module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basis | {
"line": 152,
"column": 2
} | {
"line": 156,
"column": 85
} | {
"line": 158,
"column": 0
} | [
{
"pp": "basis_hd : ℝ → ℝ\nbasis_tl : Basis\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\n⊢ WellFormedBasis (basis_hd :: basis_tl ++ [Real.log ∘ (basis_hd :: basis_tl).getLast ⋯])",
"ppTerm": "?m.16",
"assigned": true,
"usedConstants": [
"List.getLast",
"Eq.mpr",
"Real",
... | [] | apply h_basis.push
· simp [Real.tendsto_log_atTop.comp, h_basis.right]
· intro g hg
simpa [List.getLast_of_getLast?_eq_some hg] using Real.isLittleO_log_id_atTop.comp_tendsto <|
Real.tendsto_log_atTop.comp <| h_basis.tendsto_atTop <| List.mem_of_getLast? hg | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basic | {
"line": 187,
"column": 4
} | {
"line": 187,
"column": 60
} | {
"line": 189,
"column": 0
} | [
{
"pp": "c : ℝ\nbasis_hd : ℝ → ℝ\nbasis_tl : List (ℝ → ℝ)\nh_basis : WellFormedBasis (basis_hd :: basis_tl)\n⊢ Majorized (fun x ↦ c) basis_hd 0",
"ppTerm": "?m.47",
"assigned": true,
"usedConstants": [
"Real",
"congrArg",
"true_or",
"Membership.mem",
"Tactic.ComputeAsym... | [] | exact Majorized.const <| h_basis.tendsto_atTop (by simp) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Basic | {
"line": 203,
"column": 53
} | {
"line": 206,
"column": 77
} | {
"line": 208,
"column": 0
} | [
{
"pp": "basis : Basis\nn : Fin (List.length basis)\nr : ℝ\n⊢ (monomialRpow basis (↑n) r).toFun = basis[n] ^ r",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"IsRightCancelAdd.addRightStrictMono_of_addRightMono",
"instNeZeroNatHAdd_1",
"Real.instPow",
"Real",
... | [] | by
cases basis with
| nil => grind
| cons basis_hd basis_tl => cases n using Fin.cases <;> simp [monomialRpow] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Predicates | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 33
} | {
"line": 99,
"column": 0
} | [
{
"pp": "hd : ℝ\ntl : UnitMonomial\n⊢ FirstNonzeroIsPos (hd :: tl) ↔ 0 < hd ∨ hd = 0 ∧ tl.FirstNonzeroIsPos",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Predicates.0.Tactic.ComputeAsymptotics.UnitMonomial.FirstNonzero... | [] | grind [FirstNonzeroIsPos, sign] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Predicates | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 33
} | {
"line": 99,
"column": 0
} | [
{
"pp": "hd : ℝ\ntl : UnitMonomial\n⊢ FirstNonzeroIsPos (hd :: tl) ↔ 0 < hd ∨ hd = 0 ∧ tl.FirstNonzeroIsPos",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Predicates.0.Tactic.ComputeAsymptotics.UnitMonomial.FirstNonzero... | [] | grind [FirstNonzeroIsPos, sign] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Predicates | {
"line": 97,
"column": 2
} | {
"line": 97,
"column": 33
} | {
"line": 99,
"column": 0
} | [
{
"pp": "hd : ℝ\ntl : UnitMonomial\n⊢ FirstNonzeroIsPos (hd :: tl) ↔ 0 < hd ∨ hd = 0 ∧ tl.FirstNonzeroIsPos",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Predicates.0.Tactic.ComputeAsymptotics.UnitMonomial.FirstNonzero... | [] | grind [FirstNonzeroIsPos, sign] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 892,
"column": 6
} | {
"line": 893,
"column": 17
} | {
"line": 894,
"column": 4
} | [
{
"pp": "case succ.refine_2.e_a.zero\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nω0 : Ordinal.{0} := ω ^ a0.repr\nα' : Ordinal.{0} := ω0 * ↑↑n + a'.repr\nα0 : 0 < α'\nω00 : 0 < ω0 ^ ↑k\nh : a'.repr + ↑0 < ω ^ a0.repr\nR' : Ordinal.{0} := (op... | [] | have : R = 0 := by cases k <;> simp [R, opowAux]
simp [this] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.SetTheory.Ordinal.Notation | {
"line": 892,
"column": 6
} | {
"line": 893,
"column": 17
} | {
"line": 894,
"column": 4
} | [
{
"pp": "case succ.refine_2.e_a.zero\na0 a' : ONote\nN0 : a0.NF\nNa' : a'.NF\nd : ω ∣ a'.repr\ne0 : a0.repr ≠ 0\nn : ℕ+\nNo : (a0.oadd n a').NF\nk : ℕ\nω0 : Ordinal.{0} := ω ^ a0.repr\nα' : Ordinal.{0} := ω0 * ↑↑n + a'.repr\nα0 : 0 < α'\nω00 : 0 < ω0 ^ ↑k\nh : a'.repr + ↑0 < ω ^ a0.repr\nR' : Ordinal.{0} := (op... | [] | have : R = 0 := by cases k <;> simp [R, opowAux]
simp [this] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 281,
"column": 2
} | {
"line": 282,
"column": 5
} | {
"line": 284,
"column": 0
} | [
{
"pp": "b₁ b₂ b₃ : ℝ → ℝ\nbs₁ bs₂ bs₃ : Basis\nf₁ : ℝ → ℝ\ng₁ : MultiseriesExpansion bs₁ → MultiseriesExpansion bs₂\nf₂ : ℝ → ℝ\ng₂ : MultiseriesExpansion bs₂ → MultiseriesExpansion bs₃\nms : Multiseries b₁ bs₁\n⊢ map (f₂ ∘ f₁) (g₂ ∘ g₁) ms = map f₂ g₂ (map f₁ g₁ ms)",
"ppTerm": "?m.26",
"assigned": tr... | [] | simp [map, ← Stream'.Seq.map_comp]
rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Defs | {
"line": 281,
"column": 2
} | {
"line": 282,
"column": 5
} | {
"line": 284,
"column": 0
} | [
{
"pp": "b₁ b₂ b₃ : ℝ → ℝ\nbs₁ bs₂ bs₃ : Basis\nf₁ : ℝ → ℝ\ng₁ : MultiseriesExpansion bs₁ → MultiseriesExpansion bs₂\nf₂ : ℝ → ℝ\ng₂ : MultiseriesExpansion bs₂ → MultiseriesExpansion bs₃\nms : Multiseries b₁ bs₁\n⊢ map (f₂ ∘ f₁) (g₂ ∘ g₁) ms = map f₂ g₂ (map f₁ g₁ ms)",
"ppTerm": "?m.26",
"assigned": tr... | [] | simp [map, ← Stream'.Seq.map_comp]
rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | {
"line": 390,
"column": 2
} | {
"line": 392,
"column": 6
} | {
"line": 394,
"column": 0
} | [
{
"pp": "coef exp : ℝ\nm : UnitMonomial\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\n⊢ { coef := coef, unit := exp :: m }.toFun (basis_hd :: basis_tl) =\n basis_hd ^ exp * { coef := coef, unit := m }.toFun basis_tl",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Commo... | [] | ext x
simp [toFun]
ring | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.ComputeAsymptotics.Multiseries.Monomial.Basic | {
"line": 390,
"column": 2
} | {
"line": 392,
"column": 6
} | {
"line": 394,
"column": 0
} | [
{
"pp": "coef exp : ℝ\nm : UnitMonomial\nbasis_hd : ℝ → ℝ\nbasis_tl : Basis\n⊢ { coef := coef, unit := exp :: m }.toFun (basis_hd :: basis_tl) =\n basis_hd ^ exp * { coef := coef, unit := m }.toFun basis_tl",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Mathlib.Tactic.Ring.Commo... | [] | ext x
simp [toFun]
ring | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Tactic.ITauto | {
"line": 156,
"column": 2
} | {
"line": 156,
"column": 62
} | {
"line": 157,
"column": 2
} | [
{
"pp": "case var.true\na✝ : Nat\n⊢ Ordering",
"ppTerm": "?var.true",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals": []
},
{
"pp": "case var.false\na✝ : Nat\n⊢ Ordering",
"ppTerm": "?var.false",
"assigned": false,
"usedConstants": [],
"usedFVars... | [
"case var.true\na✝ : Nat\n⊢ Ordering",
"case var.false\na✝ : Nat\n⊢ Ordering",
"case var.and'\na✝³ : Nat\na✝² : AndKind\na✝¹ a✝ : IProp\n⊢ Ordering",
"case var.or\na✝² : Nat\na✝¹ a✝ : IProp\n⊢ Ordering",
"case var.imp\na✝² : Nat\na✝¹ a✝ : IProp\n⊢ Ordering",
"case true.var\na✝ : Nat\n⊢ Ordering",
"case ... | case or.or p₁ p₂ q₁ q₂ => exact (p₁.cmp q₁).then (p₂.cmp q₂) | Lean.Elab.Tactic.evalCase | Lean.Parser.Tactic.case |
Mathlib.Tactic.NormNum.Irrational | {
"line": 90,
"column": 4
} | {
"line": 90,
"column": 47
} | {
"line": 91,
"column": 2
} | [
{
"pp": "case a\na b x y : ℕ\nhab : a.Coprime b\nhxy : x.Coprime y\nh : a * x = b * y\n⊢ a ∣ y",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.eq_of_mul_eq_mul_of_coprime_aux"
],
"usedFVars": [
"a",
"b",
... | [] | exact eq_of_mul_eq_mul_of_coprime_aux hab h | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Tactic.NormNum.Irrational | {
"line": 90,
"column": 4
} | {
"line": 90,
"column": 47
} | {
"line": 91,
"column": 2
} | [
{
"pp": "case a\na b x y : ℕ\nhab : a.Coprime b\nhxy : x.Coprime y\nh : a * x = b * y\n⊢ a ∣ y",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.eq_of_mul_eq_mul_of_coprime_aux"
],
"usedFVars": [
"a",
"b",
... | [] | exact eq_of_mul_eq_mul_of_coprime_aux hab h | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Tactic.NormNum.Irrational | {
"line": 90,
"column": 4
} | {
"line": 90,
"column": 47
} | {
"line": 91,
"column": 2
} | [
{
"pp": "case a\na b x y : ℕ\nhab : a.Coprime b\nhxy : x.Coprime y\nh : a * x = b * y\n⊢ a ∣ y",
"ppTerm": "?a✝",
"assigned": true,
"usedConstants": [
"_private.Mathlib.Tactic.NormNum.Irrational.0.Tactic.NormNum.eq_of_mul_eq_mul_of_coprime_aux"
],
"usedFVars": [
"a",
"b",
... | [] | exact eq_of_mul_eq_mul_of_coprime_aux hab h | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Tactic.Simproc.FinsetInterval | {
"line": 46,
"column": 6
} | {
"line": 46,
"column": 17
} | {
"line": 46,
"column": 18
} | [
{
"pp": "n : ℕ\ns : Finset ℕ\nhs : Icc 0 n = s\n⊢ Iio (n + 1) = s",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Finset.Iio_eq_Ico",
"Finset",
"OrderBot.toBot",
"Finset.Iio",
"Preorder.toLE",
"Nat.instLocallyFiniteOrde... | [
"n : ℕ\ns : Finset ℕ\nhs : Icc 0 n = s\n⊢ Ico ⊥ (n + 1) = s"
] | Iio_eq_Ico, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.UniformSpace.Ascoli | {
"line": 343,
"column": 6
} | {
"line": 343,
"column": 56
} | {
"line": 343,
"column": 57
} | [
{
"pp": "ι : Type u_1\nX : Type u_2\nα : Type u_3\ninst✝¹ : TopologicalSpace X\ninst✝ : UniformSpace α\nF : ι → X → α\n𝔖 : Set (Set X)\n𝔖_compact : ∀ K ∈ 𝔖, IsCompact K\nF_eqcont : ∀ K ∈ 𝔖, EquicontinuousOn F K\nℱ : Filter ι\nf : X → α\n⊢ Tendsto (⇑(UniformOnFun.ofFun 𝔖) ∘ F) ℱ (𝓝 ((UniformOnFun.ofFun 𝔖)... | [
"ι : Type u_1\nX : Type u_2\nα : Type u_3\ninst✝¹ : TopologicalSpace X\ninst✝ : UniformSpace α\nF : ι → X → α\n𝔖 : Set (Set X)\n𝔖_compact : ∀ K ∈ 𝔖, IsCompact K\nF_eqcont : ∀ K ∈ 𝔖, EquicontinuousOn F K\nℱ : Filter ι\nf : X → α\n⊢ Tendsto (⇑(UniformOnFun.ofFun 𝔖) ∘ F) ℱ (𝓝 ((UniformOnFun.ofFun 𝔖) f)) ↔\n ... | ← Filter.tendsto_comap_iff (g := (⋃₀ 𝔖).restrict), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.CWComplex.Classical.Graph | {
"line": 57,
"column": 2
} | {
"line": 57,
"column": 32
} | {
"line": 58,
"column": 2
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\ne : cell C 1\n⊢ (∃ x, (OneSkeletonGraph C).IsLoopAt e x) ↔ ∃ x, cellFrontier 1 e = closedCell 0 x",
"ppTerm": "?m.43",
"assigned": true,
"usedConstants": [
"Graph.IsLoopAt",
"Topology.RelCWComplex.cellFro... | [
"X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\ne : cell C 1\nx : cell C 0\n⊢ (OneSkeletonGraph C).IsLoopAt e x ↔ cellFrontier 1 e = closedCell 0 x"
] | refine exists_congr fun x ↦ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Topology.Convenient.ContinuousMapGeneratedBy | {
"line": 51,
"column": 6
} | {
"line": 51,
"column": 51
} | {
"line": 52,
"column": 4
} | [
{
"pp": "ι : Type t\nX : ι → Type u\ninst✝² : (i : ι) → TopologicalSpace (X i)\nY : Type v\ninst✝¹ : TopologicalSpace Y\nZ : Type v'\ninst✝ : TopologicalSpace Z\ng : Y → Z\n⊢ ContinuousGeneratedBy X g ↔ Continuous (⇑WithGeneratedByTopology.equiv.symm ∘ g ∘ ⇑WithGeneratedByTopology.equiv)",
"ppTerm": "?m.30"... | [
"ι : Type t\nX : ι → Type u\ninst✝² : (i : ι) → TopologicalSpace (X i)\nY : Type v\ninst✝¹ : TopologicalSpace Y\nZ : Type v'\ninst✝ : TopologicalSpace Z\ng : Y → Z\n⊢ ContinuousGeneratedBy X g ↔ Continuous[_, inst✝] (g ∘ ⇑WithGeneratedByTopology.equiv)"
] | IsGeneratedBy.equiv_symm_comp_continuous_iff, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 108,
"column": 2
} | {
"line": 110,
"column": 63
} | {
"line": 112,
"column": 0
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nhC : IsClosed C\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\n⊢ IsClosed (C1 C ho)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Continuous",
"Pi.topologicalSpace",
... | [] | refine hC.inter ?_
have h : Continuous (fun (f : I → Bool) ↦ f (term I ho)) := continuous_apply (term I ho)
exact IsClosed.preimage h (t := {true}) (isClosed_discrete _) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 108,
"column": 2
} | {
"line": 110,
"column": 63
} | {
"line": 112,
"column": 0
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nhC : IsClosed C\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\n⊢ IsClosed (C1 C ho)",
"ppTerm": "?m.24",
"assigned": true,
"usedConstants": [
"Continuous",
"Pi.topologicalSpace",
... | [] | refine hC.inter ?_
have h : Continuous (fun (f : I → Bool) ↦ f (term I ho)) := continuous_apply (term I ho)
exact IsClosed.preimage h (t := {true}) (isClosed_discrete _) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Category.Profinite.Nobeling.ZeroLimit | {
"line": 183,
"column": 2
} | {
"line": 183,
"column": 23
} | {
"line": 184,
"column": 2
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no₁ o₂ : Ordinal.{u}\nh : o₁ ≤ o₂\n⊢ smaller C o₁ ⊆ smaller C o₂",
"ppTerm": "?m.12",
"assigned": true,
"usedConstants": [
"Int.instAddCommGroup",
"Profinite.NobelingProof.GoodProducts.smaller",
... | [
"I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no₁ o₂ : Ordinal.{u}\nh : o₁ ≤ o₂\ng : LocallyConstant ↑(π C fun x ↦ ord I x < o₁) ℤ\nhg : g ∈ range (π C fun x ↦ ord I x < o₁)\n⊢ (πs C o₁) g ∈ smaller C o₂"
] | rintro f ⟨g, hg, rfl⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 473,
"column": 4
} | {
"line": 475,
"column": 42
} | {
"line": 476,
"column": 2
} | [
{
"pp": "case pos\nI : Type u\nC : Set (I → Bool)\ninst✝² : LinearOrder I\ninst✝¹ : WellFoundedLT I\no : Ordinal.{u}\nhsC : contained C (Order.succ o)\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\ninst✝ : Inhabited I\nl : Products I\nhl : ↑l ≠ []\nhlh : (↑l).head! = term I ho\nhlc : List.IsChain (fun x1 x2 ↦ x1 >... | [] | rw [if_pos (swapTrue_eq_true _ _), if_neg]
· rfl
· simp [mem_C'_eq_false C ho x x.prop] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 473,
"column": 4
} | {
"line": 475,
"column": 42
} | {
"line": 476,
"column": 2
} | [
{
"pp": "case pos\nI : Type u\nC : Set (I → Bool)\ninst✝² : LinearOrder I\ninst✝¹ : WellFoundedLT I\no : Ordinal.{u}\nhsC : contained C (Order.succ o)\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\ninst✝ : Inhabited I\nl : Products I\nhl : ↑l ≠ []\nhlh : (↑l).head! = term I ho\nhlc : List.IsChain (fun x1 x2 ↦ x1 >... | [] | rw [if_pos (swapTrue_eq_true _ _), if_neg]
· rfl
· simp [mem_C'_eq_false C ho x x.prop] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 933,
"column": 2
} | {
"line": 933,
"column": 38
} | {
"line": 934,
"column": 2
} | [
{
"pp": "X : Type u_1\nt : TopologicalSpace X\nC D : Set X\ninst✝¹ : T2Space X\ninst✝ : RelCWComplex C D\nn : ℕ\nj : cell C n\nI : (m : ℕ) → Finset (cell C m)\nhI : cellFrontier n j ⊆ D ∪ ⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, closedCell m j\nx : X\nxmem : ∃ i < n, ∃ i_1 ∈ I i, x ∈ closedCell i i_1\n⊢ ∃ i, ↑i < ↑n ∧ ∃ ... | [
"X : Type u_1\nt : TopologicalSpace X\nC D : Set X\ninst✝¹ : T2Space X\ninst✝ : RelCWComplex C D\nn : ℕ\nj✝ : cell C n\nI : (m : ℕ) → Finset (cell C m)\nhI : cellFrontier n j✝ ⊆ D ∪ ⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, closedCell m j\nx : X\ni : ℕ\niltn : i < n\nj : cell C i\nleft✝ : j ∈ I i\nxmem : x ∈ closedCell i j\n⊢... | obtain ⟨i, iltn, j, _, xmem⟩ := xmem | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Topology.ContinuousMap.SecondCountableSpace | {
"line": 62,
"column": 6
} | {
"line": 62,
"column": 54
} | {
"line": 63,
"column": 4
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nS : Set (Set X)\nT : Set (Set Y)\nhS₁ : ∀ K ∈ S, IsCompact K\nhT : IsTopologicalBasis T\nhS₂ : ∀ (f : C(X, Y)) (x : X), ∀ V ∈ T, f x ∈ V → ∃ K ∈ S, K ∈ 𝓝 x ∧ MapsTo (⇑f) K V\nf : C(X, Y)\nK : Set X\nhK : IsCompact K\n... | [] | exact fun g hg ↦ hg.mono hKs (sUnion_subset hTU) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.ContinuousMap.SecondCountableSpace | {
"line": 96,
"column": 78
} | {
"line": 98,
"column": 58
} | {
"line": 99,
"column": 4
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝⁴ : TopologicalSpace X\ninst✝³ : TopologicalSpace Y\ninst✝² : SecondCountableTopology X\ninst✝¹ : LocallyCompactSpace X\ninst✝ : SecondCountableTopology Y\nthis : ∀ (U : ↑(countableBasis X)), LocallyCompactSpace ↑↑U\nK : (U : ↑(countableBasis X)) → CompactExhaustion ↑↑U... | [] | by
rw [← (isBasis_countableBasis _).mem_nhds_iff]
exact (hVo.preimage (map_continuous f)).mem_nhds hxV | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Convenient.Localization | {
"line": 46,
"column": 8
} | {
"line": 46,
"column": 40
} | {
"line": 46,
"column": 40
} | [
{
"pp": "ι : Type t\nX : ι → Type u\ninst✝ : (i : ι) → TopologicalSpace (X i)\n⊢ (morphismPropertyWithGeneratedByTopologyEquiv X).IsInvertedBy (toContinuousGeneratedByCat X)",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"GeneratedByTopCat.adjCounit",
"CategoryTheory.IsIso",
... | [] | rintro _ _ _ ⟨Z⟩; infer_instance | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Convenient.Localization | {
"line": 46,
"column": 8
} | {
"line": 46,
"column": 40
} | {
"line": 46,
"column": 40
} | [
{
"pp": "ι : Type t\nX : ι → Type u\ninst✝ : (i : ι) → TopologicalSpace (X i)\n⊢ (morphismPropertyWithGeneratedByTopologyEquiv X).IsInvertedBy (toContinuousGeneratedByCat X)",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"GeneratedByTopCat.adjCounit",
"CategoryTheory.IsIso",
... | [] | rintro _ _ _ ⟨Z⟩; infer_instance | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Convenient.Localization | {
"line": 52,
"column": 8
} | {
"line": 52,
"column": 40
} | {
"line": 52,
"column": 40
} | [
{
"pp": "ι : Type t\nX : ι → Type u\ninst✝ : (i : ι) → TopologicalSpace (X i)\n⊢ (morphismPropertyWithGeneratedByTopologyEquiv X).IsInvertedBy toGeneratedByTopCat",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"GeneratedByTopCat.adjCounit",
"CategoryTheory.IsIso",
"Categ... | [] | rintro _ _ _ ⟨Z⟩; infer_instance | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Convenient.Localization | {
"line": 52,
"column": 8
} | {
"line": 52,
"column": 40
} | {
"line": 52,
"column": 40
} | [
{
"pp": "ι : Type t\nX : ι → Type u\ninst✝ : (i : ι) → TopologicalSpace (X i)\n⊢ (morphismPropertyWithGeneratedByTopologyEquiv X).IsInvertedBy toGeneratedByTopCat",
"ppTerm": "?m.22",
"assigned": true,
"usedConstants": [
"GeneratedByTopCat.adjCounit",
"CategoryTheory.IsIso",
"Categ... | [] | rintro _ _ _ ⟨Z⟩; infer_instance | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Convenient.HomSpace | {
"line": 87,
"column": 2
} | {
"line": 90,
"column": 53
} | {
"line": 92,
"column": 0
} | [
{
"pp": "case refine_2\nι : Type t\nX : ι → Type u\ninst✝⁴ : (i : ι) → TopologicalSpace (X i)\nY : Type v\ninst✝³ : TopologicalSpace Y\nZ : Type v'\ninst✝² : TopologicalSpace Z\nT : Type v''\ninst✝¹ : TopologicalSpace T\ninst✝ : ∀ (i j : ι), IsGeneratedBy X (X i × X j)\ng : Y × Z → T\nh :\n ∀ (i₁ : ι) (f₁ : C(... | [] | · rw [continuousGeneratedBy_def]
intro i f
exact (h i (ContinuousMap.snd.comp f) i (ContinuousMap.fst.comp f)).comp
(Continuous.prodMk continuous_id continuous_id) | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.Homotopy.HSpaces | {
"line": 200,
"column": 25
} | {
"line": 200,
"column": 33
} | {
"line": 200,
"column": 33
} | [
{
"pp": "X : Type u\ninst✝ : TopologicalSpace X\nx y : X\nθ : ↑I\nγ : Path x y\n⊢ γ 1 = y",
"ppTerm": "?m.73",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRing",
"Eq.mpr",
"Real.partialOrder",
"Real",
"congrArg",
"Real.semiring",
"Set.Elem",
... | [
"X : Type u\ninst✝ : TopologicalSpace X\nx y : X\nθ : ↑I\nγ : Path x y\n⊢ y = y"
] | γ.target | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Instances.PNat | {
"line": 42,
"column": 30
} | {
"line": 42,
"column": 96
} | {
"line": 44,
"column": 0
} | [
{
"pp": "⊢ (Filter.cocompact ℕ+).NeBot",
"ppTerm": "?m.4",
"assigned": true,
"usedConstants": [
"PNat.instMetricSpace",
"Denumerable.pnat",
"congrArg",
"Filter.NeBot",
"_private.Mathlib.Topology.Instances.PNat.0.PNat.instNoncompactSpace._simp_1",
"PseudoMetricSpac... | [] | by simp only [Filter.cocompact_eq_cofinite, Filter.cofinite_neBot] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Homotopy.HomotopyGroup | {
"line": 172,
"column": 2
} | {
"line": 174,
"column": 27
} | {
"line": 176,
"column": 0
} | [
{
"pp": "case mpr\nN : Type u_1\nM : Type u_3\ny : M ⊕ N → ↑I\n⊢ y ∘ Sum.inl ∈ Cube.boundary M ∨ y ∘ Sum.inr ∈ Cube.boundary N → y ∈ Cube.boundary (M ⊕ N)",
"ppTerm": "?mpr",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRing",
"Real.partialOrder",
"Real",
"Set.Icc.... | [] | · rintro (⟨m, hm⟩ | ⟨n, hn⟩)
· exact ⟨Sum.inl m, hm⟩
· exact ⟨Sum.inr n, hn⟩ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.Homotopy.HomotopyGroup | {
"line": 292,
"column": 6
} | {
"line": 292,
"column": 28
} | {
"line": 292,
"column": 29
} | [
{
"pp": "case inl\nN : Type u_1\nX : Type u_2\ninst✝¹ : TopologicalSpace X\nx : X\ninst✝ : DecidableEq N\ny : N → ↑I\nj : N\nHj : y j = 0 ∨ y j = 1\np : Ω (↑(Ω^ { j_1 // j_1 ≠ j } X x)) const\n⊢ (↑(p.toContinuousMap (y j)) fun j_1 ↦ y ↑j_1) = x",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": ... | [
"case inl.inl\nN : Type u_1\nX : Type u_2\ninst✝¹ : TopologicalSpace X\nx : X\ninst✝ : DecidableEq N\ny : N → ↑I\nj : N\np : Ω (↑(Ω^ { j_1 // j_1 ≠ j } X x)) const\nHj : y j = 0\n⊢ (↑(p.toContinuousMap (y j)) fun j_1 ↦ y ↑j_1) = x",
"case inl.inr\nN : Type u_1\nX : Type u_2\ninst✝¹ : TopologicalSpace X\nx : X\nin... | rcases Hj with Hj | Hj | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Topology.Homotopy.HomotopyGroup | {
"line": 574,
"column": 2
} | {
"line": 574,
"column": 34
} | {
"line": 575,
"column": 2
} | [
{
"pp": "N : Type u_1\nX : Type u_2\ninst✝¹ : TopologicalSpace X\nx : X\ninst✝ : DecidableEq N\ni j : N\nf : ↑(Ω^ N X x)\n⊢ ⟦symmAt i f⟧ = ⟦symmAt j f⟧",
"ppTerm": "?m.21",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Real",
"GenLoop.toLoop",
"Path.symm",
"Pi.topolog... | [
"N : Type u_1\nX : Type u_2\ninst✝¹ : TopologicalSpace X\nx : X\ninst✝ : DecidableEq N\ni j : N\nf : ↑(Ω^ N X x)\n⊢ ⟦fromLoop i (Path.symm (toLoop i f))⟧ = ⟦fromLoop j (Path.symm (toLoop j f))⟧"
] | simp_rw [← fromLoop_symm_toLoop] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Topology.MetricSpace.CoveringNumbers | {
"line": 401,
"column": 44
} | {
"line": 401,
"column": 69
} | {
"line": 402,
"column": 6
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝¹ : PseudoEMetricSpace X\ninst✝ : PseudoEMetricSpace Y\nA : Set X\nε : ℝ≥0\nf : X → Y\nhf : Isometry f\nhf_inj : InjOn f A\nC : Set Y\nhC_subset : C ⊆ f '' A\nhC_cover : IsCover ε (f '' A) C\nx : ↑C\n⊢ ∃ y ∈ A, f y = ↑x",
"ppTerm": "?m.115",
"assigned": true,
... | [] | simpa using hC_subset x.2 | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Topology.MetricSpace.CoveringNumbers | {
"line": 411,
"column": 4
} | {
"line": 411,
"column": 27
} | {
"line": 412,
"column": 4
} | [
{
"pp": "case refine_2\nX : Type u_1\nY : Type u_2\ninst✝¹ : PseudoEMetricSpace X\ninst✝ : PseudoEMetricSpace Y\nA : Set X\nε : ℝ≥0\nf : X → Y\nhf : Isometry f\nhf_inj : InjOn f A\nC' : Set X\nhC'_subset : C' ⊆ A\nhC_subset : f '' C' ⊆ f '' A\nhC_cover : IsCover ε A C'\n⊢ C'.encard ≤ (f '' C').encard",
"ppT... | [
"case refine_2\nX : Type u_1\nY : Type u_2\ninst✝¹ : PseudoEMetricSpace X\ninst✝ : PseudoEMetricSpace Y\nA : Set X\nε : ℝ≥0\nf : X → Y\nhf : Isometry f\nhf_inj : InjOn f A\nC' : Set X\nhC'_subset : C' ⊆ A\nhC_subset : f '' C' ⊆ f '' A\nhC_cover : IsCover ε A C'\n⊢ InjOn f C'"
] | rw [InjOn.encard_image] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.UniformSpace.Closeds | {
"line": 210,
"column": 2
} | {
"line": 210,
"column": 65
} | {
"line": 211,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : UniformSpace α\nU : Set (α × α)\nhU : U ∈ 𝓤 α\n⊢ ∃ ia ∈ 𝓤 α,\n ∀ x ∈ hausdorffEntourage ia,\n closure[inst✝.toTopologicalSpace] x.1 ⊆ SetRel.preimage U (closure[inst✝.toTopologicalSpace] x.2) ∧\n closure[inst✝.toTopologicalSpace] x.2 ⊆ SetRel.image U (closure[inst... | [
"α : Type u_1\ninst✝ : UniformSpace α\nU : Set (α × α)\nhU : U ∈ 𝓤 α\nV : SetRel α α\nhV : V ∈ 𝓤 α\nhVU : V.comp V ⊆ U\n⊢ ∃ ia ∈ 𝓤 α,\n ∀ x ∈ hausdorffEntourage ia,\n closure[inst✝.toTopologicalSpace] x.1 ⊆ SetRel.preimage U (closure[inst✝.toTopologicalSpace] x.2) ∧\n closure[inst✝.toTopologicalSp... | obtain ⟨V : SetRel α α, hV, hVU⟩ := comp_mem_uniformity_sets hU | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Topology.UniformSpace.Closeds | {
"line": 226,
"column": 2
} | {
"line": 226,
"column": 65
} | {
"line": 227,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : UniformSpace α\nU : Set (α × α)\nhU : U ∈ 𝓤 α\n⊢ ∃ i ∈ 𝓤 α,\n (fun x ↦ (closure[inst✝.toTopologicalSpace] x.1, closure[inst✝.toTopologicalSpace] x.2)) ⁻¹' hausdorffEntourage i ⊆\n hausdorffEntourage U",
"ppTerm": "?m.63",
"assigned": true,
"usedConstants": [
... | [
"α : Type u_1\ninst✝ : UniformSpace α\nU : Set (α × α)\nhU : U ∈ 𝓤 α\nV : SetRel α α\nhV : V ∈ 𝓤 α\nhVU : V.comp V ⊆ U\n⊢ ∃ i ∈ 𝓤 α,\n (fun x ↦ (closure[inst✝.toTopologicalSpace] x.1, closure[inst✝.toTopologicalSpace] x.2)) ⁻¹' hausdorffEntourage i ⊆\n hausdorffEntourage U"
] | obtain ⟨V : SetRel α α, hV, hVU⟩ := comp_mem_uniformity_sets hU | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Topology.Sets.VietorisTopology | {
"line": 107,
"column": 4
} | {
"line": 107,
"column": 59
} | {
"line": 108,
"column": 4
} | [
{
"pp": "case refine_2.inr\nα : Type u_1\ninst✝ : TopologicalSpace α\ns : Set α\nh✝ : s.Nonempty\nu : Set (Set α)\nhu₁ : u ⊆ {U | IsOpen[inst✝] U}\nhu₂ : u.Finite\nhu : powerset '' u ⊆ powerset '' {U | IsOpen[inst✝] U}\nv : Set (Set α)\nhv₁ : v ⊆ {U | IsOpen[inst✝] U}\nhv₂ : v.Finite\nhv : (fun V ↦ {s | (s ∩ V)... | [
"case refine_2.inr\nα : Type u_1\ninst✝ : TopologicalSpace α\ns : Set α\nh✝ : s.Nonempty\nu : Set (Set α)\nhu₁ : u ⊆ {U | IsOpen[inst✝] U}\nhu₂ : u.Finite\nhu : powerset '' u ⊆ powerset '' {U | IsOpen[inst✝] U}\nv : Set (Set α)\nhv₁ : v ⊆ {U | IsOpen[inst✝] U}\nhv₂ : v.Finite\nhv : (fun V ↦ {s | (s ∩ V).Nonempty}) ... | rw [mem_inter_iff, mem_powerset_iff, mem_iInter₂] at hs | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.UniformSpace.Closeds | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 65
} | {
"line": 240,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : UniformSpace α\ns : Set α\nhs : ∃ᶠ (y : Set α) in Filter.comap (Prod.mk s) (𝓤 (Set α)), y ∈ {s | TotallyBounded s}\nU : Set (α × α)\nhU : U ∈ 𝓤 α\n⊢ ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ U}",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"Filter.... | [
"α : Type u_1\ninst✝ : UniformSpace α\ns : Set α\nhs : ∃ᶠ (y : Set α) in Filter.comap (Prod.mk s) (𝓤 (Set α)), y ∈ {s | TotallyBounded s}\nU : Set (α × α)\nhU : U ∈ 𝓤 α\nV : SetRel α α\nhV : V ∈ 𝓤 α\nhVU : V.comp V ⊆ U\n⊢ ∃ t, t.Finite ∧ s ⊆ ⋃ y ∈ t, {x | (x, y) ∈ U}"
] | obtain ⟨V : SetRel α α, hV, hVU⟩ := comp_mem_uniformity_sets hU | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Topology.UniformSpace.Closeds | {
"line": 456,
"column": 2
} | {
"line": 456,
"column": 33
} | {
"line": 458,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝² : UniformSpace α\ninst✝¹ : UniformSpace β\ninst✝ : UniformSpace γ\nF₁ F₂ : Closeds α\nh✝ : Inseparable F₁ F₂\nx : α\nhx₁ : x ∈ F₁\nU : SetRel α α\nhU : U ∈ 𝓤 α\nh : ↑F₁ ⊆ U.preimage ↑F₂\ny : α\nhy : y ∈ ↑F₂\nhxy : (x, y) ∈ U\n⊢ ∃ x_1 ∈ U, ∃ a, (x, a) = ... | [] | exact ⟨(x, y), hxy, y, rfl, hy⟩ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.UniformSpace.Closeds | {
"line": 538,
"column": 4
} | {
"line": 538,
"column": 50
} | {
"line": 539,
"column": 4
} | [
{
"pp": "α : Type u_1\ninst✝² : UniformSpace α\ninst✝¹ : T2Space α\ninst✝ : CompleteSpace α\n⊢ IsClosed (Set.range toCloseds)",
"ppTerm": "?m.17",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"TotallyBounded",
"TopologicalSpace.Closeds.uniformSpace",
"HEq.refl",
"Topo... | [
"case e'_3\nα : Type u_1\ninst✝² : UniformSpace α\ninst✝¹ : T2Space α\ninst✝ : CompleteSpace α\n⊢ Set.range toCloseds = {s | TotallyBounded ↑s}"
] | convert! Closeds.isClosed_setOf_totallyBounded | Mathlib.Tactic._aux_Mathlib_Tactic_Convert___macroRules_Mathlib_Tactic_convert!_1 | Mathlib.Tactic.convert! |
Mathlib.Topology.UniformSpace.Closeds | {
"line": 603,
"column": 4
} | {
"line": 603,
"column": 67
} | {
"line": 604,
"column": 4
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝³ : UniformSpace α\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\ninst✝ : CompleteSpace α\nf : Filter (Compacts α)\nx✝ : Cauchy f\nleft✝ : f.NeBot\nhf : ∀ {U : Set (α × α)}, U ∈ 𝓤 α → ∀ᶠ (K : Compacts α) (K' : Compacts α) in f, (↑K, ↑K') ∈ hausdorffEn... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝³ : UniformSpace α\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\ninst✝ : CompleteSpace α\nf : Filter (Compacts α)\nx✝ : Cauchy f\nleft✝ : f.NeBot\nhf : ∀ {U : Set (α × α)}, U ∈ 𝓤 α → ∀ᶠ (K : Compacts α) (K' : Compacts α) in f, (↑K, ↑K') ∈ hausdorffEntourage U\nl... | obtain ⟨V : SetRel α α, hV, hVU⟩ := comp_mem_uniformity_sets hU | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Topology.Sets.VietorisTopology | {
"line": 144,
"column": 2
} | {
"line": 144,
"column": 45
} | {
"line": 145,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : TopologicalSpace α\ns : Set α\n⊢ closure[TopologicalSpace.vietoris α] {t | t.Finite ∧ t ⊆ s} = 𝒫 closure[inst✝] s",
"ppTerm": "?m.15",
"assigned": true,
"usedConstants": [
"TopologicalSpace.vietoris",
"setOf",
"Set.powerset",
"Set.Finite",
... | [
"case refine_1\nα : Type u_1\ninst✝ : TopologicalSpace α\ns : Set α\n⊢ closure[TopologicalSpace.vietoris α] {t | t.Finite ∧ t ⊆ s} ⊆ 𝒫 closure[inst✝] s",
"case refine_2\nα : Type u_1\ninst✝ : TopologicalSpace α\ns K : Set α\nhKs : K ∈ 𝒫 closure[inst✝] s\n⊢ K ∈ closure[TopologicalSpace.vietoris α] {t | t.Finite ... | refine subset_antisymm ?_ (fun K hKs => ?_) | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Topology.UniformSpace.Closeds | {
"line": 617,
"column": 2
} | {
"line": 617,
"column": 66
} | {
"line": 618,
"column": 2
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝³ : UniformSpace α\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\ninst✝ : CompleteSpace α\nf : Filter (Compacts α)\nx✝ : Cauchy f\nleft✝ : f.NeBot\nhf : ∀ {U : Set (α × α)}, U ∈ 𝓤 α → ∀ᶠ (K : Compacts α) (K' : Compacts α) in f, (↑K, ↑K') ∈ hausdorffEn... | [
"α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝³ : UniformSpace α\ninst✝² : UniformSpace β\ninst✝¹ : UniformSpace γ\ninst✝ : CompleteSpace α\nf : Filter (Compacts α)\nx✝ : Cauchy f\nleft✝ : f.NeBot\nhf : ∀ {U : Set (α × α)}, U ∈ 𝓤 α → ∀ᶠ (K : Compacts α) (K' : Compacts α) in f, (↑K, ↑K') ∈ hausdorffEntourage U\nl... | simp_rw [Set.mem_preimage, Prod.map, id, mem_hausdorffEntourage] | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | Mathlib.Tactic.tacticSimp_rw___ |
Mathlib.Topology.MetricSpace.Infsep | {
"line": 298,
"column": 2
} | {
"line": 298,
"column": 15
} | {
"line": 299,
"column": 2
} | [
{
"pp": "α : Type u_1\ninst✝ : EDist α\ns : Set α\nhs : 0 < s.infsep\n⊢ s.Nontrivial",
"ppTerm": "?m.8",
"assigned": true,
"usedConstants": [
"Real",
"Real.instZero",
"Real.instLT",
"Mathlib.Tactic.Contrapose.contrapose₁",
"LT.lt",
"Zero.toOfNat0",
"Set.Nont... | [
"α : Type u_1\ninst✝ : EDist α\ns : Set α\nhs : ¬s.Nontrivial\n⊢ ¬0 < s.infsep"
] | contrapose hs | Mathlib.Tactic.Contrapose._aux_Mathlib_Tactic_Contrapose___macroRules_Mathlib_Tactic_Contrapose_contrapose_1 | Mathlib.Tactic.Contrapose.contrapose |
Mathlib.Topology.MetricSpace.GromovHausdorff | {
"line": 426,
"column": 4
} | {
"line": 433,
"column": 35
} | {
"line": 434,
"column": 4
} | [
{
"pp": "x y : GHSpace\nhxy : dist x y = 0\nΦ : x.Rep → ↥(lp (fun n ↦ ℝ) ∞)\nΨ : y.Rep → ↥(lp (fun n ↦ ℝ) ∞)\nΦisom : Isometry Φ\nΨisom : Isometry Ψ\nDΦΨ : 0 = hausdorffDist (range Φ) (range Ψ)\n⊢ x = y",
"ppTerm": "?m.968",
"assigned": true,
"usedConstants": [
"NormedCommRing.toNormedRing",
... | [
"x y : GHSpace\nhxy : dist x y = 0\nΦ : x.Rep → ↥(lp (fun n ↦ ℝ) ∞)\nΨ : y.Rep → ↥(lp (fun n ↦ ℝ) ∞)\nΦisom : Isometry Φ\nΨisom : Isometry Ψ\nDΦΨ : 0 = hausdorffDist (range Φ) (range Ψ)\nthis : range Φ = range Ψ\n⊢ x = y"
] | have : range Φ = range Ψ := by
have hΦ : IsCompact (range Φ) := isCompact_range Φisom.continuous
have hΨ : IsCompact (range Ψ) := isCompact_range Ψisom.continuous
apply (IsClosed.hausdorffDist_zero_iff_eq _ _ _).1 DΦΨ.symm
· exact hΦ.isClosed
· exact hΨ.isClosed
· exact hausdorffEDis... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Topology.Order.UpperLowerSetTopology | {
"line": 432,
"column": 43
} | {
"line": 432,
"column": 72
} | {
"line": 432,
"column": 73
} | [
{
"pp": "α : Type u_1\ninst✝ : Preorder α\na b : α\n⊢ closure[instTopologicalSpace] {toUpperSet b} ⊆ closure[instTopologicalSpace] {toUpperSet a} ↔ b ≤ a",
"ppTerm": "?m.10",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Topology.WithUpperSet.toUpperSet",
"Equiv.instEquivLike",
... | [
"α : Type u_1\ninst✝ : Preorder α\na b : α\n⊢ Iic (toUpperSet b) ⊆ Iic (toUpperSet a) ↔ b ≤ a"
] | IsUpperSet.closure_singleton, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Topology.OmegaCompletePartialOrder | {
"line": 35,
"column": 28
} | {
"line": 35,
"column": 84
} | {
"line": 35,
"column": 84
} | [
{
"pp": "case h\nα : Type u_1\ninst✝² : OmegaCompletePartialOrder α\ninst✝¹ : TopologicalSpace α\ninst✝ : IsScott α (range fun c ↦ range ⇑c)\nf : α → Prop\na b : α\nhab : a ≤ b\n⊢ (fun c ↦ range ⇑c) (Chain.pair a b hab) = {a, b}",
"ppTerm": "?h",
"assigned": true,
"usedConstants": [
"PartialOr... | [] | exact OmegaCompletePartialOrder.Chain.range_pair a b hab | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.MetricSpace.GromovHausdorff | {
"line": 704,
"column": 8
} | {
"line": 704,
"column": 45
} | {
"line": 705,
"column": 8
} | [
{
"pp": "δ : ℝ\nδpos : δ > 0\nε : ℝ := 2 / 5 * δ\nεpos : 0 < ε\ns : (p : GHSpace) → Set p.Rep\nhs : ∀ (p : GHSpace), (s p).Finite ∧ univ ⊆ ⋃ x ∈ s p, ball x ε\nN : GHSpace → ℕ := fun p ↦ Nat.card ↑(s p)\nE : (p : GHSpace) → ↑(s p) ≃ Fin (Nat.card ↑(s p)) := fun p ↦ Finite.equivFin ↑(s p)\nF : GHSpace → (n : ℕ) ... | [
"δ : ℝ\nδpos : δ > 0\nε : ℝ := 2 / 5 * δ\nεpos : 0 < ε\ns : (p : GHSpace) → Set p.Rep\nhs : ∀ (p : GHSpace), (s p).Finite ∧ univ ⊆ ⋃ x ∈ s p, ball x ε\nN : GHSpace → ℕ := fun p ↦ Nat.card ↑(s p)\nE : (p : GHSpace) → ↑(s p) ≃ Fin (Nat.card ↑(s p)) := fun p ↦ Finite.equivFin ↑(s p)\nF : GHSpace → (n : ℕ) × (Fin n → F... | rw [Fin.heq_fun₂_iff Npq Npq] at hpq' | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Separation.PerfectlyNormal | {
"line": 63,
"column": 39
} | {
"line": 63,
"column": 57
} | {
"line": 64,
"column": 8
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\nh✝ : PerfectlyNormalSpace X\ns : Set X\nhs : IsClosed[inst✝] s\nU : ℕ → Set X\nho : ∀ (n : ℕ), IsOpen[inst✝] (U n)\nhu : s = ⋂ n, U n\nthis : ∀ (n : ℕ), Disjoint s (U n)ᶜ\nf : ℕ → C(X, ℝ)\nhfs : ∀ (n : ℕ), EqOn (⇑(f n)) 0 s\nhfu : ∀ (n : ℕ), EqOn (⇑(f n)) 1 (U ... | [] | by simp [hfu i hi] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Sheaves.EtaleSpace | {
"line": 127,
"column": 4
} | {
"line": 127,
"column": 56
} | {
"line": 128,
"column": 4
} | [
{
"pp": "X : TopCat\nC : Type u\ninst✝⁴ : Category.{v, u} C\nCC : C → Type v\nFC : C → C → Type w\ninst✝³ : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝² : ConcreteCategory C FC\ninst✝¹ : Limits.HasColimits C\nF : Presheaf C X\ninst✝ : Limits.PreservesFilteredColimits (forget C)\nU : Opens ↑X\nhF_bij : ∀ (... | [
"X : TopCat\nC : Type u\ninst✝⁴ : Category.{v, u} C\nCC : C → Type v\nFC : C → C → Type w\ninst✝³ : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝² : ConcreteCategory C FC\ninst✝¹ : Limits.HasColimits C\nF : Presheaf C X\ninst✝ : Limits.PreservesFilteredColimits (forget C)\nU : Opens ↑X\nhF_bij : ∀ (x : ↑X) (hx ... | rcases hF_bij _ hg |>.surjective g.germ with ⟨f, hf⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRCases | Lean.Parser.Tactic.rcases |
Mathlib.Topology.Sheaves.LocallySurjective | {
"line": 106,
"column": 4
} | {
"line": 106,
"column": 41
} | {
"line": 107,
"column": 4
} | [
{
"pp": "case mpr\nC : Type u\ninst✝⁴ : Category.{v, u} C\nFC : C → C → Type u_1\nCC : C → Type v\ninst✝³ : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝² : ConcreteCategory C FC\nX : TopCat\nℱ 𝒢 : Presheaf C X\ninst✝¹ : Limits.HasColimits C\ninst✝ : Limits.PreservesFilteredColimits (forget C)\nT : ℱ ⟶ 𝒢\... | [
"case mpr\nC : Type u\ninst✝⁴ : Category.{v, u} C\nFC : C → C → Type u_1\nCC : C → Type v\ninst✝³ : (X Y : C) → FunLike (FC X Y) (CC X) (CC Y)\ninst✝² : ConcreteCategory C FC\nX : TopCat\nℱ 𝒢 : Presheaf C X\ninst✝¹ : Limits.HasColimits C\ninst✝ : Limits.PreservesFilteredColimits (forget C)\nT : ℱ ⟶ 𝒢\nhT : ∀ (x :... | set t_x := 𝒢.germ _ x hxU t with ht_x | Mathlib.Tactic._aux_Mathlib_Tactic_Set___elabRules_Mathlib_Tactic_setTactic_1 | Mathlib.Tactic.setTactic |
Mathlib.Topology.MetricSpace.GromovHausdorff | {
"line": 860,
"column": 8
} | {
"line": 860,
"column": 45
} | {
"line": 861,
"column": 8
} | [
{
"pp": "t : Set GHSpace\nC : ℝ\nu : ℕ → ℝ\nK : ℕ → ℕ\nulim : Tendsto u atTop (𝓝 0)\nhdiam : ∀ p ∈ t, diam univ ≤ C\nhcov : ∀ p ∈ t, ∀ (n : ℕ), ∃ s, #↑s ≤ ↑(K n) ∧ univ ⊆ ⋃ x ∈ s, ball x (u n)\nδ : ℝ\nδpos : δ > 0\nε : ℝ := 1 / 5 * δ\nεpos : 0 < ε\nn : ℕ\nhn : ∀ n_1 ≥ n, dist (u n_1) 0 < ε\nu_le_ε : u n ≤ ε\ns... | [
"t : Set GHSpace\nC : ℝ\nu : ℕ → ℝ\nK : ℕ → ℕ\nulim : Tendsto u atTop (𝓝 0)\nhdiam : ∀ p ∈ t, diam univ ≤ C\nhcov : ∀ p ∈ t, ∀ (n : ℕ), ∃ s, #↑s ≤ ↑(K n) ∧ univ ⊆ ⋃ x ∈ s, ball x (u n)\nδ : ℝ\nδpos : δ > 0\nε : ℝ := 1 / 5 * δ\nεpos : 0 < ε\nn : ℕ\nhn : ∀ n_1 ≥ n, dist (u n_1) 0 < ε\nu_le_ε : u n ≤ ε\ns : (p : GHSp... | rw [Fin.heq_fun₂_iff Npq Npq] at hpq' | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 268,
"column": 4
} | {
"line": 269,
"column": 73
} | {
"line": 271,
"column": 0
} | [] | [] | ⨅ y, f (inl x, inr y) + C ≤ f (inl x, inr default) + C := ciInf_le (HD_below_aux1 C) default
_ ≤ Cf + C := add_le_add ((fun x => hCf (mem_range_self x)) _) le_rfl | Lean.Elab.Tactic._aux_Mathlib_Tactic_Widget_Calc___elabRules_Lean_calcTactic_1 | Lean.calcSteps |
Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts | {
"line": 264,
"column": 10
} | {
"line": 266,
"column": 14
} | {
"line": 267,
"column": 8
} | [
{
"pp": "case op.op.single.single.id_single\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasProducts C\nX : TopCat\nF : Presheaf C X\nι : Type v'\nU : ι → Opens ↑X\nc : Cone (SheafConditionEqualizerProducts.diagram F U)\ni : ι\n⊢ ((Functor.const (CategoryTheory.Pairwise ι)ᵒᵖ).obj c.pt).map (Quiver.Hom.op (i... | [] | dsimp
rw [F.map_id]
simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts | {
"line": 264,
"column": 10
} | {
"line": 266,
"column": 14
} | {
"line": 267,
"column": 8
} | [
{
"pp": "case op.op.single.single.id_single\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasProducts C\nX : TopCat\nF : Presheaf C X\nι : Type v'\nU : ι → Opens ↑X\nc : Cone (SheafConditionEqualizerProducts.diagram F U)\ni : ι\n⊢ ((Functor.const (CategoryTheory.Pairwise ι)ᵒᵖ).obj c.pt).map (Quiver.Hom.op (i... | [] | dsimp
rw [F.map_id]
simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts | {
"line": 285,
"column": 10
} | {
"line": 287,
"column": 14
} | {
"line": 287,
"column": 15
} | [
{
"pp": "case op.op.pair.pair.id_pair\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasProducts C\nX : TopCat\nF : Presheaf C X\nι : Type v'\nU : ι → Opens ↑X\nc : Cone (SheafConditionEqualizerProducts.diagram F U)\na✝¹ a✝ : ι\n⊢ ((Functor.const (CategoryTheory.Pairwise ι)ᵒᵖ).obj c.pt).map (Quiver.Hom.op (id... | [] | dsimp
rw [F.map_id]
simp | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts | {
"line": 285,
"column": 10
} | {
"line": 287,
"column": 14
} | {
"line": 287,
"column": 15
} | [
{
"pp": "case op.op.pair.pair.id_pair\nC : Type u\ninst✝¹ : Category.{v, u} C\ninst✝ : HasProducts C\nX : TopCat\nF : Presheaf C X\nι : Type v'\nU : ι → Opens ↑X\nc : Cone (SheafConditionEqualizerProducts.diagram F U)\na✝¹ a✝ : ι\n⊢ ((Functor.const (CategoryTheory.Pairwise ι)ᵒᵖ).obj c.pt).map (Quiver.Hom.op (id... | [] | dsimp
rw [F.map_id]
simp | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Subpath | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 26
} | {
"line": 154,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\np : Fin 1 → X\nF : (k : Fin 0) → Path (p k.castSucc) (p k.succ)\n⊢ concat p F = refl (p 0)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Path.trans",
"Fin.succ",
"Path.conca... | [] | rw [concat, dfoldl_zero] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Subpath | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 26
} | {
"line": 154,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\np : Fin 1 → X\nF : (k : Fin 0) → Path (p k.castSucc) (p k.succ)\n⊢ concat p F = refl (p 0)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Path.trans",
"Fin.succ",
"Path.conca... | [] | rw [concat, dfoldl_zero] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Subpath | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 26
} | {
"line": 154,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\np : Fin 1 → X\nF : (k : Fin 0) → Path (p k.castSucc) (p k.succ)\n⊢ concat p F = refl (p 0)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Path.trans",
"Fin.succ",
"Path.conca... | [] | rw [concat, dfoldl_zero] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.UniformSpace.Ultra.Constructions | {
"line": 68,
"column": 4
} | {
"line": 68,
"column": 20
} | {
"line": 69,
"column": 4
} | [
{
"pp": "case refine_1\nX : Type u_1\nι : Type u_3\nU : ι → UniformSpace X\nhU : ∀ (i : ι), IsUltraUniformity X\nthis : UniformSpace X := ⨅ i, U i\n⊢ ∀ (i : (I : Set ι) × (↑I → SetRel X X)),\n i.fst.Finite →\n (∀ (a : ι) (b : a ∈ i.fst), i.snd ⟨a, b⟩ ∈ uniformity X) →\n (∀ (a : ι) (b : a ∈ i.fst)... | [
"case refine_1\nX : Type u_1\nι : Type u_3\nU : ι → UniformSpace X\nhU : ∀ (i : ι), IsUltraUniformity X\nthis : UniformSpace X := ⨅ i, U i\ni✝ : (I : Set ι) × (↑I → SetRel X X)\na✝³ : i✝.fst.Finite\na✝² : ∀ (a : ι) (b : a ∈ i✝.fst), i✝.snd ⟨a, b⟩ ∈ uniformity X\na✝¹ : ∀ (a : ι) (b : a ∈ i✝.fst), (i✝.snd ⟨a, b⟩).IsS... | rintro _ _ _ _ _ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Topology.UniformSpace.Ultra.Constructions | {
"line": 68,
"column": 4
} | {
"line": 68,
"column": 20
} | {
"line": 69,
"column": 4
} | [
{
"pp": "case refine_2\nX : Type u_1\nι : Type u_3\nU : ι → UniformSpace X\nhU : ∀ (i : ι), IsUltraUniformity X\nthis : UniformSpace X := ⨅ i, U i\n⊢ ∀ (i : (I : Set ι) × (↑I → SetRel X X)),\n i.fst.Finite →\n (∀ (a : ι) (b : a ∈ i.fst), i.snd ⟨a, b⟩ ∈ uniformity X) →\n (∀ (a : ι) (b : a ∈ i.fst)... | [
"case refine_2\nX : Type u_1\nι : Type u_3\nU : ι → UniformSpace X\nhU : ∀ (i : ι), IsUltraUniformity X\nthis : UniformSpace X := ⨅ i, U i\ni✝ : (I : Set ι) × (↑I → SetRel X X)\na✝³ : i✝.fst.Finite\na✝² : ∀ (a : ι) (b : a ∈ i✝.fst), i✝.snd ⟨a, b⟩ ∈ uniformity X\na✝¹ : ∀ (a : ι) (b : a ∈ i✝.fst), (i✝.snd ⟨a, b⟩).IsS... | rintro _ _ _ _ _ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Algebra.Group.Commute.Defs | {
"line": 174,
"column": 80
} | {
"line": 174,
"column": 87
} | {
"line": 174,
"column": 88
} | [
{
"pp": "G : Type u_1\ninst✝ : DivisionMonoid G\na b : G\nhab : Commute a b\n⊢ (a * b)⁻¹ = a⁻¹ * b⁻¹",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"id",
"MulOne.toMu... | [
"G : Type u_1\ninst✝ : DivisionMonoid G\na b : G\nhab : Commute a b\n⊢ (b * a)⁻¹ = a⁻¹ * b⁻¹"
] | hab.eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Group.Commute.Defs | {
"line": 177,
"column": 76
} | {
"line": 177,
"column": 83
} | {
"line": 177,
"column": 84
} | [
{
"pp": "G : Type u_1\ninst✝ : DivisionMonoid G\na b : G\nhab : Commute a b\n⊢ (a * b)⁻¹ = a⁻¹ * b⁻¹",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"DivInvMonoid.toInv",
"HMul.hMul",
"Monoid.toMulOneClass",
"congrArg",
"id",
"MulOne.toMu... | [
"G : Type u_1\ninst✝ : DivisionMonoid G\na b : G\nhab : Commute a b\n⊢ (b * a)⁻¹ = a⁻¹ * b⁻¹"
] | hab.eq, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Algebra.Group.Defs | {
"line": 627,
"column": 6
} | {
"line": 627,
"column": 21
} | {
"line": 627,
"column": 22
} | [
{
"pp": "M : Type u_2\nx✝¹ : Semigroup M\nx✝ : One M\nk : ℕ\nm : M\n⊢ npowRecAuto k m = npowBinRecAuto k m",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"Semigroup.toMul",
"congrArg",
"id",
"npowRecAuto",
"npowBinRec",
"npowBinRecAuto",... | [
"M : Type u_2\nx✝¹ : Semigroup M\nx✝ : One M\nk : ℕ\nm : M\n⊢ npowRecAuto k m = npowBinRec k m"
] | npowBinRecAuto, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Logic.Function.Basic | {
"line": 885,
"column": 21
} | {
"line": 885,
"column": 77
} | {
"line": 885,
"column": 77
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nγ : Sort u_3\nf : α → β\ng : α → γ\ninst✝ : Nonempty γ\nh : ∃ e, g = e ∘ f\nx✝¹ x✝ : α\nhf : f x✝¹ = f x✝\n⊢ g x✝¹ = g x✝",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Function.comp",
"id",
"Classic... | [] | rw [Classical.choose_spec h, comp_apply, comp_apply, hf] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Logic.Function.Basic | {
"line": 885,
"column": 21
} | {
"line": 885,
"column": 77
} | {
"line": 885,
"column": 77
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nγ : Sort u_3\nf : α → β\ng : α → γ\ninst✝ : Nonempty γ\nh : ∃ e, g = e ∘ f\nx✝¹ x✝ : α\nhf : f x✝¹ = f x✝\n⊢ g x✝¹ = g x✝",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Function.comp",
"id",
"Classic... | [] | rw [Classical.choose_spec h, comp_apply, comp_apply, hf] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Logic.Function.Basic | {
"line": 885,
"column": 21
} | {
"line": 885,
"column": 77
} | {
"line": 885,
"column": 77
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nγ : Sort u_3\nf : α → β\ng : α → γ\ninst✝ : Nonempty γ\nh : ∃ e, g = e ∘ f\nx✝¹ x✝ : α\nhf : f x✝¹ = f x✝\n⊢ g x✝¹ = g x✝",
"ppTerm": "?m.31",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Function.comp",
"id",
"Classic... | [] | rw [Classical.choose_spec h, comp_apply, comp_apply, hf] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Logic.Relation | {
"line": 453,
"column": 12
} | {
"line": 453,
"column": 31
} | {
"line": 454,
"column": 2
} | [
{
"pp": "case refl\nα : Type u_1\nr : α → α → Prop\na b c : α\nhab : r a b\n⊢ ReflTransGen r a b",
"ppTerm": "?refl",
"assigned": true,
"usedConstants": [
"Relation.ReflTransGen.refl",
"Relation.ReflTransGen.tail"
],
"usedFVars": [
"α",
"r",
"a",
"b",
... | [] | exact refl.tail hab | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Logic.Relation | {
"line": 453,
"column": 12
} | {
"line": 453,
"column": 31
} | {
"line": 454,
"column": 2
} | [
{
"pp": "case refl\nα : Type u_1\nr : α → α → Prop\na b c : α\nhab : r a b\n⊢ ReflTransGen r a b",
"ppTerm": "?refl",
"assigned": true,
"usedConstants": [
"Relation.ReflTransGen.refl",
"Relation.ReflTransGen.tail"
],
"usedFVars": [
"α",
"r",
"a",
"b",
... | [] | exact refl.tail hab | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Logic.Relation | {
"line": 453,
"column": 12
} | {
"line": 453,
"column": 31
} | {
"line": 454,
"column": 2
} | [
{
"pp": "case refl\nα : Type u_1\nr : α → α → Prop\na b c : α\nhab : r a b\n⊢ ReflTransGen r a b",
"ppTerm": "?refl",
"assigned": true,
"usedConstants": [
"Relation.ReflTransGen.refl",
"Relation.ReflTransGen.tail"
],
"usedFVars": [
"α",
"r",
"a",
"b",
... | [] | exact refl.tail hab | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Logic.Relation | {
"line": 664,
"column": 22
} | {
"line": 664,
"column": 57
} | {
"line": 666,
"column": 0
} | [
{
"pp": "case tail\nα : Type u_1\nβ : Type u_2\nr : α → α → Prop\np : β → β → Prop\nf : α → β\nh : r ≤ (p on f)\na i✝ b✝ c✝ : α\na✝ : TransGen r a b✝\nhcd : r b✝ c✝\nhac : (TransGen p on f) a b✝\n⊢ (TransGen p on f) a c✝",
"ppTerm": "?tail",
"assigned": true,
"usedConstants": [
"Relation.Trans... | [] | exact TransGen.tail hac (h _ _ hcd) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Logic.Relation | {
"line": 664,
"column": 22
} | {
"line": 664,
"column": 57
} | {
"line": 666,
"column": 0
} | [
{
"pp": "case tail\nα : Type u_1\nβ : Type u_2\nr : α → α → Prop\np : β → β → Prop\nf : α → β\nh : r ≤ (p on f)\na i✝ b✝ c✝ : α\na✝ : TransGen r a b✝\nhcd : r b✝ c✝\nhac : (TransGen p on f) a b✝\n⊢ (TransGen p on f) a c✝",
"ppTerm": "?tail",
"assigned": true,
"usedConstants": [
"Relation.Trans... | [] | exact TransGen.tail hac (h _ _ hcd) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Logic.Relation | {
"line": 664,
"column": 22
} | {
"line": 664,
"column": 57
} | {
"line": 666,
"column": 0
} | [
{
"pp": "case tail\nα : Type u_1\nβ : Type u_2\nr : α → α → Prop\np : β → β → Prop\nf : α → β\nh : r ≤ (p on f)\na i✝ b✝ c✝ : α\na✝ : TransGen r a b✝\nhcd : r b✝ c✝\nhac : (TransGen p on f) a b✝\n⊢ (TransGen p on f) a c✝",
"ppTerm": "?tail",
"assigned": true,
"usedConstants": [
"Relation.Trans... | [] | exact TransGen.tail hac (h _ _ hcd) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Logic.Relation | {
"line": 662,
"column": 2
} | {
"line": 664,
"column": 57
} | {
"line": 666,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nr : α → α → Prop\np : β → β → Prop\nf : α → β\nh : r ≤ (p on f)\na i✝ : α\nhab : TransGen r a i✝\n⊢ (TransGen p on f) a i✝",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Function.onFun",
"Relation.TransGen.tail",
"Relation.TransGen.s... | [] | induction hab with
| single hac => exact TransGen.single (h a _ hac)
| tail _ hcd hac => exact TransGen.tail hac (h _ _ hcd) | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalInduction | Lean.Parser.Tactic.induction |
Mathlib.Logic.Relation | {
"line": 1001,
"column": 6
} | {
"line": 1006,
"column": 56
} | {
"line": 1006,
"column": 56
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\na b : α\nh : Equivalence r\n⊢ EqvGen r a b → r a b",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Equivalence.symm",
"Equivalence.refl",
"Relation.EqvGen",
"Equivalence.trans",
"Relation.EqvGen.rec"
],
"usedFVa... | [] | intro h
induction h with
| rel => assumption
| refl => exact h.1 _
| symm => apply h.symm; assumption
| trans _ _ _ _ _ hab hbc => exact h.trans hab hbc | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Logic.Relation | {
"line": 1001,
"column": 6
} | {
"line": 1006,
"column": 56
} | {
"line": 1006,
"column": 56
} | [
{
"pp": "α : Type u_1\nr : α → α → Prop\na b : α\nh : Equivalence r\n⊢ EqvGen r a b → r a b",
"ppTerm": "?m.5",
"assigned": true,
"usedConstants": [
"Equivalence.symm",
"Equivalence.refl",
"Relation.EqvGen",
"Equivalence.trans",
"Relation.EqvGen.rec"
],
"usedFVa... | [] | intro h
induction h with
| rel => assumption
| refl => exact h.1 _
| symm => apply h.symm; assumption
| trans _ _ _ _ _ hab hbc => exact h.trans hab hbc | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Option.Basic | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 7
} | {
"line": 55,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nH : Function.Injective f\na : α\no : Option α\n⊢ f a ∈ Option.map f o ↔ a ∈ o",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Option.instMembership",
"Option.some.injEq",
"Option.some",
... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Option.Basic | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 7
} | {
"line": 55,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nH : Function.Injective f\na : α\no : Option α\n⊢ f a ∈ Option.map f o ↔ a ∈ o",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Option.instMembership",
"Option.some.injEq",
"Option.some",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Option.Basic | {
"line": 53,
"column": 2
} | {
"line": 53,
"column": 7
} | {
"line": 55,
"column": 0
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nf : α → β\nH : Function.Injective f\na : α\no : Option α\n⊢ f a ∈ Option.map f o ↔ a ∈ o",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Option.instMembership",
"Option.some.injEq",
"Option.some",
... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Option.Basic | {
"line": 115,
"column": 6
} | {
"line": 115,
"column": 13
} | {
"line": 115,
"column": 13
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\np : α → Prop\nf : (a : α) → p a → β\nx : Option α\na : α\nh : ∀ (a : α), a ∈ x → p a\nha : a ∈ x\n⊢ f a ⋯ ∈ pmap f x h",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"Option.instMembership",
"Option.some",
... | [
"α : Type u_1\nβ : Type u_2\np : α → Prop\nf : (a : α) → p a → β\nx : Option α\na : α\nh : ∀ (a : α), a ∈ x → p a\nha✝ : a ∈ x\nha : x = some a\n⊢ pmap f x h = some (f a ⋯)"
] | mem_def | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Order.Defs.LinearOrder | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 85
} | {
"line": 154,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b : α\n⊢ max a b = if b ≤ a then a else b",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"_private.Mathlib.Order.Defs.LinearOrder.0.max_def'._simp_1_2",
"congrArg",
"PartialOrder.toPreorder",
"St... | [] | obtain h | h | h := lt_trichotomy a b <;> simp [le_of_lt, not_le_of_gt, h, max_def] | Lean.Parser.Tactic.«_aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tactic_<;>__1» | Lean.Parser.Tactic.«tactic_<;>_» |
Mathlib.Order.Defs.LinearOrder | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 85
} | {
"line": 154,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b : α\n⊢ max a b = if b ≤ a then a else b",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"_private.Mathlib.Order.Defs.LinearOrder.0.max_def'._simp_1_2",
"congrArg",
"PartialOrder.toPreorder",
"St... | [] | obtain h | h | h := lt_trichotomy a b <;> simp [le_of_lt, not_le_of_gt, h, max_def] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Defs.LinearOrder | {
"line": 152,
"column": 2
} | {
"line": 152,
"column": 85
} | {
"line": 154,
"column": 0
} | [
{
"pp": "α : Type u_1\ninst✝ : LinearOrder α\na b : α\n⊢ max a b = if b ≤ a then a else b",
"ppTerm": "?m.9",
"assigned": true,
"usedConstants": [
"Preorder.toLT",
"_private.Mathlib.Order.Defs.LinearOrder.0.max_def'._simp_1_2",
"congrArg",
"PartialOrder.toPreorder",
"St... | [] | obtain h | h | h := lt_trichotomy a b <;> simp [le_of_lt, not_le_of_gt, h, max_def] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.Basic | {
"line": 937,
"column": 4
} | {
"line": 939,
"column": 55
} | {
"line": 940,
"column": 2
} | [
{
"pp": "case refine_1\nα : Type u_2\nβ : Type u_3\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nx y : α × β\nh : x < y\n⊢ x.fst < y.fst ∧ x.snd ≤ y.snd ∨ x.fst ≤ y.fst ∧ x.snd < y.snd",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"LE.le.lt_of_not_ge",
"Preorder.toLT",
... | [] | by_cases h₁ : y.1 ≤ x.1
· exact Or.inr ⟨h.1.1, LE.le.lt_of_not_ge h.1.2 fun h₂ ↦ h.2 ⟨h₁, h₂⟩⟩
· exact Or.inl ⟨LE.le.lt_of_not_ge h.1.1 h₁, h.1.2⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.Basic | {
"line": 937,
"column": 4
} | {
"line": 939,
"column": 55
} | {
"line": 940,
"column": 2
} | [
{
"pp": "case refine_1\nα : Type u_2\nβ : Type u_3\ninst✝¹ : Preorder α\ninst✝ : Preorder β\nx y : α × β\nh : x < y\n⊢ x.fst < y.fst ∧ x.snd ≤ y.snd ∨ x.fst ≤ y.fst ∧ x.snd < y.snd",
"ppTerm": "?refine_1",
"assigned": true,
"usedConstants": [
"LE.le.lt_of_not_ge",
"Preorder.toLT",
... | [] | by_cases h₁ : y.1 ≤ x.1
· exact Or.inr ⟨h.1.1, LE.le.lt_of_not_ge h.1.2 fun h₂ ↦ h.2 ⟨h₁, h₂⟩⟩
· exact Or.inl ⟨LE.le.lt_of_not_ge h.1.1 h₁, h.1.2⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Operations | {
"line": 235,
"column": 2
} | {
"line": 235,
"column": 7
} | {
"line": 237,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\nγ : Type w\nf : α → γ\ns : Set α\nt : Set β\n⊢ (f '' s) ×ˢ t = (fun x ↦ (f x.fst, x.snd)) '' s ×ˢ t",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"Set.ext",
"Eq.mpr",
"and_true",
"SProd.sprod",
"congrAr... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Set.Operations | {
"line": 235,
"column": 2
} | {
"line": 235,
"column": 7
} | {
"line": 237,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\nγ : Type w\nf : α → γ\ns : Set α\nt : Set β\n⊢ (f '' s) ×ˢ t = (fun x ↦ (f x.fst, x.snd)) '' s ×ˢ t",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"Set.ext",
"Eq.mpr",
"and_true",
"SProd.sprod",
"congrAr... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Operations | {
"line": 235,
"column": 2
} | {
"line": 235,
"column": 7
} | {
"line": 237,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\nγ : Type w\nf : α → γ\ns : Set α\nt : Set β\n⊢ (f '' s) ×ˢ t = (fun x ↦ (f x.fst, x.snd)) '' s ×ˢ t",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"Set.ext",
"Eq.mpr",
"and_true",
"SProd.sprod",
"congrAr... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Data.Set.Operations | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 7
} | {
"line": 241,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\nγ : Type w\nf : α → γ\ns : Set α\nt : Set β\n⊢ t ×ˢ (f '' s) = (fun x ↦ (x.fst, f x.snd)) '' t ×ˢ s",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"Set.ext",
"Eq.mpr",
"SProd.sprod",
"congrArg",
"Set.mem... | [] | aesop | Aesop.evalAesop | Aesop.Frontend.Parser.aesopTactic |
Mathlib.Data.Set.Operations | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 7
} | {
"line": 241,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\nγ : Type w\nf : α → γ\ns : Set α\nt : Set β\n⊢ t ×ˢ (f '' s) = (fun x ↦ (x.fst, f x.snd)) '' t ×ˢ s",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"Set.ext",
"Eq.mpr",
"SProd.sprod",
"congrArg",
"Set.mem... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Data.Set.Operations | {
"line": 239,
"column": 2
} | {
"line": 239,
"column": 7
} | {
"line": 241,
"column": 0
} | [
{
"pp": "α : Type u\nβ : Type v\nγ : Type w\nf : α → γ\ns : Set α\nt : Set β\n⊢ t ×ˢ (f '' s) = (fun x ↦ (x.fst, f x.snd)) '' t ×ˢ s",
"ppTerm": "?m.29",
"assigned": true,
"usedConstants": [
"Set.instSProd",
"Set.ext",
"Eq.mpr",
"SProd.sprod",
"congrArg",
"Set.mem... | [] | aesop | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Order.BoundedOrder.Lattice | {
"line": 89,
"column": 4
} | {
"line": 93,
"column": 23
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case ind\nα : Type u_1\ninst✝² : Preorder α\ninst✝¹ : WellFoundedGT α\ninst✝ : OrderTop α\nP : α → Prop\nhind : ∀ (N : α), N ≠ ⊤ → P N → ∃ M, M > N ∧ P M\nhexists : ¬P ⊤\nx : α\nIH : ∀ (y : α), x < y → ¬P y\n⊢ ¬P x",
"ppTerm": "?ind",
"assigned": true,
"usedConstants": [
"False",
... | [] | by_cases hx : x = ⊤
· exact hx ▸ hexists
· intro hx'
obtain ⟨M, hM, hM'⟩ := hind x hx hx'
exact IH _ hM hM' | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Order.BoundedOrder.Lattice | {
"line": 89,
"column": 4
} | {
"line": 93,
"column": 23
} | {
"line": 95,
"column": 0
} | [
{
"pp": "case ind\nα : Type u_1\ninst✝² : Preorder α\ninst✝¹ : WellFoundedGT α\ninst✝ : OrderTop α\nP : α → Prop\nhind : ∀ (N : α), N ≠ ⊤ → P N → ∃ M, M > N ∧ P M\nhexists : ¬P ⊤\nx : α\nIH : ∀ (y : α), x < y → ¬P y\n⊢ ¬P x",
"ppTerm": "?ind",
"assigned": true,
"usedConstants": [
"False",
... | [] | by_cases hx : x = ⊤
· exact hx ▸ hexists
· intro hx'
obtain ⟨M, hM, hM'⟩ := hind x hx hx'
exact IH _ hM hM' | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
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