module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.Topology.Sheaves.Skyscraper | {
"line": 63,
"column": 67
} | {
"line": 63,
"column": 78
} | {
"line": 63,
"column": 79
} | [
{
"pp": "X : TopCat\np₀ : ↑X\ninst✝² : (U : Opens ↑X) → Decidable (p₀ ∈ U)\nC : Type v\ninst✝¹ : Category.{w, v} C\ninst✝ : HasTerminal C\nA : C\nU V : (Opens ↑X)ᵒᵖ\ni : U ⟶ V\nh : p₀ ∈ unop V\n⊢ p₀ ∈ unop U",
"ppTerm": "?m.112",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"used... | [
"X : TopCat\np₀ : ↑X\ninst✝² : (U : Opens ↑X) → Decidable (p₀ ∈ U)\nC : Type v\ninst✝¹ : Category.{w, v} C\ninst✝ : HasTerminal C\nA : C\nU V : (Opens ↑X)ᵒᵖ\ni : U ⟶ V\nh : p₀ ∈ unop V\n⊢ p₀ ∈ unop U"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.PerfectlyNormal | {
"line": 83,
"column": 12
} | {
"line": 83,
"column": 29
} | {
"line": 83,
"column": 30
} | [
{
"pp": "case pos\nX : Type u_1\ninst✝ : TopologicalSpace X\ns t : Set X\nf g : C(X, ℝ)\nx : X\nh : ∀ (s : Set X), IsClosed[inst✝] s → ∃ f, s = {x | f x = 0} ∧ ∀ (x : X), f x ∈ Icc 0 1\nhs : IsClosed[inst✝] {x | f x = 0}\nht : IsClosed[inst✝] {x | g x = 0}\nhst : Disjoint {x | f x = 0} {x | g x = 0}\nhf : s = {... | [
"case pos\nX : Type u_1\ninst✝ : TopologicalSpace X\ns t : Set X\nf g : C(X, ℝ)\nx : X\nh : ∀ (s : Set X), IsClosed[inst✝] s → ∃ f, s = {x | f x = 0} ∧ ∀ (x : X), f x ∈ Icc 0 1\nhs : IsClosed[inst✝] {x | f x = 0}\nht : IsClosed[inst✝] {x | g x = 0}\nhst : Disjoint {x | f x = 0} {x | g x = 0}\nhf : s = {x | f x = 0}... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sheaves.LocallySurjective | {
"line": 108,
"column": 4
} | {
"line": 108,
"column": 51
} | {
"line": 110,
"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 :... | obtain ⟨V, hxV, s, rfl⟩ := ℱ.exists_germ_eq s_x | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalObtain | Lean.Parser.Tactic.obtain |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 315,
"column": 6
} | {
"line": 315,
"column": 17
} | {
"line": 315,
"column": 18
} | [
{
"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)),... | [
"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)), cf ≤ f x\nZ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 343,
"column": 6
} | {
"line": 343,
"column": 17
} | {
"line": 343,
"column": 18
} | [
{
"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)),... | [
"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)), cf ≤ f x\nZ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 370,
"column": 6
} | {
"line": 370,
"column": 17
} | {
"line": 370,
"column": 18
} | [
{
"pp": "case refine_2.refine_1\nX : Type u\nY : Type v\ninst✝³ : MetricSpace X\ninst✝² : MetricSpace Y\ninst✝¹ : CompactSpace X\ninst✝ : CompactSpace Y\nthis : Tendsto (fun t ↦ 2 * ↑(maxVar X Y) * t) (𝓝 0) (𝓝 (2 * ↑(maxVar X Y) * 0))\n⊢ Tendsto (fun t ↦ 2 * ↑(maxVar X Y) * t) (𝓝 0) (𝓝 0)",
"ppTerm": "?... | [
"case refine_2.refine_1\nX : Type u\nY : Type v\ninst✝³ : MetricSpace X\ninst✝² : MetricSpace Y\ninst✝¹ : CompactSpace X\ninst✝ : CompactSpace Y\nthis : Tendsto (fun t ↦ 2 * ↑(maxVar X Y) * t) (𝓝 0) (𝓝 (2 * ↑(maxVar X Y) * 0))\n⊢ Tendsto (fun t ↦ 2 * ↑(maxVar X Y) * t) (𝓝 0) (𝓝 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 418,
"column": 19
} | {
"line": 418,
"column": 30
} | {
"line": 418,
"column": 31
} | [
{
"pp": "X : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : MetricSpace Y\ninst✝³ : CompactSpace X\ninst✝² : CompactSpace Y\ninst✝¹ : Nonempty X\ninst✝ : Nonempty Y\nx : X\n⊢ BddBelow (range fun y ↦ (candidatesBDist X Y) (inl x, inr y))",
"ppTerm": "?m.93",
"assigned": false,
"usedConstants": ... | [
"X : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : MetricSpace Y\ninst✝³ : CompactSpace X\ninst✝² : CompactSpace Y\ninst✝¹ : Nonempty X\ninst✝ : Nonempty Y\nx : X\n⊢ BddBelow (range fun y ↦ (candidatesBDist X Y) (inl x, inr y))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 427,
"column": 19
} | {
"line": 427,
"column": 30
} | {
"line": 427,
"column": 31
} | [
{
"pp": "X : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : MetricSpace Y\ninst✝³ : CompactSpace X\ninst✝² : CompactSpace Y\ninst✝¹ : Nonempty X\ninst✝ : Nonempty Y\ny : Y\n⊢ BddBelow (range fun x ↦ (candidatesBDist X Y) (inl x, inr y))",
"ppTerm": "?m.290",
"assigned": false,
"usedConstants":... | [
"X : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : MetricSpace Y\ninst✝³ : CompactSpace X\ninst✝² : CompactSpace Y\ninst✝¹ : Nonempty X\ninst✝ : Nonempty Y\ny : Y\n⊢ BddBelow (range fun x ↦ (candidatesBDist X Y) (inl x, inr y))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 520,
"column": 19
} | {
"line": 520,
"column": 30
} | {
"line": 520,
"column": 31
} | [
{
"pp": "X : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : Nonempty X\ninst✝² : MetricSpace Y\ninst✝¹ : CompactSpace Y\ninst✝ : Nonempty Y\nf : Cb X Y\nh : f ∈ candidatesB X Y\nr : ℝ\nhr : HD (optimalGHDist X Y) < r\nz : X\nI1 : ⨆ x, ⨅ y, (optimalGHDist X Y) (inl x, inr y) < r\n⊢... | [
"X : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : Nonempty X\ninst✝² : MetricSpace Y\ninst✝¹ : CompactSpace Y\ninst✝ : Nonempty Y\nf : Cb X Y\nh : f ∈ candidatesB X Y\nr : ℝ\nhr : HD (optimalGHDist X Y) < r\nz : X\nI1 : ⨆ x, ⨅ y, (optimalGHDist X Y) (inl x, inr y) < r\n⊢ BddAbove (r... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 533,
"column": 19
} | {
"line": 533,
"column": 30
} | {
"line": 533,
"column": 31
} | [
{
"pp": "X : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : Nonempty X\ninst✝² : MetricSpace Y\ninst✝¹ : CompactSpace Y\ninst✝ : Nonempty Y\nf : Cb X Y\nh : f ∈ candidatesB X Y\nr : ℝ\nhr : HD (optimalGHDist X Y) < r\nA : ∀ x ∈ range (optimalGHInjl X Y), ∃ y ∈ range (optimalGHInjr... | [
"X : Type u\nY : Type v\ninst✝⁵ : MetricSpace X\ninst✝⁴ : CompactSpace X\ninst✝³ : Nonempty X\ninst✝² : MetricSpace Y\ninst✝¹ : CompactSpace Y\ninst✝ : Nonempty Y\nf : Cb X Y\nh : f ∈ candidatesB X Y\nr : ℝ\nhr : HD (optimalGHDist X Y) < r\nA : ∀ x ∈ range (optimalGHInjl X Y), ∃ y ∈ range (optimalGHInjr X Y), dist ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sion | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 13
} | {
"line": 98,
"column": 14
} | [
{
"pp": "E : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝ : LinearOrder β\nX : Set E\nY : Set F\nf : E → F → β\na : E\nb : β\ny y' : ↑Y\nha : ∀ x ∈ X, max (f a ↑y) (f a ↑y') ≤ max (f x ↑y) (f x ↑y')\nhb : b < max (f a ↑y) (f a ↑y')\nx : E\nhx : x ∈ X\nhx1 : ⟨x, hx⟩ ∈ sublevelLeft X f b ↑y\nhx2 : ⟨x, hx⟩ ∈ sublev... | [
"E : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝ : LinearOrder β\nX : Set E\nY : Set F\nf : E → F → β\na : E\nb : β\ny y' : ↑Y\nha : ∀ x ∈ X, max (f a ↑y) (f a ↑y') ≤ max (f x ↑y) (f x ↑y')\nhb : b < max (f a ↑y) (f a ↑y')\nx : E\nhx : x ∈ X\nhx1 : ⟨x, hx⟩ ∈ sublevelLeft X f b ↑y\nhx2 : ⟨x, hx⟩ ∈ sublevelLeft X f b... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Spectral.ConstructibleTopology | {
"line": 78,
"column": 2
} | {
"line": 78,
"column": 14
} | {
"line": 79,
"column": 2
} | [
{
"pp": "case inl\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\ns : Set X\nhs : s ∈ {s | IsOpen[inst✝¹] s ∧ IsCompact s}\n⊢ IsCompact s",
"ppTerm": "?inl",
"assigned": true,
"usedConstants": [
"And.right",
"IsOpen",
"IsCompact"
],
"usedFVars": [
... | [
"case inr\nX : Type u_1\ninst✝¹ : TopologicalSpace X\ninst✝ : CompactSpace X\ns : Set X\nhs : s ∈ {s | IsClosed[inst✝¹] s ∧ IsCompact sᶜ}\n⊢ IsCompact s"
] | · exact hs.2 | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.Subpath | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 79
} | {
"line": 84,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\na b : X\nγ : Path a b\nt₀ t₁ : ↑I\n⊢ range ⇑(γ.subpath t₀ t₁) = ⇑γ '' uIcc t₀ t₁",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Set.range_comp",
"Eq.mpr",
"Real",
"Set.Icc.convexComb",
"Path.range_subpathAux... | [] | rw [← range_subpathAux, ← range_comp, subpath, coe_mk', ContinuousMap.coe_mk] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.Topology.Subpath | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 79
} | {
"line": 84,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\na b : X\nγ : Path a b\nt₀ t₁ : ↑I\n⊢ range ⇑(γ.subpath t₀ t₁) = ⇑γ '' uIcc t₀ t₁",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Set.range_comp",
"Eq.mpr",
"Real",
"Set.Icc.convexComb",
"Path.range_subpathAux... | [] | rw [← range_subpathAux, ← range_comp, subpath, coe_mk', ContinuousMap.coe_mk] | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Topology.Subpath | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 79
} | {
"line": 84,
"column": 0
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\na b : X\nγ : Path a b\nt₀ t₁ : ↑I\n⊢ range ⇑(γ.subpath t₀ t₁) = ⇑γ '' uIcc t₀ t₁",
"ppTerm": "?m.18",
"assigned": true,
"usedConstants": [
"Set.range_comp",
"Eq.mpr",
"Real",
"Set.Icc.convexComb",
"Path.range_subpathAux... | [] | rw [← range_subpathAux, ← range_comp, subpath, coe_mk', ContinuousMap.coe_mk] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Subpath | {
"line": 206,
"column": 2
} | {
"line": 206,
"column": 27
} | {
"line": 206,
"column": 28
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\np : Fin 2 → X\nF : (k : Fin 1) → Path (p k.castSucc) (p k.succ)\n⊢ (concat p F).Homotopic (F 0)",
"ppTerm": "?m.13",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Path.trans",
"Fin.succ",
"congr... | [
"X : Type u_1\ninst✝ : TopologicalSpace X\np : Fin 2 → X\nF : (k : Fin 1) → Path (p k.castSucc) (p k.succ)\n⊢ ((Path.refl (p 0)).trans (F 0)).Homotopic (F 0)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Subpath | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 27
} | {
"line": 211,
"column": 28
} | [
{
"pp": "X : Type u_1\ninst✝ : TopologicalSpace X\np : Fin 3 → X\nF : (k : Fin 2) → Path (p k.castSucc) (p k.succ)\n⊢ (concat p F).Homotopic ((F 0).trans (F 1))",
"ppTerm": "?m.20",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Path.trans",
"Fin.succ"... | [
"X : Type u_1\ninst✝ : TopologicalSpace X\np : Fin 3 → X\nF : (k : Fin 2) → Path (p k.castSucc) (p k.succ)\n⊢ (((Path.refl (p 0)).trans (F 0)).trans (F 1)).Homotopic ((F 0).trans (F 1))"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sion | {
"line": 259,
"column": 4
} | {
"line": 259,
"column": 15
} | {
"line": 259,
"column": 16
} | [
{
"pp": "E : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nX : Set E\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\nne_X : X.Nonempty\nkX : IsCompact X\nhfy : ∀ y ∈ Y, LowerSem... | [
"E : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nX : Set E\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\nne_X : X.Nonempty\nkX : IsCompact X\nhfy : ∀ y ∈ Y, LowerSemicontinuousO... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.Path | {
"line": 81,
"column": 45
} | {
"line": 82,
"column": 9
} | {
"line": 82,
"column": 10
} | [
{
"pp": "X : Type u_1\ninst✝¹ : UniformSpace X\nx y z : X\ninst✝ : CompleteSpace X\n⊢ IsComplete (Set.range _root_.toContinuousMap)",
"ppTerm": "?m.14",
"assigned": true,
"usedConstants": [
"Real.instIsOrderedRing",
"Path.continuousMapClass",
"Eq.mpr",
"Real.partialOrder",
... | [
"X : Type u_1\ninst✝¹ : UniformSpace X\nx y z : X\ninst✝ : CompleteSpace X\n⊢ IsComplete {f | f 0 = x ∧ f 1 = y}"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sion | {
"line": 269,
"column": 4
} | {
"line": 269,
"column": 71
} | {
"line": 270,
"column": 6
} | [
{
"pp": "E : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nX : Set E\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\nne_X : X.Nonempty\nkX : IsCompact X\nhfy : ∀ y ∈ Y, LowerSem... | [
"E : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nX : Set E\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\nne_X : X.Nonempty\nkX : IsCompact X\nhfy : ∀ y ∈ Y, LowerSemicontinuousO... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.Ultra.Constructions | {
"line": 77,
"column": 4
} | {
"line": 77,
"column": 49
} | {
"line": 77,
"column": 50
} | [
{
"pp": "X✝ : Type u_1\nY : Type u_2\nι : Type u_3\nX : ι → Type u_4\nU : (i : ι) → UniformSpace (X i)\nh : ∀ (i : ι), IsUltraUniformity (X i)\nthis : IsUltraUniformity ((x : ι) → X x)\n⊢ IsUltraUniformity ((i : ι) → X i)",
"ppTerm": "?m.19",
"assigned": true,
"usedConstants": [
"Pi.uniformSpa... | [
"X✝ : Type u_1\nY : Type u_2\nι : Type u_3\nX : ι → Type u_4\nU : (i : ι) → UniformSpace (X i)\nh : ∀ (i : ι), IsUltraUniformity (X i)\nthis : IsUltraUniformity ((x : ι) → X x)\n⊢ IsUltraUniformity ((i : ι) → X i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sion | {
"line": 275,
"column": 4
} | {
"line": 275,
"column": 30
} | {
"line": 275,
"column": 31
} | [
{
"pp": "E : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nX : Set E\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\nne_X : X.Nonempty\nkX : IsCompact X\nhfy : ∀ y ∈ Y, LowerSem... | [
"E : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nX : Set E\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\nne_X : X.Nonempty\nkX : IsCompact X\nhfy : ∀ y ∈ Y, LowerSemicontinuousO... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.Ultra.Basic | {
"line": 141,
"column": 31
} | {
"line": 141,
"column": 53
} | {
"line": 141,
"column": 54
} | [
{
"pp": "X : Type u_1\ninst✝¹ : UniformSpace X\ninst✝ : IsUltraUniformity X\nx : X\n⊢ (𝓝 x).HasBasis (fun t ↦ t ∈ {s | IsClopen s} ∧ x ∈ t) id",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"setOf",
"Membership.mem",
"nhds",
"id",
"And",
"Filter.HasBas... | [
"X : Type u_1\ninst✝¹ : UniformSpace X\ninst✝ : IsUltraUniformity X\nx : X\n⊢ (𝓝 x).HasBasis (fun t ↦ IsClopen t ∧ x ∈ t) id"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.OfCompactT2 | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 29
} | {
"line": 54,
"column": 4
} | [
{
"pp": "γ : Type u_1\ninst✝² : TopologicalSpace γ\ninst✝¹ : CompactSpace γ\ninst✝ : R1Space γ\n⊢ ((𝓝ˢ (diagonal γ)).lift' fun s ↦ s ○ s) ≤ 𝓝ˢ (diagonal γ)",
"ppTerm": "?m.25",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"congrArg",
"PartialOrder.toPreorder",
"instTopolo... | [
"γ : Type u_1\ninst✝² : TopologicalSpace γ\ninst✝¹ : CompactSpace γ\ninst✝ : R1Space γ\n𝓝Δ : Filter (γ × γ) := 𝓝ˢ (diagonal γ)\n⊢ (𝓝Δ.lift' fun s ↦ s ○ s) ≤ 𝓝Δ"
] | set 𝓝Δ := 𝓝ˢ (diagonal γ) | Mathlib.Tactic._aux_Mathlib_Tactic_Set___elabRules_Mathlib_Tactic_setTactic_1 | Mathlib.Tactic.setTactic |
Mathlib.Topology.UniformSpace.Ultra.Completion | {
"line": 42,
"column": 32
} | {
"line": 42,
"column": 43
} | {
"line": 42,
"column": 44
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝² : UniformSpace X\ninst✝¹ : UniformSpace Y\ninst✝ : IsUltraUniformity X\nx✝¹ : SetRel X X\nx✝ : x✝¹ ∈ 𝓤 X ∧ x✝¹.IsSymm ∧ x✝¹.IsTrans\nleft✝ : x✝¹ ∈ 𝓤 X\nhU : x✝¹.IsSymm\nright✝ : x✝¹.IsTrans\n⊢ SetRel.IsSymm ((CauchyFilter.gen ∘ id) x✝¹)",
"ppTerm": "?m.29",
... | [
"X : Type u_1\nY : Type u_2\ninst✝² : UniformSpace X\ninst✝¹ : UniformSpace Y\ninst✝ : IsUltraUniformity X\nx✝¹ : SetRel X X\nx✝ : x✝¹ ∈ 𝓤 X ∧ x✝¹.IsSymm ∧ x✝¹.IsTrans\nleft✝ : x✝¹ ∈ 𝓤 X\nhU : x✝¹.IsSymm\nright✝ : x✝¹.IsTrans\n⊢ (CauchyFilter.gen x✝¹).IsSymm"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.Ultra.Completion | {
"line": 43,
"column": 32
} | {
"line": 43,
"column": 43
} | {
"line": 43,
"column": 44
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝² : UniformSpace X\ninst✝¹ : UniformSpace Y\ninst✝ : IsUltraUniformity X\nx✝¹ : SetRel X X\nx✝ : x✝¹ ∈ 𝓤 X ∧ x✝¹.IsSymm ∧ x✝¹.IsTrans\nleft✝¹ : x✝¹ ∈ 𝓤 X\nleft✝ : x✝¹.IsSymm\nhU : x✝¹.IsTrans\n⊢ SetRel.IsTrans ((CauchyFilter.gen ∘ id) x✝¹)",
"ppTerm": "?m.67",
... | [
"X : Type u_1\nY : Type u_2\ninst✝² : UniformSpace X\ninst✝¹ : UniformSpace Y\ninst✝ : IsUltraUniformity X\nx✝¹ : SetRel X X\nx✝ : x✝¹ ∈ 𝓤 X ∧ x✝¹.IsSymm ∧ x✝¹.IsTrans\nleft✝¹ : x✝¹ ∈ 𝓤 X\nleft✝ : x✝¹.IsSymm\nhU : x✝¹.IsTrans\n⊢ (CauchyFilter.gen x✝¹).IsTrans"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sion | {
"line": 286,
"column": 21
} | {
"line": 286,
"column": 53
} | {
"line": 286,
"column": 53
} | [
{
"pp": "case inr\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nX : Set E\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\nne_X : X.Nonempty\nkX : IsCompact X\nhfy : ∀ y ∈ Y... | [
"case inr\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nX : Set E\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\nne_X : X.Nonempty\nkX : IsCompact X\nhfy : ∀ y ∈ Y, LowerSemic... | monotone_sublevelLeft y1 htt'.le | Mathlib.Tactic.GRewrite.evalGRewriteSeq | null |
Mathlib.Topology.Sion | {
"line": 297,
"column": 13
} | {
"line": 297,
"column": 24
} | {
"line": 297,
"column": 25
} | [
{
"pp": "case empty\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : AddCommGroup F\ninst✝... | [
"case empty\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : AddCommGroup F\ninst✝³ : Module ℝ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sion | {
"line": 304,
"column": 6
} | {
"line": 304,
"column": 54
} | {
"line": 304,
"column": 55
} | [
{
"pp": "case right\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : AddCommGroup F\ninst✝... | [
"case right\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹¹ : LinearOrder β\nY : Set F\nf : E → F → β\ninst✝¹⁰ : TopologicalSpace E\ninst✝⁹ : AddCommGroup E\ninst✝⁸ : Module ℝ E\ninst✝⁷ : IsTopologicalAddGroup E\ninst✝⁶ : ContinuousSMul ℝ E\ninst✝⁵ : TopologicalSpace F\ninst✝⁴ : AddCommGroup F\ninst✝³ : Module ℝ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sion | {
"line": 516,
"column": 2
} | {
"line": 516,
"column": 48
} | {
"line": 516,
"column": 49
} | [
{
"pp": "case right\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹⁶ : LinearOrder β\nX : Set E\nY : Set F\nf : E → F → β\ninst✝¹⁵ : TopologicalSpace E\ninst✝¹⁴ : AddCommGroup E\ninst✝¹³ : Module ℝ E\ninst✝¹² : IsTopologicalAddGroup E\ninst✝¹¹ : ContinuousSMul ℝ E\nne_X : X.Nonempty\ncX : Convex ℝ X\nkX : IsC... | [
"case right\nE : Type u_1\nF : Type u_2\nβ : Type u_3\ninst✝¹⁶ : LinearOrder β\nX : Set E\nY : Set F\nf : E → F → β\ninst✝¹⁵ : TopologicalSpace E\ninst✝¹⁴ : AddCommGroup E\ninst✝¹³ : Module ℝ E\ninst✝¹² : IsTopologicalAddGroup E\ninst✝¹¹ : ContinuousSMul ℝ E\nne_X : X.Nonempty\ncX : Convex ℝ X\nkX : IsCompact X\nhf... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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