module stringlengths 16 90 | startPos dict | endPos dict | nextStartPos dict | goals listlengths 0 96 | goalsAfter listlengths 0 96 | ppTac stringlengths 1 14.5k | elaborator stringclasses 375
values | kind stringclasses 379
values |
|---|---|---|---|---|---|---|---|---|
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.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.Sion | {
"line": 522,
"column": 2
} | {
"line": 522,
"column": 48
} | {
"line": 522,
"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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