module string | startPos dict | endPos dict | nextStartPos dict | goals list | goalsAfter list | ppTac string | elaborator string | kind string |
|---|---|---|---|---|---|---|---|---|
Mathlib.MeasureTheory.Function.Jacobian | {
"line": 626,
"column": 69
} | {
"line": 628,
"column": 33
} | {
"line": 629,
"column": 4
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nhf' : ∀ x ∈ s, HasFDerivWithinAt f (f' x) s x\nR : ℝ\nhs : s ⊆ c... | [] | by
gcongr
exact (hδ (A _)).2 _ (ht _) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.ChartedSpace | {
"line": 508,
"column": 24
} | {
"line": 508,
"column": 50
} | {
"line": 509,
"column": 8
} | [
{
"pp": "case inl\nH : Type u\nH' : Type u_1\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝³ : TopologicalSpace H\ninst✝² : TopologicalSpace M\ninst✝¹ : TopologicalSpace M'\ncm : ChartedSpace H M\ncm' : ChartedSpace H M'\ninst✝ : Nonempty H\nx : M\n⊢ Sum.inl x ∈ ((ChartedSpace.chartAt x).lift_openEmbedding... | [
"case inl\nH : Type u\nH' : Type u_1\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝³ : TopologicalSpace H\ninst✝² : TopologicalSpace M\ninst✝¹ : TopologicalSpace M'\ncm : ChartedSpace H M\ncm' : ChartedSpace H M'\ninst✝ : Nonempty H\nx : M\n⊢ Sum.inl x ∈ Sum.inl '' (ChartedSpace.chartAt x).source"
] | lift_openEmbedding_source, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Manifold.ChartedSpace | {
"line": 512,
"column": 24
} | {
"line": 512,
"column": 50
} | {
"line": 513,
"column": 8
} | [
{
"pp": "case inr\nH : Type u\nH' : Type u_1\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝³ : TopologicalSpace H\ninst✝² : TopologicalSpace M\ninst✝¹ : TopologicalSpace M'\ncm : ChartedSpace H M\ncm' : ChartedSpace H M'\ninst✝ : Nonempty H\nx : M'\n⊢ Sum.inr x ∈ ((ChartedSpace.chartAt x).lift_openEmbeddin... | [
"case inr\nH : Type u\nH' : Type u_1\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝³ : TopologicalSpace H\ninst✝² : TopologicalSpace M\ninst✝¹ : TopologicalSpace M'\ncm : ChartedSpace H M\ncm' : ChartedSpace H M'\ninst✝ : Nonempty H\nx : M'\n⊢ Sum.inr x ∈ Sum.inr '' (ChartedSpace.chartAt x).source"
] | lift_openEmbedding_source, | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Geometry.Manifold.ChartedSpace | {
"line": 647,
"column": 2
} | {
"line": 647,
"column": 44
} | {
"line": 647,
"column": 45
} | [
{
"pp": "H : Type u\nM : Type u_2\ninst✝ : TopologicalSpace H\nc : ChartedSpaceCore H M\ne : PartialEquiv M H\nhe : e ∈ c.atlas\nE : e.target ∩ ↑e.symm ⁻¹' e.source = e.target\n⊢ IsOpen[inst✝] e.target",
"ppTerm": "?m.41",
"assigned": false,
"usedConstants": [],
"usedFVars": [],
"usedGoals":... | [
"H : Type u\nM : Type u_2\ninst✝ : TopologicalSpace H\nc : ChartedSpaceCore H M\ne : PartialEquiv M H\nhe : e ∈ c.atlas\nE : e.target ∩ ↑e.symm ⁻¹' e.source = e.target\n⊢ IsOpen[inst✝] e.target"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ChartedSpace | {
"line": 675,
"column": 8
} | {
"line": 675,
"column": 35
} | {
"line": 675,
"column": 36
} | [
{
"pp": "H : Type u\nH' : Type u_1\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝ : TopologicalSpace H\nc : ChartedSpaceCore H M\ne✝ e : PartialEquiv M H\nhe : e ∈ c.atlas\nthis : TopologicalSpace M := c.toTopologicalSpace\nt : Set M\ne' : PartialEquiv M H\ne'_atlas : e' ∈ c.atlas\ns : Set H\ns_open : IsOp... | [
"H : Type u\nH' : Type u_1\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝ : TopologicalSpace H\nc : ChartedSpaceCore H M\ne✝ e : PartialEquiv M H\nhe : e ∈ c.atlas\nthis : TopologicalSpace M := c.toTopologicalSpace\nt : Set M\ne' : PartialEquiv M H\ne'_atlas : e' ∈ c.atlas\ns : Set H\ns_open : IsOpen[inst✝] s\... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ChartedSpace | {
"line": 682,
"column": 6
} | {
"line": 682,
"column": 87
} | {
"line": 682,
"column": 88
} | [
{
"pp": "H : Type u\nH' : Type u_1\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝ : TopologicalSpace H\nc : ChartedSpaceCore H M\ne✝ e : PartialEquiv M H\nhe : e ∈ c.atlas\nthis✝ : TopologicalSpace M := c.toTopologicalSpace\nt : Set M\ne' : PartialEquiv M H\ne'_atlas : e' ∈ c.atlas\ns : Set H\ns_open : IsO... | [
"H : Type u\nH' : Type u_1\nM : Type u_2\nM' : Type u_3\nM'' : Type u_4\ninst✝ : TopologicalSpace H\nc : ChartedSpaceCore H M\ne✝ e : PartialEquiv M H\nhe : e ∈ c.atlas\nthis✝ : TopologicalSpace M := c.toTopologicalSpace\nt : Set M\ne' : PartialEquiv M H\ne'_atlas : e' ∈ c.atlas\ns : Set H\ns_open : IsOpen[inst✝] s... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.StructureGroupoid | {
"line": 412,
"column": 4
} | {
"line": 412,
"column": 33
} | {
"line": 412,
"column": 34
} | [
{
"pp": "H : Type u_1\ninst✝ : TopologicalSpace H\ne : OpenPartialHomeomorph H H\nh : ∀ x ∈ e.source, ∃ s, IsOpen[inst✝] s ∧ x ∈ s ∧ e.restr s ∈ {e | ∃ s, ∃ (h : IsOpen[inst✝] s), e ≈ ofSet s h}\nx : H\nhx : x ∈ e.source\ns : Set H\nhs : IsOpen[inst✝] s\nhxs : x ∈ s\ns' : Set H\nhs' : IsOpen[inst✝] s'\nhes' : e... | [
"H : Type u_1\ninst✝ : TopologicalSpace H\ne : OpenPartialHomeomorph H H\nh : ∀ x ∈ e.source, ∃ s, IsOpen[inst✝] s ∧ x ∈ s ∧ e.restr s ∈ {e | ∃ s, ∃ (h : IsOpen[inst✝] s), e ≈ ofSet s h}\nx : H\nhx : x ∈ e.source\ns : Set H\nhs : IsOpen[inst✝] s\nhxs : x ∈ s\ns' : Set H\nhs' : IsOpen[inst✝] s'\nhes' : e.restr s ≈ o... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.ExtChartAt | {
"line": 97,
"column": 90
} | {
"line": 98,
"column": 79
} | {
"line": 100,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : TopologicalSpace H\ninst✝ : TopologicalSpace M\nf : OpenPartialHomeomorph M H\nI : ModelWithCorners 𝕜 E H\n⊢ (f.extend I).target = ↑(f.extend... | [] | by
rw [f.extend_target', ← f.image_source_eq_target, ← image_comp, f.extend_coe] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.IsManifold.Basic | {
"line": 202,
"column": 24
} | {
"line": 204,
"column": 24
} | {
"line": 206,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝ : TopologicalSpace H\nφ : PartialEquiv H E\nhsource : φ.source = univ\nhtarget : φ.target = univ\nhcont : Continuous[inst✝, PseudoMetricSpace.toUniformSpace.to... | [] | by
have : range φ = φ.target := by rw [← φ.image_source_eq_target, hsource, image_univ.symm]
simp [this, htarget] | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.IsManifold.Basic | {
"line": 304,
"column": 2
} | {
"line": 304,
"column": 17
} | {
"line": 304,
"column": 18
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nh : ¬IsRCLikeNormedField 𝕜\n⊢ range ↑I = univ",
"ppTerm": "?m.13",
"assigned": false,
"usedCons... | [
"𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nh : ¬IsRCLikeNormedField 𝕜\n⊢ range ↑I = univ"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.ExtChartAt | {
"line": 255,
"column": 2
} | {
"line": 255,
"column": 64
} | {
"line": 255,
"column": 65
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : TopologicalSpace H\ninst✝ : TopologicalSpace M\nf : OpenPartialHomeomorph M H\nI : ModelWithCorners 𝕜 E H\nα : Type u_8\nl : Filter α\ng : α ... | [
"𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\ninst✝⁴ : NontriviallyNormedField 𝕜\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : TopologicalSpace H\ninst✝ : TopologicalSpace M\nf : OpenPartialHomeomorph M H\nI : ModelWithCorners 𝕜 E H\nα : Type u_8\nl : Filter α\ng : α → M\nhg : ∀ᶠ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.Basic | {
"line": 360,
"column": 4
} | {
"line": 360,
"column": 19
} | {
"line": 360,
"column": 20
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nh : IsRCLikeNormedField 𝕜\nthis✝ : RCLike 𝕜 := ⋯\nthis : NormedSpace ℝ E := ⋯\n⊢ Convex ℝ (range ↑I)",
... | [
"𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nh : IsRCLikeNormedField 𝕜\nthis✝ : RCLike 𝕜 := ⋯\nthis : NormedSpace ℝ E := ⋯\n⊢ Convex ℝ (range ↑I)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.LocalInvariantProperties | {
"line": 331,
"column": 2
} | {
"line": 332,
"column": 96
} | {
"line": 334,
"column": 0
} | [
{
"pp": "H : Type u_1\nM : Type u_2\nH' : Type u_3\nM' : Type u_4\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\ninst✝² : TopologicalSpace H'\ninst✝¹ : TopologicalSpace M'\ninst✝ : ChartedSpace H' M'\nG : StructureGroupoid H\nG' : StructureGroupoid H'\ne : OpenPartialHomeo... | [] | rw [Function.comp_apply, e.left_inv xe, ← Function.comp_assoc,
hG.liftPropWithinAt_indep_chart_source_aux (chartAt _ (g x) ∘ g) he xe, Function.comp_assoc] | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_rwSeq_1 | Lean.Parser.Tactic.rwSeq |
Mathlib.MeasureTheory.Function.Jacobian | {
"line": 889,
"column": 4
} | {
"line": 889,
"column": 98
} | {
"line": 890,
"column": 2
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nhs : MeasurableSet s\nh's : μ s ≠ ∞\nhf' : ∀ x ∈ s, HasFDerivWit... | [] | exact ENNReal.Tendsto.const_mul (ENNReal.tendsto_coe.2 tendsto_id) (Or.inr ENNReal.coe_ne_top) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Manifold.IsManifold.Basic | {
"line": 582,
"column": 74
} | {
"line": 582,
"column": 90
} | {
"line": 584,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁴ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝³ : NormedAddCommGroup E\ninst✝² : NormedSpace 𝕜 E\nF : Type u_4\ninst✝¹ : NormedAddCommGroup F\ninst✝ : NormedSpace 𝕜 F\n⊢ 𝓘(𝕜, E × F) = 𝓘(𝕜, E).prod 𝓘(𝕜, F)",
"ppTerm": "?m.37",
"assigned": true,
"usedConstants... | [] | by ext1 <;> simp | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.LocalInvariantProperties | {
"line": 355,
"column": 2
} | {
"line": 355,
"column": 39
} | {
"line": 357,
"column": 0
} | [
{
"pp": "H : Type u_1\nM : Type u_2\nH' : Type u_3\nM' : Type u_4\ninst✝⁵ : TopologicalSpace H\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\ninst✝² : TopologicalSpace H'\ninst✝¹ : TopologicalSpace M'\ninst✝ : ChartedSpace H' M'\nG : StructureGroupoid H\nG' : StructureGroupoid H'\ne : OpenPartialHomeo... | [] | exact this.comp_continuousWithinAt h1 | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.MeasureTheory.Function.Jacobian | {
"line": 959,
"column": 8
} | {
"line": 959,
"column": 89
} | {
"line": 959,
"column": 90
} | [
{
"pp": "case ha₀\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nhs : MeasurableSet s\nhf' : ∀ x ∈ s, HasFDerivWithinAt... | [
"case ha₀\nE : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nhs : MeasurableSet s\nhf' : ∀ x ∈ s, HasFDerivWithinAt f (f' x) s ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.ExtChartAt | {
"line": 537,
"column": 63
} | {
"line": 537,
"column": 74
} | {
"line": 537,
"column": 75
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : TopologicalSpace H\ninst✝¹ : TopologicalSpace M\nI : ModelWithCorners 𝕜 E H\ninst✝ : ChartedSpace H M\nx y : M\nhx : y ∈ (extChartAt I x).sou... | [
"𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : TopologicalSpace H\ninst✝¹ : TopologicalSpace M\nI : ModelWithCorners 𝕜 E H\ninst✝ : ChartedSpace H M\nx y : M\nhx : y ∈ (extChartAt I x).source\nh'x : ↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.ExtChartAt | {
"line": 647,
"column": 48
} | {
"line": 647,
"column": 80
} | {
"line": 647,
"column": 81
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : TopologicalSpace H\ninst✝¹ : TopologicalSpace M\nI : ModelWithCorners 𝕜 E H\ninst✝ : ChartedSpace H M\nx : M\ny : E\nhy : y ∈ (extChartAt I x... | [
"𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : TopologicalSpace H\ninst✝¹ : TopologicalSpace M\nI : ModelWithCorners 𝕜 E H\ninst✝ : ChartedSpace H M\nx : M\ny : E\nhy : y ∈ (extChartAt I x).target\nt ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.ExtChartAt | {
"line": 728,
"column": 51
} | {
"line": 728,
"column": 62
} | {
"line": 728,
"column": 63
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : TopologicalSpace H\ninst✝¹ : TopologicalSpace M\nI : ModelWithCorners 𝕜 E H\ninst✝ : ChartedSpace H M\ns : Set E\nx x' : M\nhx : x' ∈ (extCha... | [
"𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\ninst✝⁵ : NontriviallyNormedField 𝕜\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\ninst✝² : TopologicalSpace H\ninst✝¹ : TopologicalSpace M\nI : ModelWithCorners 𝕜 E H\ninst✝ : ChartedSpace H M\ns : Set E\nx x' : M\nhx : x' ∈ (extChartAt I x).so... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.LocalInvariantProperties | {
"line": 607,
"column": 10
} | {
"line": 607,
"column": 80
} | {
"line": 607,
"column": 81
} | [
{
"pp": "case mpr.refine_2\nH : Type u_1\ninst✝¹ : TopologicalSpace H\nG : StructureGroupoid H\ninst✝ : ClosedUnderRestriction G\ns : Set H\nx : H\nu : Set H\nf : H → H\nhu : IsOpen[inst✝¹] u\nhux : x ∈ u\nh : G.IsLocalStructomorphWithinAt f (s ∩ u) x\nhx : x ∈ s\ne : OpenPartialHomeomorph H H\nheG : e ∈ G\nhef... | [
"case mpr.refine_2\nH : Type u_1\ninst✝¹ : TopologicalSpace H\nG : StructureGroupoid H\ninst✝ : ClosedUnderRestriction G\ns : Set H\nx : H\nu : Set H\nf : H → H\nhu : IsOpen[inst✝¹] u\nhux : x ∈ u\nh : G.IsLocalStructomorphWithinAt f (s ∩ u) x\nhx : x ∈ s\ne : OpenPartialHomeomorph H H\nheG : e ∈ G\nhef : EqOn f (↑... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.LocalInvariantProperties | {
"line": 611,
"column": 29
} | {
"line": 611,
"column": 76
} | {
"line": 611,
"column": 77
} | [
{
"pp": "H : Type u_1\ninst✝¹ : TopologicalSpace H\nG : StructureGroupoid H\ninst✝ : ClosedUnderRestriction G\ns : Set H\nx : H\nf : H → H\ne' : OpenPartialHomeomorph H H\nhe'G : e' ∈ G\nhe'x : x ∈ e'.source\nh : G.IsLocalStructomorphWithinAt f s x\nhx : ↑e' x ∈ ↑e'.symm ⁻¹' s\n⊢ x ∈ s",
"ppTerm": "?m.236",... | [
"H : Type u_1\ninst✝¹ : TopologicalSpace H\nG : StructureGroupoid H\ninst✝ : ClosedUnderRestriction G\ns : Set H\nx : H\nf : H → H\ne' : OpenPartialHomeomorph H H\nhe'G : e' ∈ G\nhe'x : x ∈ e'.source\nh : G.IsLocalStructomorphWithinAt f s x\nhx : ↑e' x ∈ ↑e'.symm ⁻¹' s\n⊢ x ∈ s"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.ExtChartAt | {
"line": 824,
"column": 2
} | {
"line": 824,
"column": 13
} | {
"line": 824,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\nE' : Type u_5\nM' : Type u_6\nH' : Type u_7\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : TopologicalSpace H\ninst✝⁶ : TopologicalSpace M\nI : ModelWithCorners 𝕜 E H\ninst✝⁵ : NormedAdd... | [
"𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\nE' : Type u_5\nM' : Type u_6\nH' : Type u_7\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : TopologicalSpace H\ninst✝⁶ : TopologicalSpace M\nI : ModelWithCorners 𝕜 E H\ninst✝⁵ : NormedAddCommGroup E'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.IsManifold.ExtChartAt | {
"line": 824,
"column": 44
} | {
"line": 824,
"column": 55
} | {
"line": 824,
"column": 56
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\nE' : Type u_5\nM' : Type u_6\nH' : Type u_7\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : TopologicalSpace H\ninst✝⁶ : TopologicalSpace M\nI : ModelWithCorners 𝕜 E H\ninst✝⁵ : NormedAdd... | [
"𝕜 : Type u_1\nE : Type u_2\nM : Type u_3\nH : Type u_4\nE' : Type u_5\nM' : Type u_6\nH' : Type u_7\ninst✝¹⁰ : NontriviallyNormedField 𝕜\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\ninst✝⁷ : TopologicalSpace H\ninst✝⁶ : TopologicalSpace M\nI : ModelWithCorners 𝕜 E H\ninst✝⁵ : NormedAddCommGroup E'... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.LocalInvariantProperties | {
"line": 631,
"column": 8
} | {
"line": 631,
"column": 57
} | {
"line": 631,
"column": 58
} | [
{
"pp": "case refine_2\nH : Type u_1\ninst✝¹ : TopologicalSpace H\nG : StructureGroupoid H\ninst✝ : ClosedUnderRestriction G\ns : Set H\nx : H\nf : H → H\ne' : OpenPartialHomeomorph H H\nhe'G : e' ∈ G\na✝ : s ⊆ f ⁻¹' e'.source\nhfx : f x ∈ e'.source\nh : G.IsLocalStructomorphWithinAt f s x\nhx : x ∈ s\ne : Open... | [
"case refine_2\nH : Type u_1\ninst✝¹ : TopologicalSpace H\nG : StructureGroupoid H\ninst✝ : ClosedUnderRestriction G\ns : Set H\nx : H\nf : H → H\ne' : OpenPartialHomeomorph H H\nhe'G : e' ∈ G\na✝ : s ⊆ f ⁻¹' e'.source\nhfx : f x ∈ e'.source\nh : G.IsLocalStructomorphWithinAt f s x\nhx : x ∈ s\ne : OpenPartialHomeo... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiff.Basic | {
"line": 176,
"column": 12
} | {
"line": 176,
"column": 23
} | {
"line": 176,
"column": 24
} | [
{
"pp": "case zero\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\ns : Set M\nn : ℕ∞ω\nf : M →... | [
"case zero\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\ns : Set M\nn : ℕ∞ω\nf : M → M\nhf : Con... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiff.Basic | {
"line": 177,
"column": 16
} | {
"line": 177,
"column": 27
} | {
"line": 177,
"column": 28
} | [
{
"pp": "case succ\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\ns : Set M\nn : ℕ∞ω\nf : M →... | [
"case succ\n𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\ns : Set M\nn : ℕ∞ω\nf : M → M\nhf : Con... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiff.Defs | {
"line": 139,
"column": 48
} | {
"line": 139,
"column": 81
} | {
"line": 139,
"column": 82
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nE' : Type u_5\ninst✝² : NormedAddCommGroup E'\ninst✝¹ : NormedSpace 𝕜 E'\nH' : Type u_6\ninst✝ : Topologic... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nE' : Type u_5\ninst✝² : NormedAddCommGroup E'\ninst✝¹ : NormedSpace 𝕜 E'\nH' : Type u_6\ninst✝ : TopologicalSpace H'\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.LocalInvariantProperties | {
"line": 703,
"column": 6
} | {
"line": 703,
"column": 48
} | {
"line": 704,
"column": 6
} | [
{
"pp": "H₁ : Type u_6\ninst✝⁷ : TopologicalSpace H₁\nH₂ : Type u_7\ninst✝⁶ : TopologicalSpace H₂\nH₃ : Type u_8\ninst✝⁵ : TopologicalSpace H₃\ninst✝⁴ : ChartedSpace H₁ H₂\ninst✝³ : ChartedSpace H₂ H₃\nG₁ : StructureGroupoid H₁\ninst✝² : HasGroupoid H₂ G₁\ninst✝¹ : ClosedUnderRestriction G₁\nG₂ : StructureGroup... | [
"case refine_1\nH₁ : Type u_6\ninst✝⁷ : TopologicalSpace H₁\nH₂ : Type u_7\ninst✝⁶ : TopologicalSpace H₂\nH₃ : Type u_8\ninst✝⁵ : TopologicalSpace H₃\ninst✝⁴ : ChartedSpace H₁ H₂\ninst✝³ : ChartedSpace H₂ H₃\nG₁ : StructureGroupoid H₁\ninst✝² : HasGroupoid H₂ G₁\ninst✝¹ : ClosedUnderRestriction G₁\nG₂ : StructureGr... | refine ⟨_, hs.inter φ.open_source, ?_, ?_⟩ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Geometry.Manifold.ContMDiff.Basic | {
"line": 297,
"column": 4
} | {
"line": 297,
"column": 15
} | {
"line": 297,
"column": 16
} | [
{
"pp": "case hi\n𝕜 : Type u_1\ninst✝¹¹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁸ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁷ : TopologicalSpace M\nE' : Type u_5\ninst✝⁶ : NormedAddCommGroup E'\ninst✝⁵... | [
"case hi\n𝕜 : Type u_1\ninst✝¹¹ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁸ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁷ : TopologicalSpace M\nE' : Type u_5\ninst✝⁶ : NormedAddCommGroup E'\ninst✝⁵ : NormedSpa... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiff.Basic | {
"line": 307,
"column": 22
} | {
"line": 307,
"column": 33
} | {
"line": 307,
"column": 34
} | [
{
"pp": "n : ℕ∞ω\nE : Type u_11\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nH : Type u_12\ninst✝² : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_13\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nf g : ℝ → M\ns : ℝ\nhf : ContMDiff 𝓘(ℝ, ℝ) I n f\nhg : ContMDiff 𝓘(ℝ, ℝ) I n g... | [
"n : ℕ∞ω\nE : Type u_11\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace ℝ E\nH : Type u_12\ninst✝² : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_13\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nf g : ℝ → M\ns : ℝ\nhf : ContMDiff 𝓘(ℝ, ℝ) I n f\nhg : ContMDiff 𝓘(ℝ, ℝ) I n g\nhfg : f =ᶠ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiff.Defs | {
"line": 308,
"column": 45
} | {
"line": 308,
"column": 56
} | {
"line": 308,
"column": 57
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nM' : Type u_7\ninst✝ : TopologicalSpa... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nM' : Type u_7\ninst✝ : TopologicalSpace M'\nf : M... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiff.Defs | {
"line": 308,
"column": 45
} | {
"line": 308,
"column": 61
} | {
"line": 308,
"column": 61
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nM' : Type u_7\ninst✝ : TopologicalSpa... | [] | simpa using hy.2 | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Geometry.Manifold.ContMDiff.Defs | {
"line": 308,
"column": 45
} | {
"line": 308,
"column": 61
} | {
"line": 308,
"column": 61
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nM' : Type u_7\ninst✝ : TopologicalSpa... | [] | simpa using hy.2 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.ContMDiff.Defs | {
"line": 308,
"column": 45
} | {
"line": 308,
"column": 61
} | {
"line": 308,
"column": 61
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nM' : Type u_7\ninst✝ : TopologicalSpa... | [] | simpa using hy.2 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.ContMDiff.Defs | {
"line": 309,
"column": 6
} | {
"line": 309,
"column": 24
} | {
"line": 309,
"column": 25
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nM' : Type u_7\ninst✝ : TopologicalSpa... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nM' : Type u_7\ninst✝ : TopologicalSpace M'\nf : M... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiff.Defs | {
"line": 313,
"column": 45
} | {
"line": 313,
"column": 56
} | {
"line": 313,
"column": 57
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nM' : Type u_7\ninst✝ : TopologicalSpa... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nM' : Type u_7\ninst✝ : TopologicalSpace M'\nf : M... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiff.Defs | {
"line": 313,
"column": 45
} | {
"line": 313,
"column": 61
} | {
"line": 313,
"column": 61
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nM' : Type u_7\ninst✝ : TopologicalSpa... | [] | simpa using hy.2 | Lean.Elab.Tactic.Simpa.evalSimpa | Lean.Parser.Tactic.simpa |
Mathlib.Geometry.Manifold.ContMDiff.Defs | {
"line": 313,
"column": 45
} | {
"line": 313,
"column": 61
} | {
"line": 313,
"column": 61
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nM' : Type u_7\ninst✝ : TopologicalSpa... | [] | simpa using hy.2 | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.ContMDiff.Defs | {
"line": 313,
"column": 45
} | {
"line": 313,
"column": 61
} | {
"line": 313,
"column": 61
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nM' : Type u_7\ninst✝ : TopologicalSpa... | [] | simpa using hy.2 | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.ContMDiff.Constructions | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 97
} | {
"line": 112,
"column": 0
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nF : Type u_8\ninst✝⁴ ... | [] | exact (extChartAt I p.1).right_inv <| (extChartAt I p.1).map_source (mem_extChartAt_source _) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Manifold.ContMDiff.Constructions | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 97
} | {
"line": 112,
"column": 0
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nF : Type u_8\ninst✝⁴ ... | [] | exact (extChartAt I p.1).right_inv <| (extChartAt I p.1).map_source (mem_extChartAt_source _) | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.ContMDiff.Constructions | {
"line": 110,
"column": 4
} | {
"line": 110,
"column": 97
} | {
"line": 112,
"column": 0
} | [
{
"pp": "case refine_2\n𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nF : Type u_8\ninst✝⁴ ... | [] | exact (extChartAt I p.1).right_inv <| (extChartAt I p.1).map_source (mem_extChartAt_source _) | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Function.Jacobian | {
"line": 1042,
"column": 4
} | {
"line": 1042,
"column": 98
} | {
"line": 1043,
"column": 2
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nhs : MeasurableSet s\nh's : μ s ≠ ∞\nhf' : ∀ x ∈ s, HasFDerivWit... | [] | exact ENNReal.Tendsto.const_mul (ENNReal.tendsto_coe.2 tendsto_id) (Or.inr ENNReal.coe_ne_top) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Geometry.Manifold.ContMDiff.Constructions | {
"line": 441,
"column": 6
} | {
"line": 441,
"column": 17
} | {
"line": 441,
"column": 18
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\nM' : Type u_16\ninst✝⁶ : Topologic... | [
"𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\nM' : Type u_16\ninst✝⁶ : TopologicalSpace M'\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Normed.Operator.Prod | {
"line": 51,
"column": 8
} | {
"line": 51,
"column": 84
} | {
"line": 52,
"column": 10
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : SeminormedAddCommGroup E\ninst✝⁴ : SeminormedAddCommGroup F\ninst✝³ : SeminormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : NormedSpace 𝕜 G\nf : E →L[𝕜] F\ng : E →L... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\nG : Type u_4\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : SeminormedAddCommGroup E\ninst✝⁴ : SeminormedAddCommGroup F\ninst✝³ : SeminormedAddCommGroup G\ninst✝² : NormedSpace 𝕜 E\ninst✝¹ : NormedSpace 𝕜 F\ninst✝ : NormedSpace 𝕜 G\nf : E →L[𝕜] F\ng : E →L[𝕜] G\nx : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiff.Constructions | {
"line": 456,
"column": 6
} | {
"line": 456,
"column": 17
} | {
"line": 456,
"column": 18
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\nM' : Type u_16\ninst✝⁶ : Topologic... | [
"𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\nM' : Type u_16\ninst✝⁶ : TopologicalSpace M'\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiff.Constructions | {
"line": 452,
"column": 4
} | {
"line": 456,
"column": 23
} | {
"line": 457,
"column": 4
} | [
{
"pp": "case inr\n𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\nM' : Type u_16\ninst✝⁶ :... | [
"case inr\n𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\nM' : Type u_16\ninst✝⁶ : Topological... | have : ContDiffWithinAt 𝕜 n ((extChartAt J (g x)) ∘ g ∘ (extChartAt I x).symm)
(range I) ((extChartAt I (.inr x : M ⊕ M')) (Sum.inr x)) := by
let hg' := hg x
rw [contMDiffAt_iff] at hg'
simpa using hg'.2 | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Geometry.Manifold.ContMDiff.Constructions | {
"line": 478,
"column": 10
} | {
"line": 478,
"column": 13
} | {
"line": 479,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\nn : WithTop ℕ∞\nE' : Type u_17\nin... | [
"𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁸ : TopologicalSpace M\ninst✝⁷ : ChartedSpace H M\nn : WithTop ℕ∞\nE' : Type u_17\ninst✝⁶ : Norme... | _hx | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.Geometry.Manifold.ContMDiff.Constructions | {
"line": 491,
"column": 10
} | {
"line": 491,
"column": 13
} | {
"line": 492,
"column": 2
} | [
{
"pp": "𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM' : Type u_16\ninst✝⁸ : TopologicalSpace M'\ninst✝⁷ : ChartedSpace H M'\nn : WithTop ℕ∞\nE' : Type u_17... | [
"𝕜 : Type u_1\ninst✝¹² : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹¹ : NormedAddCommGroup E\ninst✝¹⁰ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁹ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM' : Type u_16\ninst✝⁸ : TopologicalSpace M'\ninst✝⁷ : ChartedSpace H M'\nn : WithTop ℕ∞\nE' : Type u_17\ninst✝⁶ : N... | _hx | Lean.Elab.Tactic.evalIntro | ident |
Mathlib.Geometry.Manifold.MFDeriv.Defs | {
"line": 157,
"column": 6
} | {
"line": 166,
"column": 47
} | {
"line": 167,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nE' : Type u_5\ninst✝² : NormedAddCommGroup E'\ninst✝¹ : NormedSpace 𝕜 E'\nH' : Type u_6\ninst✝ : Topologic... | [] | intro s x u f u_open xu
have : I.symm ⁻¹' (s ∩ u) ∩ Set.range I = I.symm ⁻¹' s ∩ Set.range I ∩ I.symm ⁻¹' u := by
simp only [Set.inter_right_comm, Set.preimage_inter]
rw [DifferentiableWithinAtProp, DifferentiableWithinAtProp, this]
symm
apply differentiableWithinAt_inter
have : u ... | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.MFDeriv.Defs | {
"line": 157,
"column": 6
} | {
"line": 166,
"column": 47
} | {
"line": 167,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nE' : Type u_5\ninst✝² : NormedAddCommGroup E'\ninst✝¹ : NormedSpace 𝕜 E'\nH' : Type u_6\ninst✝ : Topologic... | [] | intro s x u f u_open xu
have : I.symm ⁻¹' (s ∩ u) ∩ Set.range I = I.symm ⁻¹' s ∩ Set.range I ∩ I.symm ⁻¹' u := by
simp only [Set.inter_right_comm, Set.preimage_inter]
rw [DifferentiableWithinAtProp, DifferentiableWithinAtProp, this]
symm
apply differentiableWithinAt_inter
have : u ... | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.MeasureTheory.Function.Jacobian | {
"line": 1109,
"column": 2
} | {
"line": 1116,
"column": 63
} | {
"line": 1117,
"column": 2
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nhs : NullMeasurableSet s μ\nhf' : ∀ x ∈ s, HasFDerivWithinAt f (... | [
"E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : FiniteDimensional ℝ E\ns : Set E\nf : E → E\nf' : E → E →L[ℝ] E\ninst✝² : MeasurableSpace E\ninst✝¹ : BorelSpace E\nμ : Measure E\ninst✝ : μ.IsAddHaarMeasure\nhs : NullMeasurableSet s μ\nhf' : ∀ x ∈ s, HasFDerivWithinAt f (f' x) s x\nh... | have A : μ (f '' s) = μ (f '' t) := by
apply measure_congr
have : s = t ∪ (s \ t) := by simp [union_eq_self_of_subset_left ts]
rw [this, image_union]
refine union_ae_eq_left_of_ae_eq_empty (ae_eq_empty.mpr ?_)
apply addHaar_image_eq_zero_of_differentiableOn_of_addHaar_eq_zero _
(fun x hx ↦ ?_)... | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.Geometry.Manifold.ContMDiff.Defs | {
"line": 671,
"column": 2
} | {
"line": 671,
"column": 12
} | {
"line": 672,
"column": 4
} | [
{
"pp": "case coe\n𝕜 : Type u_1\ninst✝¹⁰ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁹ : NormedAddCommGroup E\ninst✝⁸ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace M\ninst✝⁵ : ChartedSpace H M\nE' : Type u_5\ninst✝⁴ : No... | [] | | coe n => | _private.Lean.Elab.Tactic.Induction.0.Lean.Elab.Tactic.evalCases | null |
Mathlib.Geometry.Manifold.MFDeriv.Defs | {
"line": 197,
"column": 50
} | {
"line": 197,
"column": 83
} | {
"line": 197,
"column": 84
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nE' : Type u_5\ninst✝² : NormedAddCommGroup E'\ninst✝¹ : NormedSpace 𝕜 E'\nH' : Type u_6\ninst✝ : Topologic... | [
"𝕜 : Type u_1\ninst✝⁶ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nE' : Type u_5\ninst✝² : NormedAddCommGroup E'\ninst✝¹ : NormedSpace 𝕜 E'\nH' : Type u_6\ninst✝ : TopologicalSpace H'\n... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.Algebra.Structures | {
"line": 47,
"column": 22
} | {
"line": 47,
"column": 52
} | {
"line": 47,
"column": 53
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁶ : TopologicalSpace H\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nn : ℕ∞ω\nI : ModelWithCorners 𝕜 E H\nR : Type u_4\ninst✝³ : Ring R\ninst✝² : TopologicalSpace R\ninst✝¹ : ChartedSpace H R\ninst✝ : Con... | [
"𝕜 : Type u_1\ninst✝⁷ : NontriviallyNormedField 𝕜\nH : Type u_2\ninst✝⁶ : TopologicalSpace H\nE : Type u_3\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace 𝕜 E\nn : ℕ∞ω\nI : ModelWithCorners 𝕜 E H\nR : Type u_4\ninst✝³ : Ring R\ninst✝² : TopologicalSpace R\ninst✝¹ : ChartedSpace H R\ninst✝ : ContMDiffRing I... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiff.Atlas | {
"line": 52,
"column": 2
} | {
"line": 52,
"column": 13
} | {
"line": 52,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nn : ℕ∞ω\nx : H\n⊢ ContDiffWithinAt 𝕜 n (↑(extChartAt 𝓘(𝕜, E) (↑I x)) ∘ ↑I ∘ ↑(extChartAt I x).symm) (rang... | [
"𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nn : ℕ∞ω\nx : H\n⊢ ContDiffWithinAt 𝕜 n (↑I ∘ ↑I.symm) (range ↑I) (↑I x)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiff.Atlas | {
"line": 59,
"column": 2
} | {
"line": 59,
"column": 13
} | {
"line": 59,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nn : ℕ∞ω\nx : E\nhx : x ∈ range ↑I\n⊢ ContDiffWithinAt 𝕜 n (↑(extChartAt I (↑I.symm x)) ∘ ↑I.symm ∘ ↑(extCha... | [
"𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nn : ℕ∞ω\nx : E\nhx : x ∈ range ↑I\n⊢ ContDiffWithinAt 𝕜 n (↑I ∘ ↑I.symm) (range ↑I) x"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.ContMDiff.Atlas | {
"line": 116,
"column": 2
} | {
"line": 119,
"column": 53
} | {
"line": 121,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nn : ℕ∞ω\ne : OpenPartialHomeomorph M H... | [] | refine (contMDiffOn_symm_of_mem_maximalAtlas he).comp
(I.contMDiffOn_symm.mono <| image_subset_range _ _) ?_
simp_rw [image_subset_iff, PartialEquiv.restr_coe_symm, I.toPartialEquiv_coe_symm,
preimage_preimage, I.left_inv, preimage_id']; rfl | Lean.Elab.Tactic.evalTacticSeq1Indented | Lean.Parser.Tactic.tacticSeq1Indented |
Mathlib.Geometry.Manifold.ContMDiff.Atlas | {
"line": 116,
"column": 2
} | {
"line": 119,
"column": 53
} | {
"line": 121,
"column": 0
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\nn : ℕ∞ω\ne : OpenPartialHomeomorph M H... | [] | refine (contMDiffOn_symm_of_mem_maximalAtlas he).comp
(I.contMDiffOn_symm.mono <| image_subset_range _ _) ?_
simp_rw [image_subset_iff, PartialEquiv.restr_coe_symm, I.toPartialEquiv_coe_symm,
preimage_preimage, I.left_inv, preimage_id']; rfl | Lean.Elab.Tactic.evalTacticSeq | Lean.Parser.Tactic.tacticSeq |
Mathlib.Geometry.Manifold.BumpFunction | {
"line": 145,
"column": 2
} | {
"line": 145,
"column": 23
} | {
"line": 146,
"column": 2
} | [
{
"pp": "E : Type uE\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type uH\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type uM\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nc : M\nf : SmoothBumpFunction I c\ninst✝ : FiniteDimensional ℝ E\ns : Set M\nhse : s ⊆ (extCha... | [
"case h₁\nE : Type uE\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type uH\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type uM\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nc : M\nf : SmoothBumpFunction I c\ninst✝ : FiniteDimensional ℝ E\ns : Set M\nhse : s ⊆ (extChartA... | apply Subset.antisymm | Lean.Elab.Tactic.evalApply | Lean.Parser.Tactic.apply |
Mathlib.Geometry.Manifold.BumpFunction | {
"line": 212,
"column": 38
} | {
"line": 216,
"column": 59
} | {
"line": 218,
"column": 0
} | [
{
"pp": "E : Type uE\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\nH : Type uH\ninst✝³ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type uM\ninst✝² : TopologicalSpace M\ninst✝¹ : ChartedSpace H M\nc : M\nf : SmoothBumpFunction I c\ninst✝ : FiniteDimensional ℝ E\ns : Set M\nhsc : IsClosed[in... | [] | by
rw [f.image_eq_inter_preimage_of_subset_support hs]
refine ContinuousOn.preimage_isClosed_of_isClosed
((continuousOn_extChartAt_symm _).mono f.closedBall_subset) ?_ hsc
exact IsClosed.inter isClosed_closedBall I.isClosed_range | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.BumpFunction | {
"line": 262,
"column": 2
} | {
"line": 262,
"column": 38
} | {
"line": 262,
"column": 39
} | [
{
"pp": "E : Type uE\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\nH : Type uH\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type uM\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\nc : M\nf : SmoothBumpFunction I c\ninst✝¹ : FiniteDimensional ℝ E\ninst✝ : T2Space M\n⊢ tsuppo... | [
"E : Type uE\ninst✝⁶ : NormedAddCommGroup E\ninst✝⁵ : NormedSpace ℝ E\nH : Type uH\ninst✝⁴ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type uM\ninst✝³ : TopologicalSpace M\ninst✝² : ChartedSpace H M\nc : M\nf : SmoothBumpFunction I c\ninst✝¹ : FiniteDimensional ℝ E\ninst✝ : T2Space M\n⊢ tsupport ↑f ⊆ (cha... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear | {
"line": 130,
"column": 4
} | {
"line": 130,
"column": 57
} | {
"line": 130,
"column": 58
} | [
{
"pp": "𝕜 : Type u_1\nB : Type u_2\nF : Type u_3\ninst✝⁷ : TopologicalSpace B\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nEB : Type u_4\ninst✝³ : NormedAddCommGroup EB\ninst✝² : NormedSpace 𝕜 EB\nHB : Type u_5\ninst✝¹ : TopologicalSpace HB\ninst✝ : ChartedS... | [
"𝕜 : Type u_1\nB : Type u_2\nF : Type u_3\ninst✝⁷ : TopologicalSpace B\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nEB : Type u_4\ninst✝³ : NormedAddCommGroup EB\ninst✝² : NormedSpace 𝕜 EB\nHB : Type u_5\ninst✝¹ : TopologicalSpace HB\ninst✝ : ChartedSpace HB B\nI... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.MFDeriv.Basic | {
"line": 74,
"column": 21
} | {
"line": 74,
"column": 67
} | {
"line": 74,
"column": 68
} | [
{
"pp": "𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\ns t : Set M\nx : M\nhs : UniqueMDiffAt... | [
"𝕜 : Type u_1\ninst✝⁵ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝⁴ : NormedAddCommGroup E\ninst✝³ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝² : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝¹ : TopologicalSpace M\ninst✝ : ChartedSpace H M\ns t : Set M\nx : M\nhs : UniqueMDiffAt[s] x\nht : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.VectorBundle.Basic | {
"line": 522,
"column": 2
} | {
"line": 522,
"column": 13
} | {
"line": 522,
"column": 14
} | [
{
"pp": "R : Type u_1\nB : Type u_2\nF : Type u_3\nE : B → Type u_4\ninst✝⁹ : NontriviallyNormedField R\ninst✝⁸ : (x : B) → AddCommMonoid (E x)\ninst✝⁷ : (x : B) → Module R (E x)\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace R F\ninst✝⁴ : TopologicalSpace B\ninst✝³ : TopologicalSpace (TotalSpace F E)\nin... | [
"R : Type u_1\nB : Type u_2\nF : Type u_3\nE : B → Type u_4\ninst✝⁹ : NontriviallyNormedField R\ninst✝⁸ : (x : B) → AddCommMonoid (E x)\ninst✝⁷ : (x : B) → Module R (E x)\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : NormedSpace R F\ninst✝⁴ : TopologicalSpace B\ninst✝³ : TopologicalSpace (TotalSpace F E)\ninst✝² : (x : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.FiberwiseLinear | {
"line": 255,
"column": 4
} | {
"line": 255,
"column": 71
} | {
"line": 256,
"column": 4
} | [
{
"pp": "𝕜 : Type u_1\nB : Type u_2\nF : Type u_3\ninst✝⁷ : TopologicalSpace B\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nEB : Type u_4\ninst✝³ : NormedAddCommGroup EB\ninst✝² : NormedSpace 𝕜 EB\nHB : Type u_5\ninst✝¹ : TopologicalSpace HB\ninst✝ : ChartedS... | [
"𝕜 : Type u_1\nB : Type u_2\nF : Type u_3\ninst✝⁷ : TopologicalSpace B\ninst✝⁶ : NontriviallyNormedField 𝕜\ninst✝⁵ : NormedAddCommGroup F\ninst✝⁴ : NormedSpace 𝕜 F\nEB : Type u_4\ninst✝³ : NormedAddCommGroup EB\ninst✝² : NormedSpace 𝕜 EB\nHB : Type u_5\ninst✝¹ : TopologicalSpace HB\ninst✝ : ChartedSpace HB B\nI... | rintro e e' ⟨φ, U, hU, hφ, h2φ, heφ⟩ ⟨φ', U', hU', hφ', h2φ', heφ'⟩ | _private.Lean.Elab.Tactic.RCases.0.Lean.Elab.Tactic.RCases.evalRIntro | Lean.Parser.Tactic.rintro |
Mathlib.Geometry.Manifold.VectorBundle.Basic | {
"line": 301,
"column": 45
} | {
"line": 305,
"column": 51
} | {
"line": 307,
"column": 0
} | [
{
"pp": "n : ℕ∞ω\n𝕜 : Type u_1\nB : Type u_2\nB' : Type u_3\nF : Type u_4\nM : Type u_5\nE : B → Type u_6\ninst✝¹⁸ : NontriviallyNormedField 𝕜\nEB : Type u_7\ninst✝¹⁷ : NormedAddCommGroup EB\ninst✝¹⁶ : NormedSpace 𝕜 EB\nHB : Type u_8\ninst✝¹⁵ : TopologicalSpace HB\nIB : ModelWithCorners 𝕜 EB HB\ninst✝¹⁴ : T... | [] | by
constructor
intro e e' he he'
rw [contMDiffOn_zero_iff]
exact VectorBundle.continuousOn_coordChange' e e' | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Geometry.Manifold.VectorBundle.ContMDiffSection | {
"line": 220,
"column": 6
} | {
"line": 220,
"column": 17
} | {
"line": 220,
"column": 18
} | [
{
"pp": "case h\n𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹⁰ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nF : Type u_5\ninst✝⁷ : No... | [
"case h\n𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹⁰ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nF : Type u_5\ninst✝⁷ : NormedAddCommG... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.ContMDiffSection | {
"line": 229,
"column": 4
} | {
"line": 229,
"column": 15
} | {
"line": 229,
"column": 16
} | [
{
"pp": "case h\n𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹⁰ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nF : Type u_5\ninst✝⁷ : No... | [
"case h\n𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹⁰ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nF : Type u_5\ninst✝⁷ : NormedAddCommG... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.ContMDiffSection | {
"line": 265,
"column": 4
} | {
"line": 265,
"column": 15
} | {
"line": 265,
"column": 16
} | [
{
"pp": "case h\n𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹⁰ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nF : Type u_5\ninst✝⁷ : No... | [
"case h\n𝕜 : Type u_1\ninst✝¹³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝¹² : NormedAddCommGroup E\ninst✝¹¹ : NormedSpace 𝕜 E\nH : Type u_3\ninst✝¹⁰ : TopologicalSpace H\nI : ModelWithCorners 𝕜 E H\nM : Type u_4\ninst✝⁹ : TopologicalSpace M\ninst✝⁸ : ChartedSpace H M\nF : Type u_5\ninst✝⁷ : NormedAddCommG... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactness.Paracompact | {
"line": 221,
"column": 6
} | {
"line": 221,
"column": 39
} | {
"line": 222,
"column": 8
} | [
{
"pp": "X : Type v\ninst✝³ : TopologicalSpace X\ninst✝² : WeaklyLocallyCompactSpace X\ninst✝¹ : SigmaCompactSpace X\ninst✝ : T2Space X\nι : X → Type u\np : (x : X) → ι x → Prop\nB : (x : X) → ι x → Set X\ns : Set X\nhs : IsClosed[inst✝³] s\nhB : ∀ x ∈ s, (𝓝 x).HasBasis (p x) (B x)\nK' : CompactExhaustion X :=... | [
"X : Type v\ninst✝³ : TopologicalSpace X\ninst✝² : WeaklyLocallyCompactSpace X\ninst✝¹ : SigmaCompactSpace X\ninst✝ : T2Space X\nι : X → Type u\np : (x : X) → ι x → Prop\nB : (x : X) → ι x → Set X\ns : Set X\nhs : IsClosed[inst✝³] s\nhB : ∀ x ∈ s, (𝓝 x).HasBasis (p x) (B x)\nK' : CompactExhaustion X := CompactExha... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.Compactness.Paracompact | {
"line": 220,
"column": 59
} | {
"line": 222,
"column": 84
} | {
"line": 223,
"column": 4
} | [
{
"pp": "X : Type v\ninst✝³ : TopologicalSpace X\ninst✝² : WeaklyLocallyCompactSpace X\ninst✝¹ : SigmaCompactSpace X\ninst✝ : T2Space X\nι : X → Type u\np : (x : X) → ι x → Prop\nB : (x : X) → ι x → Set X\ns : Set X\nhs : IsClosed[inst✝³] s\nhB : ∀ x ∈ s, (𝓝 x).HasBasis (p x) (B x)\nK' : CompactExhaustion X :=... | [] | by
simpa only [K'.find_shiftr] using
sdiff_subset_sdiff_right interior_subset (K'.shiftr.mem_sdiff_shiftr_find x) | [anonymous] | Lean.Parser.Term.byTactic |
Mathlib.Topology.EMetricSpace.Paracompact | {
"line": 92,
"column": 6
} | {
"line": 92,
"column": 49
} | {
"line": 92,
"column": 50
} | [
{
"pp": "α : Type u_1\ninst✝ : PseudoEMetricSpace α\npow_pos : ∀ (k : ℕ), 0 < 2⁻¹ ^ k\nhpow_le : ∀ {m n : ℕ}, m ≤ n → 2⁻¹ ^ n ≤ 2⁻¹ ^ m\nh2pow : ∀ (n : ℕ), 2 * 2⁻¹ ^ (n + 1) = 2⁻¹ ^ n\nι : Type u_1\ns : ι → Set α\nho : ∀ (a : ι), IsOpen[PseudoEMetricSpace.toUniformSpace.toTopologicalSpace] (s a)\nhcov : ∀ (x : ... | [
"α : Type u_1\ninst✝ : PseudoEMetricSpace α\npow_pos : ∀ (k : ℕ), 0 < 2⁻¹ ^ k\nhpow_le : ∀ {m n : ℕ}, m ≤ n → 2⁻¹ ^ n ≤ 2⁻¹ ^ m\nh2pow : ∀ (n : ℕ), 2 * 2⁻¹ ^ (n + 1) = 2⁻¹ ^ n\nι : Type u_1\ns : ι → Set α\nho : ∀ (a : ι), IsOpen[PseudoEMetricSpace.toUniformSpace.toTopologicalSpace] (s a)\nhcov : ∀ (x : α), ∃ i, x ∈... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.VectorBundle.Basic | {
"line": 616,
"column": 4
} | {
"line": 616,
"column": 40
} | {
"line": 617,
"column": 4
} | [
{
"pp": "n : ℕ∞ω\n𝕜 : Type u_1\nB : Type u_2\nB' : Type u_3\nF : Type u_4\nM : Type u_5\nE : B → Type u_6\ninst✝³⁸ : NontriviallyNormedField 𝕜\nEB : Type u_7\ninst✝³⁷ : NormedAddCommGroup EB\ninst✝³⁶ : NormedSpace 𝕜 EB\nHB : Type u_8\ninst✝³⁵ : TopologicalSpace HB\nIB : ModelWithCorners 𝕜 EB HB\ninst✝³⁴ : T... | [
"case refine_1\nn : ℕ∞ω\n𝕜 : Type u_1\nB : Type u_2\nB' : Type u_3\nF : Type u_4\nM : Type u_5\nE : B → Type u_6\ninst✝³⁸ : NontriviallyNormedField 𝕜\nEB : Type u_7\ninst✝³⁷ : NormedAddCommGroup EB\ninst✝³⁶ : NormedSpace 𝕜 EB\nHB : Type u_8\ninst✝³⁵ : TopologicalSpace HB\nIB : ModelWithCorners 𝕜 EB HB\ninst✝³⁴ ... | refine ContMDiffOn.clm_prodMap ?_ ?_ | Lean.Elab.Tactic.evalRefine | Lean.Parser.Tactic.refine |
Mathlib.Topology.PartitionOfUnity | {
"line": 166,
"column": 2
} | {
"line": 166,
"column": 72
} | {
"line": 166,
"column": 73
} | [
{
"pp": "ι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns : Set X\nf : PartitionOfUnity ι X s\nx : X\nhx : x ∈ s\nH : ∀ (i : ι), (f i) x ≤ 0\n⊢ ∑ᶠ (i : ι), (f i) x ≠ 1",
"ppTerm": "?m.30",
"assigned": true,
"usedConstants": [
"Eq.mpr",
"finsum_zero",
"Real.partialOrder",
... | [
"ι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns : Set X\nf : PartitionOfUnity ι X s\nx : X\nhx : x ∈ s\nH : ∀ (i : ι), (f i) x ≤ 0\n⊢ 0 ≠ 1"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Topology.PartitionOfUnity | {
"line": 204,
"column": 29
} | {
"line": 204,
"column": 49
} | {
"line": 204,
"column": 49
} | [
{
"pp": "ι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns : Set X\nρ : PartitionOfUnity ι X s\nx₀ : X\nhx₀ : x₀ ∈ s\nI : Finset ι\nhI : ρ.finsupport x₀ ⊆ I\n⊢ ∑ x ∈ I \\ ρ.finsupport x₀, (ρ x) x₀ + ∑ x ∈ ρ.finsupport x₀, (ρ x) x₀ = 1",
"ppTerm": "?m.36",
"assigned": true,
"usedConstants": [
... | [
"ι : Type u\nX : Type v\ninst✝ : TopologicalSpace X\ns : Set X\nρ : PartitionOfUnity ι X s\nx₀ : X\nhx₀ : x₀ ∈ s\nI : Finset ι\nhI : ρ.finsupport x₀ ⊆ I\n⊢ ∑ x ∈ I \\ ρ.finsupport x₀, (ρ x) x₀ + 1 = 1"
] | ρ.sum_finsupport hx₀ | Lean.Elab.Tactic.evalRewriteSeq | null |
Mathlib.Topology.ShrinkingLemma | {
"line": 319,
"column": 2
} | {
"line": 330,
"column": 34
} | {
"line": 331,
"column": 2
} | [
{
"pp": "case refine_4\nι : Type u_1\nX : Type u_2\ninst✝² : TopologicalSpace X\nu : ι → Set X\ns : Set X\ninst✝¹ : T2Space X\ninst✝ : LocallyCompactSpace X\nv : PartialRefinement u s fun w ↦ IsCompact (closure w)\nhs : IsCompact s\ni : ι\nhi : i ∉ v.carrier\nsi : Set X := s ∩ (⋃ j, ⋃ (_ : j ≠ i), v.toFun j)ᶜ\n... | [
"case refine_5\nι : Type u_1\nX : Type u_2\ninst✝² : TopologicalSpace X\nu : ι → Set X\ns : Set X\ninst✝¹ : T2Space X\ninst✝ : LocallyCompactSpace X\nv : PartialRefinement u s fun w ↦ IsCompact (closure w)\nhs : IsCompact s\ni : ι\nhi : i ∉ v.carrier\nsi : Set X := s ∩ (⋃ j, ⋃ (_ : j ≠ i), v.toFun j)ᶜ\nhsi : si = s... | · intro j hj
rw [mem_insert_iff] at hj
by_cases h : j = i
· rw [← h]
simp only [update_self]
exact hvi.2.2.2
· apply hj.elim
· intro hji
exact False.elim (h hji)
· intro hjmemv
rw [update_of_ne h]
exact v.pred_of_mem hjmemv | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Topology.PartitionOfUnity | {
"line": 471,
"column": 2
} | {
"line": 471,
"column": 13
} | {
"line": 472,
"column": 4
} | [
{
"pp": "ι : Type u\nX : Type v\ninst✝² : TopologicalSpace X\ns : Set X\ninst✝¹ : LocallyCompactSpace X\ninst✝ : T2Space X\nhs : IsCompact s\nU : ι → Set X\nho : ∀ (i : ι), IsOpen[inst✝²] (U i)\nhf : LocallyFinite U\nhU : s ⊆ ⋃ i, U i\n⊢ ∃ f, f.IsSubordinate U ∧ ∀ (i : ι), HasCompactSupport ⇑(f i)",
"ppTerm... | [
"ι : Type u\nX : Type v\ninst✝² : TopologicalSpace X\ns : Set X\ninst✝¹ : LocallyCompactSpace X\ninst✝ : T2Space X\nhs : IsCompact s\nU : ι → Set X\nho : ∀ (i : ι), IsOpen[inst✝²] (U i)\nhf : LocallyFinite U\nhU : s ⊆ ⋃ i, U i\n⊢ ∃ f, f.IsSubordinate U ∧ ∀ (i : ι), HasCompactSupport ⇑(f i)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.PartitionOfUnity | {
"line": 384,
"column": 4
} | {
"line": 384,
"column": 69
} | {
"line": 384,
"column": 70
} | [
{
"pp": "case refine_3\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nH : Type uH\ninst✝⁵ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type uM\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\ninst✝² : FiniteDimensional ℝ E\ns : Set M\nU : M → Set M\ninst✝¹ : T2Space M\ni... | [
"case refine_3\nE : Type uE\ninst✝⁷ : NormedAddCommGroup E\ninst✝⁶ : NormedSpace ℝ E\nH : Type uH\ninst✝⁵ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type uM\ninst✝⁴ : TopologicalSpace M\ninst✝³ : ChartedSpace H M\ninst✝² : FiniteDimensional ℝ E\ns : Set M\nU : M → Set M\ninst✝¹ : T2Space M\ninst✝ : Sigma... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.AEEqOfIntegralContDiff | {
"line": 52,
"column": 2
} | {
"line": 52,
"column": 58
} | {
"line": 53,
"column": 2
} | [
{
"pp": "E : Type u_1\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace ℝ E\ninst✝¹¹ : FiniteDimensional ℝ E\nF : Type u_2\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : CompleteSpace F\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_4\ninst✝⁶ : Topol... | [
"E : Type u_1\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace ℝ E\ninst✝¹¹ : FiniteDimensional ℝ E\nF : Type u_2\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : CompleteSpace F\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace ... | have := ChartedSpace.secondCountable_of_sigmaCompact H M | Lean.Parser.Tactic._aux_Init_Tactics___macroRules_Lean_Parser_Tactic_tacticHave___1 | Lean.Parser.Tactic.tacticHave__ |
Mathlib.MeasureTheory.Function.AEEqOfIntegral | {
"line": 219,
"column": 4
} | {
"line": 219,
"column": 15
} | {
"line": 219,
"column": 16
} | [
{
"pp": "α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\nhf_int_finite : ∀ (s : Set α), MeasurableSet s → μ s < ∞ → IntegrableOn f s μ\nhf_zero : ∀ (s : Set α), MeasurableSet s → μ s < ∞ → ∫ (x : α) in s, f x ∂μ = 0\nt : Set α\nht : MeasurableSet t\nhμt : μ t ≠ ∞\nh_neg : 0 ≤ᵐ[μ.restrict t] -f\n... | [
"α : Type u_1\nm0 : MeasurableSpace α\nμ : Measure α\nf : α → ℝ\nhf_int_finite : ∀ (s : Set α), MeasurableSet s → μ s < ∞ → IntegrableOn f s μ\nhf_zero : ∀ (s : Set α), MeasurableSet s → μ s < ∞ → ∫ (x : α) in s, f x ∂μ = 0\nt : Set α\nht : MeasurableSet t\nhμt : μ t ≠ ∞\nh_neg : 0 ≤ᵐ[μ.restrict t] -f\nx : α\nhx : ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.AEEqOfIntegral | {
"line": 252,
"column": 4
} | {
"line": 252,
"column": 45
} | {
"line": 253,
"column": 2
} | [
{
"pp": "α : Type u_1\nE : Type u_2\nm0 : MeasurableSpace α\nμ : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nf g : α → E\nhf_int_finite : ∀ (s : Set α), MeasurableSet s → μ s < ∞ → IntegrableOn f s μ\nhg_int_finite : ∀ (s : Set α), MeasurableSet s → μ s < ∞ → Int... | [] | exact sub_eq_zero.mpr (hfg_zero s hs hμs) | Lean.Elab.Tactic.evalExact | Lean.Parser.Tactic.exact |
Mathlib.Analysis.Distribution.AEEqOfIntegralContDiff | {
"line": 104,
"column": 10
} | {
"line": 104,
"column": 21
} | {
"line": 104,
"column": 22
} | [
{
"pp": "E : Type u_1\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace ℝ E\ninst✝¹¹ : FiniteDimensional ℝ E\nF : Type u_2\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : CompleteSpace F\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_4\ninst✝⁶ : Topol... | [
"E : Type u_1\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace ℝ E\ninst✝¹¹ : FiniteDimensional ℝ E\nF : Type u_2\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : CompleteSpace F\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Disintegration | {
"line": 91,
"column": 4
} | {
"line": 91,
"column": 49
} | {
"line": 92,
"column": 6
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : CompleteSpace 𝕜\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : MeasurableSpace E\ninst✝⁸ : BorelSpace E\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : MeasurableSpace F\ninst✝⁴ : BorelSpace F\nin... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : CompleteSpace 𝕜\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : MeasurableSpace E\ninst✝⁸ : BorelSpace E\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : MeasurableSpace F\ninst✝⁴ : BorelSpace F\ninst✝³ : Norme... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Measure.Haar.Disintegration | {
"line": 99,
"column": 4
} | {
"line": 99,
"column": 49
} | {
"line": 100,
"column": 6
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : CompleteSpace 𝕜\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : MeasurableSpace E\ninst✝⁸ : BorelSpace E\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : MeasurableSpace F\ninst✝⁴ : BorelSpace F\nin... | [
"𝕜 : Type u_1\nE : Type u_2\nF : Type u_3\ninst✝¹² : NontriviallyNormedField 𝕜\ninst✝¹¹ : CompleteSpace 𝕜\ninst✝¹⁰ : NormedAddCommGroup E\ninst✝⁹ : MeasurableSpace E\ninst✝⁸ : BorelSpace E\ninst✝⁷ : NormedSpace 𝕜 E\ninst✝⁶ : NormedAddCommGroup F\ninst✝⁵ : MeasurableSpace F\ninst✝⁴ : BorelSpace F\ninst✝³ : Norme... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.AEEqOfIntegralContDiff | {
"line": 114,
"column": 4
} | {
"line": 114,
"column": 24
} | {
"line": 114,
"column": 25
} | [
{
"pp": "E : Type u_1\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace ℝ E\ninst✝¹¹ : FiniteDimensional ℝ E\nF : Type u_2\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : CompleteSpace F\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_4\ninst✝⁶ : Topol... | [
"E : Type u_1\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace ℝ E\ninst✝¹¹ : FiniteDimensional ℝ E\nF : Type u_2\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : CompleteSpace F\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.AEEqOfIntegralContDiff | {
"line": 115,
"column": 2
} | {
"line": 115,
"column": 20
} | {
"line": 115,
"column": 21
} | [
{
"pp": "E : Type u_1\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace ℝ E\ninst✝¹¹ : FiniteDimensional ℝ E\nF : Type u_2\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : CompleteSpace F\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_4\ninst✝⁶ : Topol... | [
"E : Type u_1\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace ℝ E\ninst✝¹¹ : FiniteDimensional ℝ E\nF : Type u_2\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : CompleteSpace F\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.MeasureTheory.Function.AEEqOfIntegral | {
"line": 352,
"column": 2
} | {
"line": 357,
"column": 42
} | {
"line": 359,
"column": 0
} | [
{
"pp": "case refine_2\nα : Type u_1\nE : Type u_2\nm m0 : MeasurableSpace α\nμ : Measure α\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace ℝ E\ninst✝ : CompleteSpace E\nhm : m ≤ m0\nf : α → E\nhf_int_finite : ∀ (s : Set α), MeasurableSet s → μ s < ∞ → IntegrableOn f s μ\nhf_zero : ∀ (s : Set α), Measurabl... | [] | · intro s hs hμs
rw [restrict_trim hm (μ.restrict t) hs, Measure.restrict_restrict (hm s hs)]
rw [← restrict_trim hm μ ht_meas, Measure.restrict_apply hs,
trim_measurableSet_eq hm (hs.inter ht_meas)] at hμs
rw [← integral_trim hm hf_meas_m]
exact hf_zero _ (hs.inter ht_meas) hμs | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.MeasureTheory.Function.AEEqOfIntegral | {
"line": 384,
"column": 4
} | {
"line": 384,
"column": 23
} | {
"line": 384,
"column": 24
} | [
{
"pp": "E : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : CompleteSpace E\nβ : Type u_3\ninst✝² : TopologicalSpace β\ninst✝¹ : MeasurableSpace β\ninst✝ : BorelSpace β\nμ : Measure β\nf : β → E\nhf : Integrable f μ\nh'f : ∀ (s : Set β), IsClosed[inst✝²] s → ∫ (x : β) in s, f x ∂μ =... | [
"E : Type u_2\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : CompleteSpace E\nβ : Type u_3\ninst✝² : TopologicalSpace β\ninst✝¹ : MeasurableSpace β\ninst✝ : BorelSpace β\nμ : Measure β\nf : β → E\nhf : Integrable f μ\nh'f : ∀ (s : Set β), IsClosed[inst✝²] s → ∫ (x : β) in s, f x ∂μ = 0\nt : Set ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.Rademacher | {
"line": 86,
"column": 70
} | {
"line": 86,
"column": 81
} | {
"line": 86,
"column": 82
} | [
{
"pp": "E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\nC : ℝ≥0\nf : E → ℝ\nμ : Measure E\ninst✝¹ : FiniteDimensional ℝ E\ninst✝ : μ.IsAddHaarMeasure\nhf : LipschitzWith C f\nv : E\nL : ℝ →L[ℝ] E := ContinuousLinearMap.smulRight 1 v\np :... | [
"E : Type u_1\ninst✝⁵ : NormedAddCommGroup E\ninst✝⁴ : NormedSpace ℝ E\ninst✝³ : MeasurableSpace E\ninst✝² : BorelSpace E\nC : ℝ≥0\nf : E → ℝ\nμ : Measure E\ninst✝¹ : FiniteDimensional ℝ E\ninst✝ : μ.IsAddHaarMeasure\nhf : LipschitzWith C f\nv : E\nL : ℝ →L[ℝ] E := ContinuousLinearMap.smulRight 1 v\np : E\nthis : ∀... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Distribution.AEEqOfIntegralContDiff | {
"line": 187,
"column": 2
} | {
"line": 187,
"column": 27
} | {
"line": 187,
"column": 28
} | [
{
"pp": "E : Type u_1\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace ℝ E\ninst✝¹¹ : FiniteDimensional ℝ E\nF : Type u_2\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : CompleteSpace F\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_4\ninst✝⁶ : Topol... | [
"E : Type u_1\ninst✝¹³ : NormedAddCommGroup E\ninst✝¹² : NormedSpace ℝ E\ninst✝¹¹ : FiniteDimensional ℝ E\nF : Type u_2\ninst✝¹⁰ : NormedAddCommGroup F\ninst✝⁹ : NormedSpace ℝ F\ninst✝⁸ : CompleteSpace F\nH : Type u_3\ninst✝⁷ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type u_4\ninst✝⁶ : TopologicalSpace ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.ProperSpace | {
"line": 44,
"column": 61
} | {
"line": 44,
"column": 72
} | {
"line": 44,
"column": 73
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : ProperSpace E\ns : Set E\nx : E\nhx : AccPt x (𝓟 s)\nu : ℕ → ℝ\nu_pos : ∀ (n : ℕ), 0 < u n\nu_lim : Tendsto u atTop (𝓝 0)\nv : ℕ → E\nhvx : ∀ (n : ℕ), v n ≠ x\nhvu : ∀ (... | [
"𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : ProperSpace E\ns : Set E\nx : E\nhx : AccPt x (𝓟 s)\nu : ℕ → ℝ\nu_pos : ∀ (n : ℕ), 0 < u n\nu_lim : Tendsto u atTop (𝓝 0)\nv : ℕ → E\nhvx : ∀ (n : ℕ), v n ≠ x\nhvu : ∀ (n : ℕ), v n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.ProperSpace | {
"line": 62,
"column": 32
} | {
"line": 62,
"column": 58
} | {
"line": 62,
"column": 59
} | [
{
"pp": "𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : ProperSpace E\ns : Set E\nx : E\nhx : AccPt x (𝓟 s)\nu : ℕ → ℝ\nu_pos : ∀ (n : ℕ), 0 < u n\nu_lim : Tendsto u atTop (𝓝 0)\nv : ℕ → E\nhvx : ∀ (n : ℕ), v n ≠ x\nhvu : ∀ (... | [
"𝕜 : Type u_1\ninst✝³ : NontriviallyNormedField 𝕜\nE : Type u_2\ninst✝² : NormedAddCommGroup E\ninst✝¹ : NormedSpace 𝕜 E\ninst✝ : ProperSpace E\ns : Set E\nx : E\nhx : AccPt x (𝓟 s)\nu : ℕ → ℝ\nu_pos : ∀ (n : ℕ), 0 < u n\nu_lim : Tendsto u atTop (𝓝 0)\nv : ℕ → E\nhvx : ∀ (n : ℕ), v n ≠ x\nhvu : ∀ (n : ℕ), v n ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Analysis.Calculus.TangentCone.Seq | {
"line": 64,
"column": 2
} | {
"line": 64,
"column": 13
} | {
"line": 64,
"column": 14
} | [
{
"pp": "𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NormedDivisionRing 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : TopologicalSpace E\ninst✝ : ContinuousSMul 𝕜 E\nα : Type u_3\nl : Filter α\nc : α → 𝕜\nd : α → E\ny : E\nhc : Tendsto c l (Bornology.cobounded 𝕜)\nhd : Tendsto (fun n ↦ c n • d n) l (... | [
"𝕜 : Type u_1\nE : Type u_2\ninst✝⁴ : NormedDivisionRing 𝕜\ninst✝³ : AddCommGroup E\ninst✝² : Module 𝕜 E\ninst✝¹ : TopologicalSpace E\ninst✝ : ContinuousSMul 𝕜 E\nα : Type u_3\nl : Filter α\nc : α → 𝕜\nd : α → E\ny : E\nhc : Tendsto c l (Bornology.cobounded 𝕜)\nhd : Tendsto (fun n ↦ c n • d n) l (𝓝 y)\nthis ... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.PartitionOfUnity | {
"line": 817,
"column": 45
} | {
"line": 817,
"column": 56
} | {
"line": 817,
"column": 57
} | [
{
"pp": "E : Type uE\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\nH : Type uH\ninst✝⁶ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type uM\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : IsManifold I ∞ M\ninst✝¹ : SigmaCompactSpace M\ninst✝... | [
"E : Type uE\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\nH : Type uH\ninst✝⁶ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type uM\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : IsManifold I ∞ M\ninst✝¹ : SigmaCompactSpace M\ninst✝ : T2Space M... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.PartitionOfUnity | {
"line": 812,
"column": 4
} | {
"line": 818,
"column": 24
} | {
"line": 819,
"column": 2
} | [
{
"pp": "case neg\nE : Type uE\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\nH : Type uH\ninst✝⁶ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type uM\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : IsManifold I ∞ M\ninst✝¹ : SigmaCompactSpac... | [] | · have : 0 < g x := by
classical
apply lt_of_le_of_ne (g_pos x) (Ne.symm ?_)
rw [← mem_support, g_supp]
contrapose xs
exact h.trans f_supp.symm.subset (by simpa using xs)
linarith [f_pos x] | Lean.Elab.Tactic.evalTacticCDot | Lean.cdot |
Mathlib.Order.SuccPred.IntervalSucc | {
"line": 64,
"column": 2
} | {
"line": 64,
"column": 13
} | {
"line": 64,
"column": 14
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : OrderBot α\ninst✝² : SuccOrder α\ninst✝¹ : IsSuccArchimedean α\ninst✝ : LinearOrder β\nf : α → β\nhf : ∀ (a : α), f ⊥ ≤ f a\nh2f : ¬BddAbove (range f)\n⊢ ⋃ a, Ico (f a) (f (succ a)) = Ici (f ⊥)",
"ppTerm": "?m.27",
"assigned": false,
... | [
"α : Type u_1\nβ : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : OrderBot α\ninst✝² : SuccOrder α\ninst✝¹ : IsSuccArchimedean α\ninst✝ : LinearOrder β\nf : α → β\nhf : ∀ (a : α), f ⊥ ≤ f a\nh2f : ¬BddAbove (range f)\n⊢ ⋃ a, Ico (f a) (f (succ a)) = Ici (f ⊥)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Order.SuccPred.IntervalSucc | {
"line": 70,
"column": 2
} | {
"line": 70,
"column": 13
} | {
"line": 70,
"column": 14
} | [
{
"pp": "α : Type u_1\nβ : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : OrderBot α\ninst✝² : SuccOrder α\ninst✝¹ : IsSuccArchimedean α\ninst✝ : LinearOrder β\nf : α → β\nhf : ∀ (a : α), f ⊥ ≤ f a\nh2f : ¬BddAbove (range f)\n⊢ ⋃ a, Ioc (f a) (f (succ a)) = Ioi (f ⊥)",
"ppTerm": "?m.27",
"assigned": false,
... | [
"α : Type u_1\nβ : Type u_2\ninst✝⁴ : LinearOrder α\ninst✝³ : OrderBot α\ninst✝² : SuccOrder α\ninst✝¹ : IsSuccArchimedean α\ninst✝ : LinearOrder β\nf : α → β\nhf : ∀ (a : α), f ⊥ ≤ f a\nh2f : ¬BddAbove (range f)\n⊢ ⋃ a, Ioc (f a) (f (succ a)) = Ioi (f ⊥)"
] | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
Mathlib.Geometry.Manifold.PartitionOfUnity | {
"line": 825,
"column": 4
} | {
"line": 825,
"column": 46
} | {
"line": 825,
"column": 47
} | [
{
"pp": "E : Type uE\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\nH : Type uH\ninst✝⁶ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type uM\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : IsManifold I ∞ M\ninst✝¹ : SigmaCompactSpace M\ninst✝... | [
"E : Type uE\ninst✝⁸ : NormedAddCommGroup E\ninst✝⁷ : NormedSpace ℝ E\nH : Type uH\ninst✝⁶ : TopologicalSpace H\nI : ModelWithCorners ℝ E H\nM : Type uM\ninst✝⁵ : TopologicalSpace M\ninst✝⁴ : ChartedSpace H M\ninst✝³ : FiniteDimensional ℝ E\ninst✝² : IsManifold I ∞ M\ninst✝¹ : SigmaCompactSpace M\ninst✝ : T2Space M... | simpa using | Lean.Elab.Tactic.Simpa.evalSimpa | null |
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