module stringlengths 17 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 377
values | kind stringclasses 381
values |
|---|---|---|---|---|---|---|---|---|
Mathlib.Topology.Sion | {
"line": 265,
"column": 4
} | {
"line": 265,
"column": 15
} | {
"line": 265,
"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.Sion | {
"line": 275,
"column": 4
} | {
"line": 275,
"column": 71
} | {
"line": 276,
"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.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": 281,
"column": 4
} | {
"line": 281,
"column": 30
} | {
"line": 281,
"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": 142,
"column": 31
} | {
"line": 142,
"column": 53
} | {
"line": 142,
"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[inst✝¹.toTopologicalSpace] s} ∧ x ∈ t) id",
"ppTerm": "?m.11",
"assigned": true,
"usedConstants": [
"Set.ofPred",
"Membership.mem",
"nhds",
"id",
... | [
"X : Type u_1\ninst✝¹ : UniformSpace X\ninst✝ : IsUltraUniformity X\nx : X\n⊢ (𝓝 x).HasBasis (fun t ↦ IsClopen[inst✝¹.toTopologicalSpace] t ∧ x ∈ t) id"
] | 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.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 ∈ uniformity X ∧ x✝¹.IsSymm ∧ x✝¹.IsTrans\nleft✝ : x✝¹ ∈ uniformity X\nhU : x✝¹.IsSymm\nright✝ : x✝¹.IsTrans\n⊢ SetRel.IsSymm ((CauchyFilter.gen ∘ id) x✝¹)",
"ppTerm... | [
"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 ∈ uniformity X ∧ x✝¹.IsSymm ∧ x✝¹.IsTrans\nleft✝ : x✝¹ ∈ uniformity 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 ∈ uniformity X ∧ x✝¹.IsSymm ∧ x✝¹.IsTrans\nleft✝¹ : x✝¹ ∈ uniformity X\nleft✝ : x✝¹.IsSymm\nhU : x✝¹.IsTrans\n⊢ SetRel.IsTrans ((CauchyFilter.gen ∘ id) x✝¹)",
"ppTer... | [
"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 ∈ uniformity X ∧ x✝¹.IsSymm ∧ x✝¹.IsTrans\nleft✝¹ : x✝¹ ∈ uniformity 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": 292,
"column": 21
} | {
"line": 292,
"column": 53
} | {
"line": 292,
"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.UniformSpace.OfCompactT2 | {
"line": 53,
"column": 4
} | {
"line": 53,
"column": 29
} | {
"line": 55,
"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.Sion | {
"line": 303,
"column": 13
} | {
"line": 303,
"column": 24
} | {
"line": 303,
"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": 310,
"column": 6
} | {
"line": 310,
"column": 54
} | {
"line": 310,
"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": 523,
"column": 2
} | {
"line": 523,
"column": 48
} | {
"line": 523,
"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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