module stringlengths 16 90 | startPos dict | endPos dict | goals listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 366
values | kind stringclasses 370
values |
|---|---|---|---|---|---|---|
Mathlib.Topology.CWComplex.Classical.Graph | {
"line": 68,
"column": 15
} | {
"line": 68,
"column": 55
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\ne : cell C 1\nh : (cellFrontier 1 e).Subsingleton\nx : cell C 0\nhxy : cellFrontier 1 e = {↑(map 0 x) ![], ↑(map 0 x) ![]}\n⊢ cellFrontier 1 e = closedCell 0 x",
"usedConstants": [
"Real",
"congrArg",
"Topo... | simp [hxy, closedCell_zero_eq_singleton] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.CWComplex.Classical.Graph | {
"line": 68,
"column": 15
} | {
"line": 68,
"column": 55
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nC : Set X\ninst✝ : CWComplex C\ne : cell C 1\nh : (cellFrontier 1 e).Subsingleton\nx : cell C 0\nhxy : cellFrontier 1 e = {↑(map 0 x) ![], ↑(map 0 x) ![]}\n⊢ cellFrontier 1 e = closedCell 0 x",
"usedConstants": [
"Real",
"congrArg",
"Topo... | simp [hxy, closedCell_zero_eq_singleton] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.CWComplex.Classical.Finite | {
"line": 313,
"column": 19
} | {
"line": 313,
"column": 27
} | [
{
"pp": "X : Type u_2\ninst✝¹ : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\nfinite : _root_.Finite ((n : ℕ) × cell C n)\nh✝ : IsEmpty ((n : ℕ) × cell C n)\n⊢ ∀ (b : ℕ), 0 ≤ b → IsEmpty (cell C b)",
"usedConstants": [
"Nat.instMulZeroClass",
"LinearOrderedCommMonoidWithZero.toIsBot... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.CWComplex.Classical.Finite | {
"line": 313,
"column": 19
} | {
"line": 313,
"column": 27
} | [
{
"pp": "X : Type u_2\ninst✝¹ : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\nfinite : _root_.Finite ((n : ℕ) × cell C n)\nh✝ : IsEmpty ((n : ℕ) × cell C n)\n⊢ ∀ (b : ℕ), 0 ≤ b → IsEmpty (cell C b)",
"usedConstants": [
"Nat.instMulZeroClass",
"LinearOrderedCommMonoidWithZero.toIsBot... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.CWComplex.Classical.Finite | {
"line": 313,
"column": 19
} | {
"line": 313,
"column": 27
} | [
{
"pp": "X : Type u_2\ninst✝¹ : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\nfinite : _root_.Finite ((n : ℕ) × cell C n)\nh✝ : IsEmpty ((n : ℕ) × cell C n)\n⊢ ∀ (b : ℕ), 0 ≤ b → IsEmpty (cell C b)",
"usedConstants": [
"Nat.instMulZeroClass",
"LinearOrderedCommMonoidWithZero.toIsBot... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Compactness.DeltaGeneratedSpace | {
"line": 133,
"column": 2
} | {
"line": 133,
"column": 41
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ntX : TopologicalSpace X\ntY : TopologicalSpace Y\ninst✝ : DeltaGeneratedSpace X\n⊢ LocPathConnectedSpace X",
"usedConstants": [
"Pi.Function.module",
"NormedCommRing.toSeminormedCommRing",
"Real",
"NonUnitalCommRing.toNonUnitalNonAssocCommRing",
... | exact LocPathConnectedSpace.coinduced _ | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.Category.Compactum | {
"line": 323,
"column": 10
} | {
"line": 324,
"column": 32
} | [
{
"pp": "case h.h\nX : Compactum\nF : Ultrafilter X.A\nx : X.A\nfsu : Type u_1 := Finset (Set (Ultrafilter X.A))\nssu : Type u_1 := Set (Set (Ultrafilter X.A))\nι : fsu → ssu := fun x ↦ ↑x\nT0 : ssu := {S | ∃ A ∈ F, S = basic A}\nAA : Set (Ultrafilter X.A) := X.str ⁻¹' {x}\nT1 : ssu := insert AA T0\nT2 : Set (S... | intro
apply Filter.univ_sets | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Category.Compactum | {
"line": 323,
"column": 10
} | {
"line": 324,
"column": 32
} | [
{
"pp": "case h.h\nX : Compactum\nF : Ultrafilter X.A\nx : X.A\nfsu : Type u_1 := Finset (Set (Ultrafilter X.A))\nssu : Type u_1 := Set (Set (Ultrafilter X.A))\nι : fsu → ssu := fun x ↦ ↑x\nT0 : ssu := {S | ∃ A ∈ F, S = basic A}\nAA : Set (Ultrafilter X.A) := X.str ⁻¹' {x}\nT1 : ssu := insert AA T0\nT2 : Set (S... | intro
apply Filter.univ_sets | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 228,
"column": 47
} | {
"line": 232,
"column": 10
} | [
{
"pp": "X : Type u_1\nt : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\nn : ℕ\ni : cell C n\n⊢ ∃ I, cellFrontier n i ⊆ D ∪ ⋃ m, ⋃ (_ : m < n), ⋃ j ∈ I m, closedCell m j",
"usedConstants": [
"Real",
"pseudoMetricSpacePi",
"Real.instZero",
"congrArg",
"Topology.RelC... | by
rcases mapsTo n i with ⟨I, hI⟩
use I
rw [mapsTo_iff_image_subset] at hI
exact hI | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Category.Profinite.Nobeling.Span | {
"line": 51,
"column": 48
} | {
"line": 55,
"column": 98
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝ : LinearOrder I\ns : Finset I\nl : Products I\nhl : Products.isGood (π C fun x ↦ x ∈ s) l\n⊢ Products.eval C l = (πJ C s) (Products.eval (π C fun x ↦ x ∈ s) l)",
"usedConstants": [
"Int.instAddCommGroup",
"Int.instAddCommMonoid",
"LocallyConst... | by
ext f
simp only [πJ, LocallyConstant.comapₗ, LinearMap.coe_mk, AddHom.coe_mk,
LocallyConstant.coe_comap, Function.comp_apply]
exact (congr_fun (Products.evalFacProp C (· ∈ s) (Products.prop_of_isGood C (· ∈ s) hl)) _).symm | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 333,
"column": 2
} | {
"line": 333,
"column": 10
} | [
{
"pp": "X : Type u_1\nt : TopologicalSpace X\nC : Set X\ninst✝¹ : CWComplex C\ninst✝ : T2Space X\nA : Set X\nasubc : A ⊆ C\nthis : IsClosed[t] A ↔ (∀ (n : ℕ) (j : cell C n), IsClosed[t] (A ∩ closedCell n j)) ∧ IsClosed[t] (A ∩ ∅)\n⊢ IsClosed[t] A ↔ ∀ (n : ℕ) (j : cell C n), IsClosed[t] (A ∩ closedCell n j)",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 400,
"column": 6
} | {
"line": 400,
"column": 34
} | [
{
"pp": "case e_s.h\nX : Type u_1\nt : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\ne : cell C 1\nf : Fin 1 → ℝ\n⊢ f 0 = 1 ∨ f 0 = -1 ↔ f = -1 ∨ f = 1",
"usedConstants": [
"Eq.mpr",
"NegZeroClass.toNeg",
"Inhabited.default",
"Real",
"Pi.instNeg",
"congrArg",... | eq_const_of_unique (f := f), | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 462,
"column": 4
} | {
"line": 462,
"column": 28
} | [
{
"pp": "X : Type u_1\nt : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\nthis : D ∪ ⋃ n, ⋃ j, openCell n j = D ∪ ⋃ m, ⋃ (_ : ↑m < ⊤), ⋃ j, closedCell m j\n⊢ D ∪ ⋃ n, ⋃ j, openCell n j = C",
"usedConstants": [
"ENat.instNatCast",
"instTopENat",
"Iff.of_eq",
"congrArg",
... | simpa [union] using this | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 462,
"column": 4
} | {
"line": 462,
"column": 28
} | [
{
"pp": "X : Type u_1\nt : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\nthis : D ∪ ⋃ n, ⋃ j, openCell n j = D ∪ ⋃ m, ⋃ (_ : ↑m < ⊤), ⋃ j, closedCell m j\n⊢ D ∪ ⋃ n, ⋃ j, openCell n j = C",
"usedConstants": [
"ENat.instNatCast",
"instTopENat",
"Iff.of_eq",
"congrArg",
... | simpa [union] using this | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.CWComplex.Classical.Basic | {
"line": 462,
"column": 4
} | {
"line": 462,
"column": 28
} | [
{
"pp": "X : Type u_1\nt : TopologicalSpace X\nC D : Set X\ninst✝ : RelCWComplex C D\nthis : D ∪ ⋃ n, ⋃ j, openCell n j = D ∪ ⋃ m, ⋃ (_ : ↑m < ⊤), ⋃ j, closedCell m j\n⊢ D ∪ ⋃ n, ⋃ j, openCell n j = C",
"usedConstants": [
"ENat.instNatCast",
"instTopENat",
"Iff.of_eq",
"congrArg",
... | simpa [union] using this | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Category.Profinite.Nobeling.Basic | {
"line": 124,
"column": 25
} | {
"line": 124,
"column": 33
} | [
{
"pp": "case h.h\nI : Type u\nJ K : I → Prop\ninst✝¹ : (i : I) → Decidable (J i)\ninst✝ : (i : I) → Decidable (K i)\nh : ∀ (i : I), J i → K i\nx : I → Bool\ni : I\n⊢ (if J i then if K i then x i else false else false) = if J i then x i else false",
"usedConstants": [
"congrArg",
"Bool.and",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Category.Profinite.Nobeling.Basic | {
"line": 134,
"column": 4
} | {
"line": 134,
"column": 25
} | [
{
"pp": "case h.refine_2\nI : Type u\nC : Set (I → Bool)\nJ K : I → Prop\ninst✝¹ : (i : I) → Decidable (J i)\ninst✝ : (i : I) → Decidable (K i)\nh : ∀ (i : I), J i → K i\ny : I → Bool\nhy : y ∈ C\n⊢ Proj J y ∈ Proj J '' Proj K '' C",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Function.comp"... | rw [← Set.image_comp] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Category.Profinite.Nobeling.Basic | {
"line": 161,
"column": 2
} | {
"line": 161,
"column": 10
} | [
{
"pp": "case h.a.h\nI : Type u\nC : Set (I → Bool)\nJ K L : I → Prop\ninst✝² : (i : I) → Decidable (J i)\ninst✝¹ : (i : I) → Decidable (K i)\ninst✝ : (i : I) → Decidable (L i)\nhJK : ∀ (i : I), J i → K i\nhKL : ∀ (i : I), K i → L i\nx : ↑(π C L)\ni : I\n⊢ (if J i then if K i then ↑x i else false else false) = ... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Category.Profinite.Nobeling.Basic | {
"line": 167,
"column": 2
} | {
"line": 167,
"column": 10
} | [
{
"pp": "case h.a.h\nI : Type u\nC : Set (I → Bool)\nJ K : I → Prop\ninst✝¹ : (i : I) → Decidable (J i)\ninst✝ : (i : I) → Decidable (K i)\nh : ∀ (i : I), J i → K i\nx : ↑C\ni : I\n⊢ (if J i then if K i then ↑x i else false else false) = if J i then ↑x i else false",
"usedConstants": [
"congrArg",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Category.Profinite.Nobeling.Basic | {
"line": 435,
"column": 2
} | {
"line": 435,
"column": 14
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\nh : ⊤ ≤ span ℤ (Set.range (Products.eval C))\n⊢ span ℤ (Set.range (Products.eval C)) ≤ span ℤ (Set.range (eval C))",
"usedConstants": [
"Int.instAddCommGroup",
"Eq.mpr",
"Int.instAddCommMonoid",
... | rw [span_le] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Category.Profinite.Nobeling.Basic | {
"line": 558,
"column": 10
} | {
"line": 558,
"column": 19
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nx : I → Bool\n⊢ (x ∈ π C fun x ↦ ord I x < o) → ∀ (i : I), x i = true → ord I i < o",
"usedConstants": [
"Ordinal.instLinearOrder",
"Preorder.toLT",
"Ordinal.partialOrder",
"Par... | ⟨_, _, h⟩ | Lean.Elab.Tactic.evalIntro | Lean.Parser.Term.anonymousCtor |
Mathlib.Topology.Category.Profinite.Nobeling.Induction | {
"line": 125,
"column": 2
} | {
"line": 146,
"column": 29
} | [
{
"pp": "S : Profinite\n⊢ IsClosedEmbedding (ι S)",
"usedConstants": [
"Iff.mpr",
"Set.ext",
"Eq.mpr",
"False",
"isClopen_compl_iff",
"Pi.t2Space",
"Continuous",
"_private.Mathlib.Topology.Category.Profinite.Nobeling.Induction.0.Profinite.Nobeling.isClosedEmbe... | apply Continuous.isClosedEmbedding
· dsimp +unfoldPartialApp [ι]
refine continuous_pi ?_
intro C
rw [← IsLocallyConstant.iff_continuous]
refine ((IsLocallyConstant.tfae _).out 0 3).mpr ?_
rintro ⟨⟩
· refine IsClopen.isOpen (isClopen_compl_iff.mp ?_)
convert! C.2
ext x
simp
... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Category.Profinite.Nobeling.Induction | {
"line": 125,
"column": 2
} | {
"line": 146,
"column": 29
} | [
{
"pp": "S : Profinite\n⊢ IsClosedEmbedding (ι S)",
"usedConstants": [
"Iff.mpr",
"Set.ext",
"Eq.mpr",
"False",
"isClopen_compl_iff",
"Pi.t2Space",
"Continuous",
"_private.Mathlib.Topology.Category.Profinite.Nobeling.Induction.0.Profinite.Nobeling.isClosedEmbe... | apply Continuous.isClosedEmbedding
· dsimp +unfoldPartialApp [ι]
refine continuous_pi ?_
intro C
rw [← IsLocallyConstant.iff_continuous]
refine ((IsLocallyConstant.tfae _).out 0 3).mpr ?_
rintro ⟨⟩
· refine IsClopen.isOpen (isClopen_compl_iff.mp ?_)
convert! C.2
ext x
simp
... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 334,
"column": 2
} | {
"line": 334,
"column": 10
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\nthis : Set.range (sum_to C ho) = Set.range Subtype.val ∪ Set.range Subtype.val\n⊢ Set.range (sum_to C ho) = GoodProducts (π C fun x ↦ ord I x < o) ∪ MaxProducts C... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Compactness.CompactSystem | {
"line": 89,
"column": 4
} | {
"line": 89,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\nS : Set (Set α)\nh : ∀ (C : ℕ → Set α), (∀ (i : ℕ), C i ∈ S) → (∀ (n : ℕ), (dissipate C n).Nonempty) → (⋂ i, C i).Nonempty\nh✝ : Nonempty α\ns : ℕ → Set α\nh' : ∀ (i : ℕ), s i ∈ insert Set.univ S\nhd : ∀ (n : ℕ), (dissipate s n).Nonempty\nh₀ : ∀ (n : ℕ), s n ∉ S\n⊢ (⋂ i, s i).No... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Compactness.CompactSystem | {
"line": 89,
"column": 4
} | {
"line": 89,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\nS : Set (Set α)\nh : ∀ (C : ℕ → Set α), (∀ (i : ℕ), C i ∈ S) → (∀ (n : ℕ), (dissipate C n).Nonempty) → (⋂ i, C i).Nonempty\nh✝ : Nonempty α\ns : ℕ → Set α\nh' : ∀ (i : ℕ), s i ∈ insert Set.univ S\nhd : ∀ (n : ℕ), (dissipate s n).Nonempty\nh₀ : ∀ (n : ℕ), s n ∉ S\n⊢ (⋂ i, s i).No... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Compactness.CompactSystem | {
"line": 89,
"column": 4
} | {
"line": 89,
"column": 12
} | [
{
"pp": "case pos\nα : Type u_1\nS : Set (Set α)\nh : ∀ (C : ℕ → Set α), (∀ (i : ℕ), C i ∈ S) → (∀ (n : ℕ), (dissipate C n).Nonempty) → (⋂ i, C i).Nonempty\nh✝ : Nonempty α\ns : ℕ → Set α\nh' : ∀ (i : ℕ), s i ∈ insert Set.univ S\nhd : ∀ (n : ℕ), (dissipate s n).Nonempty\nh₀ : ∀ (n : ℕ), s n ∉ S\n⊢ (⋂ i, s i).No... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Compactness.CompactSystem | {
"line": 83,
"column": 79
} | {
"line": 103,
"column": 21
} | [
{
"pp": "α : Type u_1\nS : Set (Set α)\nh : IsCompactSystem S\n⊢ IsCompactSystem (insert Set.univ S)",
"usedConstants": [
"Mathlib.Tactic.Push.not_forall_eq",
"Set.ext",
"Set.dissipate",
"Eq.mpr",
"False",
"IsCompactSystem.iff_nonempty_iInter",
"Set.univ_nonempty._s... | by
rcases isEmpty_or_nonempty α with hα | _
· simp
rw [IsCompactSystem.iff_nonempty_iInter] at h ⊢
intro s h' hd
by_cases! h₀ : ∀ n, s n ∉ S
· simp_all
classical
let n := Nat.find h₀
let s' := fun i ↦ if s i ∈ S then s i else s n
have h₁ : ∀ i, s' i ∈ S := by grind
have h₂ : ⋂ i, s i = ⋂ i, s' i :... | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Compactness.CompactSystem | {
"line": 134,
"column": 2
} | {
"line": 134,
"column": 41
} | [
{
"pp": "α : Type u_1\nS : Set (Set α)\nhpi : IsPiSystem S\n⊢ IsCompactSystem S ↔\n ∀ (C : ℕ → Set α), Directed (fun x1 x2 ↦ x1 ⊇ x2) C → (∀ (i : ℕ), C i ∈ S) → ⋂ i, C i = ∅ → ∃ n, C n = ∅",
"usedConstants": [
"Eq.mpr",
"congrArg",
"Set.iInter",
"Directed",
"Membership.mem",... | rw [← isCompactSystem_insert_empty_iff] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Category.Profinite.Nobeling.Successor | {
"line": 614,
"column": 2
} | {
"line": 614,
"column": 34
} | [
{
"pp": "I : Type u\nC : Set (I → Bool)\ninst✝¹ : LinearOrder I\ninst✝ : WellFoundedLT I\no : Ordinal.{u}\nhC : IsClosed C\nhsC : contained C (Order.succ o)\nho : o < Ordinal.type fun x1 x2 ↦ x1 < x2\nh₁ : ⊤ ≤ Submodule.span ℤ (Set.range (eval (π C fun x ↦ ord I x < o)))\n⊢ LinearIndependent ℤ (eval (C' C ho)) ... | dsimp [SumEval, ModuleCat.ofHom] | Lean.Elab.Tactic.evalDSimp | Lean.Parser.Tactic.dsimp |
Mathlib.Topology.ContinuousMap.Interval | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 27
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : LinearOrder α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : OrderTopology α\na b c : α\ninst✝² : Fact (a ≤ b)\ninst✝¹ : Fact (b ≤ c)\nE : Type u_2\ninst✝ : TopologicalSpace E\nx : ↑(Icc a c)\nhx : ↑x ≤ b\nfg : { fg // fg.1 ⊤ = fg.2 ⊥ }\n⊢ (concatCM fg) x = (↑fg).1 ⟨↑x, ⋯⟩",
"usedCon... | exact concat_left fg.2 hx | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.ContinuousMap.Interval | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 27
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : LinearOrder α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : OrderTopology α\na b c : α\ninst✝² : Fact (a ≤ b)\ninst✝¹ : Fact (b ≤ c)\nE : Type u_2\ninst✝ : TopologicalSpace E\nx : ↑(Icc a c)\nhx : ↑x ≤ b\nfg : { fg // fg.1 ⊤ = fg.2 ⊥ }\n⊢ (concatCM fg) x = (↑fg).1 ⟨↑x, ⋯⟩",
"usedCon... | exact concat_left fg.2 hx | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.ContinuousMap.Interval | {
"line": 142,
"column": 2
} | {
"line": 142,
"column": 27
} | [
{
"pp": "α : Type u_1\ninst✝⁵ : LinearOrder α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : OrderTopology α\na b c : α\ninst✝² : Fact (a ≤ b)\ninst✝¹ : Fact (b ≤ c)\nE : Type u_2\ninst✝ : TopologicalSpace E\nx : ↑(Icc a c)\nhx : ↑x ≤ b\nfg : { fg // fg.1 ⊤ = fg.2 ⊥ }\n⊢ (concatCM fg) x = (↑fg).1 ⟨↑x, ⋯⟩",
"usedCon... | exact concat_left fg.2 hx | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Compactness.CountablyCompact | {
"line": 357,
"column": 25
} | {
"line": 357,
"column": 33
} | [
{
"pp": "E : Type u_2\ninst✝ : TopologicalSpace E\nA : Set E\nhA : IsCountablyCompact A\nhl : IsLindelof A\nι : Type u_2\nU : ι → Set E\nhUo : ∀ (i : ι), IsOpen[inst✝] (U i)\nhAU : A ⊆ ⋃ i, U i\nh : Nonempty ι\nf : ℕ → ι\nhf : A ⊆ ⋃ n, U (f n)\nt : Finset ℕ\nht : A ⊆ ⋃ i ∈ t, (U ∘ f) i\n⊢ A ⊆ ⋃ i ∈ Finset.image... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Compactness.CountablyCompact | {
"line": 357,
"column": 25
} | {
"line": 357,
"column": 33
} | [
{
"pp": "E : Type u_2\ninst✝ : TopologicalSpace E\nA : Set E\nhA : IsCountablyCompact A\nhl : IsLindelof A\nι : Type u_2\nU : ι → Set E\nhUo : ∀ (i : ι), IsOpen[inst✝] (U i)\nhAU : A ⊆ ⋃ i, U i\nh : Nonempty ι\nf : ℕ → ι\nhf : A ⊆ ⋃ n, U (f n)\nt : Finset ℕ\nht : A ⊆ ⋃ i ∈ t, (U ∘ f) i\n⊢ A ⊆ ⋃ i ∈ Finset.image... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Compactness.CountablyCompact | {
"line": 357,
"column": 25
} | {
"line": 357,
"column": 33
} | [
{
"pp": "E : Type u_2\ninst✝ : TopologicalSpace E\nA : Set E\nhA : IsCountablyCompact A\nhl : IsLindelof A\nι : Type u_2\nU : ι → Set E\nhUo : ∀ (i : ι), IsOpen[inst✝] (U i)\nhAU : A ⊆ ⋃ i, U i\nh : Nonempty ι\nf : ℕ → ι\nhf : A ⊆ ⋃ n, U (f n)\nt : Finset ℕ\nht : A ⊆ ⋃ i ∈ t, (U ∘ f) i\n⊢ A ⊆ ⋃ i ∈ Finset.image... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Compactness.CountablyCompact | {
"line": 358,
"column": 17
} | {
"line": 358,
"column": 25
} | [
{
"pp": "E : Type u_2\ninst✝ : TopologicalSpace E\nA : Set E\nhA : IsCountablyCompact A\nhl : IsLindelof A\nι : Type u_2\nU : ι → Set E\nhUo : ∀ (i : ι), IsOpen[inst✝] (U i)\nhAU : A ⊆ ⋃ i, U i\nh : IsEmpty ι\n⊢ A ⊆ ⋃ i ∈ ∅, U i",
"usedConstants": [
"subset_refl._simp_1",
"False",
"Iff.of_... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Compactness.CountablyCompact | {
"line": 358,
"column": 17
} | {
"line": 358,
"column": 25
} | [
{
"pp": "E : Type u_2\ninst✝ : TopologicalSpace E\nA : Set E\nhA : IsCountablyCompact A\nhl : IsLindelof A\nι : Type u_2\nU : ι → Set E\nhUo : ∀ (i : ι), IsOpen[inst✝] (U i)\nhAU : A ⊆ ⋃ i, U i\nh : IsEmpty ι\n⊢ A ⊆ ⋃ i ∈ ∅, U i",
"usedConstants": [
"subset_refl._simp_1",
"False",
"Iff.of_... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Compactness.CountablyCompact | {
"line": 358,
"column": 17
} | {
"line": 358,
"column": 25
} | [
{
"pp": "E : Type u_2\ninst✝ : TopologicalSpace E\nA : Set E\nhA : IsCountablyCompact A\nhl : IsLindelof A\nι : Type u_2\nU : ι → Set E\nhUo : ∀ (i : ι), IsOpen[inst✝] (U i)\nhAU : A ⊆ ⋃ i, U i\nh : IsEmpty ι\n⊢ A ⊆ ⋃ i ∈ ∅, U i",
"usedConstants": [
"subset_refl._simp_1",
"False",
"Iff.of_... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.DerivedSet | {
"line": 116,
"column": 4
} | {
"line": 116,
"column": 12
} | [
{
"pp": "case neg\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : T1Space X\nU : Set X\nhs : IsPreconnected U\na b : Set X\nh : U ⊆ a ∪ b\nha : (U ∩ derivedSet a).Nonempty\nhb : (U ∩ derivedSet b).Nonempty\nhu : ¬U.Nontrivial\nx : X\nhx : U = {x}\n⊢ (U ∩ (derivedSet a ∩ derivedSet b)).Nonempty",
"usedCo... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Filter | {
"line": 139,
"column": 4
} | {
"line": 139,
"column": 21
} | [
{
"pp": "α : Type u_2\nl : Filter α\n⊢ ⋂ s ∈ l, {x | x ≤ 𝓟 s} = {x | x ≤ l}",
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"Iff.of_eq",
"congrArg",
"Set.iInter",
"PartialOrder.toPreorder",
"setOf",
"Preorder.toLE",
"Membership.mem",
"id",... | le_principal_iff, | Mathlib.Tactic._aux_Mathlib_Tactic_SimpRw___elabRules_Mathlib_Tactic_tacticSimp_rw____1 | null |
Mathlib.Topology.Homotopy.LocallyContractible | {
"line": 177,
"column": 2
} | {
"line": 177,
"column": 28
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : StronglyLocallyContractibleSpace X\nx : X\nU : Set X\nhU : U ∈ 𝓝 x\nV : Set X\nhVU : id V ⊆ U\nhVmem : V ∈ 𝓝 x\nhVcontractible : ContractibleSpace ↑V\n⊢ ∃ V, ∃ (hVU : V ⊆ U), V ∈ 𝓝 x ∧ (ContinuousMap.inclusion hVU).Nullhomotopic",
"usedConstants... | refine ⟨V, hVU, hVmem, ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Topology.Homotopy.HSpaces | {
"line": 125,
"column": 44
} | {
"line": 125,
"column": 66
} | [
{
"pp": "M : Type u\ninst✝² : MulOneClass M\ninst✝¹ : TopologicalSpace M\ninst✝ : ContinuousMul M\n⊢ { toFun := Function.uncurry Mul.mul, continuous_toFun := ⋯ }.comp ((const M 1).prodMk (ContinuousMap.id M)) =\n ContinuousMap.id M",
"usedConstants": [
"MulOne.toOne",
"ContinuousMap.mk",
... | by ext1; apply one_mul | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Instances.CantorSet | {
"line": 307,
"column": 4
} | {
"line": 308,
"column": 70
} | [
{
"pp": "case h.refine_1\nx : ℝ\nh : x ∈ cantorSet\n⊢ x ∈ {x | ∃ a, (∀ (i : ℕ), a i ≠ 1) ∧ ofDigits a = x}",
"usedConstants": [
"Real",
"ofDigits_cantorToTernary",
"cantorToTernary_ne_one",
"cantorToTernary",
"Fin.instOfNat",
"Ne",
"instOfNatNat",
"And",
... | use cantorToTernary x
exact ⟨fun _ ↦ cantorToTernary_ne_one, ofDigits_cantorToTernary h⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Instances.CantorSet | {
"line": 307,
"column": 4
} | {
"line": 308,
"column": 70
} | [
{
"pp": "case h.refine_1\nx : ℝ\nh : x ∈ cantorSet\n⊢ x ∈ {x | ∃ a, (∀ (i : ℕ), a i ≠ 1) ∧ ofDigits a = x}",
"usedConstants": [
"Real",
"ofDigits_cantorToTernary",
"cantorToTernary_ne_one",
"cantorToTernary",
"Fin.instOfNat",
"Ne",
"instOfNatNat",
"And",
... | use cantorToTernary x
exact ⟨fun _ ↦ cantorToTernary_ne_one, ofDigits_cantorToTernary h⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.EMetricSpace.PairReduction | {
"line": 447,
"column": 2
} | {
"line": 448,
"column": 30
} | [
{
"pp": "T : Type u_1\ninst✝² : PseudoEMetricSpace T\na c : ℝ≥0∞\nJ : Finset T\ninst✝¹ : DecidableEq T\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nha : 1 < a\nf : T → E\nhJ : J.Nonempty\ns : T\nhs : s ∈ J\nt : T\nht : t ∈ J\nhst : edist ⟨s, hs⟩ ⟨t, ht⟩ ≤ c\nP : ℕ → Prop := fun l ↦ s ∈ (logSizeBallSeq J hJ a c ... | have htP : ((logSizeBallSeq J hJ a c l).point, t) ∈ pairSetSeq J a c l := by
simp [pairSetSeq, hJ, htB] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Topology.EMetricSpace.PairReduction | {
"line": 494,
"column": 4
} | {
"line": 494,
"column": 12
} | [
{
"pp": "case inl.inr\nT : Type u_1\ninst✝¹ : PseudoEMetricSpace T\na : ℝ≥0∞\nn : ℕ\nc : ℝ≥0∞\nE : Type u_2\ninst✝ : PseudoEMetricSpace E\nha1 : a ≤ 1\nx₀ : T\nhJ_card : ↑(#{x₀}) ≤ a ^ n\nhJ : Nonempty ↥{x₀}\n⊢ ∃ K ⊆ {x₀} ×ˢ {x₀},\n ↑(#K) ≤ a * ↑(#{x₀}) ∧\n (∀ (s t : T), (s, t) ∈ K → edist s t ≤ ↑n * c)... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Homotopy.HomotopyGroup | {
"line": 377,
"column": 2
} | {
"line": 377,
"column": 13
} | [
{
"pp": "case refine_1\nN : Type u_1\nX : Type u_2\ninst✝¹ : TopologicalSpace X\nx : X\ninst✝ : DecidableEq N\ni : N\np q : ↑(Ω^ N X x)\nH : Path.Homotopy (toLoop i p) (toLoop i q)\n⊢ ∀ (x_1 : N → ↑I), (homotopyFrom i H).toFun (0, x_1) = ↑p x_1",
"usedConstants": []
},
{
"pp": "case refine_2\nN : Ty... | pick_goal 3 | Batteries.Tactic.«_aux_Batteries_Tactic_PermuteGoals___elabRules_Batteries_Tactic_tacticPick_goal-__1» | Batteries.Tactic.«tacticPick_goal-_» |
Mathlib.Topology.Homotopy.HomotopyGroup | {
"line": 496,
"column": 6
} | {
"line": 497,
"column": 33
} | [
{
"pp": "N✝ : Type u_1\nX : Type u_2\ninst✝² : TopologicalSpace X\nx : X\ninst✝¹ : DecidableEq N✝\nN : Type ?u.92556\ninst✝ : Unique N\np : Ω X x\n⊢ { toFun := fun c ↦ p (c default), continuous_toFun := ⋯ } ∈ Ω^ N X x",
"usedConstants": [
"Real.instIsOrderedRing",
"Inhabited.default",
"Rea... | rintro y ⟨i, iH | iH⟩ <;> cases Unique.eq_default i <;> apply (congr_arg p iH).trans
exacts [p.source, p.target] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Homotopy.HomotopyGroup | {
"line": 496,
"column": 6
} | {
"line": 497,
"column": 33
} | [
{
"pp": "N✝ : Type u_1\nX : Type u_2\ninst✝² : TopologicalSpace X\nx : X\ninst✝¹ : DecidableEq N✝\nN : Type ?u.92556\ninst✝ : Unique N\np : Ω X x\n⊢ { toFun := fun c ↦ p (c default), continuous_toFun := ⋯ } ∈ Ω^ N X x",
"usedConstants": [
"Real.instIsOrderedRing",
"Inhabited.default",
"Rea... | rintro y ⟨i, iH | iH⟩ <;> cases Unique.eq_default i <;> apply (congr_arg p iH).trans
exacts [p.source, p.target] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Homotopy.HomotopyGroup | {
"line": 572,
"column": 59
} | {
"line": 575,
"column": 84
} | [
{
"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⟧",
"usedConstants": [
"Eq.mpr",
"Real",
"GenLoop.toLoop",
"Path.symm",
"DivInvOneMonoid.toInvOneClass",
"HomotopyGroup.au... | by
simp_rw [← fromLoop_symm_toLoop]
let inv := fun (G) (_ : Group G) ↦ ((·⁻¹) : G → G)
exact congr_fun (congr_arg (inv <| HomotopyGroup N X x) <| auxGroup_indep i j) ⟦f⟧ | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.MetricSpace.Closeds | {
"line": 41,
"column": 10
} | {
"line": 41,
"column": 31
} | [
{
"pp": "α : Type u_1\ninst✝ : PseudoEMetricSpace α\ns t : Set α\nδ : ℝ≥0∞\nh : ⨆ x ∈ s, infEDist x t < δ ∧ ⨆ y ∈ t, infEDist y s < δ\n| (s, t).1 ⊆ SetRel.preimage {p | edist p.1 p.2 < δ} (s, t).2 ∧ (s, t).2 ⊆ SetRel.image {p | edist p.1 p.2 < δ} (s, t).1",
"usedConstants": [
"PseudoEMetricSpace.toWea... | enter [2, 2, 1, 1, _] | Lean.Elab.Tactic.Conv.evalEnter | Lean.Parser.Tactic.Conv.enter |
Mathlib.Topology.MetricSpace.Closeds | {
"line": 52,
"column": 15
} | {
"line": 52,
"column": 36
} | [
{
"pp": "α : Type u_1\ninst✝ : PseudoEMetricSpace α\ns t : Set α\nδ : ℝ≥0∞\nh :\n (s, t).1 ⊆ SetRel.preimage {p | edist p.1 p.2 ≤ δ} (s, t).2 ∧ (s, t).2 ⊆ SetRel.image {p | edist p.1 p.2 ≤ δ} (s, t).1\n| (s, t).1 ⊆ SetRel.preimage {p | edist p.1 p.2 ≤ δ} (s, t).2 ∧ (s, t).2 ⊆ SetRel.image {p | edist p.1 p.2 ≤ ... | enter [2, 2, 1, 1, _] | Lean.Elab.Tactic.Conv.evalEnter | Lean.Parser.Tactic.Conv.enter |
Mathlib.Topology.MetricSpace.CoveringNumbers | {
"line": 323,
"column": 40
} | {
"line": 323,
"column": 61
} | [
{
"pp": "X : Type u_1\ninst✝ : PseudoEMetricSpace X\nA : Set X\nε : ℝ≥0\nh : packingNumber ε A ≠ ⊤\nx : X\nhxA : x ∈ A\nh_dist : ∀ y ∈ maximalSeparatedSet ε A, (x, y) ∉ {x | edist x.1 x.2 ≤ ↑ε}\nC : Set X := {x} ∪ maximalSeparatedSet ε A\nhx_not_mem : x ∉ maximalSeparatedSet ε A\n⊢ ∀ y ∈ maximalSeparatedSet ε A... | by simpa using h_dist | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.UniformSpace.Closeds | {
"line": 79,
"column": 4
} | {
"line": 82,
"column": 34
} | [
{
"pp": "case a\nα : Type u_1\nU V : SetRel α α\n⊢ hausdorffEntourage U ○ hausdorffEntourage V ⊆ hausdorffEntourage (U ○ V)",
"usedConstants": [
"Eq.mpr",
"SetRel",
"congrArg",
"Membership.mem",
"Set.instIsTransSubset",
"Prod.mk",
"Set.instReflSubset",
"HasSub... | intro ⟨s₁, s₃⟩ ⟨s₂, ⟨h₁₂, h₂₁⟩, ⟨h₂₃, h₃₂⟩⟩
simp only at *
grw [mem_hausdorffEntourage, preimage_comp, ← h₂₃, ← h₁₂, image_comp, ← h₂₁, ← h₃₂]
exact ⟨subset_rfl, subset_rfl⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.UniformSpace.Closeds | {
"line": 79,
"column": 4
} | {
"line": 82,
"column": 34
} | [
{
"pp": "case a\nα : Type u_1\nU V : SetRel α α\n⊢ hausdorffEntourage U ○ hausdorffEntourage V ⊆ hausdorffEntourage (U ○ V)",
"usedConstants": [
"Eq.mpr",
"SetRel",
"congrArg",
"Membership.mem",
"Set.instIsTransSubset",
"Prod.mk",
"Set.instReflSubset",
"HasSub... | intro ⟨s₁, s₃⟩ ⟨s₂, ⟨h₁₂, h₂₁⟩, ⟨h₂₃, h₃₂⟩⟩
simp only at *
grw [mem_hausdorffEntourage, preimage_comp, ← h₂₃, ← h₁₂, image_comp, ← h₂₁, ← h₃₂]
exact ⟨subset_rfl, subset_rfl⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.MetricSpace.GromovHausdorff | {
"line": 135,
"column": 2
} | {
"line": 135,
"column": 64
} | [
{
"pp": "p : GHSpace\n⊢ toGHSpace p.Rep = p",
"usedConstants": [
"GromovHausdorff.toGHSpace",
"GromovHausdorff.rep_gHSpace_compactSpace",
"id",
"GromovHausdorff.GHSpace",
"GromovHausdorff.rep_gHSpace_nonempty",
"GromovHausdorff.repGHSpaceMetricSpace",
"GromovHausdor... | change toGHSpace (Quot.out p : NonemptyCompacts ℓ_infty_ℝ) = p | Lean.Elab.Tactic.evalChange | Lean.Parser.Tactic.change |
Mathlib.Topology.UniformSpace.Closeds | {
"line": 455,
"column": 2
} | {
"line": 455,
"column": 30
} | [
{
"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\n⊢ ∃ x_1 ∈ U, ∃ a, (x, a) = x_1 ∧ a ∈ ↑F₂",
"usedConstants": []... | obtain ⟨y, hy, hxy⟩ := h hx₁ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Topology.MetricSpace.HausdorffAlexandroff | {
"line": 73,
"column": 2
} | {
"line": 74,
"column": 34
} | [
{
"pp": "X : Set (ℕ → Bool)\nh_closed : IsClosed X\nh_nonempty : X.Nonempty\n⊢ ∃ f, Continuous f ∧ Set.range f = X",
"usedConstants": [
"LipschitzWith",
"Continuous",
"Pi.topologicalSpace",
"instTopologicalSpaceBool",
"instDiscreteTopologyBool",
"Membership.mem",
"E... | obtain ⟨f, fs, frange, hf⟩ := PiNat.exists_lipschitz_retraction_of_isClosed h_closed h_nonempty
exact ⟨f, hf.continuous, frange⟩ | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.MetricSpace.HausdorffAlexandroff | {
"line": 73,
"column": 2
} | {
"line": 74,
"column": 34
} | [
{
"pp": "X : Set (ℕ → Bool)\nh_closed : IsClosed X\nh_nonempty : X.Nonempty\n⊢ ∃ f, Continuous f ∧ Set.range f = X",
"usedConstants": [
"LipschitzWith",
"Continuous",
"Pi.topologicalSpace",
"instTopologicalSpaceBool",
"instDiscreteTopologyBool",
"Membership.mem",
"E... | obtain ⟨f, fs, frange, hf⟩ := PiNat.exists_lipschitz_retraction_of_isClosed h_closed h_nonempty
exact ⟨f, hf.continuous, frange⟩ | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.MetricSpace.Infsep | {
"line": 429,
"column": 68
} | {
"line": 431,
"column": 36
} | [
{
"pp": "α : Type u_1\ninst✝ : PseudoMetricSpace α\ns : Finset α\nhs : s.offDiag = ∅\n⊢ (↑s).infsep = 0",
"usedConstants": [
"Eq.mpr",
"PseudoEMetricSpace.toWeakPseudoEMetricSpace",
"Real",
"Real.instZero",
"Finset.inf'",
"congrArg",
"Finset",
"Finset.not_none... | by
rw [← Finset.not_nonempty_iff_eq_empty] at hs
rw [Finset.coe_infsep, dif_neg hs] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.MetricSpace.Snowflaking | {
"line": 476,
"column": 2
} | {
"line": 477,
"column": 63
} | [
{
"pp": "X : Type u_1\nα : ℝ\nhα₀ : 0 < α\nhα₁ : α ≤ 1\ninst✝ : PseudoMetricSpace X\nx : Snowflaking X α hα₀ hα₁\nr : ℝ\nhr : 0 ≤ r\n⊢ ⇑toSnowflaking ⁻¹' ball x r = ball (ofSnowflaking x) (r ^ α⁻¹)",
"usedConstants": [
"Eq.mpr",
"Metric.Snowflaking.instPseudoMetricSpace",
"Real.instPow",
... | rw [toSnowflaking.preimage_eq_iff_eq_image, image_toSnowflaking_ball _ (by positivity),
toSnowflaking_ofSnowflaking, Real.rpow_inv_rpow hr hα₀.ne'] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.MetricSpace.Snowflaking | {
"line": 476,
"column": 2
} | {
"line": 477,
"column": 63
} | [
{
"pp": "X : Type u_1\nα : ℝ\nhα₀ : 0 < α\nhα₁ : α ≤ 1\ninst✝ : PseudoMetricSpace X\nx : Snowflaking X α hα₀ hα₁\nr : ℝ\nhr : 0 ≤ r\n⊢ ⇑toSnowflaking ⁻¹' ball x r = ball (ofSnowflaking x) (r ^ α⁻¹)",
"usedConstants": [
"Eq.mpr",
"Metric.Snowflaking.instPseudoMetricSpace",
"Real.instPow",
... | rw [toSnowflaking.preimage_eq_iff_eq_image, image_toSnowflaking_ball _ (by positivity),
toSnowflaking_ofSnowflaking, Real.rpow_inv_rpow hr hα₀.ne'] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.MetricSpace.Snowflaking | {
"line": 476,
"column": 2
} | {
"line": 477,
"column": 63
} | [
{
"pp": "X : Type u_1\nα : ℝ\nhα₀ : 0 < α\nhα₁ : α ≤ 1\ninst✝ : PseudoMetricSpace X\nx : Snowflaking X α hα₀ hα₁\nr : ℝ\nhr : 0 ≤ r\n⊢ ⇑toSnowflaking ⁻¹' ball x r = ball (ofSnowflaking x) (r ^ α⁻¹)",
"usedConstants": [
"Eq.mpr",
"Metric.Snowflaking.instPseudoMetricSpace",
"Real.instPow",
... | rw [toSnowflaking.preimage_eq_iff_eq_image, image_toSnowflaking_ball _ (by positivity),
toSnowflaking_ofSnowflaking, Real.rpow_inv_rpow hr hα₀.ne'] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.NatEmbedding | {
"line": 62,
"column": 4
} | {
"line": 62,
"column": 95
} | [
{
"pp": "case neg.refine_3\nX : Type u_1\ninst✝² : TopologicalSpace X\ninst✝¹ : T2Space X\ninst✝ : Infinite X\nx : X\nhx : (𝓝[≠] x).NeBot\nthis✝ : Std.Symm Disjoint\nS : Finset (Set X)\nhS : ∀ x_1 ∈ S, (fun U ↦ U.Nonempty ∧ IsOpen[inst✝²] U ∧ Uᶜ ∈ 𝓝 x) x_1\nthis : (⋂ U ∈ S, interior Uᶜ) \\ {x} ∈ 𝓝[≠] x\ny : ... | · exact disjoint_left.2 fun z hzU ⟨_, hzU'⟩ ↦ interior_subset (mem_iInter₂.1 hzU' U hU) hzU | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.Order.UpperLowerSetTopology | {
"line": 243,
"column": 24
} | {
"line": 243,
"column": 91
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : TopologicalSpace α\ninst✝ : Topology.IsUpperSet α\ns : Set α\nS : Set (Set α)\n⊢ (∀ s ∈ S, IsOpen[inst✝¹] s) → IsOpen[inst✝¹] (⋂₀ S)",
"usedConstants": [
"Eq.mpr",
"IsUpperSet",
"Preorder.toLE",
"Members... | simpa only [isOpen_iff_isUpperSet] using isUpperSet_sInter (α := α) | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Topology.Order.UpperLowerSetTopology | {
"line": 243,
"column": 24
} | {
"line": 243,
"column": 91
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : TopologicalSpace α\ninst✝ : Topology.IsUpperSet α\ns : Set α\nS : Set (Set α)\n⊢ (∀ s ∈ S, IsOpen[inst✝¹] s) → IsOpen[inst✝¹] (⋂₀ S)",
"usedConstants": [
"Eq.mpr",
"IsUpperSet",
"Preorder.toLE",
"Members... | simpa only [isOpen_iff_isUpperSet] using isUpperSet_sInter (α := α) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Order.UpperLowerSetTopology | {
"line": 243,
"column": 24
} | {
"line": 243,
"column": 91
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\nγ : Type u_3\ninst✝² : Preorder α\ninst✝¹ : TopologicalSpace α\ninst✝ : Topology.IsUpperSet α\ns : Set α\nS : Set (Set α)\n⊢ (∀ s ∈ S, IsOpen[inst✝¹] s) → IsOpen[inst✝¹] (⋂₀ S)",
"usedConstants": [
"Eq.mpr",
"IsUpperSet",
"Preorder.toLE",
"Members... | simpa only [isOpen_iff_isUpperSet] using isUpperSet_sInter (α := α) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Order.ScottTopology | {
"line": 262,
"column": 4
} | {
"line": 262,
"column": 26
} | [
{
"pp": "case refine_2\nα : Type u_1\nβ : Type u_2\ninst✝⁵ : Preorder α\ninst✝⁴ : TopologicalSpace α\ninst✝³ : Preorder β\ninst✝² : TopologicalSpace β\ninst✝¹ : IsScott β univ\nf : α → β\nD : Set (Set α)\ninst✝ : IsScott α D\nhD : ∀ (a b : α), a ≤ b → {a, b} ∈ D\nhf : Continuous[inst✝⁴, inst✝²] f\nt : Set α\nh₀... | exact hfcb <| hb _ hcd | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Topology.MetricSpace.GromovHausdorff | {
"line": 662,
"column": 6
} | {
"line": 662,
"column": 37
} | [
{
"pp": "case refine_2\nδ : 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 : GHS... | let hi := ((E q) ⟨y, ys⟩).is_lt | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticLet___1 | Lean.Parser.Tactic.tacticLet__ |
Mathlib.Topology.Order.LawsonTopology | {
"line": 220,
"column": 2
} | {
"line": 220,
"column": 10
} | [
{
"pp": "α : Type u_1\ninst✝² : Preorder α\nL S : TopologicalSpace α\ninst✝¹ : IsLawson α\ninst✝ : IsScott α univ\ns : Set α\nh : IsLowerSet s\n⊢ IsLowerSet s ∧ DirSupClosed s ↔ DirSupClosed s",
"usedConstants": [
"congrArg",
"Preorder.toLE",
"DirSupClosed",
"iff_self",
"And",
... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Partial | {
"line": 69,
"column": 2
} | {
"line": 69,
"column": 11
} | [
{
"pp": "case mpr\nX : Type u_1\nY : Type u_2\ninst✝¹ : TopologicalSpace X\ninst✝ : TopologicalSpace Y\nf : X →. Y\nhf : ∀ {x : X} {y : Y}, y ∈ f x → PTendsto' f (𝓝 x) (𝓝 y)\ns : Set Y\nos : IsOpen[inst✝] s\nx : X\ny : Y\nys : y ∈ s\nfxy : (x, y) ∈ f.graph'\nt : Set X\nh : f.preimage s ⊆ t\n⊢ t ∈ 𝓝 x",
"... | grw [← h] | Mathlib.Tactic._aux_Mathlib_Tactic_GRewrite_Elab___macroRules_Mathlib_Tactic_grwSeq_1 | Mathlib.Tactic.grwSeq |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 343,
"column": 4
} | {
"line": 344,
"column": 51
} | [
{
"pp": "case refine_2\nX : Type u\nY : Type v\ninst✝³ : MetricSpace X\ninst✝² : MetricSpace Y\ninst✝¹ : Nonempty X\ninst✝ : Nonempty Y\nf g : Cb X Y\ncg : ℝ\nhcg : cg ∈ lowerBounds (range ⇑g)\nHcg : ∀ (x : (X ⊕ Y) × (X ⊕ Y)), cg ≤ g x\ncf : ℝ\nhcf : cf ∈ lowerBounds (range ⇑f)\nHcf : ∀ (x : (X ⊕ Y) × (X ⊕ Y)),... | · change BddBelow (range fun x : X => g (inl x, inr y))
exact ⟨cg, forall_mem_range.2 fun i => Hcg _⟩ | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.MetricSpace.GromovHausdorff | {
"line": 940,
"column": 2
} | {
"line": 940,
"column": 50
} | [
{
"pp": "X : ℕ → Type\ninst✝² : (n : ℕ) → MetricSpace (X n)\ninst✝¹ : ∀ (n : ℕ), CompactSpace (X n)\ninst✝ : ∀ (n : ℕ), Nonempty (X n)\nd : ℕ → ℝ := fun n ↦ (1 / 2) ^ n\n⊢ CompleteSpace GHSpace",
"usedConstants": [
"Real.instIsOrderedRing",
"pow_pos",
"Real.partialOrder",
"Real",
... | have : ∀ n : ℕ, 0 < d n := fun _ ↦ by positivity | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Topology.Separation.PerfectlyNormal | {
"line": 91,
"column": 10
} | {
"line": 91,
"column": 18
} | [
{
"pp": "case pos\nX : Type u_1\ninst✝ : TopologicalSpace X\nh : ∀ (s : Set X), IsClosed[inst✝] s → ∃ f, s = ⇑f ⁻¹' {0} ∧ ∀ (x : X), f x ∈ Icc 0 1\ns : Set X\nhs : IsClosed[inst✝] s\nhse : s = ∅\n⊢ IsGδ s",
"usedConstants": [
"congrArg",
"True",
"Set.instEmptyCollection",
"of_eq_true... | simp_all | Lean.Elab.Tactic.evalSimpAll | Lean.Parser.Tactic.simpAll |
Mathlib.Topology.Separation.PerfectlyNormal | {
"line": 91,
"column": 10
} | {
"line": 91,
"column": 18
} | [
{
"pp": "case pos\nX : Type u_1\ninst✝ : TopologicalSpace X\nh : ∀ (s : Set X), IsClosed[inst✝] s → ∃ f, s = ⇑f ⁻¹' {0} ∧ ∀ (x : X), f x ∈ Icc 0 1\ns : Set X\nhs : IsClosed[inst✝] s\nhse : s = ∅\n⊢ IsGδ s",
"usedConstants": [
"congrArg",
"True",
"Set.instEmptyCollection",
"of_eq_true... | simp_all | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Separation.PerfectlyNormal | {
"line": 91,
"column": 10
} | {
"line": 91,
"column": 18
} | [
{
"pp": "case pos\nX : Type u_1\ninst✝ : TopologicalSpace X\nh : ∀ (s : Set X), IsClosed[inst✝] s → ∃ f, s = ⇑f ⁻¹' {0} ∧ ∀ (x : X), f x ∈ Icc 0 1\ns : Set X\nhs : IsClosed[inst✝] s\nhse : s = ∅\n⊢ IsGδ s",
"usedConstants": [
"congrArg",
"True",
"Set.instEmptyCollection",
"of_eq_true... | simp_all | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Sheaves.EtaleSpace | {
"line": 112,
"column": 14
} | {
"line": 116,
"column": 77
} | [
{
"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 : ∀ (... | by
rintro ⟨⟨base, s⟩, hs⟩
simp only
congr 2
rw [leftInverse_surjInv (hF_bij _ _), surjInv_eq (hF_bij _ _).surjective] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Sheaves.Flasque | {
"line": 99,
"column": 2
} | {
"line": 99,
"column": 69
} | [
{
"pp": "X : TopCat\nU : Opens ↑X\nF G : Sheaf AddCommGrpCat X\ng : F ⟶ G\ns : ↑(G.obj.obj (op U))\nc : Set (Under g s)\nh : IsChain (fun x y ↦ Nonempty (y ⟶ x)) c\nf : ↑c → Opens ↑X := fun x ↦ unop (StructuredArrow.right ↑x).fst\nt : ToType (F.obj.obj (op (iSup f)))\nht : IsGluing F.obj f (fun x ↦ (StructuredA... | have le₁ : iSup f ≤ U := iSup_le <| fun j => leOfHom j.1.hom.1.unop | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts | {
"line": 231,
"column": 10
} | {
"line": 233,
"column": 16
} | [
{
"pp": "case zero\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 c' : Cone ((diagram U).op ⋙ F)\nf : c ⟶ c'\n⊢ f.hom ≫ (coneEquivFunctorObj F U c').π.app WalkingParallelPair.zero =\n (coneEquivFunctorObj F U c).π.app WalkingPara... | · dsimp
ext
simp | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts | {
"line": 231,
"column": 10
} | {
"line": 233,
"column": 16
} | [
{
"pp": "case one\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 c' : Cone ((diagram U).op ⋙ F)\nf : c ⟶ c'\n⊢ f.hom ≫ (coneEquivFunctorObj F U c').π.app WalkingParallelPair.one =\n (coneEquivFunctorObj F U c).π.app WalkingParall... | · dsimp
ext
simp | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Data.Nat.BinaryRec | {
"line": 61,
"column": 26
} | {
"line": 61,
"column": 66
} | [
{
"pp": "case zero.false\n⊢ bit false 0 = 0 ↔ 0 = 0 ∧ false = false",
"usedConstants": [
"cond",
"Nat.bit",
"HMul.hMul",
"congrArg",
"and_self",
"instMulNat",
"instOfNatNat",
"iff_self",
"instHAdd",
"And",
"Iff",
"HAdd.hAdd",
"Nat... | simp [bit, Nat.two_mul, ← Nat.add_assoc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Nat.BinaryRec | {
"line": 61,
"column": 26
} | {
"line": 61,
"column": 66
} | [
{
"pp": "case zero.true\n⊢ bit true 0 = 0 ↔ 0 = 0 ∧ true = false",
"usedConstants": [
"cond",
"Nat.bit",
"False",
"HMul.hMul",
"congrArg",
"Bool.true_eq_false",
"instMulNat",
"instOfNatNat",
"iff_self",
"Bool.true",
"instHAdd",
"And",
... | simp [bit, Nat.two_mul, ← Nat.add_assoc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Nat.BinaryRec | {
"line": 61,
"column": 26
} | {
"line": 61,
"column": 66
} | [
{
"pp": "case succ.false\nn✝ : Nat\n⊢ bit false (n✝ + 1) = 0 ↔ n✝ + 1 = 0 ∧ false = false",
"usedConstants": [
"cond",
"Nat.bit",
"False",
"HMul.hMul",
"and_true",
"congrArg",
"and_self",
"Nat.add_eq_zero_iff._simp_1",
"false_and",
"instMulNat",
... | simp [bit, Nat.two_mul, ← Nat.add_assoc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Data.Nat.BinaryRec | {
"line": 61,
"column": 26
} | {
"line": 61,
"column": 66
} | [
{
"pp": "case succ.true\nn✝ : Nat\n⊢ bit true (n✝ + 1) = 0 ↔ n✝ + 1 = 0 ∧ true = false",
"usedConstants": [
"cond",
"Nat.bit",
"False",
"HMul.hMul",
"congrArg",
"and_self",
"Nat.add_eq_zero_iff._simp_1",
"false_and",
"Bool.true_eq_false",
"instMulN... | simp [bit, Nat.two_mul, ← Nat.add_assoc] | Lean.Elab.Tactic.evalSimp | Lean.Parser.Tactic.simp |
Mathlib.Logic.Relation | {
"line": 233,
"column": 2
} | {
"line": 233,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nγ : Sort u_3\nδ : Sort u_4\nε : Sort u_5\nζ : Sort u_6\nr : α → β → Prop\nf₁ : α → γ\ng₁ : β → δ\nf₂ : γ → ε\ng₂ : δ → ζ\n⊢ Relation.Map (Relation.Map r f₁ g₁) f₂ g₂ = Relation.Map r (f₂ ∘ f₁) (g₂ ∘ g₁)",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relati... | grind [Relation.Map] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.Logic.Relation | {
"line": 233,
"column": 2
} | {
"line": 233,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nγ : Sort u_3\nδ : Sort u_4\nε : Sort u_5\nζ : Sort u_6\nr : α → β → Prop\nf₁ : α → γ\ng₁ : β → δ\nf₂ : γ → ε\ng₂ : δ → ζ\n⊢ Relation.Map (Relation.Map r f₁ g₁) f₂ g₂ = Relation.Map r (f₂ ∘ f₁) (g₂ ∘ g₁)",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relati... | grind [Relation.Map] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Logic.Relation | {
"line": 233,
"column": 2
} | {
"line": 233,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nγ : Sort u_3\nδ : Sort u_4\nε : Sort u_5\nζ : Sort u_6\nr : α → β → Prop\nf₁ : α → γ\ng₁ : β → δ\nf₂ : γ → ε\ng₂ : δ → ζ\n⊢ Relation.Map (Relation.Map r f₁ g₁) f₂ g₂ = Relation.Map r (f₂ ∘ f₁) (g₂ ∘ g₁)",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relati... | grind [Relation.Map] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Logic.Relation | {
"line": 283,
"column": 2
} | {
"line": 283,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nr : α → α → Prop\nf : α → β\nx✝ : α\n⊢ ∀ {y : α}, r x✝ y → (Relation.Map r f f on f) x✝ y",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relation.le_onFun_map._proof_1_2"
]
}
] | grind [Relation.Map] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.Logic.Relation | {
"line": 292,
"column": 2
} | {
"line": 292,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nr : β → β → Prop\nf : α → β\nx✝ : β\n⊢ ∀ {y : β}, Relation.Map (r on f) f f x✝ y → r x✝ y",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relation.map_onFun_le._proof_1_2"
]
}
] | grind [Relation.Map] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.Logic.Relation | {
"line": 299,
"column": 2
} | {
"line": 299,
"column": 22
} | [
{
"pp": "case h.h.a\nα : Sort u_1\nβ : Sort u_2\nr : β → β → Prop\nf : α → β\nhsurj : Surjective f\nx y : β\nx✝¹ : ∃ a, f a = x\nx✝ : ∃ a, f a = y\n⊢ Relation.Map (r on f) f f x y ↔ r x y",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relation.map_onFun_eq_of_surjective._proof_1_2"
]
}
... | grind [Relation.Map] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.Logic.Relation | {
"line": 303,
"column": 2
} | {
"line": 303,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nr : α → α → Prop\nf : α → β\n⊢ Relation.Map (Relation.Map r f f on f) f f = Relation.Map r f f",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relation.map_onFun_map_eq_map._proof_1_2"
]
}
] | grind [Relation.Map] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.Logic.Relation | {
"line": 303,
"column": 2
} | {
"line": 303,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nr : α → α → Prop\nf : α → β\n⊢ Relation.Map (Relation.Map r f f on f) f f = Relation.Map r f f",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relation.map_onFun_map_eq_map._proof_1_2"
]
}
] | grind [Relation.Map] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Logic.Relation | {
"line": 303,
"column": 2
} | {
"line": 303,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nr : α → α → Prop\nf : α → β\n⊢ Relation.Map (Relation.Map r f f on f) f f = Relation.Map r f f",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relation.map_onFun_map_eq_map._proof_1_2"
]
}
] | grind [Relation.Map] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Logic.Relation | {
"line": 307,
"column": 2
} | {
"line": 307,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nr : β → β → Prop\nf : α → β\n⊢ (Relation.Map (r on f) f f on f) = (r on f)",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relation.onFun_map_onFun_eq_onFun._proof_1_2"
]
}
] | grind [Relation.Map] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.Logic.Relation | {
"line": 307,
"column": 2
} | {
"line": 307,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nr : β → β → Prop\nf : α → β\n⊢ (Relation.Map (r on f) f f on f) = (r on f)",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relation.onFun_map_onFun_eq_onFun._proof_1_2"
]
}
] | grind [Relation.Map] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Logic.Relation | {
"line": 307,
"column": 2
} | {
"line": 307,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nr : β → β → Prop\nf : α → β\n⊢ (Relation.Map (r on f) f f on f) = (r on f)",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relation.onFun_map_onFun_eq_onFun._proof_1_2"
]
}
] | grind [Relation.Map] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Logic.Relation | {
"line": 311,
"column": 2
} | {
"line": 311,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nr : β → β → Prop\nf : α → β\na₁ a₂ : α\n⊢ Relation.Map (r on f) f f (f a₁) (f a₂) ↔ r (f a₁) (f a₂)",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relation.onFun_map_onFun_iff_onFun._proof_1_2"
]
}
] | grind [Relation.Map] | Lean.Elab.Tactic.evalGrind | Lean.Parser.Tactic.grind |
Mathlib.Logic.Relation | {
"line": 311,
"column": 2
} | {
"line": 311,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nr : β → β → Prop\nf : α → β\na₁ a₂ : α\n⊢ Relation.Map (r on f) f f (f a₁) (f a₂) ↔ r (f a₁) (f a₂)",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relation.onFun_map_onFun_iff_onFun._proof_1_2"
]
}
] | grind [Relation.Map] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Logic.Relation | {
"line": 311,
"column": 2
} | {
"line": 311,
"column": 22
} | [
{
"pp": "α : Sort u_1\nβ : Sort u_2\nr : β → β → Prop\nf : α → β\na₁ a₂ : α\n⊢ Relation.Map (r on f) f f (f a₁) (f a₂) ↔ r (f a₁) (f a₂)",
"usedConstants": [
"_private.Mathlib.Logic.Relation.0.Relation.onFun_map_onFun_iff_onFun._proof_1_2"
]
}
] | grind [Relation.Map] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
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