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.Order.NhdsSet | {
"line": 62,
"column": 6
} | {
"line": 62,
"column": 29
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderClosedTopology α\na b : α\n⊢ Ioi a ∈ 𝓝ˢ (Ici b) ↔ a < b",
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"instClosedIicTopology",
"Set.Ioi",
"Preorder.toLT",
"Set.Ici",
... | isOpen_Ioi.mem_nhdsSet, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.Order.NhdsSet | {
"line": 61,
"column": 64
} | {
"line": 62,
"column": 45
} | [
{
"pp": "α : Type u_1\ninst✝² : LinearOrder α\ninst✝¹ : TopologicalSpace α\ninst✝ : OrderClosedTopology α\na b : α\n⊢ Ioi a ∈ 𝓝ˢ (Ici b) ↔ a < b",
"usedConstants": [
"Filter.instMembership",
"Eq.mpr",
"instClosedIicTopology",
"Set.Ioi",
"Preorder.toLT",
"Set.Ici",
... | by
rw [isOpen_Ioi.mem_nhdsSet, Ici_subset_Ioi] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.Order.NhdsSet | {
"line": 186,
"column": 2
} | {
"line": 186,
"column": 35
} | [
{
"pp": "α : Type u_1\ninst✝³ : LinearOrder α\ninst✝² : TopologicalSpace α\ninst✝¹ : OrderTopology α\na : α\ninst✝ : (𝓝[>] a).NeBot\nthis : Nonempty ↑(Ioi a)\nc : α\nhc : a < c\n⊢ ∃ i', a < i' ∧ Iic i' ⊆ Iio c",
"usedConstants": [
"Eq.mpr",
"Preorder.toLT",
"congrArg",
"PartialOrder... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.PartialSups | {
"line": 37,
"column": 2
} | {
"line": 37,
"column": 43
} | [
{
"pp": "L : Type u_1\ninst✝² : SemilatticeSup L\ninst✝¹ : TopologicalSpace L\ninst✝ : ContinuousSup L\nα : Type u_2\nl : Filter α\nf : ℕ → α → L\ng : ℕ → L\nn : ℕ\nhf : ∀ k ≤ n, Tendsto (f k) l (𝓝 (g k))\n⊢ Tendsto (fun a ↦ (partialSups fun x ↦ f x a) n) l (𝓝 ((partialSups g) n))",
"usedConstants": [
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.PartialSups | {
"line": 49,
"column": 2
} | {
"line": 49,
"column": 43
} | [
{
"pp": "L : Type u_1\ninst✝³ : SemilatticeSup L\ninst✝² : TopologicalSpace L\ninst✝¹ : ContinuousSup L\nX : Type u_2\ninst✝ : TopologicalSpace X\nf : ℕ → X → L\nn : ℕ\nx : X\nhf : ∀ k ≤ n, ContinuousAt (f k) x\n⊢ ContinuousAt ((partialSups f) n) x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Order.PartialSups | {
"line": 57,
"column": 2
} | {
"line": 57,
"column": 43
} | [
{
"pp": "L : Type u_1\ninst✝³ : SemilatticeSup L\ninst✝² : TopologicalSpace L\ninst✝¹ : ContinuousSup L\nX : Type u_2\ninst✝ : TopologicalSpace X\nf : ℕ → X → L\nn : ℕ\ns : Set X\nx : X\nhf : ∀ k ≤ n, ContinuousWithinAt (f k) s x\n⊢ ContinuousWithinAt ((partialSups f) n) s x",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.DisjointCover | {
"line": 68,
"column": 25
} | {
"line": 68,
"column": 88
} | [
{
"pp": "ι : Type u_1\nX : Type u_2\ninst✝³ : TopologicalSpace X\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : T2Space X\ninst✝ : CompactSpace X\nU : ι → Opens X\nhU : IsOpenCover U\nn : ℕ\nV : Fin n → Clopens X\nhVle : ∀ (j : Fin n), ∃ i, ↑(V j) ⊆ ↑(U i)\nhVun : univ ⊆ ⋃ j, ↑(V j)\nW : Fin n → Clopens X\nhWle... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.DisjointCover | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 49
} | [
{
"pp": "X : Type u_1\ninst✝¹ : TopologicalSpace X\nS : Set (X × X)\ninst✝ : CompactSpace X\nhS : S ∈ 𝓝ˢ (diagonal X)\nU : X → Set X\nhUo : ∀ (x : X), IsOpen[inst✝¹] (U x)\nhUx : ∀ (x : X), x ∈ U x\nhUp : ∀ (x : X), U x ×ˢ U x ⊆ S\nt : Finset X\nht : univ ⊆ ⋃ i ∈ t, U i\n⊢ ⋃ i, U ↑i = univ",
"usedConstants... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.DisjointCover | {
"line": 147,
"column": 4
} | {
"line": 147,
"column": 58
} | [
{
"pp": "X : Type u_1\nV : Type u_2\ninst✝⁴ : TopologicalSpace X\ninst✝³ : TopologicalSpace V\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : T2Space X\ninst✝ : CompactSpace X\nS : Set (V × V)\nf : C(X, V)\nhS : S ∈ 𝓝ˢ (diagonal V)\nn : ℕ\nE : Fin n → Clopens X\nhEne : ∀ (i : Fin n), E i ≠ ⊥\nhES : ∀ (i : Fin n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.DisjointCover | {
"line": 150,
"column": 4
} | {
"line": 150,
"column": 63
} | [
{
"pp": "X : Type u_1\nV : Type u_2\ninst✝⁴ : TopologicalSpace X\ninst✝³ : TopologicalSpace V\ninst✝² : TotallyDisconnectedSpace X\ninst✝¹ : T2Space X\ninst✝ : CompactSpace X\nS : Set (V × V)\nf : C(X, V)\nhS : S ∈ 𝓝ˢ (diagonal V)\nn : ℕ\nE : Fin n → Clopens X\nhEne : ∀ (i : Fin n), E i ≠ ⊥\nhES : ∀ (i : Fin n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 321,
"column": 6
} | {
"line": 321,
"column": 17
} | [
{
"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)),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 349,
"column": 6
} | {
"line": 349,
"column": 17
} | [
{
"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)),... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 376,
"column": 6
} | {
"line": 376,
"column": 17
} | [
{
"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)",
"usedConstan... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 424,
"column": 19
} | {
"line": 424,
"column": 30
} | [
{
"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))",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 433,
"column": 19
} | {
"line": 433,
"column": 30
} | [
{
"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))",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 526,
"column": 19
} | {
"line": 526,
"column": 30
} | [
{
"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⊢... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.MetricSpace.GromovHausdorffRealized | {
"line": 539,
"column": 19
} | {
"line": 539,
"column": 30
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sheaves.Skyscraper | {
"line": 63,
"column": 67
} | {
"line": 63,
"column": 78
} | [
{
"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",
"usedConstants": []
}
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.PerfectlyNormal | {
"line": 83,
"column": 12
} | {
"line": 83,
"column": 29
} | [
{
"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 = {... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Separation.PerfectlyNormal | {
"line": 117,
"column": 2
} | {
"line": 117,
"column": 56
} | [
{
"pp": "X : Type u_1\nY : Type u_2\ninst✝² : TopologicalSpace X\ninst✝¹ : TopologicalSpace Y\ne : X → Y\nhe : IsEmbedding e\ninst✝ : PerfectlyNormalSpace Y\nt : Set X\nht : IsClosed[inst✝²] t\nf : C(Y, ℝ)\nhf : ∀ (x : Y), f x ∈ Icc 0 1\nhc : IsClosed[inst✝¹] (⇑f ⁻¹' {0}) ∧ e '' t = ⇑f ⁻¹' {0} ∩ range e\n⊢ t = ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sheaves.LocallySurjective | {
"line": 108,
"column": 4
} | {
"line": 108,
"column": 51
} | [
{
"pp": "case mpr.imageSieve_mem\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 ... | 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.Sion | {
"line": 98,
"column": 2
} | {
"line": 98,
"column": 13
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Spectral.ConstructibleTopology | {
"line": 72,
"column": 2
} | {
"line": 72,
"column": 14
} | [
{
"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",
"usedConstants": [
"And.right",
"IsOpen",
"IsCompact"
]
},
{
"pp": "case inr\nX : Type u_1\ninst✝¹ : TopologicalSpace ... | · exact hs.2 | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.Sion | {
"line": 259,
"column": 4
} | {
"line": 259,
"column": 15
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Subpath | {
"line": 82,
"column": 2
} | {
"line": 82,
"column": 79
} | [
{
"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",
"usedConstants": [
"Set.range_comp",
"Eq.mpr",
"Real",
"Set.Icc.convexComb",
"Path.range_subpathAux",
"Real.lattice",
"Real.instZero... | 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
} | [
{
"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",
"usedConstants": [
"Set.range_comp",
"Eq.mpr",
"Real",
"Set.Icc.convexComb",
"Path.range_subpathAux",
"Real.lattice",
"Real.instZero... | 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
} | [
{
"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",
"usedConstants": [
"Set.range_comp",
"Eq.mpr",
"Real",
"Set.Icc.convexComb",
"Path.range_subpathAux",
"Real.lattice",
"Real.instZero... | rw [← range_subpathAux, ← range_comp, subpath, coe_mk', ContinuousMap.coe_mk] | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Topology.Sion | {
"line": 269,
"column": 4
} | {
"line": 269,
"column": 71
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sion | {
"line": 275,
"column": 4
} | {
"line": 275,
"column": 30
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Subpath | {
"line": 206,
"column": 2
} | {
"line": 206,
"column": 27
} | [
{
"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)",
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Path.trans",
"Fin.succ",
"congrArg",
"Path.concat",
"Function.co... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Subpath | {
"line": 211,
"column": 2
} | {
"line": 211,
"column": 27
} | [
{
"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))",
"usedConstants": [
"Eq.mpr",
"instNeZeroNatHAdd_1",
"Path.trans",
"Fin.succ",
"congrArg",
"Path.concat",
... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sion | {
"line": 286,
"column": 21
} | {
"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... | monotone_sublevelLeft y1 htt'.le | Mathlib.Tactic.evalGRewriteSeq | null |
Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts | {
"line": 207,
"column": 10
} | {
"line": 208,
"column": 17
} | [
{
"pp": "case zero.one.left.w\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 ((diagram U).op ⋙ F)\ni j : ι\n⊢ (𝟙 c.pt ≫ Pi.lift fun b ↦ c.π.app (op (Pairwise.pair b.1 b.2))) ≫\n limit.π (Discrete.functor fun p ↦ F.obj (... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sheaves.SheafCondition.EqualizerProducts | {
"line": 212,
"column": 10
} | {
"line": 213,
"column": 17
} | [
{
"pp": "case zero.one.right.w\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 ((diagram U).op ⋙ F)\ni j : ι\n⊢ (𝟙 c.pt ≫ Pi.lift fun b ↦ c.π.app (op (Pairwise.pair b.1 b.2))) ≫\n limit.π (Discrete.functor fun p ↦ F.obj ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sion | {
"line": 297,
"column": 13
} | {
"line": 297,
"column": 24
} | [
{
"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✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sion | {
"line": 304,
"column": 6
} | {
"line": 304,
"column": 54
} | [
{
"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✝... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Sion | {
"line": 517,
"column": 2
} | {
"line": 517,
"column": 48
} | [
{
"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... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.Path | {
"line": 81,
"column": 45
} | {
"line": 82,
"column": 9
} | [
{
"pp": "X : Type u_1\ninst✝¹ : UniformSpace X\nx y z : X\ninst✝ : CompleteSpace X\n⊢ IsComplete (Set.range _root_.toContinuousMap)",
"usedConstants": [
"Real.instIsOrderedRing",
"Path.continuousMapClass",
"Eq.mpr",
"Real.partialOrder",
"Real",
"IsComplete",
"Set.Ic... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.Ultra.Basic | {
"line": 141,
"column": 31
} | {
"line": 141,
"column": 53
} | [
{
"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",
"usedConstants": [
"setOf",
"Membership.mem",
"nhds",
"id",
"And",
"Filter.HasBasis",
"IsClopen",
"UniformSpace.to... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.Ultra.Constructions | {
"line": 77,
"column": 4
} | {
"line": 77,
"column": 49
} | [
{
"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)",
"usedConstants": [
"Pi.uniformSpace_eq",
"Pi.uniformSpace",
"Unifo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.ProdApproximation | {
"line": 111,
"column": 2
} | {
"line": 111,
"column": 13
} | [
{
"pp": "X : Type u_5\nY : Type u_6\nR : Type u_7\ninst✝⁹ : TopologicalSpace X\ninst✝⁸ : TopologicalSpace Y\ninst✝⁷ : CommRing R\ninst✝⁶ : TopologicalSpace R\ninst✝⁵ : IsTopologicalRing R\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : CompactSpace Y\ninst✝¹ : T2Space Y\ninst✝ : TotallyDisconnectedSpace ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.ProdApproximation | {
"line": 111,
"column": 27
} | {
"line": 111,
"column": 50
} | [
{
"pp": "X : Type u_5\nY : Type u_6\nR : Type u_7\ninst✝⁹ : TopologicalSpace X\ninst✝⁸ : TopologicalSpace Y\ninst✝⁷ : CommRing R\ninst✝⁶ : TopologicalSpace R\ninst✝⁵ : IsTopologicalRing R\ninst✝⁴ : CompactSpace X\ninst✝³ : T2Space X\ninst✝² : CompactSpace Y\ninst✝¹ : T2Space Y\ninst✝ : TotallyDisconnectedSpace ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.UniformSpace.OfCompactT2 | {
"line": 52,
"column": 4
} | {
"line": 52,
"column": 29
} | [
{
"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)",
"usedConstants": [
"instTopologicalSpaceProd",
"Set.diagonal",
"Prod",
"nhdsSet",
"Filter"
]
}
] | set 𝓝Δ := 𝓝ˢ (diagonal γ) | Mathlib.Tactic._aux_Mathlib_Tactic_Set___elabRules_Mathlib_Tactic_setTactic_1 | Mathlib.Tactic.setTactic |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.