pp": "case swap.some.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nc : α\nh₁ : f a = some c\nh₂ : f b = none\n⊢ lookmap f (b :: a :: l) ~ lookmap f (a :: b :: l)",
"ppTerm": "?swap... | [
"case swap.some.none\nα : Type u_1\nf : α → Option α\nl₁ l₂ : List α\na b : α\nl : List α\nH : Pairwise (fun a b ↦ ∀ (c : α), c ∈ f a → ∀ (d : α), d ∈ f b → a = b ∧ c = d) (b :: a :: l)\nc : α\nh₁ : f a = some c\nh₂ : f b = none\n⊢ b :: c :: l ~ c :: b :: l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Condensed.Light.Sequence | {
"line": 360,
"column": 70
} | {
"line": 360,
"column": 81
} | {
"line": 360,
"column": 82
} | [
{
"pp": "R : Type\ninst✝ : CommRing R\nX Y : LightCondMod R\np : X ⟶ Y\nhp : Epi p\nS : LightProfinite\nf : (free R).obj (S ⊗ ℕ∪{∞}).toCondensed ⟶ Y\nT : LightProfinite\nπ : T ⟶ S ⊗ ℕ∪{∞}\ng : (free R).obj T.toCondensed ⟶ X\nhπ : Epi π\ncomm : (lightProfiniteToLightCondSet ⋙ free R).map π ≫ f = g ≫ p\nS' T' : L... | [
"R : Type\ninst✝ : CommRing R\nX Y : LightCondMod R\np : X ⟶ Y\nhp : Epi p\nS : LightProfinite\nf : (free R).obj (S ⊗ ℕ∪{∞}).toCondensed ⟶ Y\nT : LightProfinite\nπ : T ⟶ S ⊗ ℕ∪{∞}\ng : (free R).obj T.toCondensed ⟶ X\nhπ : Epi π\ncomm : (lightProfiniteToLightCondSet ⋙ free R).map π ≫ f = g ≫ p\nS' T' : LightProfinit... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.AList | {
"line": 323,
"column": 2
} | {
"line": 323,
"column": 22
} | {
"line": 323,
"column": 23
} | [
{
"pp": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nc : Sigma β\nl : List (Sigma β)\nh : (c :: l).NodupKeys\n⊢ { entries := c :: l, nodupKeys := h } = insert c.fst c.snd { entries := l, nodupKeys := ⋯ }",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"AList.mk... | [
"α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nc : Sigma β\nl : List (Sigma β)\nh : (c :: l).NodupKeys\n⊢ l = kerase c.fst l"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.DenselyOrdered | {
"line": 33,
"column": 4
} | {
"line": 33,
"column": 52
} | {
"line": 35,
"column": 0
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : DenselyOrdered α\ns t : Finset α\ninst✝² : NoMaxOrder α\ninst✝¹ : NoMinOrder α\ninst✝ : Nonempty α\nH : ∀ x ∈ s, ∀ y ∈ t, x < y\nhs : ¬s.Nonempty\nht : ¬t.Nonempty\n⊢ ∃ b, (∀ x ∈ s, x < b) ∧ ∀ y ∈ t, b < y",
"ppTerm": "?neg✝",
"assigned":... | [] | exact Nonempty.elim ‹_› fun p ↦ ⟨p, by simp_all⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Data.Finset.DenselyOrdered | {
"line": 33,
"column": 4
} | {
"line": 33,
"column": 52
} | {
"line": 35,
"column": 0
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : DenselyOrdered α\ns t : Finset α\ninst✝² : NoMaxOrder α\ninst✝¹ : NoMinOrder α\ninst✝ : Nonempty α\nH : ∀ x ∈ s, ∀ y ∈ t, x < y\nhs : ¬s.Nonempty\nht : ¬t.Nonempty\n⊢ ∃ b, (∀ x ∈ s, x < b) ∧ ∀ y ∈ t, b < y",
"ppTerm": "?neg✝",
"assigned":... | [] | exact Nonempty.elim ‹_› fun p ↦ ⟨p, by simp_all⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Finset.DenselyOrdered | {
"line": 33,
"column": 4
} | {
"line": 33,
"column": 52
} | {
"line": 35,
"column": 0
} | [
{
"pp": "case neg\nα : Type u_1\ninst✝⁴ : LinearOrder α\ninst✝³ : DenselyOrdered α\ns t : Finset α\ninst✝² : NoMaxOrder α\ninst✝¹ : NoMinOrder α\ninst✝ : Nonempty α\nH : ∀ x ∈ s, ∀ y ∈ t, x < y\nhs : ¬s.Nonempty\nht : ¬t.Nonempty\n⊢ ∃ b, (∀ x ∈ s, x < b) ∧ ∀ y ∈ t, b < y",
"ppTerm": "?neg✝",
"assigned":... | [] | exact Nonempty.elim ‹_› fun p ↦ ⟨p, by simp_all⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.List.Sigma | {
"line": 252,
"column": 6
} | {
"line": 254,
"column": 38
} | {
"line": 254,
"column": 38
} | [
{
"pp": "α : Type u\nα' : Type u'\nβ : Type v\nf : α → α'\nhf : Function.Injective f\nhd : (_ : α) × β\ntl : List ((_ : α) × β)\nih : tl.NodupKeys → (map (Sigma.map f fun x ↦ id) tl).NodupKeys\nnd : ¬hd.fst ∈ tl.keys ∧ tl.NodupKeys\nh : (Sigma.map f (fun x ↦ id) hd).fst ∈ (map (Sigma.map f fun x ↦ id) tl).keys\... | [] | simp only [keys, map_map] at h ⊢
obtain ⟨x, hm, he⟩ := mem_map.mp h
exact mem_map.mpr ⟨x, hm, hf he⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Sigma | {
"line": 252,
"column": 6
} | {
"line": 254,
"column": 38
} | {
"line": 254,
"column": 38
} | [
{
"pp": "α : Type u\nα' : Type u'\nβ : Type v\nf : α → α'\nhf : Function.Injective f\nhd : (_ : α) × β\ntl : List ((_ : α) × β)\nih : tl.NodupKeys → (map (Sigma.map f fun x ↦ id) tl).NodupKeys\nnd : ¬hd.fst ∈ tl.keys ∧ tl.NodupKeys\nh : (Sigma.map f (fun x ↦ id) hd).fst ∈ (map (Sigma.map f fun x ↦ id) tl).keys\... | [] | simp only [keys, map_map] at h ⊢
obtain ⟨x, hm, he⟩ := mem_map.mp h
exact mem_map.mpr ⟨x, hm, hf he⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finmap | {
"line": 306,
"column": 4
} | {
"line": 306,
"column": 15
} | {
"line": 306,
"column": 16
} | [
{
"pp": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nf : { f // ∀ (i : α), (f.2 i).isSome = true ↔ i ∈ f.1 }\ni : α\nx : β i\nleft✝¹ : ⟨i, x⟩.fst ∈ (↑f).1\nhx : (↑f).2 ⟨i, x⟩.fst = some ⟨i, x⟩.snd\ny : β i\nleft✝ : ⟨i, y⟩.fst ∈ (↑f).1\nhy : (↑f).2 ⟨i, y⟩.fst = some ⟨i, y⟩.snd\n⊢ ⟨i, x⟩ = ⟨i, y⟩",
"pp... | [
"α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\nf : { f // ∀ (i : α), (f.2 i).isSome = true ↔ i ∈ f.1 }\ni : α\nx : β i\nleft✝¹ : ⟨i, x⟩.fst ∈ (↑f).1\nhx : (↑f).2 ⟨i, x⟩.fst = some ⟨i, x⟩.snd\ny : β i\nleft✝ : ⟨i, y⟩.fst ∈ (↑f).1\nhy : (↑f).2 ⟨i, y⟩.fst = some ⟨i, y⟩.snd\n⊢ x = y"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sigma | {
"line": 455,
"column": 46
} | {
"line": 455,
"column": 67
} | {
"line": 455,
"column": 68
} | [
{
"pp": "α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na₁ a₂ : α\nl : List (Sigma β)\nh : a₁ ≠ a₂\np✝ : a₁ ∈ l.keys\nw✝² : β a₂\nw✝¹ w✝ : List (Sigma β)\nleft✝ : ¬a₂ ∈ w✝¹.keys\np : a₁ ∈ (w✝¹ ++ ⟨a₂, w✝²⟩ :: w✝).keys\nq : a₂ ∈ (w✝¹ ++ ⟨a₂, w✝²⟩ :: w✝).keys\n⊢ a₁ ∈ (w✝¹ ++ w✝).keys",
"ppTerm": "?m.75",
... | [
"α : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na₁ a₂ : α\nl : List (Sigma β)\nh : a₁ ≠ a₂\np✝ : a₁ ∈ l.keys\nw✝² : β a₂\nw✝¹ w✝ : List (Sigma β)\nleft✝ : ¬a₂ ∈ w✝¹.keys\np : a₁ ∈ (w✝¹ ++ ⟨a₂, w✝²⟩ :: w✝).keys\nq : a₂ ∈ (w✝¹ ++ ⟨a₂, w✝²⟩ :: w✝).keys\n⊢ (∃ x, ⟨a₁, x⟩ ∈ w✝¹) ∨ ∃ x, ⟨a₁, x⟩ ∈ w✝"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finset.PiInduction | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 28
} | {
"line": 52,
"column": 29
} | [
{
"pp": "ι : Type u_1\nα : ι → Type u_2\ninst✝² : Finite ι\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → DecidableEq (α i)\nr : (i : ι) → α i → Finset (α i) → Prop\nH_ex : ∀ (i : ι) (s : Finset (α i)), s.Nonempty → ∃ x ∈ s, r i x (s.erase x)\np : ((i : ι) → Finset (α i)) → Prop\nh0 : p fun x ↦ ∅\nstep : ∀ (g : (i ... | [
"ι : Type u_1\nα : ι → Type u_2\ninst✝² : Finite ι\ninst✝¹ : DecidableEq ι\ninst✝ : (i : ι) → DecidableEq (α i)\nr : (i : ι) → α i → Finset (α i) → Prop\nH_ex : ∀ (i : ι) (s : Finset (α i)), s.Nonempty → ∃ x ∈ s, r i x (s.erase x)\np : ((i : ι) → Finset (α i)) → Prop\nh0 : p fun x ↦ ∅\nstep : ∀ (g : (i : ι) → Finse... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.AList | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 28
} | {
"line": 83,
"column": 2
} | [
{
"pp": "α : Type u_1\nM : Type u_2\ninst✝² : Zero M\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq M\nl : AList fun _x ↦ M\n⊢ l.lookupFinsupp.support = (filter (fun x ↦ decide (x.snd ≠ 0)) l.entries).keys.toFinset",
"ppTerm": "?m.27",
"assigned": true,
"usedConstants": [
"instDecidableNot",
... | [
"α : Type u_1\nM : Type u_2\ninst✝² : Zero M\ninst✝¹ : DecidableEq α\ninst✝ : DecidableEq M\nl : AList fun _x ↦ M\n⊢ (filter (fun x ↦ decide (x.snd ≠ 0)) l.entries).keys.toFinset =\n (filter (fun x ↦ decide (x.snd ≠ 0)) l.entries).keys.toFinset"
] | dsimp only [lookupFinsupp] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.Data.Finsupp.AList | {
"line": 91,
"column": 60
} | {
"line": 93,
"column": 39
} | {
"line": 95,
"column": 0
} | [
{
"pp": "α : Type u_1\nM : Type u_2\ninst✝¹ : Zero M\ninst✝ : DecidableEq α\nl : AList fun _x ↦ M\na : α\n⊢ l.lookupFinsupp a = 0 ↔ a ∉ l ∨ 0 ∈ lookup a l",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"False",
"Option.ctorIdx",
... | [] | by
rw [lookupFinsupp_apply, ← lookup_eq_none]
rcases lookup a l with - | m <;> simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Data.Finsupp.AList | {
"line": 119,
"column": 6
} | {
"line": 119,
"column": 17
} | {
"line": 119,
"column": 18
} | [
{
"pp": "case neg\nα : Type u_1\nM : Type u_2\ninst✝ : Zero M\nf : α →₀ M\na : α\nh : ¬f a = 0\n⊢ ⟨a, f a⟩ ∈ f.toAList.entries",
"ppTerm": "?neg✝",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"Prod.toSigma",
"congrArg",
"Finset",
"List.ma... | [
"case neg\nα : Type u_1\nM : Type u_2\ninst✝ : Zero M\nf : α →₀ M\na : α\nh : ¬f a = 0\n⊢ ¬f a = 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.NeLocus | {
"line": 44,
"column": 2
} | {
"line": 45,
"column": 32
} | {
"line": 45,
"column": 33
} | [
{
"pp": "α : Type u_1\nN : Type u_3\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : Zero N\nf g : α →₀ N\na : α\n⊢ a ∈ f.neLocus g ↔ f a ≠ g a",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"Finsupp.instFunLike",
"Eq.mpr",
"instDecidableNot",
"Finset.instU... | [
"α : Type u_1\nN : Type u_3\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : Zero N\nf g : α →₀ N\na : α\n⊢ f a ≠ g a → f a ≠ 0 ∨ g a ≠ 0"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.NeLocus | {
"line": 83,
"column": 14
} | {
"line": 83,
"column": 73
} | {
"line": 83,
"column": 74
} | [
{
"pp": "α : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁴ : DecidableEq α\ninst✝³ : DecidableEq N\ninst✝² : Zero N\ninst✝¹ : DecidableEq M\ninst✝ : Zero M\nf g : α →₀ N\nF : N → M\nF0 : F 0 = 0\nx : α\n⊢ x ∈ (mapRange F F0 f).neLocus (mapRange F F0 g) → x ∈ f.neLocus g",
"ppTerm": "?m.31",
"assigned": t... | [
"α : Type u_1\nM : Type u_2\nN : Type u_3\ninst✝⁴ : DecidableEq α\ninst✝³ : DecidableEq N\ninst✝² : Zero N\ninst✝¹ : DecidableEq M\ninst✝ : Zero M\nf g : α →₀ N\nF : N → M\nF0 : F 0 = 0\nx : α\n⊢ f x = g x → F (f x) = F (g x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Finsupp.NeLocus | {
"line": 138,
"column": 2
} | {
"line": 138,
"column": 35
} | {
"line": 138,
"column": 36
} | [
{
"pp": "α : Type u_1\nN : Type u_3\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : AddGroup N\nf₁ f₂ g : α →₀ N\n⊢ (f₁ - g).neLocus (f₂ - g) = f₁.neLocus f₂",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"AddGroup.toSubtractionMonoid",
"Eq.mpr",
"congrArg",
... | [
"α : Type u_1\nN : Type u_3\ninst✝² : DecidableEq α\ninst✝¹ : DecidableEq N\ninst✝ : AddGroup N\nf₁ f₂ g : α →₀ N\n⊢ (f₁ + -g).neLocus (f₂ + -g) = f₁.neLocus f₂"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Sigma | {
"line": 749,
"column": 4
} | {
"line": 753,
"column": 35
} | {
"line": 755,
"column": 0
} | [
{
"pp": "case cons\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns : Sigma β\ntail✝ : List (Sigma β)\nih : ∀ {l₂ : List (Sigma β)}, b ∈ dlookup a (tail✝.kunion l₂) ↔ b ∈ dlookup a tail✝ ∨ ¬a ∈ tail✝.keys ∧ b ∈ dlookup a l₂\nl₂ : List (Sigma β)\n⊢ b ∈ dlookup a ((s :: tail✝).kunion l₂) ↔ b ... | [] | obtain ⟨a'⟩ := s
by_cases h₁ : a = a'
· subst h₁
simp
· simp [h₁, @ih (kerase a' l₂)] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Sigma | {
"line": 749,
"column": 4
} | {
"line": 753,
"column": 35
} | {
"line": 755,
"column": 0
} | [
{
"pp": "case cons\nα : Type u\nβ : α → Type v\ninst✝ : DecidableEq α\na : α\nb : β a\ns : Sigma β\ntail✝ : List (Sigma β)\nih : ∀ {l₂ : List (Sigma β)}, b ∈ dlookup a (tail✝.kunion l₂) ↔ b ∈ dlookup a tail✝ ∨ ¬a ∈ tail✝.keys ∧ b ∈ dlookup a l₂\nl₂ : List (Sigma β)\n⊢ b ∈ dlookup a ((s :: tail✝).kunion l₂) ↔ b ... | [] | obtain ⟨a'⟩ := s
by_cases h₁ : a = a'
· subst h₁
simp
· simp [h₁, @ih (kerase a' l₂)] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Finsupp.Sigma | {
"line": 90,
"column": 2
} | {
"line": 90,
"column": 13
} | {
"line": 90,
"column": 14
} | [
{
"pp": "κ : Type u_1\nι : κ → Type u_2\nM : Type u_3\ninst✝ : Zero M\nk : κ\nf g : ι k →₀ M\nh : f.embSigma = g.embSigma\ni : ι k\nthis : f.embSigma ⟨k, i⟩ = g.embSigma ⟨k, i⟩\n⊢ f i = g i",
"ppTerm": "?m.38",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"κ : Type u_1\nι : κ → Type u_2\nM : Type u_3\ninst✝ : Zero M\nk : κ\nf g : ι k →₀ M\nh : f.embSigma = g.embSigma\ni : ι k\nthis : f.embSigma ⟨k, i⟩ = g.embSigma ⟨k, i⟩\n⊢ f i = g i"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Holor | {
"line": 151,
"column": 4
} | {
"line": 151,
"column": 14
} | {
"line": 152,
"column": 4
} | [
{
"pp": "α : Type\nds₁ ds₂ ds₃ : List ℕ\ninst✝ : Semigroup α\nx : Holor α ds₁\ny : Holor α ds₂\nz : Holor α ds₃\nt : HolorIndex (ds₁ ++ ds₂ ++ ds₃)\n⊢ (x ⊗ y ⊗ z) t = cast ⋯ (x ⊗ (y ⊗ z)) t",
"ppTerm": "?m.40",
"assigned": true,
"usedConstants": [
"Semigroup.toMul",
"cast",
"id",
... | [
"α : Type\nds₁ ds₂ ds₃ : List ℕ\ninst✝ : Semigroup α\nx : Holor α ds₁\ny : Holor α ds₂\nz : Holor α ds₃\nt : HolorIndex (ds₁ ++ ds₂ ++ ds₃)\n⊢ x t.take.take * y t.take.drop * z t.drop = cast ⋯ (fun t ↦ x t.take * (y t.drop.take * z t.drop.drop)) t"
] | unfold mul | Lean.Elab.Tactic.evalUnfold | Lean.Parser.Tactic.unfold |
Mathlib.Data.Holor | {
"line": 242,
"column": 28
} | {
"line": 242,
"column": 82
} | {
"line": 242,
"column": 83
} | [
{
"pp": "α : Type\nd : ℕ\nds : List ℕ\ninst✝ : Semiring α\nx : Holor α (d :: ds)\ni : ℕ\nhid : i < d\nb : ↥(Finset.range d)\na✝ : b ∈ (Finset.range d).attach\nhbi : b ≠ ⟨i, ⋯⟩\n⊢ i ≠ ↑b",
"ppTerm": "?m.106",
"assigned": true,
"usedConstants": [
"Finset",
"Membership.mem",
"id",
... | [
"α : Type\nd : ℕ\nds : List ℕ\ninst✝ : Semiring α\nx : Holor α (d :: ds)\ni : ℕ\nhid : i < d\nb : ↥(Finset.range d)\na✝ : b ∈ (Finset.range d).attach\nhbi : b ≠ ⟨i, ⋯⟩\n⊢ ¬i = ↑b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Holor | {
"line": 280,
"column": 6
} | {
"line": 280,
"column": 59
} | {
"line": 280,
"column": 60
} | [
{
"pp": "α : Type\nds : List ℕ\ninst✝¹ : Mul α\ninst✝ : AddMonoid α\nm n : ℕ\ny x₁ x₂ : Holor α ds\nhx₁ : x₁.CPRankMax1\nhx₂ : CPRankMax m x₂\nhy : CPRankMax n y\nthis : CPRankMax (m + n + 1) (x₁ + (x₂ + y))\n⊢ CPRankMax (m + 1 + n) (x₁ + x₂ + y)",
"ppTerm": "?m.245",
"assigned": true,
"usedConstant... | [
"α : Type\nds : List ℕ\ninst✝¹ : Mul α\ninst✝ : AddMonoid α\nm n : ℕ\ny x₁ x₂ : Holor α ds\nhx₁ : x₁.CPRankMax1\nhx₂ : CPRankMax m x₂\nhy : CPRankMax n y\nthis : CPRankMax (m + n + 1) (x₁ + (x₂ + y))\n⊢ CPRankMax (m + (n + 1)) (x₁ + (x₂ + y))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.CardIntervalMod | {
"line": 61,
"column": 2
} | {
"line": 62,
"column": 76
} | {
"line": 63,
"column": 2
} | [
{
"pp": "a b r : ℤ\nhr : 0 < r\nx : ℤ\n⊢ x ∈ {x ∈ Ioc a b | r ∣ x} ↔ x ∈ map { toFun := fun x ↦ x * r, inj' := ⋯ } (Ioc ⌊↑a / ↑r⌋ ⌊↑b / ↑r⌋)",
"ppTerm": "?m.59",
"assigned": true,
"usedConstants": [
"Int.decidableDvd",
"Iff.mpr",
"Int.cast",
"Eq.mpr",
"GroupWithZero.toM... | [
"a b r : ℤ\nhr : 0 < r\nx : ℤ\n⊢ ((a < x ∧ x ≤ b) ∧ ∃ c, x = c * r) ↔\n ∃ a_1, (a < a_1 * r ∧ a_1 * r ≤ b) ∧ { toFun := fun x ↦ x * r, inj' := ⋯ } a_1 = x"
] | simp only [mem_map, mem_filter, mem_Ioc, floor_lt, le_floor, div_lt_iff₀, le_div_iff₀,
dvd_iff_exists_eq_mul_left, cast_pos.2 hr, ← cast_mul, cast_lt, cast_le] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Holor | {
"line": 327,
"column": 4
} | {
"line": 327,
"column": 19
} | {
"line": 328,
"column": 4
} | [
{
"pp": "α : Type\ninst✝ : Semiring α\nd : ℕ\nds : List ℕ\nx : Holor α (d :: ds)\nh_summands : ∀ (i : ↥(Finset.range d)), CPRankMax ds.prod (unitVec d ↑i ⊗ x.slice ↑i ⋯)\nh_dds_prod : (d :: ds).prod = (Finset.range d).card * ds.prod\nthis : CPRankMax ((Finset.range d).attach.card * ds.prod) (∑ i ∈ (Finset.range... | [
"α : Type\ninst✝ : Semiring α\nd : ℕ\nds : List ℕ\nx : Holor α (d :: ds)\nh_summands : ∀ (i : ↥(Finset.range d)), CPRankMax ds.prod (unitVec d ↑i ⊗ x.slice ↑i ⋯)\nh_dds_prod : (d :: ds).prod = (Finset.range d).card * ds.prod\nthis : CPRankMax ((Finset.range d).attach.card * ds.prod) (∑ i ∈ (Finset.range d).attach, ... | rw [h_dds_prod] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Data.Int.Lemmas | {
"line": 56,
"column": 2
} | {
"line": 56,
"column": 44
} | {
"line": 57,
"column": 4
} | [
{
"pp": "a b : ℤ\nha : a ≤ 0\nhb : b ≤ 0\n⊢ a.natAbs = b.natAbs ↔ a = b",
"ppTerm": "?m.11",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a b : ℤ\nha : a ≤ 0\nhb : b ≤ 0\n⊢ a.natAbs = b.natAbs ↔ a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.Lemmas | {
"line": 61,
"column": 2
} | {
"line": 61,
"column": 35
} | {
"line": 61,
"column": 36
} | [
{
"pp": "a b : ℤ\nha : 0 ≤ a\nhb : b ≤ 0\n⊢ a.natAbs = b.natAbs ↔ a = -b",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a b : ℤ\nha : 0 ≤ a\nhb : b ≤ 0\n⊢ a.natAbs = b.natAbs ↔ a = -b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.Lemmas | {
"line": 65,
"column": 2
} | {
"line": 65,
"column": 35
} | {
"line": 65,
"column": 36
} | [
{
"pp": "a b : ℤ\nha : a ≤ 0\nhb : 0 ≤ b\n⊢ a.natAbs = b.natAbs ↔ -a = b",
"ppTerm": "?m.13",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a b : ℤ\nha : a ≤ 0\nhb : 0 ≤ b\n⊢ a.natAbs = b.natAbs ↔ -a = b"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.Int.Lemmas | {
"line": 91,
"column": 2
} | {
"line": 91,
"column": 30
} | {
"line": 92,
"column": 4
} | [
{
"pp": "a : ℤ\nx✝ : a ∈ Iic 0\nb : ℤ\nhb : b ∈ Iic 0\nhab : a < b\n⊢ b.natAbs < a.natAbs",
"ppTerm": "?m.14",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
}
] | [
"a : ℤ\nx✝ : a ∈ Iic 0\nb : ℤ\nhb : b ∈ Iic 0\nhab : a < b\n⊢ b.natAbs < a.natAbs"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Data.List.Intervals | {
"line": 62,
"column": 54
} | {
"line": 62,
"column": 70
} | {
"line": 63,
"column": 2
} | [
{
"pp": "n m l : ℕ\nthis : n ≤ l ∧ l < n + (m - n) ↔ n ≤ l ∧ l < m\n⊢ l ∈ Ico n m ↔ n ≤ l ∧ l < m",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"List.mem_range'_1._simp_1",
"congrArg",
"List.range'",
"HSub.hSub",
"Membership.mem",
"instSubNat",
"... | [] | simp [Ico, this] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.List.Intervals | {
"line": 62,
"column": 54
} | {
"line": 62,
"column": 70
} | {
"line": 63,
"column": 2
} | [
{
"pp": "n m l : ℕ\nthis : n ≤ l ∧ l < n + (m - n) ↔ n ≤ l ∧ l < m\n⊢ l ∈ Ico n m ↔ n ≤ l ∧ l < m",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"List.mem_range'_1._simp_1",
"congrArg",
"List.range'",
"HSub.hSub",
"Membership.mem",
"instSubNat",
"... | [] | simp [Ico, this] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.List.Intervals | {
"line": 62,
"column": 54
} | {
"line": 62,
"column": 70
} | {
"line": 63,
"column": 2
} | [
{
"pp": "n m l : ℕ\nthis : n ≤ l ∧ l < n + (m - n) ↔ n ≤ l ∧ l < m\n⊢ l ∈ Ico n m ↔ n ≤ l ∧ l < m",
"ppTerm": "?m.26",
"assigned": true,
"usedConstants": [
"List.mem_range'_1._simp_1",
"congrArg",
"List.range'",
"HSub.hSub",
"Membership.mem",
"instSubNat",
"... | [] | simp [Ico, this] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
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